- Email: [email protected]
The timetable of life: The timing of events in the lives of organisms
Mathl. Comput. Modelling Vol. 19, No. 6-8, pp. 171-240, 1994
Pergamon 08957177(94)E0050-W
Copyright@1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0895-7177/94 $7.00 + 0.00
The Timetable of Life: The Timing of Events in the Lives of Organisms*
32 Willow Dr., Ste. 1B Ocean, NJ 07712, U.S.A. Abstract-This paper offers an empirical mathematical formula (geometric series) for the ages at which “events” can occur in organisms. These “events” include fertilization, events in the fertilized ovum, developmental events in the embryo and fetus, birth, mating, and other postnatal events throughout the remainder of life. A theory is presented for the foregoing timing of events by the building of an mRNA molecule one unit at a time. The formula is derived from the hypothetical molecule-building process. It is shown that the majority of species have ranges of gestation ages that are indicative of subspecies using several successive event ages from the formula. On a time scale of evolution, these subspecies march randomly toward higher event ages, which is the process of heterochrony.
1. INTRODUCTION This
mini-monograph
organisms.
presents
It presents
a novel partial
also a completely
theory
from event to event. It is a synthesis and extension The assertions given in the following introductory per against published
data. In this Introduction,
potentially important
ing.
are verified in the body of the pa-
its structure without
substantiation
distraction.
and apparently new to biology and medicine.
or life scientist,
in medicine
or life science.
The author,
being not a
has resorted to unusual words and usages to express intended
The reader might be helped by reference to the appended
unfamiliar
of that timing
papers [l-3].
italics are used to designate statements believed by the author to be both
Some terms used herein are not common physician
of three previous paragraphs
of events in the lives of
of the regularity
the assertions are made without
in order to focus on the theory and to emphasize In this Introduction,
of the timing
novel demonstration
Glossary
(Appendix
mean-
B) for any
or unclear words or usages.
tThe author acknowledges gratitude to the late Robert H. Cavins, his high school chemistry teacher, for having been taught to expect to see in nature and science “the perfection of nature.” Of all of the persons who have studied the author’s papers and discussed them in depth, no one has been more helpful than B. Fairchild. He, along with a few others, notably T. Oren and J. McCoy, have been generous with their assessment of the work, urging that the author’s findings deserve the utmost investigation by life scientists as being probably important scientific discoveries. The author thanks A. Leissa of the Ohio State University, for having recognized early his research ability by recommending admission to Sigma Xi. The author thanks the late George Hamilton and the late Willard Constantinides, two outstanding mechanical engineers, who shared their skills in numerical calculus with the author. These skills were key to identifying the “logarhythm of life” in the noisy published data on event ages. The author is thankful that this journal provides such a large canvss for so ambitious a paper. *This paper was typeset in d&-m and galley proofs to authors provided from the offices of the Guest Editor.
171
A. B. CLYMER
172 1.1. Events The
life of an individual
“events,” events _ _ _ _ _ ~ ~ _ _ _ _ ~ _ ~ _ ~
organism
each of which starts
include
can be thought
of as consisting
or stops one or more localized
of a lifelong
developments
sequence
or activities.
of
These
the following categories:
Mating Birth of a mammal Laying of an insect, fish, reptile or bird egg Hatching of an insect, fish, reptile or bird egg The start of a metamorphosis of an insect First appearance of a particular structure or tissue in an animal
or plant
Appearance of a new control loop (homeostatic function) Single cell or embryo mitosis First appearance of a new protein (enzyme, hormone, etc.) in an animal or plant Initiation of a new state of a tissue (e.g., eyelids open or close in a fetus) Migration of birds, mammals, shellfish, etc. Appearance of a new reflex Appearance of a new problem-solving capability or language skill Change or shedding of skin, fur, antlers, color, shell, etc. First appearance of a biorhythm, e.g., menarche Start or stop of hibernation First appearance of a new behavior or physical capability First appearance of an organism’s susceptibility to a drug Start or stop of construction of a chambered shell Establishment of an organism’s sex Death (perhaps for some species an event)
Not all of these events occur in every species, One extremely
important
characteristic
it occurs.
Here age is measured
1.2. The
Series
Apparently, are precisely ages”
from zero at the time of fertilization
it has not been seriously timed
are members
using bisexual
(which
has often
of a single
as a possibility,
been pointed
mathematical
not only that
out by others),
series for all events
the post-fertilization
that
series given by a certain
all such events those
but also that in all species
“event
(at least those
data for several hundred
mammalian
been found in the author’s two successive
searches
which has the value 1.0472, species.
No previously
of the geometric
was obtained
obtained
formula
by fitting
gestation
for event ages has
of the literature.
event ages are only 4.72%
Aj is age in days at the jth event. degree of precision
age of every event is a member
constant to the jth power. Here age is given in days, and j is any integer,
plus, minus or zero. The constant,
sufficiently
considered
when
of the ovum.
reproduction).
It is hypothesized
Note that
of course.
of an event is the age (or ages) of the organism
Hence,
apart.
to test the formula
That
in data that is unusual in biology and medicine.
precise to afford a meaningful
is, Aj+l
= l.O472Aj,
against observed
where
data requires a
Most published
data are not
check.
It follows from the formula that the event ages are equally spaced on a logarithmic spacing being the same for all events and species.
This rhythm
time scale, the
might be called the Yogarhythm
of life.” The
formula
is equivalent
to a list of possible
event ages (see Table
1).
Any species
“uses”
some subset of this list, but the ages used do not have to be consecutive. It is postulated that the “in use” by living things since the beginning of sexual same list of possible event ages has been reproduction.
Many events in one species
might bring on no event.
might occur at one event age; some other
event ages
Timetable Table la. Event ages. All time post-fertilization for humans.)
of Life
173
(PF) in Tables la-c.
(In Table Id, they are postnatal
In Table la, the integers i are those associated with the formula Ai = 21( 1.0472)i,
which gives the same series of ages as given by Aj = 21(1.0472)j,
days.
-155
IO.39613 123.768
I
-242
IO.4299 125.80
-232
IO.6819 140.91
-224
IO.9862 159.17
-221
1.1325 67.95
The up to 350 or so event ages “used” by a species are the entries in the timetable of the events in the species. The set of timetables of all species might be called the “timetable of life.” The human timetable, in particular, should be invaluable in medicine and for monitoring and managing development, as would be timetables for many other species in veterinary medicine. The science of time in development might be called “chrontogeny” (chron + ontogeny). 1.3. Multiple
Event
Ages
For many events, the age of occurrence (event age) is observed to be very sharply a day or two variation over a year interval, as for the swallows of Capistrano, the Hinkley migrating, or the occurrence of ragweed pollen in Illinois on August, 21). In events, there are two or more peaks in the frequency distribution over time, and in the ages of occurrence are found to be smeared randomly over some wide range. Most events species.
in most species
are hypothesized
It is a fact that most mammalian
(age at birth),
some as many
to have more
fixed (e.g., vultures of some
other
still others
than one event age per event per
species have more than one possible gestation
period
as 8 or 9. Each of these event ages is given by the formula, and
174
A. B. CLYMER Table lb. Event ages. All time post-fertilization for humans.)
(PF) in Tables la-c.
In Table lb, the integers i are those associated
with the formula Ai = 21(1.0472)i,
which gives the same series of ages as given by Aj = 21( l.O472)j,
I
-103
-76
15.142
908.51
-75
15.857
951.39
-74
16.605
996.30
-71
19.069
1144.14
(In Table Id, they are postnatal
days
-32
1 4.8003 1115.21
-22
t 7.6132 1182.72
1 4.359 1261.53 I
those for one species event has several The
are consecutive
list of event
event
ages in the list than
The
substantially
of theory Molecule
It is postulated molecular
in error,
I
12.6443
-11
to find experimental Building
303.46
distribution
for an
a published
or observational
This
observed
between
event
age as
two consecutive
is an instance
of the unusual
errors.
Process
that the formula
building process
tentatively
if it lies closer to the midpoint
to one of the ages in the list.
is a mathematical
description
of the temporal
outcome
of a
by which structural units are added one at a time. The times to build
molecules
of consecutive
sizes (numbers
according
to the formula.
A derivation
building
76.07
in the list. In such a case, the frequency
ages can be used to identify
probably
1.4.
3.1696
peaks.
being
application
-41
of consecutive of the formula,
structural adduced
units)
herein,
are in the ratio
suggests
1.0472,
one hypothetical
mechanism.
Addition
of one structural
same or a qualitatively
unit to a timer
different
at the next later event age.
molecule
event, depending
would seem to offer the possibility
on the nature
of the added unit, in either
of the case
Timetable Table lc. Event ages. All time post-fertilization for humans.)
of Life
175
(PF) in Tables la-c.
In Table lc, the integers i are those associated
(In Table Id, they are postnatal
with the formula Ai = 21(1.0472)i,
which gives the same series of ages ss given by Aj = 21(1.0472)j,
days.
1Event i 1Months 1
1 Days 1 1
75
1 21.930 1 667.5
80
1 27.617 1 840.6
I
87
1 38.141 11160.9
99
1 66.335 12019.1
I
1.5.
A Theory
102
1 76.179 12318.7 I
103
1 79.774 12428.1
I
of Biorhythms
An intriguing theory of biorhythms (not new) is that repeated building of a timer molecule on the same substrate results in the same event over and over at equal intervals of time. This concept is consistent with the theory herein. Moreover, the biorhythm periods check well against the nearest members of the list of event ages. 1.6. Synchronizations Some important synchronizations are enabled by the timer molecules. For example, from generation to generation a mammalian species can maintain a fairly stable relationship to the annual calendar (hence, seasonal climate) in its event timing. Similarly, for species with much shorter lives, a synchronization can be maintained over lunar months or solar days. Also, in many species, it is advantageous to maintain a synchronization between successive generations and/or between mates. Synchronization is an important characteristic in ecosystems also, such as a prey species appearing when a predator arrives during its migration. A change of climatic temperature alters observed event ages, possibly upsetting synchronizations that are vital to the survival of some species and even of the entire ecosystem. The effects
176
A. B. CLYMER Table Id. Human postnatal (PN) events. Assuming 277.894 days PF gestation period.
1 year = 12 months = 365.25 days.
87
12.41761 29.011
I
1
93
13.43081 41.170
94
13.62871 43.544
97
(4.28001
I
51.360
1
I
130 122.3322 1267.99
1 78
Il.33781
16.0541
I
140 135.8642 1430.37
of global warming upon ecosystems, There
appears
in individual 1.7.
to be no timing mechanism
organisms.
of a tissue growth process
the dimension
level; all timing seems to be caused
for development,
values of j the dimensions Another Darwin’s
“quantum
to a difference
application finches,
is a “quantized”
will take only certain
stop event ages, assuming
1.8.
on the ecosystem
It then has consequences
shift, are conceivably
heretofore. ecosystems
and evolution.
Quantization
The result that
via change of event ages due to thermal
than other effects of warming considered
more devastating
a constant numbers.”
growth
rate.
which one can postulate
dimension.
Quantized
by the difference
One might choose
In paleontology,
of event ages, assuming
might be the geometric
tissue
values determined
means
of the start
and
to call the corresponding
one could work backwards
from observed
that the tissue growth rate has been constant.
parameters
(e.g., lengths
and radii) of the beaks of
are quantized.
Evolution
Mutations of evolution
by jumps
of j by one unit for this or that event constitute
of a species,
as far as size is concerned.
the postulated
As a rule, the individuals
mechanism
with larger values
Timetable of Life
177
of j for the same growth-end event can out-compete those with smaller j’s, since size usually offers advantage. It takes only 15 unit increments of j to double an event age, and just a few doublings of size would transform an eohippus (dawn horse) into a horse. As a species evolves, its event ages tend to increase incrementally, in general. Exceptions would be dwarfs and pygmies, which might have descended from larger ancestors by temporary and local decrease of the j’s. This shifting of the timing of developmental events is called heterochrony. Note added in proof: S. J. Gould [4] has maintained that growth is a continuum but that evolution involves discrete increments. This observation is in agreement with the theory herein. Those primate species having the greatest numbers of event ages per event are found to be those that are evolving fastest. One would be inclined to form the hypothesis that this is true of all species, not just primates, on the argument that there is nothing special about primate evolution. Species that have not evolved “recently” (on an evolutionary time scale) are usually found to have a single age for each event. A species stops evolving if it finds a set of event ages that are a local optimum in mutation space for dealing with its environment. The foregoing items in italics are believed by the author to constitute an expanded, structured and more definitive account of the roles and mechanisms of timing in biology and medicine than has been available heretofore.
2. EVENTS
AND
PROCESSES
2.1. Events In the Introduction, a list has been given of the most common and recognized events that occur in organisms. They are like the turning on and off of switches, which start or stop processes. Events per se have a negligible duration. These events are milestones in the development of an organism. The times at which they occur, expressed as the post-fertilization (or post-pollination for a plant [5]) age of the organism, constitute a set of parameters which define a species to a major extent. The list of events and their event ages for a species is its “timetable.” It is difficult to define “event” other than to use the empirical approach that a legitimate “event” category is one that succeeds in being fitted by the series. 2.2.
Processes
Many events start processes resulting
in tissue growth,
in less growth, Similarly,
because
if there
in certain
will be proportional
there is less time available before the process is stopped
apparent
discontinuities is in reality Changes
interruptions
continuous
or transients. However,
and smooth
quite recently
Previous
the amount
event. because
of growth
as seen by the naked eye is continuous,
to the theory
herein,
started
large spurts
of size variables the apparent
and stopped
of growth
[6]. Th ese spurts can be interpreted
can have continuity
at event
in the lengths
ages.
of babies
as pulses of growth hormone
of which die out quickly, but not until surprising
have occurred.
3. SERIES 3.1.
by another
for growth.
only during processes Indeed,
event results
there will be more growth,
Of course time derivatives
according
at event ages, the consequences
of growth
event,
If the growth rate is constant,
available
can begin or end at event ages.
released perhaps
stopping
The overall course of development
at event ages.
have been reported amounts
for growth.
to the time interval
Note added in proof:
The process might be cell reproduction,
In this case a delay in the growth starting
is a delay in the process
there will be more time available
without
cells or a tissue.
for example.
OF EVENT
AGES
Series
Researchers in embryology have recognized that the development of an embryo follows a fairly rigid schedule. The best known works that have attempted to exhibit a universal series of definite times are those by Witschi [7] and by Streeter [8]. Another list in the literature is the Carnegie stages, which also are expressed as small integer stages, but they have only human application 191.
178
A. B. CLYMER
Witschi presented a list of 36 “standard stages,” each an integer number of days after fertilization, at which embryos presumably first reach a definable level of development. In Witschi’s list, the intervals between successive ages increase generally with age from one day to two days. Thus, Witschi saw developmental stages as getting further apart as development proceeds. Similarly, Streeter presented a set of “horizons” which he believed represented definable levels of development. These too are embryo ages in integer numbers of days. Like Witschi he used intervals of one to two days. Neither list was completely regular in any sense, so neither list had the look of a simple natural law. No formula would be a very good fit for either series because of their irregularities. Table 2 shows the Streeter and Witschi series compared with a certain geometric series mentioned in the Introduction and to be discussed further in Section 3.2. The general agreement is of interest, in the sense that it gives an absolute magnitude check on the geometric series and its slope. The overall outcome is 22 successes out of 37, or 59% success. This result is not particularly impressive. However, if one looks only or 79% success. For the Streeter data, apparently Witschi is showing events, Refer to Figure 1 (in Section 5) for 3.2. The Geometric
at the Witschi data, one obtains 15 successes and 4 failures, there are 6 successes and 10 failures, or 38% success. Thus, while Streeter is showing stages between events. definitions of success (S) and failure (F).
Series of Event
Ages
Table 1 gives a listing of the geometric series over the entire range of observed event times. To repeat and amplify on the statement of this series in the Introduction, the series can be defined by the formula Aj = (l.O472)j, where Aj is the age in days at which the jth event occurs, 1.0472 is an empirical constant, and j is any integer (positive, negative or zero). The table includes, for convenience, a portion in which the zero is translated from fertilization to a typical time of human birth, in order to allow entry with postnatal ages of human postnatal events. The series was written earlier [l], in the form Ai = 21 (1.0472)i, where i is any integer and 21 is another empirical constant. This is the formula upon which Table 1 is based. By noting that the value 1 day (24.01 hrs) appears in the list of values calculated for Ai, one can replace the constant 21 days with the constant 1 day and define j to be a translation (shifted version) of i. That is where the formula above containing j instead of i came from. Actually, a different value was first used for the constant “1.0472” (namely, 1.05946, which is the twelfth root of two, as reported in [l]), but the form of the equation was the same. Going to the value 1.0472 improved the fit notably; there were no longer oscillations of the sign of the error. Presumably, the oscillations were an interference pattern between the periodicity of the formula in logtime and the postulated periodicity of the reported data in logtime. The constant value 1.0472 is very close to the 15th root of two, which might be just coincidence. The author has no explanation or rationalization, other than to recall his concept of a logarithmic spiral with radii (see Appendix C, Section 2). There is a problem with the series that needs to be discussed. At smaller and smaller values of i or j, the event ages get down into the range of a few seconds. Somewhere in that range it must become impossible to manufacture any mRNA molecule so fast. Moreover, as age decreases, the values of i and j approach negative infinity, and an infinity of events must take place in a very short time, according to the formula. At some point the formula must cease to be credible. However, this defect does not prevent the formula from being useful over the entire practical range. The foregoing problem might be taken care of by putting an offset constant on the right hand side of the formula to represent the time taken by steps other than mRNA building. This constant would have to be very small, in order that it not disturb the accuracy of fit away from small event ages.
Timetable
of Life
179
Table 2.
Day
18
Nearest
Witchi’s
Event
Standard
Age (days)
Stage
Streeter’s Horizon
Percent Error
success or Failure
18.29 19.15 20.05 14
_
0
_
X
t-o.05
S
S
23
23.03
_
_
_
_
24
24.12
15
XI
-0.5
25
25.26
_
_
_
SS _
26
26.45
_
XII
-1.73
F
27
26.45
16
XIII
+2.04
F,F
28
27.70
17
+1.07
S
18
_ 1
XIV
)
0
)
SS
31 32
31.81
33
33.31
34
I
22
I
I
I
XVI
I
23 XVII
-.94
I
s,s
+2.03
F
t.34
s.s
35
34.88
24
36
36.52
25
37
36.52
_
XVIII
+1.30
38
38.25
26 _
_
-.66
S
XIX
+1.92
F
38.25
I
(
27 41 42
28
43
-
45
46.00
46
46.00
47
46.00
48
48.17
_
50
32
I
/[
F F
_
-.13
S
-2.29
F
I
I
XXI
31 _
[ -1.44
xx
XXIII
49
I
_
+.14
I -2.14
I
I
S F
+2.13
F
-.35
S
0
_
-.88
S
Another interesting limit question relates to what happens if one constructs a closer and closer set of event ages by decreasing the spacing factor indefinitely below 1.0472 toward unity. The event ages will eventually become so close that all reported events are successes [lo]. However, that case is not of interest. The case with the factor 1.0472 is believed by the author to be a local optimum on the curve of percentage success versus e in the spacing factor 1 + e. The value .0472 for e seems to make contact with something significant in the real world. It would be desirable to demonstrate this curve for a set of values of e by calculation with some body of data such as gestation data. The foregoing discussion was not correctly presented in [l]. 3.3. Species
Timetables
If a species has existed long enough to have reached an equilibrium, in the sense of having no possible improvement of itself by unit changes in the quantum numbers j of its events, then MCM 19:6-8-H
A. B. CLYMER
180
there will be exactly one event age per event for that species. The more common situation is for a species to have two or more event ages per event, which is suboptimal and, hence, not an equilibrium “design” of the organism in a specified environment. For a given species, one can collect the known event descriptions and their ages of occurrence into a timetable for the species. Most of the events will probably have more than one event age (see Section 6 for further information), so several columns will be needed at the left for the various ages for the event described in the column at the right. There will probably be little or no information about correlations of event ages between events and, hence, about the different combinations of event ages that occur in an individual for a number of events. For example, one could try to do a timetable for all humans having a particular gestation period. Such a timetable would facilitate event management by physicians and veterinarians. The sequence of events is not always exactly the same for a species. For example, usually a girl entering puberty will have first onset of breast buds, then pubic hair, but this sequence is reversed in about 25% of cases [ll]. This might be due to thermal variance or it might be due to different subspecies defined in terms of the quantum numbers of events. In all timetables, the formula would provide the necessary framework in time. 3.4. Timing
in Simulations
of Living
Systems
The author has long been interested in the problems associated with simulating a living system of any kind. The series of event ages provides a made-to-order and simple scheme for introducing events into simulations [l]. Moreover, in the field of discrete event simulation, which is widely applied in industrial engineering and operations analysis, there is one “world view,” which fits the series neatly. As defined by Pritsker 1121, “In the event-oriented world view a system is modeled by defining the changes that occur at event times.” If it is desired to deal not only with events at scattered event ages but also with continuous processes in terms of regular small discrete jumps in time, one can use a “combined” language, which permits both types of simulation at once. The logarithm of conceptual age has been used before as a modified time scale for presenting findings about development [13]. 3.5. Series of Events The author has investigated some of the series defined by algorithms, such as “same time next year.” Such a series can be selected from Table 1. To get “same time next year,” one selects the event age closest to each integer year, as in the following list:
This event series consists of the closest event age to integer years after fertilization. A species which mates annually might use such a series to time its mating; it would be an alternative to a circannual rhythm for this purpose. There are five other event series which tend to repeat annually at a particular time of year. They consist of annual integer years plus approximations to the following numbers of months: 2.5, 4, 6, 7.5 and 10.
Timetableof Life Similarly, there are event series that provide approximately
181 “the year after next same time,”
“next lunar month same time,” “tomorrow same time,” etc. The author has no evidence that any of these event series is used by any species. Nevertheless, the potential is there, and they ought to be looked for [3]. 4. 4.1. Thermal
DISPERSION
FACTORS
Effects upon Event Ages
4.1.1. Effects of steady-state
temperature change
The relationship between temperature and the age at which an event occurs is given approximately by a hyperbola, concave upward. Here temperature is the x axis, and the age at the event is the y axis. The lowest point represents the minimum possible time until the event. There are two vertical asymptotes, between which is the portion of the hyperbola that is of interest. The hyperbola changes with species and event. A surprisingly small temperature change can shift an event age substantially. Given the hyperbola for a species, one can obtain from it a correction to event age corresponding to any change of steady-state temperature. If the typical temperature of a species’ environment is on the left branch of the hyperbola, then a small increase of temperature will speed up the growth of the event molecule, and a decrease of temperature will slow it down. The opposite is true for a species normally located on its right branch. An approximation to the true curve is given by a hyperbolic equation:
Aj= (T -
K Tl)(TZ - T)’
where K, Tl and T2 are empirical constants varying with species and event. The only range of temperature T of concern is between Tl and Ts. Tl and Ts are asymptotes at which an event would take forever (the organism could die if the event were essential to continued life). Effects other than mere event age change can be brought about by temperature change. Extremes of temperature result in fetal deformities and even death. Another phenomenon caused by temperature change is control of sex in a reptile such as the leatherback turtle: a warm nest produces all females, and a cooler nest produces all males [14]. However, for alligators it is the reverse [ 151. Such phenomena associated with variable temperature can be researched by computer simulation using the foregoing formula to determine event ages on the fly. Actually, the timer site in the affected cells might be buried under thermal capacity and insulation, leading to substantial lags of local somatic temperature behind ambient temperature changes. Many of these situations could be modeled by systems of thermal ordinary differential equations, such as for example: 1. Turtle eggs in a nest under sand 2. A human fetus in utero under normal conditions 3. Bird eggs in a nest under a parent bird 4. Postnatal development of an animal 5. A joey in a marsupial pouch 6. Competition among nestmates or littermates for growth 7. A pregnant woman in a hot tub or sauna 8. Hibernation of ground squirrels with varying outside weather.
A. B. CLYMER
182
4.1.2.Effects
of thermal
variation
If ambient temperature undergoes small changes that are random in time, the resulting event age can be calculated from the random traversal of the hyperbola. Here it is assumed for simplicity that the ambient temperature applies also at the site of the timing of the event. The condition for completion of the event time is
I ()
A~
dt
Aj[T(t)l=l,
from which Aj can be found, given Aj[T(t)] from the previous formula. 4.1.3.Indirect
effects
of temperature
Temperature also has many indirect effects upon event ages observed. In the case of gestation period, as affected by various factors that play a thermal role, examples are: 1. If mother is lactating, temperature is reduced (loss of enthalpy). 2. Mother’s age (affects heat storage, insulating layers and metabolism). 3. Number and sex of litter mates (act as heat storage elements). Human twins are born 19 days earlier than a single child. A sheep single birth occurs 0.6 day later than a twin birth, and a guinea pig single birth 3.7 days later than a litter of 6. Likewise an Alaskan mink has less than one day reduction in gestation period due to multiple birth [16]. 4. Seasons spanned by gestation (determine ambient temperature range). An Alaskan mink has a shorter gestation period when it is born in spring further on toward summer. A zebu calves with a longer gestation period in November by three days than in October [16]. August conceptions for goats give a 1.5 day longer gestation than do February conceptions [16], the gestation period being of the order of five months. 5. Food available and consumed (metabolism generates heat). 6. Exercise (generates heat). 7. Altitude delays mating (it is colder at altitude), the timing of which could affect the gestation period by changing the time of year somewhat and hence the ambient temperature). Some of the factors that have thermal effects are wind, clothing or fur, diurnal and seasonal temperature fluctuations, thermal homeostasis by the animal, beds or dens, blood circulation, etc. The hyperbolic curve underlying these phenomena differs between species, even if event age is normalized. The available data show markedly different regimes of slope at the operating point: _ Slime mold: 7% increase of speed per “C increase. - Fetus (species unspecified): 1% speedup of gestation per “C increase. - Frog mitosis: 15% increase in speed per “C increase [17]. _ Rat gestation period increased 2.5 days (11.4%) for 11.5”C increase, or 1% per “C. Data from [18]. - Ferret gestation period decreased 2.08 days for a 15°C increase in temperature [18]. _ Rhesus monkey gestation period increased 1 day for 2’C increase [18]. _ Bat gestation period increased 5 days for about 15°C cooling [18]. _ Dynoflagellate alga Gonyaulax slows down when warmer [19]. Thus, a hyperbola can entertain an operating point on either side of the lowest point, and so the slope can be either positive or negative for different species. The positioning of the operating point at normal temperature for a species is not understood by the author. Note that a change of 4.72% in gestation period moves a species from one event age to another. Hence, small temperature changes can have large influence on percentage difference between an observed event age and the theoretical age.
Timetable
of Life
183
The young of the tree shrew Tupaia are in danger at any temperature under 20°C (see [20]). The normal temperature of its environment is 25°C. Thus, a shift of as little as 5°C for a long time can be a serious threat Also, the temperature
to this tree shrew species’ existence.
width
of the hyperbola
differs between
events
and species.
Some eggs
have a hyperbola width (temperature difference between asymptotes) of roughly PC, such as from 32°C to 40°C. Then these eggs cannot be left long at temperatures varying more than 4’C either way about the temperature of fastest development. Also “. . . loggerhead turtle eggs incubated in sand outside the 24°C to 34’C temperature range may not hatch” [14]. These facts are of grave concern in relation to global warming. An interesting set of thermal effects has been reported by Fagerstone [21], in the case of the Wyoming ground squirrel in Colorado. The date of spring emergence from hibernation is earlier if: 1. It was a warm winter 2. There
(average
air temperature
over past 5 months).
was little or no snow cover at emergence.
3. The den faced south, 4. The individual
therefore
was heavier
getting
more sun.
than most, hence warmer.
5. The date is not before the endogenously hibernation.
timed
Note that all of these factors seem to involve the basic cause of variation in date of emergence
(but thermally
affected)
a resulting time-averaged from the value determined
age to terminate
thermal variation by the series.
as
Likewise the time of autumnal immergence for hibernation is variable. The typical sequence of time of immergence is adult male, adult female, subadult, and juveniles, that is, in order of weight. This is a thermal effect, it would seem. Also females that weaned litters entered immergence four days earlier than those who had not done so, presumably because of the loss of body heat through lactation. The body temperature at the time a particular tissue is developing has a large effect upon the amount of development that occurs in the tissue. An example might be a dyslexic, in whom the right hemisphere can be very well developed, which the language areas in the left hemisphere are typically underdeveloped. Because of effects of this kind, there might be some basis for the zodiac which predicts different personalities determined by birth date. 4.2.
Other
Factors
Affecting
Reported
Data
Reported event ages are affected also by some natural processes nocuous steps in obtaining and processing data for publication:
and by some apparently
in-
times. 1. Use of crude or indirect inaccurate ways to measure event or fertilization of the definition of an event, so that something else happening at another 2. Misunderstandings time is noted instead. An example is birth: does one look for the first sign of the birth process, the first exposure of the fetus, or completion of the process? is bimodal, the average will miss both peaks and so 3. Averaging of data (if the distribution will be a failure; averaging is not harmless even if the distribution is unimodal or trimodal, because information in the frequency distribution such as the existence of peaks, which is usually quite meaningful, is lost). 4. Roundoff of observed event age to fewer significant digits can make data too crude to be useful in comparing with the event age list. 5. Use of large time units which enable an event age to be reported crudely as a small integer, presumably to avoid the issue of error magnitude; use of large time units, such as integer months instead of days, can make data too crude to check against the event age list or other reported observations. 6. Confusion between events and stages (periods between events), such as in many publications in embryology.
A. B. CLYMER
184
7. Some organisms have found ways to avoid the use of times fixed in advance for event occurrence. A plant which produces seeds is an example; it germinates not as a timed event but whenever its criterion on physical conditions is satisfied. Another example is offered by almost all crow-like birds, who lay a second clutch of eggs if they lose the first. 8. Some organisms have put two timed events in a series, as an improvement upon a single event with an unsatisfactory event time. Examples are species in which the female stores sperm for a long period of time before allowing fertilization to take place or else stores the embryo in a dormant state: - Cavia porcellus, Bos taurus, sheep: fertilization a few hours after ovulation [22] - Canis familiaris: fertilization several days after ovulation [22] - Felis catus: fertilization 2 days after ovulation [22] - Golden hamster Mesocricetus auratus: fertilization 2 hrs after ovulation [22] - Mus muscolus: fertilization 5 hrs after ovulation [22] - Rattus rattus: fertilization 4 hrs after ovulation [22] - Rabbit Oryctolagus cuniculus: fertilization immediately after ovulation [22] - River otter: delayed implantation [23] - Skunk, weasel, tammar wallaby, bat, armadillo, kangaroo, nutria, red panda: delayed implantation [24] - Fisher: 9-10 months delay [24] - Hippopotamus: mother can delay birth when disturbed - Stoat: 10 month delay [25] - Armadillo: can delay a year or more - Seal: dormant 3 months, grows 8 or 9 months - 100 species of mammals delay implantation [23,24] 9. Like averaging, range cropping, according to some rule of thumb for disqualifying outliers, can be destructive of information in a frequency distribution having two or more peaks. 10. Most published data for egg hatching are measured from laying, unfortunately not from fertilization. Data from fertilization to laying are not easily obtained. 4.3. Stability and Thermodynamics The Second Law of Thermodynamics
is unquestionably true (that organization and energy
must always degenerate toward the state of disorder). It would appear that this requirement is violated by the living, the precisely timed development, and the evolution of organisms, in which there is an ongoing reaching for greater organization. The answer lies in the fact that life is possible only in a region in which conditions are sufficiently constant. If a large enough random disturbance comes along for a long enough time, life is wiped out to some extent in the region. Indeed, it has been stated that at least 99% of the species that ever existed have subsequently become extinct, presumably because of severe conditions arising and enduring. A possible understanding of this fact is provided herein (Section 4.1.3), namely, in that eggs and other immature offspring are fatally vulnerable to temperature excursions outside a narrow band. Another interesting aspect of thermodynamics in relation to life is that the building of timing molecules, a process which produces orderly structure, is accomplished by random motions of and within molecules. Clearly this is not impossible, but it is extremely precarious with respect to temperature variations.
5. FITS TO PUBLISHED 5.1. Some Notable
DATA
Sets of Data
5.1.1. Clawed toad ovum cleavages The data in Table 3 show a surprising agreement between observed ages of ovum cleavages for Xenopus laevis (clawed toad) at 21°C ( see [26]) and the nearest event ages from Table 1.
Timetable
of Life
185
Table 3.
I
I
I
390 min
11
396.09 min
F
-1.56
In Table 3, it can be seen that only two of the 11 observed data lie more than 1.18% away from an event age listed in Table 1. The figure 1.18% is one quarter of 4.72%, which is the distance between any two consecutive entries in Table 1. Hence, an error of less than 1.18% means that an observed datum is closer to an event age in Table 1 than to the midpoint between two successive values in the table. Such a case is called here a “success” (S). A “failure” (F) is a case in which the error is more than 1.18% (but less than 3.54%), it being closer to the midpoint than to a tabular entry. Refer to Figure 1 for a depiction of success and failure. --+ +
I
I
success 2.36%
II
I -
+
failure 2.36% +
III1
-
4.72%
+
j-l
-+
success +1.18% t
II
-
+
j+l
j
I
I +
_i+Z
Figure 1. Definitions of Failure (F) and Success (S). The + points indicate event ages with serial numbers given below in terms of j. A “success”
(often designated
herein by S) is an observed event time oc-
curring no more than one quarter of an interevent spacing from an event age in either direction.
The spacing for two successive event ages is 4.72%, so the
width of “success” band is k l.lS%,
or a total width of 2.36%, centered at an
integer value of j. A “failure”
(often designated
herein by F) lies in the band between two
success bands. It too is 2.36% wide, so successes and failures are equally likely a priori. Thus, a success occurs when an observed datum comes closer to an event age than to the midpoint between ages.
The example in Table 3 shows a slightly higher degree of success than is usual, namely, 9 successes out of 11, or 82%. It is presented here partly to enable a prediction to be made on the basis of the formula: if the two disagreements in Table 3 are due to excessive rounding in the observed (reported, at least) data, then it is predicted that the calculated tabular values will be found to be better representations than the reported values are. If this prediction were to be found to be true, it would be very persuasive on behalf of the formula underlying Table 1. Most scientists
A. B. CLYMER
186
would prefer the linear regularity of the reported ages, which would have to be abandoned if the formula gives a better fit. A complication of experiment and analysis arises due to the extreme thermal sensitivity of event ages for these early events [27]. 5.1.2. Piaget’s developmental
stage transitions
The data in Table 4 show an agreement of event ages with the postnatal transition ages between Piaget’s stages in the development of human intelligence from Table Id (postnatal). Table 4. Piaget’s data for the development
of intelligence.
Five of the six results are successes (S), a finding which is not significant. The implication would be that a new functional structure appears to be incorporated into the developing brain at approximately two-year intervals, giving it new capabilities in problem solving, but this conclusion cannot be drawn from the data given. 5.1.3.
Early
embryo
events
Table 5 shows the data found for cleavages and implantations. Overall, there are 18 successes to 10 failures, or 64% success. This percentage is in line with results for gestation data. See also [2, Table 11, for more data concerning fertilized ova and events in embryos and fetuses. 5.1.4.
Gestation
data
The largest body of data, thus far found by the author, are the gestation periods of 672 species reported mainly in [16]. These data are included in Table Al in Appendix A. About 70% of them lie closer to event ages than to midpoints. This distribution is enormously statistically significant. The probability of it occurring by chance is 2.54 x 10mz3 (see [l]). This finding establishes the validity of the formula, for gestation data at least, beyond any reasonable doubt. Comparably good results are obtained for most other gestation data obtained subsequently. Most of them are included in Table Al in Appendix A. An exception is the table by Harvey and Clutton-Brock (281, in which only means are given, averaging over even bimodal and quadrimodal distributions. The results show how grave this mistake in data processing can be: 33 successes and 41 failures, or 45% success. The primate gestation data given by King and Mitchell [20], which are incorporated in Table Al in Appendix A, in themselves make a nice cameo study. Successes are Sl%, failures 39%.
Timetable
of Life
187
Table 5. Data found for cleavages and implantations.
Cricetus aumtus [22]
1 Frog [17, Chapter 181
Frog [17, Chapter 201
One of the more interesting animals for its gestation data is the wildebeest. Different authors say that all calves are born in a three day period or three week period. The explanation seems to be that the gnu, or black wildebeest, has a reported gestation period of 8 to 8 l/2 months, or 243.5 to 258.7 days, whereas the blue wildebeest has a reported gestation period in the range from 249 to 255 days. The event ages in this time period are 242.0 and 253.4 days. Apparently, then, the blue wildebeest has a single peak, hence, a narrow range, while the black wildebeest spans two peaks, hence is bimodal with a wider range. The three day range is within the three week range. As Hemingway [31] puts it, “. . . all the calves . . . are born within a three-week period and most of these during three halcyon days.” The Asdell gestation data were fitted by a trial and error process. An initial guess for the unknown constant (finally found to be 1.0472), together with a multiplicative constant chosen to equal 21 (chosen because the largest set of identical published event ages was 21 days for many species of rodent), was used to calculate a complete set of tentative event ages over the range of interest. The resulting errors of fit showed waves of positive and negative errors. It was noticed that one particular value of the constant, found to be 1.0472, made the error go to essentially zero amplitude, and visible waves were absent.
A. B. CLYMER
188
Table 6. Estrous cycle data.
Species (Ref.)
Farmed fallow deer,
Wide range, shouldn’t
Pere David’s deer [33]
Bimodal?
Peaks at
Lemur,
ago crasszcau
Cercocebus atterimus Mangabey, Cercocebus torquatus [20]
33.4d
33.3 d
+.30
s
Table 6 is continued on the next page.
Timetable of Life
189
Table 6. continued.
Rhesus monkey,
Later it was found that one of the event ages was very close to one day (24.01 hrs). Then the formula could be simplified to merely 1.0472 to the jth power, in days (with a multiplicative constant of 1 day suppressed but implied). 5.1.5.
Estrous
cycle
data
There are nearly as many failures as successes in Table 6. That is, there is no evidence here that the series applies to estrous data. The question of whether the stop or start of each estrous period is an event remains open. The human menstrual period is commonly spoken of as being 28 days. If menstruation is a multimodal event with five event ages, then one would expect to find a frequency distribution with peaks at the five event ages closest to 28 days, namely, 25.254, 26.446, 27.695, 29.002, and 30.37 days. However, no source found by the author shows any sign of peaks; the distribution is essentially bell-shaped with some small deviations. Perhaps the peaks are broadened by thermal variation or imprecise determination of onset of estrus. 5.1.6.
Events
in lives of religious
leaders
A list of 23 notable events in the lives of religious leaders gave 12 successes and 11 failures. That is, such “events” (divine vision, left home seeking truth, entered politics, crucifixion, vision of God, new religion conceived, etc.) are not biological events in the sense used herein, and the series does not apply. 5.1.7.
Distribution
of gestation
range
as percent
of mean
A study of the frequency distribution of the quotients of ranges to rneans has led to some important results. The data shown in Table 7 are for gestation periods. The list shown in Table 7, which is equivalent to a histogram, shows 9 peaks, each close to an integer multiple of 4.72%. That is, range is quantized. All data were obtained from Asdell [16], and they are all gestation data. This list is the clearest evidence for the existence of multimodal event ages. The slight displacements of some actual peaks from theoretical peaks are ascribed to inconsistent lopping off of tails in frequency distributions to get published ranges. One can get a fair estimate of the number 1.0472 by using the peak locations in the table. For example, the last peak appears to be at 43%. Dividing by 9 (it is the gth peak) and by lOO%, one obtains 431900 = .0478, whence one has for the spacing constant the value 1.0478, which is quite close to 1.0472. This result is important in that it affords a totally independent “ballpark” check of the approximate magnitude of the constant “1.0472” gotten from gestation data per se by regression. This observation should still any doubts that 1.0472 is approximately the best fitting value of the spacing constant.
A. B. CLYMER
190
Table 7.
I
7-7.99
2
8-8.99
6
9-9.99
3
10-10.99
3
11-11.99
3
12-12.99
0
13-13.99
6
14-14.99
3
15-15.99
4
16-16.99
1
17-17.99
1
18-18.99
3
19-19.99
0
28-28.99
1
*Both actual and theoretical
2
peak.
Actual peak 2 x 4.72 = 9.44
Theoretical
peak
Actual peak 13
x
4.72 = 14.16 1Theoretical
4 x 4.72 = 18.88
16 x 4.72 = 28.32
peak
Peak*
1
Peak*
I
Timetable
of Life
191
5.1.8. Opening and closing eyelids The eyelids of embryos of certain animals change state between open and closed at fairly predictable
post-fertilization
ages, as shown in Table 8. Table 8.
Species
Reported
Eyelid Event
NearyLfvent
% Error
S or F
Age Opossum
Close
12.25 d
12.07 d
+1.47
F
Ezat
Close
18
18.29
-1.61
F
Swine Guinea Die: Opossum
Close
1
Ooen
50 I
Open
59*
50.44 I
62*
57.93
-.88 1 -1-1.85
1 I
s F
63.52
-2.39
F
Opossum
Open
72
72.95
-1.32
F
Man
Close
70
69.66
+.49
S
Sheep
Open
84
83.78
+.26
Swine
Open
90
91.87
-2.08
1
F
Man
Open
139.1
1 +.64
I
S
I
140
I
S
*These two data are from [41]; all others are from (221. Note the large inconsistency
in “opossum open” data.
The results are S = 9 and F = 6, or 60% success. Part of the trouble is that all data are reported in integer days, a bad habit in pediatrics and development books. The resulting roundoff drives the percent success closer to 50% (purely random). 5.1.9. Red Howler Monkey gestation The Red Howler Monkey gestation data make an interesting case for analysis. the data published by Crockett and Sekulic [42]
Table 9 shows
Table 9.
The author’s int.erpretation is that the 6 animals were in two different event age subspecies: five at or near 192.2 days event age and between event ages 183.5 days and 192.2 days. Thus, the event age series seems to be very helpful in analyzing reported data.
A. B. CLYMER
192
5.1.10.
Viral
events
The author has found only very few viral timing data [43], which are shown in Table 10. Table 10. Event
Reported Time
DNA enters cell Replication
Near~~~vent
S or F
say. time zero
of DNA
I
5min
1 4.954min
Start of synthesis of head and tail proteins
8 min
7.857 min
I )
F
Completed
13min
I 13.05 min
I
S
virus
s
I
These data are too few to allow a conclusion to be drawn, but more data should be sought. 5.1.11.
Scientific
contributions
Table 11 shows some data for the ages at which some great scientists made their contribution. Table 11.
Table 11 is continued on the next page.
Timetable
of Life
193
Table 11. continued.
% Error
S,F
1P. Curie 1Joliet-Curie 1H. Lorentz
R.A. Millikan
-0.42
1C.V.
S
-0.04
s
-1.38
F
+1.5
F
-1.83
F
f0.92
s
-0.75
s
-1.14
s
C. J. Davisson
+1.39
F
G.P. Thompsor
+2.26
F
+1.09
s
-0.73
s
-1.83
F
J. Chadwick
R. Descartes
In Table
11, there are 48 successes
more significant contribution
and 23 failures,
is that scientific
The statistical
or 68% success.
were given to trying to identify
was made, using several sources.
The implication event ages.
if more attention
creativity
significance
mean, for this to be a firm conclusion;
The table
the exact month
would
be
when each
Too many of the data are reported as integer years. is made possible
is not high enough, it is only an indication.
by substance
release events at
being only three sigmas
from the
A. B. CLYMER
194
5.1.12.
Menarche
and menopause
Menarche is an event which is quite variable in its age of occurrence. Historically, it has shown a steady and substantial decline with time by three years in 200 years. This relationship might be due to the increase in the warmth of clothing, housing, schools, etc., over the past couple of centuries. At a given time, there is about a 5-year range of ages of occurrence of menarche. This range spans several event ages: 9.966, 10.867, 11.811, 12.800, 13.835, 14.919 years. No data have been found by the author which would indicate the presence of any peaks in the frequency distribution. Weight is a factor, probably through its thermal effect. Menopause has an unusually wide range of occurrence, hence, event ages. The author has found no presentation of data that resolve the supposed peaks. 5.1.13.
Chambered
nautilus
A study by N. Landman was reported in 1988 in which radioactivity measurements were made of the ages of the chambers of a fully grown chambered nautilus [44]. These data are quite well fitted by the event age list. The given facts were: “. . . the nautilus hatched in 1957 with seven chambers and added eight more in the course of the next year. Over the next decade the animal formed new chambers at a diminishing rate: the last fully sealed chamber took seven months to form and was completed in 1968, a year before the animal was netted . . . The shell has 31 chambers in all.” In order to match these observations, the series must be fitted to the given data to get the overall-best-fitting by choosing an event age when the first chamber is started. The choice made was to start the first chamber at event age 1.993 months (i = 23). The other choice that had to be made was the number of event ages per chamber built. The best fit was to take every third event age as the start of a new chamber. Then, having thus fixed two parameters, all other information about the building process can be read from the event age list, as shown in Table 12. The agreement between the predictions of the series with the reported data is within one digit (month or chamber) in each case. Perhaps the differences can be ascribed to experimental error and temperature variation, The agreement is good enough to support the statement that the growth of the chambered nautilus is an exponential function, as in the formula and as asserted by Landman and Cochran [45]. The chambered nautilus provides the only good example available now of a lifelong longitudinal verification of the series. It would be promising and worthwhile to seek and analyze similar data for other creatures having periodic structures. One question remaining is whether no building takes place after the second and third event age of a set of three, the only building occurring after the first event age and until the second event age of the set. 5.1.14.
White
and black children’s
development
Geber [46] has presented data for the postnatal behavioral development of black and white children (see Table 13). The result is only 33% successes. Perhaps this indicates that the “events” are really interevent stages rather than events. 5.1.15.
The central
nervous
system
The brain, like any other organ, has its events in the development process. Some of these are to apply “insulation” to “wiring” already in place, in order to start it operating. Growth of new neurons is confined to prenatal development.
Timetable
of Life
Table 12.
Table 13.
M’3! 19:6-8-N
195
A. B. CLYMER
196
One technique for observing present, the research permits a be compared with the formula. growth processes in certain age
newly functioning areas of the brain is with an EEG [47]. At resolution of time only to integer years, so their findings cannot However, it has been shown already that there are well defined ranges.
Functionally the brain contains hierarchies of sensory, multisensory and abstract pattern recognizers, each of which puts out a signal when it recognizes something in its category. For example, a frog recognizes a fly in motion nearby. Each pattern recognition unit consists of several inputs conveying signals indicating whether elements of the pattern are present, and an output signal when enough key inputs are present to indicate the whole pattern. The brain contains also hierarchies of pattern generators, each of which elaborates an abstract or general command into individual muscle action instructions. At the top is a command such as “Get that fly,” and the lower pattern generators convert this command into detailed instructions to tongue muscles [48]. It is postulated that these capabilities first appear at event ages. They might be a necessary condition for the physical and behavioral changes noted in Section 5.1.2. If such patterns are built-in before birth or the final metamorphosis, they can be used as a basis for constructive behavior, such as building a web or nest, learning a mating dance or song, etc. This might be the basis of instinct: genetically produced blueprints for key tasks. Similarly, such a system can be the basis for a simple organism simulator. 5.1.16.
Other bodies of data
It is known that many species from butterflies to lobsters to fish to birds to land mammals to whales migrate. Most of the data are quite nonquantitative, speaking in terms of a month by name but with no dates given. The author has been unable to collect enough good migration data to permit an analysis. There seem to be wide ranges of migration dates for a particular species. The range might be due to thermal variance or multimodal event spectra. There is one paper on the “migration” of toads in Wales [49]. It is about male and female toads going to the nearest pond for mating. Due to the frequent occurrence of deterrence from cold weather, which reduces drastically the daily attendance at a pond, and due to the small resolution of published data graphs, one cannot analyze the available data very well. However, the author thinks he can see evidence of a trimodal attendance spectrum, which suggests the possibility of multimodality. Bird migration is better documented. They have an event which produces “flight frenzy” or restlessness which is neuromuscular excitation for flight. It stops at the end point age of migration [50]. The distribution of migration arrival times is quite broad for most bird species. Perhaps the explanation is related to there being different generations or ages in a flight season of a species, or different points of origin being at different distances away from the destination. Bird molting is also under the control of an inner timer. Butterflies migrate also. However, the cycle is not performed by any one generation; several generations of monarch are involved in one round trip (511. Each of these generations has a different set of event times appropriate to its role in the migration cycle. Another category of events for which mainly inadequate data are available is mammalian prenatal development. It is the custom in this field to report all events to the nearest integer day, but such data are not desirable for testing the series of event ages given by the formula. Perhaps in the future these data will be obtained and reported in decimal days, or at least integer days and hours. Child behavior development is another field with excessively crude event ages reported. Although the data of Piaget (Section 5.1.2) appear to be marginally successful, it must be borne in mind that the reported data are ranges in years expressed in small integers. The data reported by Geber [46], Section 5.1.14 herein, suffer from the same defect, but they too seem to succeed.
Timetable of Life
197
In this field, also, it would be desirable to strive for more precision in measurement and reporting of event ages. One interesting observation [l] is that the formula has very surprising success in its fit to the series of times obtained by multiplying or dividing 24 hrs by 2, successively. There are 18 octaves of success in this run. The success is due to the proximity of 1.0472 to the 15th root of two. Cell cycle times give a fair body of data [52]. A sample of 25 kinds of cells gave 68% successes, which is statistically significant at the 3% level [l]. Cell mitosis data given in [l] have 83% successes, which is significant at the 1% level. A body of 94 mammalian prenatal events gave 65 successes, a result which is significant at the 2% level. A table of single cells and early stages of sea urchins, nematodes, mice and frogs [2], is significantly fitted by the formula at the 4% level. 5.2. Goodness 5.2.1. Error
and Significance of Fits
distribution
The differences between published and nearest calculated event ages are the errors of fit. For gestation data their frequency distribution is well enough described by a bell-shaped curve. See Table 14. Its standard deviation (sigma) is a factor of about 1.012. The fact that the errors are distributed like a bell-shaped curve is suggestive that they are random in magnitude and distributed in a Gaussian manner. Really the distribution is lognormal, but it is so narrow that a Gaussian distribution is a good approximation. Table 14.
This error distribution is nearly Gaussian, indicating that the errors are random, approximately. The peak is at zero error. The fact that there is no substantial offset of the peak from zero indicates that there is no constant error offset. The positive tail shows a small rise at the end, which could be a folding back of the tail in the next error class. This long tail would be consistent with the lognormal identification of the distribution. A well-intentioned reviewer of [53] noticed that some of the small integer numbers are fitted by the series better than would be expected from chance. On this basis, he extrapolated to the fallacious conclusion that the series worked only because of this arithmetical coincidence. On that basis, the paper was rejected. It is time to set the record straight. It is true that the first eight integer months are successes [l], regardless of what event might occur then. It is easy to delete such data in the interest of reducing statistical bias. On the other hand, integer days from one to 70 score only 40% success. The same is true of small integer hours, the first ten of which score 80% successes, regardless of event, but the success rate drops off to the expected level (50%) above the first 25 integer hours. Integer weeks also are biased, the first ten giving 80% success and the second ten giving 70% success.
A. B. CLYMER
198
To test the overall importance of the foregoing small integer problems, the author reran the gestation data analysis, deleting all integer hours up to 24, all integer days up to 21, all integer weeks up to 20, and all integer months up to 12. The result was 76% at low event ages and 58% at high event ages, very similar to the results with the small integer data included. 5.2.2.
Measures
of likelihood
of fit by chance
The errors of the calculated event ages relative to published values can be expressed in terms of success or failure to lie within 1.18% of the closest event age. Successes and failures are equally likely a priori. Therefore, successes (or failures) amounting to 70% or more of a large set of data being tested would be surprising, much more surprising than one might suppose. The diagram in Figure 1 (Section 5.1.1) shows how “success” and “failure” are defined. The formula for the number of standard deviations from the mean is No. of sigmas = ,prob.
deviation (as a fraction) x N f o success x prob. of failure x N]i/z’
where N is the number of cases. One can calculate the probability that exactly z of n trials of flipping a coin will be heads (or in evaluating event age data that there will be z successes) from the following formula: I
P(?
n, 4) =
qnz!(n 7L - z)! ’
where q is the probability of a head (l/2). To calculate the probability that z or more trials will be successful, one must repeat the calculation for 2, z + 1, zr+ 2, etc. up to z = n, then sum the results. 5.2.3.
Testing
for bias
Since most of the gestation data in hand are from [16], and since most of the data of all kinds are gestation data, it would be a prudent statistical check on Asdell as a source to incorporate the gestation data from Asdell into two subsets that might be chosen as follows [54]: 1. The first and second halves of the book, or 2. Odd and even chapter numbers, or 3. Draw chapter numbers out of a hat to insert into two other hats. 5.2.4.
Gestation
fit error
vs. age
The errors of fit for gestation periods of mammals are found to be 83% for animals with short gestation periods (up to 24 days) and 60% for animals with the longest gestation periods. It is believed that the difference is due to the fact that the longer period is more likely to include major temperature variations, which disturb gestation periods as they do all other event ages. The longer period brings in wider deviations from normal temperature. 5.2.5.
Overall
goodness
of fit
To obtain an overall measure of fit of all data to the series, one could find the total numbers of successes and failures, then divide successes by total and multiply by 100%. This is done below. Table 15 is a collection of all of the fitting results obtained by the author as of 1986 [l]. To add the data found meanwhile would not make a significant difference in outcome. Note from the table that the overall success rate of 922 events is 70%. This is far higher a result than is reasonably likely by chance. It is 12.4 standard deviations from the mean. The gestation data by themselves give 9.88 standard deviations from the mean. The implication is that there is indeed a regularity in nature which is very similar to the formula or series.
Timetable of Life
199
Table 15. Body of Data
References
Mammalian gestation
(
672
1
69
1 See Appendix A, Table Al
Bird incubation Deriods
1
14
1
64
I 1551
Reptile incubation or gestation periods Insect metamorphosis Development of Rana pipiens, 18’C Biological rhythms T4 virus building
10
80
[551
9
89
[55-571
23
65
7
100
Various 117,431
1581
1
100
24
83
P71
4
75
156,591
Mammalian prenatal events
94
69
[I71
Mammalian eyelid opening or closing
13
69
[I71
Cell cycle times of normal and cancer cells
25
68
[521
9
77
I601
20
90
[26,61,62]
122
70
Cell mitosis Start of synthesis of a compound
Slime mold stage start times Events in fertilized ova All of above events including 650 successes
Considering that the empirical formula was fitted only to gestation data, it is remarkable that it then fits also such a wide variety of other event data.
6. MULTIMODALITY 6.1. Distribution
of Range/Mean
Data
The gestation data include many figures given as ranges of values. Interestingly, the ranges divided by the means tend to cluster strongly around small integers multiplied by 0.0472, as portrayed by the frequency distribution, Table 7. This can be interpreted to mean that different species can have different numbers of event ages for gestation. For example, a species, having a range that just includes three successive event ages for a particular event, will contain individuals with various ones of the three event ages. The reported range will be about 3 x 0.0472 = 0.1416 multiplied by the mean. A species can have as many as 8 or 9 event ages per event.
6.2. Other
Evidence
of Multimodality
In some cases, the literature provides gestation data for each of a substantial number of organisms. In such a case, a frequency distribution can be plotted. It will be easy then to see that reported event data usually cluster around two or more event ages. The peaks are not necessarily of equal height; they usually have a bell-shaped envelope over the peaks. Asdell [16] gives no direct data for multimodality of gestation ages. However, he states that the guinea pig has a bimodal distribution of estrous cycle periods (peaks at 16 and 17 days). Hence, one should be alert for multimodality of all events in all species, with the expectation that most will show it. 6.3. Significance
of Multimodality
If an event has a multimodal event age distribution for a particular species, the implication is that the species has two or more subspecies differing at least in this respect. These subspecies have different timetables. Geographical samples of organisms could have differing frequency distributions of event ages. These data could be useful in finding the geographical origins of individual organisms. Perhaps the greatest significance of multimodality of event times is that it gives a species more options (subspecies), enabling a better chance of survival of some subspecies.
200
A. B. CLYMER
7. THE MOLECULE-BUILDING 7.1. Description
PROCESS
of the Process
A conjectured concept of the process of timing is that each of a set of neighboring cells builds a certain type of molecule over a period of time which might range from seconds to years. When the molecule is completed in all cells simultaneously, it produces an event having physiological or anatomical consequences. The building process can take a long time because the molecule is built one unit at a time in series, in contrast to most organic chemical building processes that are distributed, parallel, and are expedited by an enzyme. The building is imagined to consist of moving one unit along the molecule by thermal impacts from one end to the other, where it is then attached. The “molecule” is believed to be mRNA. The fixed end is believed to be attached to a gene on a chromosome. As the molecule gets longer, new units take longer to be installed. Addition of deuterium oxide to the fluid in the nucleus also makes the process take longer, indicating that water has a role in the process dynamics. stochastic simulation of this construction process would be interesting. A further stochastic
A
process can be operating.
If a unit is being moved along by cilia-like molecular extensions, there might be circumstances when the advancement of the unit does not occur. It could be as if the unit took 19 steps forward and one step nowhere, thus adding 5% to the duration of the assembly of the unit. Consider the probability of a unit making it all the way through a gauntlet in which at each step there is a probability of failure to advance. Then the probability of completion of the total trip is the product of the probabilities of making it through each step. As more steps are added, the probability of completion in a fixed time decreases. The probability of completion in a longer time increases. That is, the longer the trip, the slower the progress. This effect could make the time of completion of a molecule a nonlinear function of molecule length. The foregoing description is not all new; see, e.g., [63]. It is now recognized that, in Drosophila and E. coli at least, the length of time until expression of a gene is determined by the time of transcription. The mRNA building process is capable of being simulated, even if somewhat speculatively. In [l] the process was erroneously described as being analogous to the tiltboard game Pigs in Clover. In this game, all balls are to be rolled into holes in the board and kept there. However, this is a parallel process, which is known to go quickly, whereas mRNA building is believed to be a serial building process, one unit at a time. The roles of temperature in the mRNA building process are not fully understood by the author. It will be clear, however, that increase of temperature would speed up thermal agitation that is moving units. But also increase of temperature could thwart the desired movement by changing the mix of molecular modes being excited. 7,2. Derivation of the Formula The process described in Section 7.1 can be modeled to yield a formula for the time required to assemble a molecule having a given number of units. Consider the trip required of a unit to add one unit to a molecule already existing. The time is proportional to the number of units to be traversed from one end to the other, i.e., to the molecule size. However, there is an additional time required, because some of the steps were not traversed on the first try, and they must be repeated. Moreover, not all of those repeated will be successful the second time. Thus, a series of contributions to time taken is obtained:
tj(l + k + k2 + k3 +e +.),
Timetable of Life
of size j and k is the fraction
where tj is the time to traverse
a molecule
try. However,
in parentheses
the sum of terms
vice versa). Now it will be clear that the post-fertilization
201
to be repeated
on each
is, say, (1 + e), where e can be found from k (or age at which a molecule
of size j + 1 is completed
is: A~+I = Aj(l + e).
I
This is the desired recursion formula. All other forms of the formula follow from it. It is known, empirically, that e = .0472. It is simple to calculate k if it is noted that the series 1 + Ic + k2 + k3 + . . . is merely the reciprocal of 1 - k. Then,
&=l+e, which is readily particular step.
solved to give k = .04507. This is the fraction of units that must repeat a All steps are essentially alike, so k and e are constants over all species and
events. The effect of temperature upon k or e is not easy to determine. Likewise, it is not obvious how to determine the effect of deuterium in the water, except that it increases the masses of the water molecules enough to have a surprisingly large effect upon time of assembly. 7.3.
Some Questions
The foregoing theory is so incomplete and uncertain that numerous questions arise. One would wish to know the roles of the DNA in the chromosomes, of the genes, of the mRNA, and of the ribosomes. Probably the process is somewhat as described for bacteria by Hendricks [64]: like circumferential bands on an earthworm, puffs appear on chromosomes for production of mRNA by activation of a particular gene, and the mRNA causes a ribosome to build a polypeptide chain (protein), which, along with other identical protein molecules from other cells, helps to cause an event. Presumably, it is the building of the mRNA which is of concern in Sections 7.1 and 7.2. Does an enzyme do the reading of the gene, causing the assembly of an appropriate unit on the end of the mRNA being built there by moving along the axis of the mRNA to the end? What tells an mRNA molecule that it is completed and may go on its way? What could go wrong to let another unit build on at the end? Is it an error in the DNA which then produces a longer mRNA molecule? Does it matter which ribosome the mRNA finds first, or will any one do? Presumably, any will do. What decides between a single event and a biorhythm? That is, what makes mRNA or a ribosome stop directing the manufacture of a protein ? Is the decision made at the gene or at the ribosome? What can start a biorhythm at a time other than the event age equal to the biorhythm period? An example would be menarche, starting not until the second decade but having a periodicity of a lunar month. How can mRNA building survive cell division? How can mutations of mRNA be passed on to the next generation, if at all? Is it possible that low frequency electromagnetic waves (e.g., at or below powerline frequencies) can cause bending resonance and fracture of mRNA molecules, later producing wrong proteins and wrong processes in cells?
8. BIORHYTHMS 8.1. Postulated
Production of Biorhythms
Theories of biorhythm production have been incomplete and vague. For example, a reviewer of [50] refers to “. . . our almost complete ignorance of the physiological processes involved in generating circannual rhythmicity.”
A. B. CLYMER
202
The genes were implicated by Feldman [65]: “. . . the clock mechanism is somehow encoded in the genes.” Direct association of a biorhythm with regulation of protein synthesis is pointed out in a review of [66]: “Recent experiments . . . indicate that biological rhythms may arise directly from the regulatory mechanisms of protein synthesis.” As mentioned in the Introduction, the theory in Section 7 leads to the concept that a biorhythm is produced if the molecule building process does not stop when a molecule (protein, i.e., hormone, enzyme, etc.) is completed and released, so that the process can be repeated over and over synchronously in some set of cells. associated with the first building.
The period of the resulting biorhythm is the event age
However, it is not a new idea that repeated rebuilding of a molecule accounts for biorhythms. Johnson and Hastings [19] make the following statement citing basic references: “. . . many models of the clock’s biochemistry have been proposed that variously involve sequential gene transcription, membrane properties, ion transport, mitochondrial oxidative phosphorylation, cyclic nucleotide levels, messenger RNA production, or translation on 80s ribosomes.” Also “. . . a particular messenger RNA transcribed from the gene locus undergoes a 15-fold oscillation in its amount during the circadian cycle,” and “Perhaps this oscillating RNA is involved in coupling genetic information to overt rhythmicity.” Another source on the repetition of mRNA building to get a biorhythm is [67]. Some biorhythms, such as the human female’s monthly period, occur at an age which is different from the period. This might be called two events in series: menarche, then the period. The author has not given much attention to series events, because it has seemed as if an all-parallel model accounted for events well enough. However, it might turn out that some of the errors in the application of the formula are due to series events being analyzed as if parallel. The only data found in the literature on this question relate to the slime mold [SO], in which most but not all event producing processes are in parallel. It would appear, then, that greater attention should be paid to series events in all species. There has been some confusion of terminology in the science of biorhythms. The term “biological clock” implies to the author a continuously interrogable reckoning of time. The term “timer” is less ambitious, being applied to a particular tick of time (an event age). The term “oscillator” is most appropriate when the waveform of a biorhythm is sinusoidal. A timer resulting in a switchlike action or a pulse can maintain an oscillation with a sinusoidal waveform in a second order system. For each case of oscillation, the second order system must be identified. 8.2. Biorhythm
Periods
on Event
Age List
Several of the event ages are significantly close to the periods of known biorhythms. One is 24.01 hours (the circadian rhythm which approximates most closely one day). Another is the next larger event age, which is observed as the circadian rhythm in humans, namely, 25.15 hrs. One year is represented as 366.5 days. A lunar month appears as 27.695 days. A week is the event age at 6.9424 days. From these remarkable matches, it might be concluded that the parameters of the formula evolved to give the formula these properties. Thus, it appears to be promising to check any other known biorhythm periods for any species against event ages in the list. This is done to some extent in Table 16. Another possible check is to test an absurdly chosen astronomical cycle time against the series. For example, the period of Venus as seen from the earth is 583.923 d, according to Feynman [68]. The nearest event age is 581.2d, giving an error of only +0.47%, which is a success. Since it is inconceivable that Venus could have any biological influence on earth, the agreement must be regarded as a meaningless coincidence.
Timetable of Life
203
Table 16. Some biorhythm periods compared with event ages.
Rhythm of body
Javanese human
This agreement is remarkable (3.9 sigmas from the expected value that the successes are due to chance). There have been hundreds of investigations of the effects of various light-dark schedules upon the timing of biorhythms. The phenomenon is well established, but theory is sparse. It is not apparent to the author how the theory herein can be extended to account for these light exposure test results. NOTE ADDED IN PROOF. It appears that not only normal but also mutant organisms have biological rhythms whose periods are event ages, as shown in Table 16. An example is Drosophila, which has a mutant perS with 19 hr period (cf. 19.07 hrs) and a mutant per’ with 29 hr period (cf. 28.88 hrs). See [75].
204
A. B. CLYMER
9. SYNCHRONIZATIONS 9.1.
With
Calendar
and Seasons
One of the properties of the list of event ages is that it has a tendency for certain dates to be listed for a run of years, give or take a few days [3]. Hence, these ages can be selected to make a certain event occur at nearly the same time every year for some number of years. See Section 3.5. It is almost as if there were a circannual rhythm producing the event. However, this is not necessarily the case, because there are some events which use some but not all of these event ages. Examples might be black bear, lion or shark mating, which is skipped every other year [76,77], humpback whale which calves at two to four year intervals [78], or African elephant, which has a calf every third or fourth year. Of course, it might be a rhythm with a two year period. As a result of such cases there arises a question of the occurrence of such rhythms versus absolute timing. It is difficult to tell which occurs in many cases. It would be necessary to obtain a large body of precise data in order to choose between the two possible theories in particular
cases.
There is an overall pattern of the event ages which seem to repeat from year to year. There are streaks of such ages. Most of the streaks are short, but a few run to 10 or more years. The irregularities of these streaks constitute a signature which could enable a meaningful check of observed data against an absolute timing hypothesis. 9.2. With
Solar Days
and Lunar Months
The same pattern shows up when one works with lunar months or solar days as units for the event age list. It works because one lunar month, one solar day, and one solar year are all in the list of event ages (a surprising coincidence). One is led to speculate that the constants in the formula defining the event age series were “selected” over evolution to include these event ages. To have its event ages synchronized with lunar months guarantees synchronization with tides, which are essential mechanisms for many organisms. Other organisms exploit the phases of the moon per se for the light conditions provided. 9.3.
With
Mate
It might be the case for some species that a pair must be synchronized in order to reproduce. Synchronization of the entire species would insure this condition. Another possibility is that a sperm might have to be synchronized with an ovum in order to achieve fertilization. This condition could be met by providing a large number of sperm running on variously shifted timers, so that the ovum could make a selection on the basis of timing. 9.4.
Between
Generations
If the time of year (or lunar month or day) of mating by parents is the fertilization time of the offspring (no storage of sperm), their sets of timers can be synchronized to the calendar year (or lunar month or day). If mating is an event having an event age tied indirectly to the calendar, such as by being repeated every year or twice a year, then so will the timetable of the offspring be tied to the calendar (including eventually the dates of mating). Then each generation will follow the calendar (apparently). Such relationships between generations can give rise to subspecies which mate at different times of year and have other events at different sets of event ages. 9.5. Within
Ecosystems
It is crucial for the stability and well-being of an ecosystem to maintain its system of event age timetables. If a prey species stops appearing at the time and place it is needed by a predator species, the predators will suffer, perhaps fatally. This result, in turn, could affect another species adversely, such as a plant to be pollinated.
Timetable of Life
205
One of the mechanisms that exist potentially for the disruption of ecosystems is climatic drift. As physical conditions (particularly temperature) shift within an ecosystem, its event ages, as observed, change also, possibly altering the functional relationships among species. Still more important is the impact on an ecosystem when some of its species are wiped out by an unusual temperature change. The young are especially vulnerable. The cause of death might be the consequence of a developmental event prevented by temperature from ever occurring. Even quite a modest temperature change in the environment of a young organism or egg can have fatal results, as shown by the data in Section 4.1. One can imagine the demise of the dinosaurs as having been perhaps due to this danger. Considering this thermal sensitivity, it is remarkable that nearly 1% of the species that ever existed still do. Organisms that have thermal homeostasis are able to cope better against environmental temperature shifts. However, this advantage is lacking before the thermal homeostatic system develops in the adult organism. Organisms living in shallow fresh water have only a temporary protection against a temperature change in the air because of the finite thermal capacity of the water. The same is true of organisms living in the shallow or upper water of an ocean. The shapes, sizes and locations of the curves of event age vs. temperature could conceivably have evolved somewhat to be wider and shallower, if that is physicochemically possible.
10. QUANTIZATION 10.1.
Quantized
Growth
A growth process takes place between two event ages corresponding to the growth start and stop events. The growth rate might be constant, if the process were driven by release of a growth stimulator at a constant rate. If the growth stimulating substance is released by the very cells that are being created in the growth process, then the growth would be exponential, i.e., progressively faster. If the growth is at a constant rate, say for simplicity, then the resulting final magnitude of some characteristic dimension will be directly proportional to the time period between events. The event integers j at the beginning and end of the growth period may be thought of as quantum numbers that characterize the growth process. To specify these quantum numbers amounts to specifying the two event ages and, hence, their difference. Another possible pattern of a local growth is in the form of a pulse (brief and intense), as was recently regrated for lengths of babies [6]. This growth would be caused by a pulse of a growth promoting substance at an event age, according to the theory herein. 10.2.
Dimension
Spectra
Since most events have multimodal occurrence times (see Section 6), it follows that a growth process in a species can result in different quantized lengths in different individual organisms. One then has a spectrum of possible dimensions, each with its own amplitude representing relative frequency of occurrence.
11. EVOLUTION 11.1. 11.1.1.
The
Trend
Subspecies
in Event differing
Times
in Evolution
in event
ages
Subspecies differing in event ages are important in evolution. They may be portrayed for an event by a spectrum of event ages. Typically, this spectrum consists of several peaks, each at an event age, the event ages being consecutive. Each peak may be thought of as a subspecies. The envelope (curve tangent to the tops of the peaks) is a bell-shaped curve. This picture plays a prominent part in the process of evolution.
A. B. CLYMER
206
11.1.2.
Marching of event age subspecies sets
A bell-shaped spectrum of subspecies is not a stable configuration. Indeed, it has a standard dynamics. Normally, the subspecies at the highest event age has advantages over the other species by virtue of its larger size, due to longer periods of growth. Accordingly, the later peak will usually grow at the expense of the other peaks. The same is true of the second peak; it will grow at the expense of earlier peaks. The result is that the envelope glides smoothly to higher ages, enclosing a gradually changing set of event ages, since subspecies will be dropped off by extinction at the early end and added by mutation at the high age end. The progression of sizes with time in evolution can reach remarkable extremes of size. Examples are giraffe legs and necks, dinosaurs, whales, mammoths, etc. Since a doubling in event ages takes 15 event age intervals, several doublings of size are understandable and credible over the eons of evolution. 11.1.3.
Dwarf species
It is not necessarily true that marching of the envelope will be to higher ages. There can be local climatic and ecosystem conditions which favor a smaller body. In such a case, one observes a marching to lower ages, producing smaller species, such as human dwarfs or pygmies. If the smaller body size is compatible with long-enduring physical conditions, the dwarf species can optimize (find the best set of event quantum numbers j, one per event per species) and become stable (no longer evolving). If the envelope drift to lower ages is too slow to keep up with a shift in climate or other physical conditions, a species can become extinct. The degeneration of a species can be accelerated by an abnormal temperature over a long period. Likewise, a species can become extinct by not being able to move its envelope to higher ages fast enough. 11.1.4.
Multimodality
of different events
In the foregoing material, there are discussions of a subspecies comprised of individuals having the same event age for a particular event. However, there can also be subspecies defined in terms of the event ages of all of their events. It is unknown what correlations there might be in nature concerning the various event ages for a pair of events in one species, for example. One might expect to find an individual using consistently a high or a low event age for every event, if each event were a growth trigger or stopper. 11.1.5.
Speed of evolution of a species vs. multimodality
It has been observed by the author that the rate of evolution of a primate species, which correlates with its position in the tree (fastest for those farther out from the trunk), correlates also with its degree of multimodality of gestation period. Then one could generalize to the hypothesis that the rate of evolution of any species correlates with the degree of multimodality of its event ages for any of its events. A special case, yet obeying the principle, would be a species no longer evolving and having only one event age per event. One possible explanation of the general correlation would be that a rapidly evolving species, with its envelope rapidly moving to higher ages, would not have time to lose its peaks at lower ages at that same rate, making the envelope span more event ages. In fact, the same could be true of a species whose envelope is moving rapidly to lower ages during some unusual circumstances of long duration. The process of delaying an event to the next later (occasionally earlier) event age, or the evolutionary change in the timing of developmental events, is called heterochrony [63,79-851. The work of Matsuda [83] is said, by McCune [83], to be a “gold mine of examples of heterochrony.”
Timetable of Life
207
NOTE ADDED IN PROOF. See also [86]. According to Marx [79], “There is a great deal of evidence indicating that new species often emerge because the timing of some developmental events is altered so that they occur earlier or later with respect to other events than they normally would. This proposed mode of evolution is called heterochrony.” Likewise, Vermeij [81] says that “. . . shifts in the timing of developmental events have been frequent in the history of life . . .” Studies of Drosophila and E. coli have shown that ‘L.. . delays in gene expression are determined by the length of time required to transcribe the gene itself . . .” [63]. In the terminology of the present paper, a “delay in gene expression” is an “event age.” The mechanism of the molecular events that cause heterochrony Perhaps the mechanism described in Section 7.1 is involved.
11.2.
Evolution
11.2.1.
of Timer
Mutations
are not understood
[63,80].
Molecules
of timer
molecules
The process of evolution on a molecular scale can be viewed in part in terms of the progressive change by mutations of event-causing molecules. A timer molecule, if it were to mutate, could do so by adding a unit building block on its end. With the molecule now taking longer to build, an organism larger in some respect might result, giving it advantages. Thus, competition would usually favor mutations of timer molecules to make them longer.
11.2.2.
Environmental
constraints
on timer
evolution
Winter presents problems to many species. Generally, with exceptions, a species avoids trying to rear its young from a start in winter. Therefore, a mutation of event age extending birth too close to winter could be unsuccessful. A trend to age, could be For example, cold problem
increase event supported by young born in in the species’
ages, while blocked by disadvantages of increasing a particular event getting around the blockage, such as by migration, hibernation, etc. a place where winter is warm, thanks to migration, would avoid the original winter location.
More generally, one would expect to find examples problems.
of many
“ingenious”
solutions
to evolution
blockage
11.2.3.
Some
unanswered
questions
The author has no insight into the process of timer molecule be passed along to offspring.
11.3. 11.3.1.
Transients Effects
and
Evolution
of an ecosystem
mutation
or how a mutation
might
in an Ecosystem upon
development
The successful development of individuals of a particular species requires favorable interaction with many other species in an ecosystem. For example, other species are required as food, for pollination in some cases, and for other services. Likewise, the species is itself used less often by other species as food if there are related species present as alternative foods. In addition, the physical conditions are affected by other species, enabling enjoyment of favorable environment for development. Thus, trees provide shelter against the sun and wind.
A. B. CLYMER
208
11.3.2.
Stability
of an ecosystem
Stability of an ecosystem overall tends to stabilize the event age spectra of species living there, and the reverse is also true. A diversified ecosystem is knitted by a network of interactions among species. For example, a migrating bird species passing through an ecosystem can take as food the eggs of horseshoe crabs being laid at that time. Also hatches of several insect species in succession in a river provide more and better diet for the fish and young of birds. Also, a temporary loss of one food source can be compensated by another food source. By use of niches by species, many more species can be fitted into an ecosystem, increasing its variety and stability. Niches reduce competition among species, providing a better living for all. The local ecosystem forms an important part of the environment of a species. As such, the environment can help to shape the course of the evolution of a species. 11.4.
Quantization
in Evolution
It has been shown in Section 10 that one obtains a spectrum of a dimension for a multimodal species as a result of growth in development. These spectra shift to ever increasing ages and dimensions in evolution as a result of mutations in event ages. Conversely, going back in time, as in paleobioscience, one finds spectra shifted to ever shorter event ages and dimensions. For example, given an ancient bone fossil, one could use such spectra, together with a knowledge of event ages of a species versus evolutionary time, as an aid to dating of the bone. A case in point would be to make careful measurements of the dimensions (lengths, radii, etc.) of the beaks of Darwin’s finches as they are today. One would expect to find the frequency distributions quantized.
12. CONCLUSIONS 12.1.
Conclusions
Regarding
Life Science
The conclusions of this paper deal mostly with matters in life science. The most important are the following: 1. Development is marked by events that start or stop processes. The processes in development are localized and of discrete duration, with overlapping in time. Growth is intermittent in any location. All events are revealed by sudden changes in the concentration of some substance somewhere in the organism. Life consists of the consequences of a precisely timed series of biological events. 2. Events occur at one of the post-fertilization ages given by the geometric series in which each event age is 1.0472 times the age at the last previous event. One day is very close to being a member of the series. So are most biorhythm periods. Since there are about three hundred event ages in the range of concern, whereas there are millions of species, each with thousands of events, the series permits remarkable condensation of data. Another fascinating property of the series is that the spacings of the logarithms of the event ages are all identical, i.e., a linear series. Some events are exceptions. For example, plant seeds germinate in response to physical criteria, not timing. 3. Building of the mRNA molecules that achieve event timing is believed to take place on DNA, unit by unit, i.e., on the chromosomes of any cell. The resulting mRNA molecule moves to a ribosome to direct the start and stop of the building of a protein which participates in the new process. Building of the mRNA would be the time-taking step, the others being relatively fast. The foregoing building process is sufficient as a model from which to derive the geometric series of event ages. 4. The geometric series of event ages is considered to have been sufficiently well established against published data herein that it can be used to identify suspicious (possibly erroneous) data. The frequency distribution of errors of fit is Gaussian. Such a pattern could result
Timetable of Life
from temperature
209
variation, improper data processing, etc. Data newly being found in the
literature are members of the same statistical
family that was fitted; error magnitudes and
distributions are similar. 5. Most events occur for a particular species at two or more consecutive event ages. It has been concluded that one should expect to find growth to be quantized, i.e., clustering around certain values. This distribution would result from multiplying a constant growth rate by the difference of the starting and stopping event ages. If the event ages are multimodal, then so will be the resulting growth dimension. The same would be true of migration distance, duration of hibernation, etc. 6. Most biorhythms are shown herein to have periods that closely match event ages. This agreement is explained by assuming that the molecule building for one event age can be merely repeated over and over to produce a biorhythm. 7. Event ages as observed are affected significantly by temperature change. The curve is a hyperbola with an asymptote at each of two critical temperatures at which event ages becomes infinite. Since the asymptotes are not very far apart, a small temperature shift can greatly delay or prevent a vital event from occurring. 8. Evolution could be modeled in some respects as a flea or frog race: an ensemble of racers intermittently jumping to the next higher event age in a stochastic manner. These event age changes would be caused by mutations of mRNA by one unit each time. A species that is evolving rapidly would have a large number of event ages per event, say 8 or 9. This relationship is true for primates, at least. 9. If the event age formula and series survive evaluation by others, they will introduce a new requirement for precision in measurement and reporting of event age data. 10. The biological time of each organism is mathematically structured. 12.2.
Conclusions
Regarding
Medicine
The availability of patient event timetables and improved means for locally causing events that do not occur naturally should result in improved monitoring and management of child and adult development. Similar timetables for other species should permit the same developmental management to be applied in veterinary medicine, zoo management, etc. In general medicine and medical research, it would be desirable to have event age data for malaria parasites, nucleus-invading organisms, various cancer cells, mental illnesses that have any temporal causation, etc. Timetables would be useful also in determining an appropriate time for administration of a drug whose effect depends sharply upon patient age. Physicians and life scientists have always held a deep respect for the system and beauty in organisms. The system aspect is now enhanced by the inclusion of simple mathematics with general scope of application. In general, it is understood that medical applications emerge from advances in the life sciences. Thus, one could expect progress in medicine from the advances in chrontogenetic science postulated in Section 12.1. 12.3.
Conclusions
Regarding
Planet
Management
It has been shown that major losses of life can result from modest changes in atmospheric temperature. Eggs and young are particularly vulnerable. Surely this problem of potential species and ecosystem extinctions deserves massive research. The postulated cause is the impact of temperature change upon the age of occurrence of one or more events. Beings who would presume to manage entire ecosystems and planets must know much about timing in the lives of organisms.
A. B. CLYMER
210
12.4.
Some
Remaining
Questions
Of the many questions remaining, the following are especially interesting: 1. Does the event age list apply in any way to bacteria, viruses, cancer cells, plants, etc.? 2. Are the mRNA and/or protein molecules, that are presumed here to be responsible for events and event ages, quantized in molecular weight, as might be suggested by the findings of Savageau as reported by Lewin [87]? 3. Is the molecule building process described in Section 7 a valid theory? observed, or observed not to occur?
Can any of it be
4. Why do some mutations of mRNA molecules produce no change in the resulting events while others do?
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.
27. 28. 29. 30. 31.
A.B. Clymer, Simulations of the timing of nature, In Proc. Sot. for Comp. Simulation Conf. on Simulations at the Frontier of Science, pp. 3-22, SCS, San Diego, CA, (1986). A.B. Clymer, The precise timing of events in disease and development, In Proc. SCS Summer Computer SimzLlation ConJ., San Diego, CA, pp. 42&430, Sot. for Comp. Simulation, (1987). A.B. Clymer, Patterns of timing in living systems, In Proc. SCS Simulators Conf., San Diego, CA, SCS, (1988). S.J. Gould, Bully for Brontosaurus, W.W. Norton, New York, (1991). S. Au&ad, On the nature of aging, Nut. Hist. 2, 25-56 (1992). M. Lampl, J.D. Veldhuis and M.L. Johnson, Science (October 1992). Witschi, In Biology Data Book, (Edited by Altman and Dittmer), Fed. of Amer. Sot. on Expl. Biol., Washington, DC, (1964). Streeter, Biology Data Book, (Edited by Altman and Dittmer), Fed. of Amer. Sot. on Expl. Biol., Washington, DC, (1964). R. O’Rahilly and E. Gardner, Acta Anat. 104, 122-133 (1979). A. Delaney, (personal communication), (1986). J. Brooks-Gunn, Antecedents and consequences of variations in girls’ maturational timing, J. Adolescent Health Care 9, 365-373 (1988). A.A.B. Pritsker, Papers, Experiences, Perspectives, Systems Publ. Corp., W. Lafayette, IN, (1990). C.F.A. Moorees, Variability of dental and facial development, In The Biology of Human Variation, Annals of the NY Academy of Sciences, (Edited by J. Brozek), Volume 134, pp. 846-857, (1966). D.A. Nelson, Life history and environmental requirements of loggerhead sea turtles, Technical Report EL-86-2, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS, (1986). S.B. Hrdy, Daughters or sons, Nat. Hist., 63-83 (1988). S. A. Asdell, Patterns of Mammalian Reproduction, Cornell Univ. Press, Ithica, NY, (1964). Altman and Dittmer, Editors, Biology Data Book, Fed. Amer. Sot. on Expl. Biol., Washington, DC, (1964). P. A. Racey, Environmental factors affecting the length of gestation in mammals, In Environmental Factors in Mammal Reproduction, pp. 199-213, Univ. Park Press, Baltimore, MD, (1981). C.H. Johnson and J.W. Hastings, The elusive mechanism of the circannual clock, Amer. Sci. 74, 29-36 (1986). King and Mitchell, Breeding primates in zoos, In Comparative Primate Biology, Vol. 2B, Behavior, Cognition and Motivation, pp. 219-261, A.R. Liss, New York, (1986). K.A. Fagerstone, The annual cycle of Wyoming ground squirrels in Colorado, J. Mamm. 69,678-687 (1988). Altman and Dittmer, Editors, Growth, Including Reproduction and Morphological Development, FASEB, Washington, DC, (1962). L.S. Earley, On the rebound, Nat. Parks, 35-38 (1992). T. Verde, Mothers in waiting, Nat. Wildlije 30, 16-20 (1992). M. Sandell, Stop-and-go stoats, Nat. Hist. 97, 55-65 (1988). M. Kirschner et al., Initiation of the cell cycle and establishment of bilateral symmetry in xenopus eggs, In The Cell Surface: Mediators of Developmental Processes, (Edited by Subtelny and Weasells), pp. 187-216, Academic Press, New York, (1980). M.J. Whitaker and R.A. Steinhardt, Ionic regulation of egg activation, Q. Rev. of Biophys. 15, 593-666 (1982). P.H. Harvey and T.H. Clutton-Brock, Life history variation in primates, Evol. 39, 559-581 (1985). C.G. Hartman, The irregularity of the menstrual cycle, In Science and the Safe Period, R.E. Krieger Publ. Co., Huntington, NY, (1972). Arey, Developmental Anatomy, Sixth Edition, Saunders, Philadelphia, (1956). J. Hemingway, Despite long odds, mighty herds still plunge across the Serengeti, Smithsonian 17, 50-61 (1987).
Timetable 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48.
49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62.
63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80.
of Life
211
G.W. Asher, Oestrus cycle and breeding season of farmed fallow deer, Dana dama, J. Repro. Fert. 75, 521-529 (1985). J.D. Curlewis, Estrous cycles and the breeding season of the Pere David’s deer hind, J. Repro. Fed. 82, 119-126 (1988). D.G. Kleiman, Maternal behavior of the Green Acouchi (Myoprocta prathi Pocock), A South American caviomorph rodent, Behavior 43, 44-84 (1972). E. Linden, Bonobos, Nat. Geogr., 46-53 (March 1992). Van Horn, Valerio et al. Hampton and Hampton. Lorenz. Dixson. Glander. Tobach, Aronson and Shaw, Editors, The Biopsychology of Development, Academic Press, NY, (1971). C.M. Crockett and R. Sekulic, Gestation length in Red Howler Monkeys, Amer. J. Primatology 3, 291-294 (1982). W.B. Wood and R.S. Edgar, Building a bacterial virus, Sci. Amer. 217, 60-74 (1967). J.H., The Nautilus and the born, Sci. Amer., 22-23 (January 1988). N.H. Landman and J.K. Cochran, Growth and longevity of Nautilus, In Nautilus, (Edited by N.H. Landman and W.B. Saunders), (1989). M. Geber, The psychomotor development of African children in the first year and the influence of maternal behavior, J. Sot. Psych. 47 (1958). R.W. Thatcher, R.A. Walker and S. Giudice, Human cerebral hemispheres develop at different rates and ages, Science 236, 1110-1123 (1987). A.B. Clymer, Roles of simulation in the application of expert systems in emergency management operations, In Proc. First Symposium in the Application of Expert Systems in Emergency Management Operations, FEMA/NBS, Washington, DC, (1985). F.M. Slater, S.P. Gittins and J.D. Harrison, The timing and duration of the breeding migration of the common toad (Bufo bufo) at the Llandrindod Wells Lake, Mid-Wales, Br. J. Herpetology 6, 424-426 (1985). E. Gwinner, Internal rhythms, bird migration, Sci. Amer. 254, 84-92 (1988). L.P. Brower, A place in the sun, Animal Kingdom 91 (4), 42-51 (1988). R. Baserga, Multiplication and Division in Mammalian Cells, Marcel Dekker, New York, (1976). A.B. Clymer, Development: A timed series of molecular events, Science (submitted 1967, in review by author). J.H.S. Bradley, (personal communication), (1986). Diagram group, Comparisons, St. Martin’s Press, New York, (1980). F.C. Kafatos and N. Feder, Cytodifferentiation during insect metamorphosis, the galea of silkmoths, Science 161, 470-472 (1968). W.J. Gehring, The molecular basis of development, Sci. Amer. 253, 152B-162 (October 1985). S.B. Oppenheimer and R.L.C. Chao, Atlas of Embryonic Development, Allyn and Bacon, Boston, (1944). J.D. Wilson, F.W. George and J.E. Griffin, The hormonal control of sexual development, Science 211, 1278-1284 (1981). D.R. Soll, Timers in developing systems, Science 203, 841-849 (1979). M. Poenie et al., Changes of free calcium levels with stages of the cell division cycle, Nature 315, 147-149 (1985). R.P. Elinson, The amphibian egg cortex in fertilization and early development, In The Cell Surface: Mediator of Development Processes, (Edited by Subtelny and Wessells), pp. 217-234, Academic Press, New York, (1980). C.S. Thummel, Mechanisms of transcriptional timing in Drosophila, Science 255, 39-40 (1992). S.B. Hendricks, Metabolic control of timing, Science 141, 21-27 (1963). J.F. Feldman, Genetic approaches to circadian clocks, Ann. rev., Plant Physiol. 33, 583-608 (1982). B.C. Goodwin, Temporal Organization in Cells. A Dynamic Theory of Cellular Control Processes, Academic Press, London, (1963). C.F. Ehret and E. Trucco, J. Theor. Biol. 15, 240 (1967). R.F. Feynman, Surely You’re Jo&g, Mr. Feynman, Norton, New York, (1985). Suter and Rawson. Living Clocks. Boslough. Zernbavel. Martin and Menacker. Klevecz. J.S. Takahashi, Circadian clock genes are ticking, Science 258, 238-239 (October 9, 1992). P. McConnell, Bears . in New Jersey.?, New Jersey Outdoors, 3-5 (1987). P.E. Ross, Man bites shark, Sci. Amer., 31 (1990). T. Bedell, There’s a whale, there’s a whale, Skylines, 17-20, 32-33 (September 1986). J.L. Marx, Clues to developmental timing, Science 226, 425-426 (1984). J.L. Marx, Evolution’s link to development explored, Science 240, 880-882 (1988).
MCM 19:6-8-O
212 81. 82. 83. 84. 85. 86. 87. 88. 89. 90.
91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103.
A. B. CLYMER G.J. Vermeij, Review of Evolutionary IPrends, (Edited by K.J. McNamara, Univ. of Arizona Press, Tucson, 1990), Science 251, 1374-1375 (1991). P. Mabee, Review of The Evolution of Ontogeny, (Edited by M.L. McKinney and K.J. McNamara, Plenum, New York, 1991), Science 254, 874-875 (1991). A.R. McCune, Review of Animal Evolution in Changing Environments, (Edited by R. Matsuda, Wiley-Interscience, New York, 1987), Science, 300-301 (1988). J. Hanken, Development and evolution in amphibians, Amer. Sci. 77, 336-343 (1989). D.A. Powers, Fish as model systems, Science 246, 352-358 (1989). D.L. Slocum, Review of Developmental Patterning of the Verterbrate Limb, (Edited by Hinchliffe, Hurle, and Summerbell, Plenum, New York, 1991), Science 257, 1570-1571 (September 11, 1992). R. Lewin, Unexpected size pattern in bacterial proteins, Science 232, 825-826 (1986). S.J. Gould, Justice Scalia’s misunderstanding, Nat. Hi&., 14-21 (1987). A.B. Clymer, Dear John (letter), Simulation, v-vii (1967). A.B. Clymer, Development: A timed series of molecular events, Submitted to T. Theor. Biol., March 1968, rejected (author’s paper A.B. Clymer, The regularity of the timing of developmental events, submitted BS an abstract to the 31th ACEMB, October 1978, also was rejected). S.J. Gould, Nat. Hist. 20 (February 1984). J. Bronowski, The educated man in 1984, Science 123, 710 (1956). A.G. Thorne and M.H. Wolpoff, The multiregional evolution of humans, Sci. Amer., 76-83 (April 1992). F. Crick, Lessons from biology, Nat. Hi&., 32-39 (November 1988). S.J. Gould, Letter, Science 232, 439 (1986). Adams, Smithsonian horizons, Smithsonian (issue unknown). G. Lakoff, What Categories Reveal about the Mind, Univ. of Chicago Press; L.H. Brody, Lib. J. 78 (1987). A.B. Clymer, A model of abuse, In Proc. Conf. on Emergency Planning, Society for Computer Simulation, San Diego, CA, pp. 54-60, (1987). R.L. Armstrong, Review of Theories of the Earth and Universe, (Edited by S.W. Carey, Stanford Univ. Press, 1988), Amer. Sci. 77, 382-384 (1989). Sir J.A. Thomson, The Great Biologists, Books for Libraries Press, Freeport, New York, (1932). W. Bagehot, Physics and Politics, Knopf, New York, (1948). U. Windhorst, How brainlike is the spinal cord 7, In Studies of Brain l%nction, p. 15, Springer-Verlag, (1988). J.H.M. Thornley and I.R. Johnson, Plant and Crop Modelling, Clarendon Press, Oxford, (1990).
Timetable
of Life
213
APPENDIX A GESTATION DATA Table Al.
Comparision
of event times with reported gestation periods.
*These are events ages
closest to published gestation data. l*S = Success, F = Failure (see Section 5.1.1).
Species Name
* Refs
-
111 - 121
13741
[51 El 171 172’1
[71 - [71 - 171 I71 -IT -IT PI [71
“402 hrs with 14 month-old”
-VT [71 Tr 171 171 - 171 171
20.05d
(Dipodomys merriami Mearns)
17.00d and 23.00d
cf 23.03d
S
Hamster
“20 to 22 days” = 20.00d to 22.00d
cf 20.05dz cf 21.99d
S S
tvery unlikely spread. SAlso, expect peak at 21.00d.
-FT (71
A. B. CLYMER
214 Table Al.
Continued.
Comparision
of event times with reported gestation
periods.
‘These
are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
First Species Name
Event
Published
Interpretation
Gestation
and
Data
Comments*
Time Common
Applicable
Name
(Latin Name)
to Species
S,F Refs **
20.05d
(
cf 20.05d
F
19.15d
<
cf 19.15dt cf 21.00d
20.05d
(
-S -S -F -S -S -S S s
20.05d 20.05d 19.15d
= 20.50d to 21.00d
( Micro&
oeconomus Pallas)l “20 to 21 20.00d to 1“20 to 21 ( :erbil, I= 20.00d __IG. simoni Lataste) [ “19 to 22 E3onbieda
days” = 21:OOd days, usually 20” to 21.00d days, usually 20”
= 19.00d to 22.00d 20.05d 20.05d 21.00d 20.05d 21.00d 21.00d 21.00d 21.00d 20.00d
F‘ersian house mouse Elouse mouse (wild), Mus musculus L.) i Dasyurinae Dasyurops naculatus Kerr) I :ommon shrew, _( Soricidae sorez Araneusl ( :lider -1 Sorex fumeus Miller) Sihort-tailed shrew EIarvest mouse, .I R. montanus) ‘ygmy mouse,
“20 days” = 20.00d “20.24& 0.12 days” = 20.24d “3 wks” = 21.00d “20 days” = 20.00d
cf cf cf cf cf cf cf
20.05d 21.00d 20.05d 21.00d 20.05d 21.00d 19.15d
:f 21.00d and 21.99dz cf 20.05d cf 20.05d cf 21.00d cf 20.05d
“3 weeks” = 21.00d “3 weeks or less” = 21.00d “5 lay betw. 21 and 23 days” I= 21.00d to 23.00d ( “21 days” = 21.00d
j “20 days” = 20.00d
cf 21.00d cf 21.00d cf 21. OOd cf 23.03d* cf 21.00d cf 21.00d
21.00d 21.00d
.L (
21.00d
21.99d 21.00d 21.00d 21.00d 21.99d
-
S
s s s-S S -
S
(” ? J
cf 21.00d
s
cf 21.00d
s
I
cf cf cf cf
(
= 21.00d to 22.00d
piorway rat .( albino, laboratory) Jorway rat .; albino, laboratory) E3lack rat EIormouse, .( M. avellanarius L.) IIormouse, ( E. auercinus L.1
1Also, expect
pea at
20.05d
IExpect peak at 20.05d and 21.00d ‘Expect peak at 21.99d too.
“avg.. .21.8 days” = 21.80d
21.00d 21.00d 21.99d 21.99d
-
S -s -S S
“about 21 days” = 21.00d “21 days” = 21.00d “21 days” = 21.00d
cf 21.00d
s
cf 21.00d cf 21.00d
s s
“22 days” = 22.00d
cf 21.99d
s -
~ 171 171 171 [71 -
[71 [71
- 171 [71
S
sS
.( 21.00d 21.00d
-
cf 21.00d cf 21.00d
(
21.00d
sS
s s sS
( r~ F EEuropean field mouse,
21.00d 21.00d
S
1
.; 21.00d
s-
-
171 -
PO1 - [71 - [71 [71 [71 -
[71
-
[71 - [71 [71 Jl_ 171 [71 [71 - [71 171 [71 [71 - (71 [71 171
Timetable Table Al.
Continued.
Comparision
of Life
215
of event times with reported gestation
events ages closest to published gestation data. “S
periods.
*These are
= Success, F = Failure (see Section 5.1.1).
First Event
Species Name
Published
Time Applicable
Common Name
Gestation
to Species
(Latin Name)
Data
21.00d
klce rar
Refs.
“Variously given as 25 or from 21 to 24 days” = 21.00d, 24.00d, and 25.00d “21 to 24 days” = 21.00d to 24.00d “22.5 days”
21.99d 21.99d 21.99d 21.00d 23.03d 21.99d 23.03d 23.03d 21.00d 23.03d 21.03d 24.12d
bird, (N. persicus Blanford) Jird, (M. vinogmdovi Heptner) (Thallomys namaquensis A. Smith) (Rattus hawaiiensis Stone) Suslik, (Citellus Townsendii) Suslik, (Citellus Suslicus) Columbian ground squirrel (U.S.A. and Canada) Harvest mouse, (R. megalotis) White-footed mouse, (P. calif.) Cotton mouse Wood mouse Gerbil,
“22 days” “21.5 to 23 days” = 21.50d to 23.00d “may be 22 days or more” = 22.00d “not lees than 21 days” = 21.00d “at least 23 days” = 23.00d “22 to 26 days” = 22.0d to 26.00d “23 to 24 days, usually the latter” = 23.00d to 24.00d “23 to 24 days” = 23.00d to 24.00d “range 21 to 25 days” = 21.00d to 25.00d “22.9 days” = 22.90d “23.2 days” = 23.20d “about 24 days” I
cf 23.03d
I= 24.00d 23.03d 23.03d
23.03d
1(Citellus 1townsendii Bachman) 1(Rattus assimilis Gould)
1Multimammate
rat
“at least 23 days” I
I = 23.Orld 1“22 to 24 days, _
I
~-
---
with 22.8 the avg. and with 60% at 23 days” = 22.00d 1to 23.00d, 24.00d 1“23.1f.7 days” I= 23.10d
Possibly peak also at 21.99d and 23.03d. L TPossibly peak also at 21.99d and 23.03d. *Is 22.5d an average across a distribution from 22 to 23d? *Should show 3 peaks in between. *Should show 3 peaks in between. *Apparently peaks near 22, 23, and 24 days. OPerhaps peaks also at 21.99d and 24.12d.
I I I
1 S
216
A. B. CLYMER Table Al.
Continued.
Comparision of event times with reported gestation periods.
*These are
events ages closest to published gestation data. l*S = Success, F = Failure (see Section 5.1.1).
Common Name
IPerhaps *Perhaps *Perhaps *Possible *Possible OPerhaps OPerhaps
peaks also at 26.45d and 27.69d. peaks also at 26.45d, 27.69d and 29.00d. peaks also at 29.OOd and 30.37d. peak also at 30.37d. peak also at 30.37d. peaks also at 27.69, 29.00d, and 30.37d. peak at 31.80d too.
Timetable Table Al.
Continued.
Comparision
of Life
of event times with reported gestation periods.
events ages closest to published gestation data. “S
Common Name
(Mawnota
monax
mona
31.084~0.02 days, D = 0.83d,
Note broad distribution
covers 30.37d and 31.8Od.
SPerhaps distribution covers 31.8Od and 33.31d. *Perhaps peaks also at 29.OOd and 30.37d.
*These are
= Success, F = Failure (see Section 5.1.1).
218
A. B. CLYMER Table Al.
Continued.
Comparision
of event times with reported gestation
periods.
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
First Species Name
Event Time
Published
I nterpretation
Applicable
Common Name
Gestation
and
to Species
(Latin Name)
Data
Comments*
30.37d 30.37d 30.37d 30.37d 30.37d 30.37d 33.31d 30.37d
F‘rairle aog, _( Cynomys ludovicianus Ord) c California ground squirrel ( Citellus fulvus Lkhtenstein) EIastern chipmunk _L Eutamias quadrimaculatus Gray) F‘lying squirrel, (Glaucomys abrinus Shaw) mouse : &sshopper F‘ocket gopher
31.80d
5Vood rat, _( N. floridana Ord) VVood rat, _( N. fuscipes Baird) VVood rat,
30.37d 34.88d 34.88d
_L N. lepida Thomas) Iilound-tailed muskrat P E
31.8Od 33.31d
27.6Qd 38.25d 38.25d 34.88d 34.88d 36.52d 40.05d 38.25d 41.94d 41.94d 41.94d
40.05d 41.94d 38.25d 40.05d
C:ommon European mole S nowshoe hare Eiuropean red squirrel r )warf mongoose L,ittle northern chipmunk, Eutamias sibiricus Laxmann) _i Mystromys albicandatus A. Smith) Ebrush wallaby C:ray Kangaroo Rlat Kangaroo h4ole, (Mogera latouchei Thomas) J ack rabbit
F‘lying squirrel, _i Glaucomys sabrinus Shaw) \‘srying hare \‘olcano rabbit, diazi) _L Romerolagus Swamp rabbit
G ray squirrel _& ~&TIM griseus Ord) Perhaps peaks also at 31.80d and 33.31d. 43.92d 43.92d
SPossible peaks also at 33.31d and 34.88d. *Perhaps peaks also at 36.52 and 38.25d. *Perhaps peaks also at 36.52 and 38.25d. *Perhaps peaks at all three of these event ages.
“30 to 35 days”
cf 30.37d
W **
Refs
-
-
= 30.00d to 35.00d “probably 30 days” = 30.00d “about 1 month” = 30.42d
cf 34.88dt cf 30.37d cf 30.37d
-F -S -F S
“31 days” = 31.00d “31 days” = 31.00d “1 month” = 30.42d
cf 30.37d cf 30.37d cf 30.37d
F F s
“33 days” = 33.00d “30 days” = 30.00d “19 days”=19.00d “in captivity 32 days” = 32.00d “33 days” (2 cases) = 33.00d “32 to 36 days”
cf cf cf cf
-S -F -S S
= 32.00d to 36.00d “SC 30 days” = 30.00d
“about 4 wks” = 28.00d “38 days” = 38.00d “38 days” (1 case) = 38.00d “about 5 wks” = 35.00d “35 to 40 days” = 35.oOd to 4o.oOd “about 37 days” = 37.00d “40 days” = 40.00d “38 or 39 days” = 38.50d “probably 6 weeks”=42,00d “6 wks” = 42.00d “41 to 47 days. mean of 43” = 41.00d 43.00d 47.00d “40 days” = 40.00d “about 42 days” = 42.OOd “38 or 40 days”=38.00d (1 case in zoo) or 40.00d “39-40 days” = 39.50d (1 case) “44 days” = 44.00d “43 days or more” = 43.00d
33.31d 30.37d 19.15d 31.8Od
cf 33.31d cf 31.80d cf 36.52dJ cf 30.37d cf 34.88d cf 34.88d cf 40.05d cf 34.88d* cf 31.80d cf 31.80d cf 27.69d cf 38.25d cf 38.25d cf 34.88d cf 34.88d cf 40.05.d* cf 36.52.d cf 40.05d cf 38.25d cf 41.94d cf 41.94d rf 41.94d cf 43.92d cf 46.00d* cf 40.05d cf 41.94d cf 38.25d cf 40.05d
-
[71 [71 [71 (71 (71 [71 [71 [71 (71
S
-S -F -F S s-S S F s-S S s-S -S S F s s s s F F F s sS s F s F
171 [71 -[71 pl_ 171
(181 [71 [71 [71 [71 [71 -[71 -[71 -171 -[71 -[71 [71 [71 m P91 [71 -[71 -[71
Timetable Table Al.
Continued.
Comparision
of Life
219
of event times with reported gestation periods.
‘These
are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
First Species Name
Event
Interpretation
Time Common
Applicable to Species
American red squirrel Palm squirrel,
(finabulus pennanti Wrought07 Marmot, (Mannota bobak Mzlller) Pinon mouse African jerboa (Desmana moschata L.)
40.05d 40.05d 41.94d 46.00d I
40.05d
Himalayan marmot, (Marmoto bobak Mullerl
30.37d 41.94d 34.88d 50.44d 48.17d 50.44d 50.44d 55.31d
1Fox squirrel IGiant Rat European stoat, (h4ustela putorius eversmanni) a weasel, (M. sibirica Pallas) European badger Dwarf mongoose, (Helogale vet&a Thomas) Common European bat a bat, (Pipistrellus (Nyctalus) noctula Shreber) Fennec Bobcat Philippine tree shrew
x 50.44d 48.17d 55.31d 55.31d 55.31d 50.44d
** Data
, -‘about 40 days” = 40.00d “40 to 42 days” = 40.00d to 42.00d “about 40 days” = 40.00d “40 days” = 40.00d “42 days” = 42.00d “45 to 50 days”
English red fox European weasel Marbled polecat (Felis libyca Forster) (Felis bengalansis Kerr) Spiny Hedgehog tenrec, (Setijer setosus)
Possible peak also at 48.17d. Possible peak also at 48.17d. Possible peaks also at 55.32d and 57.93d.
Comments* cf cf cf cf
40.05d 40.05d 41.94d 40.05d
cf 40.05d cf 41.94d cf 46.00d
= 45.00d to 50.00d “about 40 days” = 40.00d
cf 50.44dt cf 40.05d
“about 44 days” = 44.00d “46 to 50 days”
cf 43.92d cf 46.00d
= 46.00d to 50.00d “42 days” = 42.00d
cf 50.44dT cf 41.94d cf 41.94d
“42 days with practically no variation” = 42.00d
I
46.00d 41.94d 40.05d
S,F ReE
Name
(Latin Name)
40.05d 40.05d
I
S s
171
171 S S
171
S S E S
[71 [71 [71
S
171
S
[71 171
s S S S
PI [71
“about 45 days” = 45.00d “42 days” = 42.00d “40 to 42 days” = 40.00d to 42.00d “about 30 days” = 30.00d
cf 46.00 cf 41.94d cf 40.05d cf 41.94d cf 30.37d
F S _s_ S
[71 [71 [71
F
[71
“6 wks” = 42.00d “about 5 wks” = 35.00d
cf 41.94d cf 41.94d
S S
[71 [71
“50 davs” = 50.00d “probably about 49 days” = 49.00d “2 case, 50 and 51 davs” = 50.50d
cf 50.44d cf 48.17d
S F
[71 [71
S S F S
171 [71 171
F S
171
F
[71
s_
[71
“approx. 56 days” = 56.00d “or < 50 days” = 50.00d “52 days” and “60 days” = 52.00d and 60.00d “49 to 55 days, with a
=
49.00d 52.00d 55.00d
cf 50.44d cf 50.44d cf 55.31d cf 50.44 cf 52.82d cf 60.66d* cf 48.17d cf 52.82d cf 55.31d cf 50.44d cf 52.83d cf 48.17d cf 55.31d cf 55.31d cf 55.31d cf 50.44d cf 52.82d cf 55.31d cf 55.31d cf 57.93d cf 60.66d
F S
S F F F F s
F S F S S
[71 [71 171 [71 WI
220
A. B. CLYMER Table Al.
Continued.
Comparision
of event times with reported gestation
events ages closest to published gestation data. “S
periods.
*These are
= Success, F = Failure (see Section 5.1.1).
First Species Name
Event Time
Common
Applicable to Species
Name
Published
Interpretation
Gestation
and
Data
Comments*
(Latin Name)
46.00
Tree shrew, (Tzlpaia glis belangeri)
60.66d
Northern coyote
60.66d
Wolf
47 days (4 cases) = 47.00d 48 days (1 case) = 48.00d 52 days (1 case) = 52.00d 54 days (2 cases) = 54.00d “59 to 63 days” “betw. 58 and 63 days” = 58.00d to 63.00d, “61.3 davs” = 61.30d.
cf cf cf cf
46.00d 48.17d 52.82d 52.82d
cf 57.93d cf 63.52d cf 60.66d
%F Hefs. **
F
[I91
s F F
s s s s s
WI [71
D51 [191 [71
F
s -S
= 60.00d to 63.00d, 60.66d
a wolf, (Canis a~rens L.) Stripe-sided jackal
57.93d 63.52d 57.93d
Pale bat Mouse lemur, (Microcebus murinus) Tree shrew, (npaia)
43.92d
60.00d 63.52d 60.00d
Indri Hairy armadillo Hair tree porcupine
63.52d 63.52d 60.66d
Dingo Gray fox Cape hunting dog
60.66d
Big-eared fox
n Dublin “60 to 63 = 60.00d “57 to 60 = 57.00d
Zoo 63d days” to 63.00d davs” to -6O.OOd
Raccoon, (PTOCyOT2
63.52d 63.52d 60.66d 60.66d
LOtOT)
Stone marten, Beech marten Striped skunk Skunk I
(L. maculicollis Lichtenstein)
IPerhaps peaks at 63.52d and 66.52d. [Perhaps peaks also at 63.52 and 66.52d.
cf cf cf cf
60.66d 63.52d 57.93d 60.66d
5 “43 davs” = 43.20d “45 days” = 45.00d “49 days” = 49.00d “49-51 days” = 49.00d to 51.00d “56 days” = 56.00d “60 days” = 60.00d “65 days” = 65.00d “60 to 70 days”
= 60.00d to 70.00d
63.52d
-
“63 days” = 63.00d “about 63 davs” = 63.00d “60 to 63 days” = 60.00d to 63.00d “80 days” = 80.00d “probably 60 to 70 days” = 60.00d to 70.00d “avg. 63 days” = 63.00d “64 days” = 64.00d “In India. 9 wks” = 63.00d
cf 45.996d cf 48.167d cf 50.44d cf cf cf cf
55.31d 60.66d 63.52d 60.66d
cf 69.66dt cf 63.52d cf 63.52d cf 60.66d cf 63.52d cf 80.00d cf 60.66d cf 69.66dr cf 63.52 cf 63.52 cf 63.52d
171 WI
S
s
[71
F
171
-S F F F F F s
[71 -IT
s s -
-VI
F S
[71
F [7) -5 [71 S
s -
-S S
[71 [71 171 PO1
-S S
[71
s -S
s -S
171
-
S
F -
F sS
g -m (71
Timetable Table Al.
Continued.
Comparision
of Life
221
of event times with reported gestation periods.
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
First Event Time
Published
Interpretation
Applicable
Common Name
Gestation
and
to Species
(Latin Name)
Data
Comments*
60.66d
(Felis chaus Gulders Taedt)
63.52d
(Felis yaguarondi Desmarest) Lynx, (Felis canadensis Kerr) Lynx,
60.66d 63.52d
)
(Felis lunx L.1 69.66d
Asiatic pipistrelle bat
ggE
S,F l
R.efs
*
“about 63 days” = 63.OOd “60 to 65 davs” = 60.00d to -65.00d “about 63 days” = 63.00d “cat in the wild 68 days” “about 2 months” = 60.87d “9 weeks” = 63.OOd “about 2 months”
= 60.87d
;I9 to 10 weeks” = 63.00d
1;o 70.00d “60 days” = 60.00d “about 70 days” = 70.00d “(litters of 6), 66.8 days” = 66.80d “about 67 to 68 days’ = 67.00d to 68.OOd “usually given as 61 to 63 days’ , = 61.00d to 63.00d “60 to 65 days” “70 “68 “71 “74 “75 “76 “67
days” days” days” days” days” days” to 77
(1 case) = 70.00d = 68.00d (1 case) = 71.00d (1 case) = 74 .OOd (2 cases) = 75.00d (2 cases) = 76.00d days”
[71
(71 (231 - 171 [71 WI
1241
= 67.00d to 77.00d “61 days” (1 case) = 61.00d “64 days” (1 case) = 64.00d “66 days” = 66.00d “63 days” = 63.00d “64 days” = 64.00d “63-70 days” = 63.00d to 7O.OOd
76.69d
1Coati
IPossible peak also at 66.52d. TPerhaps peaks also at 72.95d and 69.66d. *Possible peak also at 66.52d. *Perhaps a peak also at 80.00d.
“about 73 days” = 73.00d “about 11 to 12 weeks” = 77.00d to 84.OOd “77 days” = 77.00d
1251 I191 PI PI
222
A. B. CLYMER Table Al.
Continued.
Comparision
of event times with reported gestation
periods,
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
Common
105.5d 105.5d 105.5d
Name
African lion, (Panthera lea) Capybara, (Hydrochoeris isthmius Agouti
Goldman)
‘Perhaps a peak at 72.95d also. SPerhaps peak also at 96.20d. *Perhaps peaks also at 96.20d and 100.7d. *Possibly peaks also 96.20d and 100.7d. *Perhaps peak also at 110.5d. *2 or 3 peaks?
Gestation
“105 to 113 days” = 105.0d to 113.0d “104 and 111 days” = 104.Od and lll.Od “about 104 days” = 104.0d
cf cf cf cf cf
105.5d 110.5d 105.5d 110.5d 1055d
S F
[311
P S
[71
F
[71
Timetable Table Al.
Continued.
Comparision
of Life
of event times with reported gestation
223 periods.
‘These
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
Common
(Chinchilla
iPerhaps
Name
laniger)
peak also at 115.7d
Gestation
are
224
A. B. CLYMER Table Al.
Continued.
Comparision
of event times with reported gestation
periods.
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
Common
Name
= 158.0d to 175.Od
Perhaps 3 other peaks also. SPerhaps peak also at 145.7d. *Perhaps peak also at 145.7d. ‘Perhaps peak also at 145.7d. *Perhaps peaks also at 145.7d 152.6, 159.8d.
Timetable Table Al.
Continued.
Comparision
of Life
of event times with reported gestation periods.
events ages closest to published gestation data. “S
Species Name
Time Applicable to Species
Common
Name
(Latin Name)
Interpretation
Gestation
and
Data
Saiga Rocky Mountain goat Bar bari goat E. African dwarf goat
145.7d
Angora goat
“148.08 f
145.7d 152.6d 152.6d 152.6d 152.6d 145.7d 152.6d 159.8d 152.6d
Philippine EOat Jummaoari eoat Anglo-nubian goat Schwartzald goat (Callithriz argentata) (Cebuella pygmaea) Markhor Bharal Barbary sheep (So. Morocco) Dorset horn sheep Karakul sheep Rambouiilet sheep
‘<148.1 & .07 days” = 148.ld “150 days” = 150.0d “150.0 * .l days” = 150.0d “150.8 f .2 days” = 150.8d “154 days” = 154.0d “140-150 days” = 145.0d “about 153 days” = 153.0d “160 davs” = 160.0d “154 to 161 days” = 154.0d to 161.0d “144.1 days” = 144.ld “151.8 days” = 151.8d “143 to 159 days” = 143.0d to 159.0d “5 months” = 152.2d “about 150 davs” = 150.0d “156 days (2 &ass) = 156.0d
152.6d 152.6d 152.6d 152.6d 152.6d 159.8d 175.2d 145.7d 145.7d
159.8d 132.9d 145.7d
159.8d
Argali, Arkar Mouflon sheen Common marmoset, (Cullithrix jacchus) (Cullimico goeldii) Night monkey, (A&us trivergatus) Rhesus monkey, (Macaca radiata) Rhesus monkey, ‘Macaca silenus) sheep Hybrid marmoset, : C. penicillate, 7. jacchzls) saddle-back tamarin, ‘Saguinus fuscicollis) saddle-back tamarin, :Saguinus fuscicollis) Celebes black ape, :Cynopithecus 2. niger) Celebes black ape, 1Cynopithecus n. niger
7-r
Published
145.7d 145.7d 145.7d 145.7d
145.7d 152.6d 145.7d
*These are
= Success. F = Failure (see Section 5.1.1).
First Event
225
“145 days” = “147 davs” = “146 dais” = “146.5 days”
145.0d 147.0d 146.Od = 146.5d
.09 days” = 148.ld
“150-160 days” (‘150-153 days” = 151.5d “162 days” “173-183 days” =173.0 to 183.0d 148.9 days” ,145 days” (1 case) = 145.0d. 146 days” (1 cssej = 146.0d, 125 davs” = 125.0d.* 159 days” (1 case) = 159.0d 134-140 or more” = 134.0 to 140.0d 149 days” (1 case) = 149.0d, 157 days” (1 case) = 157.Od, ,163 days” (1 case) = 163.0d 160 to 165 days” = 160.0d to 165.0d
.Bimodal? SBimodal? lBimodal? lBimodai? *Perhaps peak also at 152.6d. *Third case anothor species? Third case seems doubful.
S,F Refs **
A. B. CLYMER
226 Table Al.
Continued.
Comparision
of event times with reported gestation
periods.
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
l:l Event
/
Applicable
SW=
Name
Common
Name
159.8d
Loris, (Loris tardigradus grandis)
152.6d 159.8d
Saki, (Pith&a) Rhesus monkey, (Macaca) Goat Ursine black-and-white colobus, (Colobus p. polykomos)
152.6d 145.7d
167.3d 139.ld
Indian langur Collared peccary, (Tayassu. tajaczl) Collared peccary, (Tayassu tajacu) a lemur, (Hapalemur griseus Link) Black lemur Slender loris Squirrel monkey,
145.7d 159.8d 152.6d 167.3d 167.3d
(Saimiri) 159.8d
Japanese monkey
1Crab-eating macaque
167.3d
Pig-tailed
152.6d
macaque
Bonnet macaque
152.6d
Sacred baboon
167.3d
Proboscis monkey, (Nasalis larva&s) Black bear
152.6d 220.7d
Grizzly bear, ( UTSUS howibilis Ord) 1
152.6d 159.8d
1Manatee 1Musk deer
fnterpretation
Gestation
and
Data
Comments*
(Latin Name)
to Species
159.8d
Published
(
“160-166 days” “166-169 days” “175 davs” “approx. 150 days” = 150.0d “162-164 days” =162.0d to 164.0d “150.8 days” “147 days” (1 case) = 147.0d “154 “169 “177 “178
days” days” days” da&
(1 (1 (1 (1
case) case) case) casej
= = = =
154.0d 169.0d 177.0d 178.0d
“168 days” = 168.0d “142 days” (1 case) = 142.0d “142-149 days” = 145.5d “160 days” = 160.0d “about 5 months” = 152.2d “171 days” = 171.0d “168-182 days” = 168.0d-182.0d
159.8d 167.3d 175.2d 152.0d 159.8d 167.3d 152.6d 145.7d 152.6d 167.3d 175.2d 175.2d 167.3d 139.ld
s s s
WI
F
[211 WI
F
[38) iI91
cf 145.7d
s
Kw
cf 159.8d
s
[71
cf 152.6d cf 167.3d cf 167.3d
s
cf cf cf cf cf cf cf cf cf cf cf cf cf cf
cf 183.5dT
“Mode 161.3 days” = 161.3d “5-6 months” = 152.2d and 182.6d 1“160 to 170 days” = 160.0d to l+O.Od “about 170 days” = 170.0d “171 days” (1 case) = 171.0d “153 days” (1 case) = 153.0d “166 days” (1 case) = 166.0d “169 days” (1 case) = 169.0d “range 154 to 183 days” =154.0d to 183.0d “about 166 days” = 166.0d
cf cf cf cf cf cf cf cf cf cf cf cf cf
(17 cases) “151 to 177 days” = 151.0d to 177.0d “spread evenly’ “216 days” (1 case) = 216.0d “245 days” (1 case) = 245.0d “258 davs” (1 case1 = 258.0d I -_I\-I “at least 152 days” = 152.0d 1“160 days” = 160.0d
cf 152.6d cf 175.2d* cf 220.7d cf 242.0d cf 253.4d* cf 152.6d cf 159.8
Possible peak also at 175.2d. $0 ne at 5 peaks? *Perhaps peak also at 159.8d. *Perhaps peaks also at 159.8d, 167.3d 175.2d. *Perhaps peak also 167.3d. *Perhaps peak also 231.ld.
S,F Refs. **
159.8dt 152.6d 183.5d 159.8d 167.3d 167.3d 167.3d l52..6d 167.3d 167.3d. 152.6d 183.5d’ 167.3d
F F
F
s
s S s
iI51 [191
F
s
F
s
s s s s
s F
F F S
--ST
s S s
Jl_ [71 WI [71
[71 [71 171
[71
s
7,211
s s
[71
F
(71
F -
F
s s-
[71 [71
Timetable Table Al.
Continued.
Comparision
of Life
227
of event times with reported gestation periods.
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
First Event
Published
Interpretation and
Time Applicable
Common Name
Gestation
to Species
(Latin Name)
Data
152.6d
“5 to 6 months”
152.6d
Blackbuck,
= 152.2d to 182.6d “5 to 6 months”
cf 183.5dt cf 152.6d
152.6d
Indian antelope (Gazelle dama Pallas)
= 152.2d to 182.8d “5 months” = 152.2d “158-166 days” = 158.0 to 166.Od “150 to 160 days” = 150.0d to 160.0d “165 to 170 days” = 167.5d “171 to 175 days” = 172.5d “170 to 174 days” = 172.0d “171 days” (1 case) = 171.0d “180 to 210 days” = 180.d to 21O.Od “6 months” = 182.6d “6 months” = 182.6d “6 months” = 182.6d “about 180 davs” = 180.0d “6 months” = 182.6d “6 months” = 182.6d
cf 182.5df cf 152.6d cf 159.8 cf 167.3d cf 152.6d cf 159.8d cf 167.3d
159.8d 152.6d
Talapoin, (Miopithecus Chamois
167.3d
Ibex
175.2d 175.2d 167.3d
Wart hog Dik-dik Impala
183.5d
Impala
183.5d 183.5d 183.5d 183.5d 183.5d 183.5d 175.2d 183.5d 183.5d 183.5d 192.ld 192.ld 183.5d 183.5d 183.5d 183.5d 167.3d 167.3d 192.ld 183.5d 192.2d 201.2d
talapoin)
Chiru. Tibetan antelooe Goral Tahr Bighorn 1Urial 1Howler monkey, (Alouatta) _ ) Mangabey, 1I\--Cercorebus1-, Weeping capuchin Squirrel monkey, Titi Chacma baboon, (Papio) Langur Giant anteater, Brazil Honey badger, Rate1 Hanglu, in Kashmir Hanglu Four-horned Antelope Springbok Hamadryss baboon Potto, (Lotis Perodicticus potto) (Genus Tar&s) Slow Lot%, 1(Nycticebus coucang) 1Grizzly bear,
( Ursus) 175.2d
1Slow Loris
I“174-175 days” = 174.5d
cf 175.2d cf 175.2d cf 167.3d cf 183.5d cf 210.7d. cf cf cf cf cf cf
183.5d 183.5d 183.5d 183.5d 183.5d 183.5d
cf 175.2d
I “about 6 months” = 182.6d “6 months” = 182.6d “184 to 193 days” =184.0d to 193.0d (14 cases) “196 days” (1 case) = 196.0d “190 days” = 190.0d “about 6 months” = 182.6d “6 months” = 182.6d “183 days” = (London Zoo) =183.0d “6 months” = 182.6d “about 171 days” = 171.0d “average 170 days” = 171.0d “193 days”
cf 183.5d cf 167.3d* cf 167.3d* cf 192.ld
“approx 6 months” = 182.6d “averaged 192.2 days”
cf 183.5d cf 192.2d
1“6.5-7 months” I= 197.8d-213.ld 1“174 days” = 174.0d
IPerhaps 3 other peaks in between. aPerhaps 3 other peaks in between. *Perhaps peak also at 192.ld and 201.2d. lBimodal? *Bimodal?
KM 19:6-B-P
cf 152.6d
Kob
cf cf cf cf cf cf cf cf cf
183.5d 183.5d 183.5d 192.ld 192.ld 192.ld 183.5d 183.5d 183.5d
cf 201.2d cf 210.7d cf 175.2d
W Hefs. **
-
S
s
s S s -
-S -S -F S s F -F F F S s s s F S s -
171 (71 [71 WI 171 [71 [71 [71 [71 171 [71 [71 [71 [71 Jl_ Pll
S
WI
S
(71 [71 [71
s-
S s F
S
Jl_ [7) [71 (71 [71
-S -F -F S
[71 [71 [401 WI
ss-
ss s-
S
S
[211 [411
F
[71 Jl_
A. B. Table Al.
Continued.
Comparision
CLYMER
of event times with reported gestation
periods.
*These are
events ages closest to published gestation data. l*S = Success, F = Failure (see Section 5.1.1).
First Species Name
Event
Common
Applicable
Name
Interpretation
Gestation
and
Data
(Latin Name)
to Species 175.2d
Vervet monkey, (Cerco-pithecus Pygerythrzls)
183.5d
Vervet monkey,
183.5d 210.7d 210.7d 210.7d 210.7d 210.7d 210.7d 201.2d
220.7d
(Cerco-pithecus Pygerythru) Indian fruit bat (2 species) Barbary ape Grivet monkey Sloth bear Hvaena. in India 1Aardvark 1Asiatic two-horned rhinoceros Pygmy hippopotamus ,I
,
210.7d
Mandrill, (Mandrillus sphinx L.) Spotted deer, Chital
201.2d
Mule deer
201.2d
White tailed deer, Virginia deer Greater kudu Harnessed bushbok Bear, Dublin Zoo (Damaliscus Korriaum
210.7d 220.7d 210.7d 210.7d
242.0d 220.7d 210.7d 210.7d 210.7d 210.7d 242.0d 220.7d 23l.ld
,175 days” (1 case) = 175.0 ‘178 days” (1 case) = 178.0 ‘203 days” (1 case) = 203.0 ‘180-213 days” I 180.0 to 213.Od ,about 6 months” = :about 210 days” = about 7 months” = ,about 7 months” = ,7 months” = 213.ld ,about 7 months” = ,7 months” = 213.ld
Ringed seal Siamang, (Symphalangus syndactylus) Reindeer, (Rangifer tarandus) Steinbok Lechwe Porcuoine I Leooard seal ITree hyrax 1Rock dsssie
[Perhaps peak also at 192.ld and 201.2d. I FBimodaI. *Perhaps 3 peaks between. *Perhaps peak at 220.7d. * Bimodal? &Perhaps peak also at 210.7d.
S,F Refs. **
Comments*
182.6d 2lO.Od 213.ld 213.ld 213.ld
,201 to 210 days” = 201.0d to 210.0d ‘184 days.” ,230 days” :9-10 months” = !73.9d-304.4d ‘220 and 270 days” = 220.0d and 270.0d ,7 to 7.5 months” = 213.ld to 228.3d l99 to 207 days” =199.0d to 207.0d (5 cases) :197 to 222 days” =197.0d to 222.0d ‘about 214 days” = 214.0d
Ooilbv
T
Published
Time
‘214 to 225 days” = 219.5d ‘7 months” = 213.ld ‘about 214 days” = 214.0d ‘214 days” = 214.0d ‘7 months” = 213.ld ‘about 240 days” = 240.0d 10 births, London Zoo) ‘8 months” = 243.5d (223-239 days” : 223.0d-239.0d 7-8 months” : 213.1-243.5d 7 months” = 213.0d 7 months” = 213.0d 210 days” about 8 months” = 243.5d 225 days” = 225.0d 7.5 months” = 228.3d
cf 220.7d*
IS
Timetable Table Al.
Continued.
Comparision
of Life
229
of event times with reported gestation periods.
*These are
events ages closest to published gestation data. l*S = Success, F = Failure (see Section 5.1.1).
Common Name
= 225.0d to 257.0d
“255 days” = 225.0d
253.4d
Orangutan,
(Pongo)
242.0d 242.0d 253.4d
Serow Musk ox Wooly monkey, (Lagothiz cana Geofloy)
“249 days” = 249.0d “251 days” = 251.0d “255 days” = 255.0d 250 to ss many as 288 days* “8 months” = 243.5d “8 months” = 243.5d “8 months and 10 days” = 253.5d
._ Perhaps peaks at 220.7d and 231.ld also. IPerhaps peaks at 220.7d and 231.ld. *Perhaps peaks at 265.4, 277.7d.
cf cf cf cf cf cf
253.4d 253.4d 291.0d 242.0d 242.0d 253.4d
S F S
PI
E
;;
S
(71
230
A. B. CLYMER Table Al.
Continued.
Comparision
of event times with reported gestation
periods,
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
Common
Name
“8 to 9 months”
= 240.0d to 270.0d “9 to 10 months”
= 258.7d to 273.9d
“about 285 days” = 285.0d
Timetable of Life Table Al.
Continued.
Comparision of event times with reported gestation periods.
231 *These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
Published Common Name
Perhaps peak also at 277.9 and 291.0 days.
Gestation
232
A. B. CLYMER Table Al.
Continued.
Comparision of event times with reported gestation periods.
*These are
events ages closest to published gestation data. “‘S = Success, F = Failure (see Section 5.1.1).
Published Common Name
Gestation
389.9 h 2.1 days”
Timetable of Life Table Al.
Continued.
Comparision
of event times with reported
events ages closest to published gestation data.
Common Name
“S
233 gestation
periods.
*These are
= Success, F = Failure (see Section 5.1.1).
Gestation
= 607.0d-641.Od “25 cases 17-24 months”
A considerable number of unselected gestation data have been collected in the large table above. These data include both published data and for each the nearest event age from the formula. By counting successes and failures, one would expect to find them nearly equal, as in the analogy of heads and tails of a coin. Quite surprisingly, however, the ratio of successes and failures is very highly improbable. For example, in the first 103 species in the table there are 85 successes and 18 failures, giving 83% success (versus the 50% expected a priori). This outcome is so improbable that it strongly supports the formula. The percentage success decreases slowly with increase of age of species, dropping to about 60% for the largest reported event ages. That is still remarkably improbable. The reason for the decrease is discussed in Section 5.2. It is problematical to determine how to deal with data given as a range. If the mean is used, then all ranges equivalent to even multiples of 1.0472 will automatically give a failure. On the other hand, if the ends of the range are used as two data, it is likely that each will be a success. The latter alternative was used. This might seem to be cheating by taking advantage of a hypothesis to improve the fit. However, if this method is not used, the difference in results is small enough to make the result still statistically astonishing. The following are references cited in Table Al.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
F. Sunquist, Of quells and quokkss, International Wildlife (July/Aug), 12-16 (1991). A.G. Lyne, Gestation period and birth in the marsupial Zsoodon macrourus, Austr. J. Zool. 22 (3), 303-309 (1974). Stodart (1966). Hughes (1962). Reynolds (1952). D. Ferrigno, The Virginia opossum, New Jersey Outdoors (May/June), 36-37 (1984). S.A. Asdell, Patterns of Mammalian Reproduction, Cornell Univ. Press, Ithaca, NY, (1964). M. Griffiths, The platypus, Sci. Amer. 258, 84-91 (1988). MacLusky and Naftolin. P. Vogel, Comparative investigations of the mode of ontogenesis of domestic soricidae, Rev. Sulsse Zool. 79 (4) 1201-1332 (1973). McAllen and Dickman (1986). HA. Griszell, A study of the southern woodchuck, Marmota monax monax, American Midland Natumlist 53 (2), 257-293 (1955). G.B. Sharman and P.E. Pilton, The life history and reproduction of the red kangaroo (Megaleia n&a), Proc. Zool. Sot. London 142 (Part l), 29-48 (January 1964). D.A. Conner, Life in a rockpile, Natural History (June), 51-59 (1983). Lush, Animal Breeding Plans, Collegiate Press, Ames, Iowa, (1937). D. Mackenzie and C. Shwarek, The Eastern Chipmonk, New Jersey Outdoors (Fall), 64 (1992).
234
A. B. CLYMER
17.
Hoogland, Infanticide in prairie dogs, lactating females kill offspring of close kin, Science 230, 1037ff (No_ vember 1985). B. Morris, Some observations on the breeding season of the hedgehog and the rearing and handling of the young, Proc. Zool. Sot. London 136, 201-206 (1961). J.J.C. Mallinson, Establishing mammal gestation periods at the Jersey Zoological Park, In International Zoo Yearbook, Husbandry, pp. 184-187, (1974). Marshall and Jolly. N.E. King and G. Mitchell, Breeding primates in zoos, In Comparative Primate Biology, Volume 2B, Behavior, Cognition and Motivation, pp. 219-261, A.R. Liss, New York, (1986). (unknown source). H. Ikeda, Old dogs, new treks, Natural History (August), 38-45 (1986). Wackemagel (1968). Eisenberg (1970). Goldman (1950). J. Scott, The leopard’s tale, SWARA 8 (6), 8-12 (1985). Baker (1984). C.P. Kofron, Seasonal reproduction of the springhare (Pedetes capensis) in Southeastern Zimbabwe, Afr. J. Ecol. 25, 185-194 (1987). San Diego Zoo signs. Bourliere (1967). P.G. Crawshaw, Top cat in a vast Brazilian marsh, Animal Kingdom (September/October), 12-19 (1987). Houston and Prestwich. Sign at the San Diego Wild Animal Park. P.L Krohn, The duration of pregnancy in rhesus monkeys Macaca mulatta, J. Zool. Sot. London 134, 595-599 (1960). Wolfe et al. (1972). Howard. Harms (1956). Sowls. Yerkes (1953). M.K. Izard, K.A. Weisenceel and R.L. Ange, Reproduction in the slow loris (Nycticebus coucang), Amer. J. Prim. 16, 331-339 (1988). Napier and Napier (1967). Gilbert, Some not-too-close encounters with a cactus that walks, Smithsonian 23, 56-67 (1992). Klingel, Sizing up a heavyweight, International Wildlife 21 (5), 4-10 (1991). C.W. Wemmer, Sociology and management, In The Biology and Management of an Extinct Species, Pere David’s Deer, (Edited by Beck and Wemmer), Noyes Publications, New Jersey, (1983). Bergernd (1983). Signs in San Diego Wild Animal Park, Columbus Zoo. unknown (1976). T. Bedell, There’s a whale, there’s a whale, Skylines, 32-33, 17-20 (September 1986). D.A. Glockner-Ferrari, Humpback whales, up close and personal, Animal Kingdom (November/December), 38-49 (1986). Tapir Res. Inst. (1971). T.V. Program. The Diagram Group, Comparisons, pp. 172-173, St. Martin’s Press, New York, (1980). Bronx Zoo sign. S.N. Austad, The adaptable opossum, Sci. Amer. 258 (2), 98-104 (February 1988).
18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.
APPENDIX B GLOSSARY Ambient temperature: Asymptote: Bimodal: Differential equation: Enthalpy: Envelope: Event : Event age: Failure:
the temperature in the vicinity of an object of concern. a vertical straight line at which a curve goes to infinity. a frequency distribution with two peaks. an equation in which the unknown appears in a rate of change term. the amount of heat in an object. a smooth curve which kisses a wiggly curve at several points. a sudden start or stop of some process involved in development or later life of an organism. the age, post-fertilization, at which an event can occur according to the formula or series. a reported age at which an event occurred which is more than 1.18% away from the nearest event age in the series.
Timetable of Life Frequency distribution: Geometric series: Histogram: Integer: Logarithmic mRNA:
time scale:
Molecule: Multimodality: Mutation: Mutation space: Quantum numbers:
Series: Simulation: Success: The formula: Thermal capacity: Timetable:
235
a graph, histogram or table showing how many items (e.g., species) there are in each class interval (e.g., range of ages). each member of the series is a certain constant times the immediate past member of the series. a stair-stepped plot of a frequency distribution using horizontal line segments between class boundaries. whole number. a scale on which logarithms of a variable are plotted. messenger ribonucleic acid, produced on a chromosome by a hypothetical slow process making it a timer, which directs the manufacture of a protein in a ribosome outside the nucleus of a cell. (as in “molecule building”) a linear molecule (mRNA), the completion of whose building constitutes a timing signal. the property of having several peaks in a frequency distribution. as used here, any change in a gene (mRNA) giving a new event age. a hypothetical space whose dimensions are all the parameters of possible mutations (one quantum number per gene?). integers associated with particular states of a system, such as possible orbits of an electron around an atom, or possible dimensions after growth of a particular tissue. a geometric series of event ages given by the formula. the process of solving a given mathematical model on a computer in a number of cases of concern. a reported age at which an event occurred which is closer than l.lS% to the nearest event age in the series. one of several equivalent forms of equation yielding the event ages, namely, Aj+l = l.O472Aj, or Aj = (l.O472)j, or 1ogAj = j log 1.0472. the amount of heat required to heat an object one degree. a table listing events and the time of occurrence of each.
APPENDIX C A LOOK BACK 1. INTRODUCTION The appendix is about the author’s struggle in the research and its “marketing.” The story is an account of one unaffiliated and unanointed man innocently bringing his work before his scientific peers in search of feedback, which is a highly discouraging process. He allowed himself to be silenced then for 19 years. That is cowardice. Then he wrote three papers in an attempt to attract attention. Nothing resulted. There followed several more years of quiet cowardice, then this paper. 2. HOW
IT GOT
STARTED
It is educational to look into how a research project got started. First it is desirable to get out of the way the mistaken idea that research proceeds from nothing by deliberate rational thought about what would be the best question to address. For example, John Wheeler has advised: “In any field, find the strangest thing, and then explore it.” Similarly, Steven Jay Gould has said: “You might almost define a good scientist as a person with the horse sense to discern the largest answerable question-and to shun useless issues t,hat sound bigger,” [88]. This ploy might be good, but it was not used in this case. So big a problem was not originally sought. In college, the author was urged to apply mathematics to biology as a part of his career. It was widely felt by mathematicians then that biology was ripe for “strengthening” by mathematics. At that time, the author made a mental note to try. In 1966, the author read a paper by Moorees [13] in which the use of the logarithm of conceptual age was mentioned as being a useful modified “time scale” variable for developmental data presentation. That could have started him to think in terms of events equally spaced on a logarithmic time scale, or the equivalent in terms of a geometric series in regular time.
A. B.
236
In January
CLYMER
1967, the author was entertaining the conceptual scheme of a log spiral with radial
lines every 36 degrees. Every turn of the spiral represented a doubling of age. The age increase between radial lines was a factor equal to the twelfth root of two. Every intersection of the spiral with a radial line stood for an event in the development of the individual whose life was thus charted. The author believed for a while that the events on a particular radial line were of the same type, in some undefined sense, but this frill was abandoned for lack of evidence. At this point, the author first went into print [89], using what few kinds of data he had found by then. The author was already pursuing science as defined by Pritsker [12]: “Science is nothing else than the search to discover unity in the wild variety of nature.. .” The next attempted paper was an article submitted to Science [53]. It was rejected. Then a paper was submitted to the Journal of Theoretical Biology [go]. It too was rejected. 3. THE RESEARCH 3.1.
Tools
Used
The author had a limited set of tools with which to work. He had the biological and medical literature, mathematical analytical tools, and a full set of conceptual schemes. He had no funding, no equipment, no laboratory or field skill or knowledge, no collaborators (all candidates ran, as from a leper), no biological knowledge (except from a high school course), no statistical expertise (except from one college course), and no connections. These limitations of tools naturally limited the types of research he could perform. Nevertheless, significant work was done, regardless of whether it all has merit. Thus, an amateur in biology, unequipped and unplaced for professional work, can do work deservingsome notice. 3.2.
The Roles of Luck
It is humbling to keep in mind that “Really sharp and noteworthy accomplishments require luck as well as hard work” (M. Freedman, U.S.C.). By pure luck, Asdell’s book full of gestation data had been published in 1964, just three years before the author needed those data. Those data were absolutely crucial, because the only other data on hand then were of little value [89]. There is perhaps an analogy with the excellent planetary measurements made by Tycho Brahe that enabled Johannes Kepler to discover and establish his laws. Similarly, by luck the author happened to see a tree diagram of the evolution of primates. That enabled him to make an easy test: did the number of event ages per event of a species correlate with the stated rate of evolution of that species? The answer was affirmative, thus suggesting a generalization to a hypothesis covering all species. By luck, the author had had graduate courses in molecular vibration and rotation. This background provided some of the concepts in the molecule building theory. By luck, the author had had a job (1942-1945) in which he was taught the skills of numerical differencing and smoothing. That is just what was needed in order to see the geometric series in the data. By luck, the author came across some data for the effect of temperature upon event ages. At first the only apparent relevance was to the errors in reported event age data, but eventually the greater importance of thermal effects was seen. 3.3. The Research Work The research work required a considerable amount of toil. Searches for data had to be performed, which required an enormous amount of reading in spite of some degree of computer automation of the task. Then the relevant material had to be copied and filed.
Timetable of Life
237
Given these hard-won data, it was necessary to analyze them. The purposes of the analyses were to detect error patterns, to compare event ages for related species, and to try to identify the series signal buried in the noise. Actually, the foregoing steps were organized into many successive campaigns with batches of data, going through the entire process for each batch. The author is able to agree heartily with Gould that “Scientific discovery. . . is a reciprocal interaction between a multifarious and confusing nature and a mind sufficiently receptive (as many are not) to extract a weak but sensible pattern from the prevailing noise.” The fact of the noise and the fact that the relationship was logarithmic together insured that the secret was kept from life scientists by nature. Occasional one-of-a-kind analyses were required. One was the listing (see Table 7) of the range-mean ratio of gestation data, which revealed the multiplicity of peaks in the frequency distribution for most species. Until then, the author had regarded the ranges of values as reflecting errors. What had seemed to be unforgivably large errors quickly became precise and meaningful structure! The given data suddenly improved greatly in apparent quality! Likewise, the errors of fit of the series to the reported event age data had to be calculated and a histogram prepared. This effort led to the conclusion that the errors are approximately Gaussian (actually lognormal because of the logarithmic time scale). The greatest task was preparing and maintaining the large table in Appendix A. Unfortunately, it could not previously be published because of its size. Therefore, the author agrees with Gould [91]: “Good science may require genius and imagination.. .but never forget that new conclusions are the fruit of hard empirical work as well.. .” Likewise, Newton is said to have discovered his revolutionary findings by thinking about them without ceasing. The author has had many such long periods caught up in questions. The intense emotions associated with creating a scientific theory are not qualitatively different from those of creating a work of art. Each is a network of problem solvings and tentative decisions. Throughout the work the author had to guard against unintentional fraud. It was easy to eschew creating or changing data, but it was difficult to remember to include bodies of data that did not agree very well with the hypothesis. Finally, by 1986 the author had enough courage, new data, and new ideas to make it desirable to publish. The publication of 1967, [89], had been highly preliminary; it was less than professional. It served no purpose but to establish priority for the format of the formula and for the concept of development. Three papers in three successive years were published [l-3]. Those papers were presented to and published by the Society for Computer Simulation, the author reasoning that his peers would be more receptive than the editors of Science. Wrong. There was a nearly total lack of persons in the audiences or among the readers who knew enough biology to understand the subject and enough system science to understand the presentation. The editor of this journal was one of the few. 4. THE
FINDINGS
In this section, the author offers some of his notions about the contribution. There are several possibly notable aspects of the series which resulted from the foregoing work: 1. It has the simplicity of a law that usually turns out to be necessary for success for a very general application. This simplicity applies to each form: the geometric series, the recursion formula, and the logarithmic equal-spacing form. 2. It introduces an unprecedented degree of precision into life science in dealing with time. 3. The series fits many important natural constants, such as: 24.01 hrs (one day), 6.9424 d (one week), 27.695 d (one lunar month), and 366.5 d (one solar year). It fits also many biorhythms (if not all). A two-parameter formula should not a priori fit so many points. Hence, these fits are quite surprising.
A. B. CLYMER
238
4. The series offers a remarkable condensation of the data of chrontology: event ages fit all events (thousands?)
a few hundred
in all species (millions), i.e., billions of species-event
combinations. 5. The errors of fit for all events-and species for which data were available are remarkably small, with some glaring exceptions. The fault seems usually to lie with the data more than with the formula for the event age series. 6. The series should be a nice help in simulating organisms. 7. According to Bronowski [92], “Science is . . . a way of giving order and therefore unity and intelligibility to the facts of nature.” The series is a candidate to be a part of this science. Given the series, it was humanly inevitable that questions would be asked which would produce the theory to explain the series. The author followed this road and then had another success experience with a theory. (At least it still looks like a success experience to the author.) The unlikelihood of all of this success has been pointed out by Ward: “. . .rarely, a scientist finds a brilliant answer to the very problem he set out to solve, and then further finds to his delight that that answer holds implications of deeper significance than the original problem seemed to suggest. That might be called serendipity in spades.” In the author’s case, there seems to have been a lot of “serendipity in spades,” if some of the hypotheses can be validated by other investigators. The theory, like the series, has many unusual aspects: 1. It sheds a new light on the processes of development, evolution, and life itself. 2. Far reaching, it relates many diverse areas. 3. It has the audacity to imply (by hypothesis) that a molecular stochastic process based on random thermal excitation can constitute a precise timer. 4. The theory contains some unifying conceptual frameworks such as species timetables, marching envelopes of event ages in evolution, the concept of the starting and stopping events of processes, synchronization and quantization. 5. The theory has enormous generality of scope, embracing all events over the lifetimes of all species (those having sexual reproduction at least). The theory also has aspects on levels ranging from molecular to global. The theory can be drawn as a network in which the pieces (hypotheses) of the theory are directly or indirectly connected. A question is whether these connections make the hypotheses any more validated than if they stood in isolation. 5. TESTS
OF THE WORK
The literature yields many criteria for a theory to be good, such as: 1. How much can it explain [93]? The theory herein seems to offer explanations over a wide range of questions. 2. How good are its predictions [94]? It is too early to answer this question. Only the author has tested it. A few predictions are stated herein. Crick’s statement is “A good theory makes not only predictions, but surprising predictions that then turn out to be true.” 3. Is the idea completely crazy (Bohr)? Some scientists are ready to pin this label on any theory that involves cycles, rhythms, overly simple mathematics, etc., but the idea of a universal list of event ages is completely crazy to almost anyone. Moreover, any chemical kineticist knows that biochemical reactions take place in milliseconds, not minutes to years, so the proposed molecule building process is completely crazy. 4. How many empirical investigations can it trigger [95]? The event ages of any event in any species can be determined by observation or experiment. Age relationships in an ecosystem can be studied. Quantization can be investigated in paleontology. The effects of temperature upon observed event ages can be determined.
Timetable of Life
239
5. Does it explain several large and independent classes of facts [96]? The formula accounts for the ages published for most of the thousand or so of observed events tested thus far. It had not been realized formerly that these large classes of facts (data) are in fact not independent but rather share membership in a smallish clan. The explanations of development and evolution afforded by the theory appear to be useful, although not complete explanations. The idea of multimodality of event ages has shed much light on the published data. 6. Has testing been done down to minute detail [97]? The most thorough testing done to date is Table Al in Appendix A. The results indicate beyond any doubt that gestation data are numerically accounted for by the formula herein. Additional testing is shown in the cameo studies in Section 5. 6. ACCEPTANCE
OF THE WORK
One should keep in mind the fact that “One of the great paradoxes of the history of technology is that the greatest progress often comes in unexpected ways.” Belief cannot be stretched in a continuous manner. It acts as if there were static friction in the system which must be overcome before there can be any change. A model of belief could be made by minor modification of the author’s model of abuse [98]. To the best of the author’s knowledge, none of the three papers [l-3] is referenced anywhere. Moreover, the author received very little informal feedback from any of the papers. The lack of wide interest in the author’s series kept him trapped in problems related to it. Had it been accepted early, he would have been free to look into entirely different problems. Thus, the need to keep trying to “sell” his earlier ideas motivated half-hearted intermittent further research on matters related to the original question, causing the author to do work he was less and less well fitted for, such as molecular biology or evolution, to try to bolster his earlier theory. It is difficult to say whether the course actually taken will prove to have been the best in the long run. The author has had the benefit of good advice regarding how to 2ake” the slings and arrows. Carey [99] urges the researcher to keep his hopes and expectations low: “. . .do not expect to be hailed as a hero when you make your great discovery. More likely you will be a ratbagmaybe failed by your examiners. Your statistics, or your observations, or your literature study, or something else will be patently deficient. Do not doubt that in our enlightened age the really important advances are and will be rejected more often than acclaimed.” Equally dire is the warning by Huang: “Once you let your idea out, it can go through several phases: First your idea is ignored; then people think it’s impossible; then impractical; then that it’s not really that original; and then that they have had that same idea themselves.” Similarly, as Arthur Koestler has pointed out, “The more original the discovery, the more obvious it seems afterwards.” In the same vein Sir Arthur Thomson has written [loo] “It seems to be a fact, though not a cheerful fact, that the recognition of a scientific conclusion depends very largely on the intellectual preparedness of the time.” Apparently the author has again been many years ahead, trying in vain to “sell” his ideas. It is the story of his life. Regardless of one’s understanding of these psychological aspects, however, lack of acceptance of one’s work is the cause of long and deep despair, as many scientists have attested. 7. THE
PAPER
IN THE AUTHOR’S
VIEW
In summary, attend the theory presented by Walter Bagenhot [loll: “One of the greatest pains to human nature is the pain of a new idea. It is, as common people say, so ‘upsetting’ it makes you think that, after all, your favourite notions may be wrong, your firmest beliefs ill-founded; it is certain that till now there was no place allotted in your mind to the new and startling inhabitant, and now that it has conquered an entrance, you do not at once see which of your old
240
A. B. CLYMER
ideas it will or will not turn out, with which of them it can be reconciled, and with which it is at essential enmity. Naturally, therefore, common men hate a new idea, and are disposed more or less to ill-treat the original man who brings it.” The ideal attitude is detachment. However, any author’s assessment of his own work is to be viewed with suspicion. The author’s view of the paper is of its contents and findings, which he has discussed in Section 5 of this Appendix. Of course he feels that it is transparently clear to the reader. However, he is aware of the truth in Windhorst’s [102] remarks: “When the great innovation appears, it will almost certainly be in a muddled, incomplete, and confusing form. To the discoverer himself it will be only half understood, to everybody else it will be a mystery.” 8. FURTHER
WORK
Much further work seems to the author to be highly desirable.
Some of the possible investiga-
tions are: 1. Analytical investigations, such as determination of the best-fitting constants for the formula by iterative least squares; simulations of many types. 2. Experiments with big samples, temperature control and other necessary refinements, blink comparators of images to seek the time something first appeared, etc. Challenge the formula with data that are much more precisely determined. 3. Checks of the data which the author has questioned or which have large errors; checks that the reader could make easily. 4. Searches for data for types of event not now analyzable. Get data capable of resolving multiple peaks in frequency distributions of observed event ages. 5. Extension of the work to earlier event times. 6. Extension of the work to species that do not use sexual reproduction. 7. Searches for the frequency distributions of event ages now given only as averages (means) or ranges. 8. More applications to medicine need to be conceived and pursued, including pediatrics, gerontology, and pharmacology, as well as general medicine and research in specialized topics. 9. Measurement of thermal effects upon crucial event ages of concern in connection with global warming. 10. Investigation of the limits of validity of the theory. 11. Spot-checks of the author’s work. 12. Use of advanced microscopy techniques to seek predicted behaviors on the molecular level. 13. Appendix A contains many criticisms, suggestions, and research ideas for others interested in gestation periods to investigate. 14. Get timing data for plant events. Standard texts, e.g., Thornley and Johnson [103], are not helpful for this work. Possibly there are significantly different temperatures for fastest growing of different plants, which would help florists and farmers. 15. See if it is possible to determine time of fertilization of a person or animal by noting the times of later events, enabling assignment to a specific event time subspecies. 16. New research never contemplated by the author (the most important of all, keeping in mind the advice to expect the unexpected).
Pergamon 08957177(94)E0050-W
Copyright@1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0895-7177/94 $7.00 + 0.00
The Timetable of Life: The Timing of Events in the Lives of Organisms*
32 Willow Dr., Ste. 1B Ocean, NJ 07712, U.S.A. Abstract-This paper offers an empirical mathematical formula (geometric series) for the ages at which “events” can occur in organisms. These “events” include fertilization, events in the fertilized ovum, developmental events in the embryo and fetus, birth, mating, and other postnatal events throughout the remainder of life. A theory is presented for the foregoing timing of events by the building of an mRNA molecule one unit at a time. The formula is derived from the hypothetical molecule-building process. It is shown that the majority of species have ranges of gestation ages that are indicative of subspecies using several successive event ages from the formula. On a time scale of evolution, these subspecies march randomly toward higher event ages, which is the process of heterochrony.
1. INTRODUCTION This
mini-monograph
organisms.
presents
It presents
a novel partial
also a completely
theory
from event to event. It is a synthesis and extension The assertions given in the following introductory per against published
data. In this Introduction,
potentially important
ing.
are verified in the body of the pa-
its structure without
substantiation
distraction.
and apparently new to biology and medicine.
or life scientist,
in medicine
or life science.
The author,
being not a
has resorted to unusual words and usages to express intended
The reader might be helped by reference to the appended
unfamiliar
of that timing
papers [l-3].
italics are used to designate statements believed by the author to be both
Some terms used herein are not common physician
of three previous paragraphs
of events in the lives of
of the regularity
the assertions are made without
in order to focus on the theory and to emphasize In this Introduction,
of the timing
novel demonstration
Glossary
(Appendix
mean-
B) for any
or unclear words or usages.
tThe author acknowledges gratitude to the late Robert H. Cavins, his high school chemistry teacher, for having been taught to expect to see in nature and science “the perfection of nature.” Of all of the persons who have studied the author’s papers and discussed them in depth, no one has been more helpful than B. Fairchild. He, along with a few others, notably T. Oren and J. McCoy, have been generous with their assessment of the work, urging that the author’s findings deserve the utmost investigation by life scientists as being probably important scientific discoveries. The author thanks A. Leissa of the Ohio State University, for having recognized early his research ability by recommending admission to Sigma Xi. The author thanks the late George Hamilton and the late Willard Constantinides, two outstanding mechanical engineers, who shared their skills in numerical calculus with the author. These skills were key to identifying the “logarhythm of life” in the noisy published data on event ages. The author is thankful that this journal provides such a large canvss for so ambitious a paper. *This paper was typeset in d&-m and galley proofs to authors provided from the offices of the Guest Editor.
171
A. B. CLYMER
172 1.1. Events The
life of an individual
“events,” events _ _ _ _ _ ~ ~ _ _ _ _ ~ _ ~ _ ~
organism
each of which starts
include
can be thought
of as consisting
or stops one or more localized
of a lifelong
developments
sequence
or activities.
of
These
the following categories:
Mating Birth of a mammal Laying of an insect, fish, reptile or bird egg Hatching of an insect, fish, reptile or bird egg The start of a metamorphosis of an insect First appearance of a particular structure or tissue in an animal
or plant
Appearance of a new control loop (homeostatic function) Single cell or embryo mitosis First appearance of a new protein (enzyme, hormone, etc.) in an animal or plant Initiation of a new state of a tissue (e.g., eyelids open or close in a fetus) Migration of birds, mammals, shellfish, etc. Appearance of a new reflex Appearance of a new problem-solving capability or language skill Change or shedding of skin, fur, antlers, color, shell, etc. First appearance of a biorhythm, e.g., menarche Start or stop of hibernation First appearance of a new behavior or physical capability First appearance of an organism’s susceptibility to a drug Start or stop of construction of a chambered shell Establishment of an organism’s sex Death (perhaps for some species an event)
Not all of these events occur in every species, One extremely
important
characteristic
it occurs.
Here age is measured
1.2. The
Series
Apparently, are precisely ages”
from zero at the time of fertilization
it has not been seriously timed
are members
using bisexual
(which
has often
of a single
as a possibility,
been pointed
mathematical
not only that
out by others),
series for all events
the post-fertilization
that
series given by a certain
all such events those
but also that in all species
“event
(at least those
data for several hundred
mammalian
been found in the author’s two successive
searches
which has the value 1.0472, species.
No previously
of the geometric
was obtained
obtained
formula
by fitting
gestation
for event ages has
of the literature.
event ages are only 4.72%
Aj is age in days at the jth event. degree of precision
age of every event is a member
constant to the jth power. Here age is given in days, and j is any integer,
plus, minus or zero. The constant,
sufficiently
considered
when
of the ovum.
reproduction).
It is hypothesized
Note that
of course.
of an event is the age (or ages) of the organism
Hence,
apart.
to test the formula
That
in data that is unusual in biology and medicine.
precise to afford a meaningful
is, Aj+l
= l.O472Aj,
against observed
where
data requires a
Most published
data are not
check.
It follows from the formula that the event ages are equally spaced on a logarithmic spacing being the same for all events and species.
This rhythm
time scale, the
might be called the Yogarhythm
of life.” The
formula
is equivalent
to a list of possible
event ages (see Table
1).
Any species
“uses”
some subset of this list, but the ages used do not have to be consecutive. It is postulated that the “in use” by living things since the beginning of sexual same list of possible event ages has been reproduction.
Many events in one species
might bring on no event.
might occur at one event age; some other
event ages
Timetable Table la. Event ages. All time post-fertilization for humans.)
of Life
173
(PF) in Tables la-c.
(In Table Id, they are postnatal
In Table la, the integers i are those associated with the formula Ai = 21( 1.0472)i,
which gives the same series of ages as given by Aj = 21(1.0472)j,
days.
-155
IO.39613 123.768
I
-242
IO.4299 125.80
-232
IO.6819 140.91
-224
IO.9862 159.17
-221
1.1325 67.95
The up to 350 or so event ages “used” by a species are the entries in the timetable of the events in the species. The set of timetables of all species might be called the “timetable of life.” The human timetable, in particular, should be invaluable in medicine and for monitoring and managing development, as would be timetables for many other species in veterinary medicine. The science of time in development might be called “chrontogeny” (chron + ontogeny). 1.3. Multiple
Event
Ages
For many events, the age of occurrence (event age) is observed to be very sharply a day or two variation over a year interval, as for the swallows of Capistrano, the Hinkley migrating, or the occurrence of ragweed pollen in Illinois on August, 21). In events, there are two or more peaks in the frequency distribution over time, and in the ages of occurrence are found to be smeared randomly over some wide range. Most events species.
in most species
are hypothesized
It is a fact that most mammalian
(age at birth),
some as many
to have more
fixed (e.g., vultures of some
other
still others
than one event age per event per
species have more than one possible gestation
period
as 8 or 9. Each of these event ages is given by the formula, and
174
A. B. CLYMER Table lb. Event ages. All time post-fertilization for humans.)
(PF) in Tables la-c.
In Table lb, the integers i are those associated
with the formula Ai = 21(1.0472)i,
which gives the same series of ages as given by Aj = 21( l.O472)j,
I
-103
-76
15.142
908.51
-75
15.857
951.39
-74
16.605
996.30
-71
19.069
1144.14
(In Table Id, they are postnatal
days
-32
1 4.8003 1115.21
-22
t 7.6132 1182.72
1 4.359 1261.53 I
those for one species event has several The
are consecutive
list of event
event
ages in the list than
The
substantially
of theory Molecule
It is postulated molecular
in error,
I
12.6443
-11
to find experimental Building
303.46
distribution
for an
a published
or observational
This
observed
between
event
age as
two consecutive
is an instance
of the unusual
errors.
Process
that the formula
building process
tentatively
if it lies closer to the midpoint
to one of the ages in the list.
is a mathematical
description
of the temporal
outcome
of a
by which structural units are added one at a time. The times to build
molecules
of consecutive
sizes (numbers
according
to the formula.
A derivation
building
76.07
in the list. In such a case, the frequency
ages can be used to identify
probably
1.4.
3.1696
peaks.
being
application
-41
of consecutive of the formula,
structural adduced
units)
herein,
are in the ratio
suggests
1.0472,
one hypothetical
mechanism.
Addition
of one structural
same or a qualitatively
unit to a timer
different
at the next later event age.
molecule
event, depending
would seem to offer the possibility
on the nature
of the added unit, in either
of the case
Timetable Table lc. Event ages. All time post-fertilization for humans.)
of Life
175
(PF) in Tables la-c.
In Table lc, the integers i are those associated
(In Table Id, they are postnatal
with the formula Ai = 21(1.0472)i,
which gives the same series of ages ss given by Aj = 21(1.0472)j,
days.
1Event i 1Months 1
1 Days 1 1
75
1 21.930 1 667.5
80
1 27.617 1 840.6
I
87
1 38.141 11160.9
99
1 66.335 12019.1
I
1.5.
A Theory
102
1 76.179 12318.7 I
103
1 79.774 12428.1
I
of Biorhythms
An intriguing theory of biorhythms (not new) is that repeated building of a timer molecule on the same substrate results in the same event over and over at equal intervals of time. This concept is consistent with the theory herein. Moreover, the biorhythm periods check well against the nearest members of the list of event ages. 1.6. Synchronizations Some important synchronizations are enabled by the timer molecules. For example, from generation to generation a mammalian species can maintain a fairly stable relationship to the annual calendar (hence, seasonal climate) in its event timing. Similarly, for species with much shorter lives, a synchronization can be maintained over lunar months or solar days. Also, in many species, it is advantageous to maintain a synchronization between successive generations and/or between mates. Synchronization is an important characteristic in ecosystems also, such as a prey species appearing when a predator arrives during its migration. A change of climatic temperature alters observed event ages, possibly upsetting synchronizations that are vital to the survival of some species and even of the entire ecosystem. The effects
176
A. B. CLYMER Table Id. Human postnatal (PN) events. Assuming 277.894 days PF gestation period.
1 year = 12 months = 365.25 days.
87
12.41761 29.011
I
1
93
13.43081 41.170
94
13.62871 43.544
97
(4.28001
I
51.360
1
I
130 122.3322 1267.99
1 78
Il.33781
16.0541
I
140 135.8642 1430.37
of global warming upon ecosystems, There
appears
in individual 1.7.
to be no timing mechanism
organisms.
of a tissue growth process
the dimension
level; all timing seems to be caused
for development,
values of j the dimensions Another Darwin’s
“quantum
to a difference
application finches,
is a “quantized”
will take only certain
stop event ages, assuming
1.8.
on the ecosystem
It then has consequences
shift, are conceivably
heretofore. ecosystems
and evolution.
Quantization
The result that
via change of event ages due to thermal
than other effects of warming considered
more devastating
a constant numbers.”
growth
rate.
which one can postulate
dimension.
Quantized
by the difference
One might choose
In paleontology,
of event ages, assuming
might be the geometric
tissue
values determined
means
of the start
and
to call the corresponding
one could work backwards
from observed
that the tissue growth rate has been constant.
parameters
(e.g., lengths
and radii) of the beaks of
are quantized.
Evolution
Mutations of evolution
by jumps
of j by one unit for this or that event constitute
of a species,
as far as size is concerned.
the postulated
As a rule, the individuals
mechanism
with larger values
Timetable of Life
177
of j for the same growth-end event can out-compete those with smaller j’s, since size usually offers advantage. It takes only 15 unit increments of j to double an event age, and just a few doublings of size would transform an eohippus (dawn horse) into a horse. As a species evolves, its event ages tend to increase incrementally, in general. Exceptions would be dwarfs and pygmies, which might have descended from larger ancestors by temporary and local decrease of the j’s. This shifting of the timing of developmental events is called heterochrony. Note added in proof: S. J. Gould [4] has maintained that growth is a continuum but that evolution involves discrete increments. This observation is in agreement with the theory herein. Those primate species having the greatest numbers of event ages per event are found to be those that are evolving fastest. One would be inclined to form the hypothesis that this is true of all species, not just primates, on the argument that there is nothing special about primate evolution. Species that have not evolved “recently” (on an evolutionary time scale) are usually found to have a single age for each event. A species stops evolving if it finds a set of event ages that are a local optimum in mutation space for dealing with its environment. The foregoing items in italics are believed by the author to constitute an expanded, structured and more definitive account of the roles and mechanisms of timing in biology and medicine than has been available heretofore.
2. EVENTS
AND
PROCESSES
2.1. Events In the Introduction, a list has been given of the most common and recognized events that occur in organisms. They are like the turning on and off of switches, which start or stop processes. Events per se have a negligible duration. These events are milestones in the development of an organism. The times at which they occur, expressed as the post-fertilization (or post-pollination for a plant [5]) age of the organism, constitute a set of parameters which define a species to a major extent. The list of events and their event ages for a species is its “timetable.” It is difficult to define “event” other than to use the empirical approach that a legitimate “event” category is one that succeeds in being fitted by the series. 2.2.
Processes
Many events start processes resulting
in tissue growth,
in less growth, Similarly,
because
if there
in certain
will be proportional
there is less time available before the process is stopped
apparent
discontinuities is in reality Changes
interruptions
continuous
or transients. However,
and smooth
quite recently
Previous
the amount
event. because
of growth
as seen by the naked eye is continuous,
to the theory
herein,
started
large spurts
of size variables the apparent
and stopped
of growth
[6]. Th ese spurts can be interpreted
can have continuity
at event
in the lengths
ages.
of babies
as pulses of growth hormone
of which die out quickly, but not until surprising
have occurred.
3. SERIES 3.1.
by another
for growth.
only during processes Indeed,
event results
there will be more growth,
Of course time derivatives
according
at event ages, the consequences
of growth
event,
If the growth rate is constant,
available
can begin or end at event ages.
released perhaps
stopping
The overall course of development
at event ages.
have been reported amounts
for growth.
to the time interval
Note added in proof:
The process might be cell reproduction,
In this case a delay in the growth starting
is a delay in the process
there will be more time available
without
cells or a tissue.
for example.
OF EVENT
AGES
Series
Researchers in embryology have recognized that the development of an embryo follows a fairly rigid schedule. The best known works that have attempted to exhibit a universal series of definite times are those by Witschi [7] and by Streeter [8]. Another list in the literature is the Carnegie stages, which also are expressed as small integer stages, but they have only human application 191.
178
A. B. CLYMER
Witschi presented a list of 36 “standard stages,” each an integer number of days after fertilization, at which embryos presumably first reach a definable level of development. In Witschi’s list, the intervals between successive ages increase generally with age from one day to two days. Thus, Witschi saw developmental stages as getting further apart as development proceeds. Similarly, Streeter presented a set of “horizons” which he believed represented definable levels of development. These too are embryo ages in integer numbers of days. Like Witschi he used intervals of one to two days. Neither list was completely regular in any sense, so neither list had the look of a simple natural law. No formula would be a very good fit for either series because of their irregularities. Table 2 shows the Streeter and Witschi series compared with a certain geometric series mentioned in the Introduction and to be discussed further in Section 3.2. The general agreement is of interest, in the sense that it gives an absolute magnitude check on the geometric series and its slope. The overall outcome is 22 successes out of 37, or 59% success. This result is not particularly impressive. However, if one looks only or 79% success. For the Streeter data, apparently Witschi is showing events, Refer to Figure 1 (in Section 5) for 3.2. The Geometric
at the Witschi data, one obtains 15 successes and 4 failures, there are 6 successes and 10 failures, or 38% success. Thus, while Streeter is showing stages between events. definitions of success (S) and failure (F).
Series of Event
Ages
Table 1 gives a listing of the geometric series over the entire range of observed event times. To repeat and amplify on the statement of this series in the Introduction, the series can be defined by the formula Aj = (l.O472)j, where Aj is the age in days at which the jth event occurs, 1.0472 is an empirical constant, and j is any integer (positive, negative or zero). The table includes, for convenience, a portion in which the zero is translated from fertilization to a typical time of human birth, in order to allow entry with postnatal ages of human postnatal events. The series was written earlier [l], in the form Ai = 21 (1.0472)i, where i is any integer and 21 is another empirical constant. This is the formula upon which Table 1 is based. By noting that the value 1 day (24.01 hrs) appears in the list of values calculated for Ai, one can replace the constant 21 days with the constant 1 day and define j to be a translation (shifted version) of i. That is where the formula above containing j instead of i came from. Actually, a different value was first used for the constant “1.0472” (namely, 1.05946, which is the twelfth root of two, as reported in [l]), but the form of the equation was the same. Going to the value 1.0472 improved the fit notably; there were no longer oscillations of the sign of the error. Presumably, the oscillations were an interference pattern between the periodicity of the formula in logtime and the postulated periodicity of the reported data in logtime. The constant value 1.0472 is very close to the 15th root of two, which might be just coincidence. The author has no explanation or rationalization, other than to recall his concept of a logarithmic spiral with radii (see Appendix C, Section 2). There is a problem with the series that needs to be discussed. At smaller and smaller values of i or j, the event ages get down into the range of a few seconds. Somewhere in that range it must become impossible to manufacture any mRNA molecule so fast. Moreover, as age decreases, the values of i and j approach negative infinity, and an infinity of events must take place in a very short time, according to the formula. At some point the formula must cease to be credible. However, this defect does not prevent the formula from being useful over the entire practical range. The foregoing problem might be taken care of by putting an offset constant on the right hand side of the formula to represent the time taken by steps other than mRNA building. This constant would have to be very small, in order that it not disturb the accuracy of fit away from small event ages.
Timetable
of Life
179
Table 2.
Day
18
Nearest
Witchi’s
Event
Standard
Age (days)
Stage
Streeter’s Horizon
Percent Error
success or Failure
18.29 19.15 20.05 14
_
0
_
X
t-o.05
S
S
23
23.03
_
_
_
_
24
24.12
15
XI
-0.5
25
25.26
_
_
_
SS _
26
26.45
_
XII
-1.73
F
27
26.45
16
XIII
+2.04
F,F
28
27.70
17
+1.07
S
18
_ 1
XIV
)
0
)
SS
31 32
31.81
33
33.31
34
I
22
I
I
I
XVI
I
23 XVII
-.94
I
s,s
+2.03
F
t.34
s.s
35
34.88
24
36
36.52
25
37
36.52
_
XVIII
+1.30
38
38.25
26 _
_
-.66
S
XIX
+1.92
F
38.25
I
(
27 41 42
28
43
-
45
46.00
46
46.00
47
46.00
48
48.17
_
50
32
I
/[
F F
_
-.13
S
-2.29
F
I
I
XXI
31 _
[ -1.44
xx
XXIII
49
I
_
+.14
I -2.14
I
I
S F
+2.13
F
-.35
S
0
_
-.88
S
Another interesting limit question relates to what happens if one constructs a closer and closer set of event ages by decreasing the spacing factor indefinitely below 1.0472 toward unity. The event ages will eventually become so close that all reported events are successes [lo]. However, that case is not of interest. The case with the factor 1.0472 is believed by the author to be a local optimum on the curve of percentage success versus e in the spacing factor 1 + e. The value .0472 for e seems to make contact with something significant in the real world. It would be desirable to demonstrate this curve for a set of values of e by calculation with some body of data such as gestation data. The foregoing discussion was not correctly presented in [l]. 3.3. Species
Timetables
If a species has existed long enough to have reached an equilibrium, in the sense of having no possible improvement of itself by unit changes in the quantum numbers j of its events, then MCM 19:6-8-H
A. B. CLYMER
180
there will be exactly one event age per event for that species. The more common situation is for a species to have two or more event ages per event, which is suboptimal and, hence, not an equilibrium “design” of the organism in a specified environment. For a given species, one can collect the known event descriptions and their ages of occurrence into a timetable for the species. Most of the events will probably have more than one event age (see Section 6 for further information), so several columns will be needed at the left for the various ages for the event described in the column at the right. There will probably be little or no information about correlations of event ages between events and, hence, about the different combinations of event ages that occur in an individual for a number of events. For example, one could try to do a timetable for all humans having a particular gestation period. Such a timetable would facilitate event management by physicians and veterinarians. The sequence of events is not always exactly the same for a species. For example, usually a girl entering puberty will have first onset of breast buds, then pubic hair, but this sequence is reversed in about 25% of cases [ll]. This might be due to thermal variance or it might be due to different subspecies defined in terms of the quantum numbers of events. In all timetables, the formula would provide the necessary framework in time. 3.4. Timing
in Simulations
of Living
Systems
The author has long been interested in the problems associated with simulating a living system of any kind. The series of event ages provides a made-to-order and simple scheme for introducing events into simulations [l]. Moreover, in the field of discrete event simulation, which is widely applied in industrial engineering and operations analysis, there is one “world view,” which fits the series neatly. As defined by Pritsker 1121, “In the event-oriented world view a system is modeled by defining the changes that occur at event times.” If it is desired to deal not only with events at scattered event ages but also with continuous processes in terms of regular small discrete jumps in time, one can use a “combined” language, which permits both types of simulation at once. The logarithm of conceptual age has been used before as a modified time scale for presenting findings about development [13]. 3.5. Series of Events The author has investigated some of the series defined by algorithms, such as “same time next year.” Such a series can be selected from Table 1. To get “same time next year,” one selects the event age closest to each integer year, as in the following list:
This event series consists of the closest event age to integer years after fertilization. A species which mates annually might use such a series to time its mating; it would be an alternative to a circannual rhythm for this purpose. There are five other event series which tend to repeat annually at a particular time of year. They consist of annual integer years plus approximations to the following numbers of months: 2.5, 4, 6, 7.5 and 10.
Timetableof Life Similarly, there are event series that provide approximately
181 “the year after next same time,”
“next lunar month same time,” “tomorrow same time,” etc. The author has no evidence that any of these event series is used by any species. Nevertheless, the potential is there, and they ought to be looked for [3]. 4. 4.1. Thermal
DISPERSION
FACTORS
Effects upon Event Ages
4.1.1. Effects of steady-state
temperature change
The relationship between temperature and the age at which an event occurs is given approximately by a hyperbola, concave upward. Here temperature is the x axis, and the age at the event is the y axis. The lowest point represents the minimum possible time until the event. There are two vertical asymptotes, between which is the portion of the hyperbola that is of interest. The hyperbola changes with species and event. A surprisingly small temperature change can shift an event age substantially. Given the hyperbola for a species, one can obtain from it a correction to event age corresponding to any change of steady-state temperature. If the typical temperature of a species’ environment is on the left branch of the hyperbola, then a small increase of temperature will speed up the growth of the event molecule, and a decrease of temperature will slow it down. The opposite is true for a species normally located on its right branch. An approximation to the true curve is given by a hyperbolic equation:
Aj= (T -
K Tl)(TZ - T)’
where K, Tl and T2 are empirical constants varying with species and event. The only range of temperature T of concern is between Tl and Ts. Tl and Ts are asymptotes at which an event would take forever (the organism could die if the event were essential to continued life). Effects other than mere event age change can be brought about by temperature change. Extremes of temperature result in fetal deformities and even death. Another phenomenon caused by temperature change is control of sex in a reptile such as the leatherback turtle: a warm nest produces all females, and a cooler nest produces all males [14]. However, for alligators it is the reverse [ 151. Such phenomena associated with variable temperature can be researched by computer simulation using the foregoing formula to determine event ages on the fly. Actually, the timer site in the affected cells might be buried under thermal capacity and insulation, leading to substantial lags of local somatic temperature behind ambient temperature changes. Many of these situations could be modeled by systems of thermal ordinary differential equations, such as for example: 1. Turtle eggs in a nest under sand 2. A human fetus in utero under normal conditions 3. Bird eggs in a nest under a parent bird 4. Postnatal development of an animal 5. A joey in a marsupial pouch 6. Competition among nestmates or littermates for growth 7. A pregnant woman in a hot tub or sauna 8. Hibernation of ground squirrels with varying outside weather.
A. B. CLYMER
182
4.1.2.Effects
of thermal
variation
If ambient temperature undergoes small changes that are random in time, the resulting event age can be calculated from the random traversal of the hyperbola. Here it is assumed for simplicity that the ambient temperature applies also at the site of the timing of the event. The condition for completion of the event time is
I ()
A~
dt
Aj[T(t)l=l,
from which Aj can be found, given Aj[T(t)] from the previous formula. 4.1.3.Indirect
effects
of temperature
Temperature also has many indirect effects upon event ages observed. In the case of gestation period, as affected by various factors that play a thermal role, examples are: 1. If mother is lactating, temperature is reduced (loss of enthalpy). 2. Mother’s age (affects heat storage, insulating layers and metabolism). 3. Number and sex of litter mates (act as heat storage elements). Human twins are born 19 days earlier than a single child. A sheep single birth occurs 0.6 day later than a twin birth, and a guinea pig single birth 3.7 days later than a litter of 6. Likewise an Alaskan mink has less than one day reduction in gestation period due to multiple birth [16]. 4. Seasons spanned by gestation (determine ambient temperature range). An Alaskan mink has a shorter gestation period when it is born in spring further on toward summer. A zebu calves with a longer gestation period in November by three days than in October [16]. August conceptions for goats give a 1.5 day longer gestation than do February conceptions [16], the gestation period being of the order of five months. 5. Food available and consumed (metabolism generates heat). 6. Exercise (generates heat). 7. Altitude delays mating (it is colder at altitude), the timing of which could affect the gestation period by changing the time of year somewhat and hence the ambient temperature). Some of the factors that have thermal effects are wind, clothing or fur, diurnal and seasonal temperature fluctuations, thermal homeostasis by the animal, beds or dens, blood circulation, etc. The hyperbolic curve underlying these phenomena differs between species, even if event age is normalized. The available data show markedly different regimes of slope at the operating point: _ Slime mold: 7% increase of speed per “C increase. - Fetus (species unspecified): 1% speedup of gestation per “C increase. - Frog mitosis: 15% increase in speed per “C increase [17]. _ Rat gestation period increased 2.5 days (11.4%) for 11.5”C increase, or 1% per “C. Data from [18]. - Ferret gestation period decreased 2.08 days for a 15°C increase in temperature [18]. _ Rhesus monkey gestation period increased 1 day for 2’C increase [18]. _ Bat gestation period increased 5 days for about 15°C cooling [18]. _ Dynoflagellate alga Gonyaulax slows down when warmer [19]. Thus, a hyperbola can entertain an operating point on either side of the lowest point, and so the slope can be either positive or negative for different species. The positioning of the operating point at normal temperature for a species is not understood by the author. Note that a change of 4.72% in gestation period moves a species from one event age to another. Hence, small temperature changes can have large influence on percentage difference between an observed event age and the theoretical age.
Timetable
of Life
183
The young of the tree shrew Tupaia are in danger at any temperature under 20°C (see [20]). The normal temperature of its environment is 25°C. Thus, a shift of as little as 5°C for a long time can be a serious threat Also, the temperature
to this tree shrew species’ existence.
width
of the hyperbola
differs between
events
and species.
Some eggs
have a hyperbola width (temperature difference between asymptotes) of roughly PC, such as from 32°C to 40°C. Then these eggs cannot be left long at temperatures varying more than 4’C either way about the temperature of fastest development. Also “. . . loggerhead turtle eggs incubated in sand outside the 24°C to 34’C temperature range may not hatch” [14]. These facts are of grave concern in relation to global warming. An interesting set of thermal effects has been reported by Fagerstone [21], in the case of the Wyoming ground squirrel in Colorado. The date of spring emergence from hibernation is earlier if: 1. It was a warm winter 2. There
(average
air temperature
over past 5 months).
was little or no snow cover at emergence.
3. The den faced south, 4. The individual
therefore
was heavier
getting
more sun.
than most, hence warmer.
5. The date is not before the endogenously hibernation.
timed
Note that all of these factors seem to involve the basic cause of variation in date of emergence
(but thermally
affected)
a resulting time-averaged from the value determined
age to terminate
thermal variation by the series.
as
Likewise the time of autumnal immergence for hibernation is variable. The typical sequence of time of immergence is adult male, adult female, subadult, and juveniles, that is, in order of weight. This is a thermal effect, it would seem. Also females that weaned litters entered immergence four days earlier than those who had not done so, presumably because of the loss of body heat through lactation. The body temperature at the time a particular tissue is developing has a large effect upon the amount of development that occurs in the tissue. An example might be a dyslexic, in whom the right hemisphere can be very well developed, which the language areas in the left hemisphere are typically underdeveloped. Because of effects of this kind, there might be some basis for the zodiac which predicts different personalities determined by birth date. 4.2.
Other
Factors
Affecting
Reported
Data
Reported event ages are affected also by some natural processes nocuous steps in obtaining and processing data for publication:
and by some apparently
in-
times. 1. Use of crude or indirect inaccurate ways to measure event or fertilization of the definition of an event, so that something else happening at another 2. Misunderstandings time is noted instead. An example is birth: does one look for the first sign of the birth process, the first exposure of the fetus, or completion of the process? is bimodal, the average will miss both peaks and so 3. Averaging of data (if the distribution will be a failure; averaging is not harmless even if the distribution is unimodal or trimodal, because information in the frequency distribution such as the existence of peaks, which is usually quite meaningful, is lost). 4. Roundoff of observed event age to fewer significant digits can make data too crude to be useful in comparing with the event age list. 5. Use of large time units which enable an event age to be reported crudely as a small integer, presumably to avoid the issue of error magnitude; use of large time units, such as integer months instead of days, can make data too crude to check against the event age list or other reported observations. 6. Confusion between events and stages (periods between events), such as in many publications in embryology.
A. B. CLYMER
184
7. Some organisms have found ways to avoid the use of times fixed in advance for event occurrence. A plant which produces seeds is an example; it germinates not as a timed event but whenever its criterion on physical conditions is satisfied. Another example is offered by almost all crow-like birds, who lay a second clutch of eggs if they lose the first. 8. Some organisms have put two timed events in a series, as an improvement upon a single event with an unsatisfactory event time. Examples are species in which the female stores sperm for a long period of time before allowing fertilization to take place or else stores the embryo in a dormant state: - Cavia porcellus, Bos taurus, sheep: fertilization a few hours after ovulation [22] - Canis familiaris: fertilization several days after ovulation [22] - Felis catus: fertilization 2 days after ovulation [22] - Golden hamster Mesocricetus auratus: fertilization 2 hrs after ovulation [22] - Mus muscolus: fertilization 5 hrs after ovulation [22] - Rattus rattus: fertilization 4 hrs after ovulation [22] - Rabbit Oryctolagus cuniculus: fertilization immediately after ovulation [22] - River otter: delayed implantation [23] - Skunk, weasel, tammar wallaby, bat, armadillo, kangaroo, nutria, red panda: delayed implantation [24] - Fisher: 9-10 months delay [24] - Hippopotamus: mother can delay birth when disturbed - Stoat: 10 month delay [25] - Armadillo: can delay a year or more - Seal: dormant 3 months, grows 8 or 9 months - 100 species of mammals delay implantation [23,24] 9. Like averaging, range cropping, according to some rule of thumb for disqualifying outliers, can be destructive of information in a frequency distribution having two or more peaks. 10. Most published data for egg hatching are measured from laying, unfortunately not from fertilization. Data from fertilization to laying are not easily obtained. 4.3. Stability and Thermodynamics The Second Law of Thermodynamics
is unquestionably true (that organization and energy
must always degenerate toward the state of disorder). It would appear that this requirement is violated by the living, the precisely timed development, and the evolution of organisms, in which there is an ongoing reaching for greater organization. The answer lies in the fact that life is possible only in a region in which conditions are sufficiently constant. If a large enough random disturbance comes along for a long enough time, life is wiped out to some extent in the region. Indeed, it has been stated that at least 99% of the species that ever existed have subsequently become extinct, presumably because of severe conditions arising and enduring. A possible understanding of this fact is provided herein (Section 4.1.3), namely, in that eggs and other immature offspring are fatally vulnerable to temperature excursions outside a narrow band. Another interesting aspect of thermodynamics in relation to life is that the building of timing molecules, a process which produces orderly structure, is accomplished by random motions of and within molecules. Clearly this is not impossible, but it is extremely precarious with respect to temperature variations.
5. FITS TO PUBLISHED 5.1. Some Notable
DATA
Sets of Data
5.1.1. Clawed toad ovum cleavages The data in Table 3 show a surprising agreement between observed ages of ovum cleavages for Xenopus laevis (clawed toad) at 21°C ( see [26]) and the nearest event ages from Table 1.
Timetable
of Life
185
Table 3.
I
I
I
390 min
11
396.09 min
F
-1.56
In Table 3, it can be seen that only two of the 11 observed data lie more than 1.18% away from an event age listed in Table 1. The figure 1.18% is one quarter of 4.72%, which is the distance between any two consecutive entries in Table 1. Hence, an error of less than 1.18% means that an observed datum is closer to an event age in Table 1 than to the midpoint between two successive values in the table. Such a case is called here a “success” (S). A “failure” (F) is a case in which the error is more than 1.18% (but less than 3.54%), it being closer to the midpoint than to a tabular entry. Refer to Figure 1 for a depiction of success and failure. --+ +
I
I
success 2.36%
II
I -
+
failure 2.36% +
III1
-
4.72%
+
j-l
-+
success +1.18% t
II
-
+
j+l
j
I
I +
_i+Z
Figure 1. Definitions of Failure (F) and Success (S). The + points indicate event ages with serial numbers given below in terms of j. A “success”
(often designated
herein by S) is an observed event time oc-
curring no more than one quarter of an interevent spacing from an event age in either direction.
The spacing for two successive event ages is 4.72%, so the
width of “success” band is k l.lS%,
or a total width of 2.36%, centered at an
integer value of j. A “failure”
(often designated
herein by F) lies in the band between two
success bands. It too is 2.36% wide, so successes and failures are equally likely a priori. Thus, a success occurs when an observed datum comes closer to an event age than to the midpoint between ages.
The example in Table 3 shows a slightly higher degree of success than is usual, namely, 9 successes out of 11, or 82%. It is presented here partly to enable a prediction to be made on the basis of the formula: if the two disagreements in Table 3 are due to excessive rounding in the observed (reported, at least) data, then it is predicted that the calculated tabular values will be found to be better representations than the reported values are. If this prediction were to be found to be true, it would be very persuasive on behalf of the formula underlying Table 1. Most scientists
A. B. CLYMER
186
would prefer the linear regularity of the reported ages, which would have to be abandoned if the formula gives a better fit. A complication of experiment and analysis arises due to the extreme thermal sensitivity of event ages for these early events [27]. 5.1.2. Piaget’s developmental
stage transitions
The data in Table 4 show an agreement of event ages with the postnatal transition ages between Piaget’s stages in the development of human intelligence from Table Id (postnatal). Table 4. Piaget’s data for the development
of intelligence.
Five of the six results are successes (S), a finding which is not significant. The implication would be that a new functional structure appears to be incorporated into the developing brain at approximately two-year intervals, giving it new capabilities in problem solving, but this conclusion cannot be drawn from the data given. 5.1.3.
Early
embryo
events
Table 5 shows the data found for cleavages and implantations. Overall, there are 18 successes to 10 failures, or 64% success. This percentage is in line with results for gestation data. See also [2, Table 11, for more data concerning fertilized ova and events in embryos and fetuses. 5.1.4.
Gestation
data
The largest body of data, thus far found by the author, are the gestation periods of 672 species reported mainly in [16]. These data are included in Table Al in Appendix A. About 70% of them lie closer to event ages than to midpoints. This distribution is enormously statistically significant. The probability of it occurring by chance is 2.54 x 10mz3 (see [l]). This finding establishes the validity of the formula, for gestation data at least, beyond any reasonable doubt. Comparably good results are obtained for most other gestation data obtained subsequently. Most of them are included in Table Al in Appendix A. An exception is the table by Harvey and Clutton-Brock (281, in which only means are given, averaging over even bimodal and quadrimodal distributions. The results show how grave this mistake in data processing can be: 33 successes and 41 failures, or 45% success. The primate gestation data given by King and Mitchell [20], which are incorporated in Table Al in Appendix A, in themselves make a nice cameo study. Successes are Sl%, failures 39%.
Timetable
of Life
187
Table 5. Data found for cleavages and implantations.
Cricetus aumtus [22]
1 Frog [17, Chapter 181
Frog [17, Chapter 201
One of the more interesting animals for its gestation data is the wildebeest. Different authors say that all calves are born in a three day period or three week period. The explanation seems to be that the gnu, or black wildebeest, has a reported gestation period of 8 to 8 l/2 months, or 243.5 to 258.7 days, whereas the blue wildebeest has a reported gestation period in the range from 249 to 255 days. The event ages in this time period are 242.0 and 253.4 days. Apparently, then, the blue wildebeest has a single peak, hence, a narrow range, while the black wildebeest spans two peaks, hence is bimodal with a wider range. The three day range is within the three week range. As Hemingway [31] puts it, “. . . all the calves . . . are born within a three-week period and most of these during three halcyon days.” The Asdell gestation data were fitted by a trial and error process. An initial guess for the unknown constant (finally found to be 1.0472), together with a multiplicative constant chosen to equal 21 (chosen because the largest set of identical published event ages was 21 days for many species of rodent), was used to calculate a complete set of tentative event ages over the range of interest. The resulting errors of fit showed waves of positive and negative errors. It was noticed that one particular value of the constant, found to be 1.0472, made the error go to essentially zero amplitude, and visible waves were absent.
A. B. CLYMER
188
Table 6. Estrous cycle data.
Species (Ref.)
Farmed fallow deer,
Wide range, shouldn’t
Pere David’s deer [33]
Bimodal?
Peaks at
Lemur,
ago crasszcau
Cercocebus atterimus Mangabey, Cercocebus torquatus [20]
33.4d
33.3 d
+.30
s
Table 6 is continued on the next page.
Timetable of Life
189
Table 6. continued.
Rhesus monkey,
Later it was found that one of the event ages was very close to one day (24.01 hrs). Then the formula could be simplified to merely 1.0472 to the jth power, in days (with a multiplicative constant of 1 day suppressed but implied). 5.1.5.
Estrous
cycle
data
There are nearly as many failures as successes in Table 6. That is, there is no evidence here that the series applies to estrous data. The question of whether the stop or start of each estrous period is an event remains open. The human menstrual period is commonly spoken of as being 28 days. If menstruation is a multimodal event with five event ages, then one would expect to find a frequency distribution with peaks at the five event ages closest to 28 days, namely, 25.254, 26.446, 27.695, 29.002, and 30.37 days. However, no source found by the author shows any sign of peaks; the distribution is essentially bell-shaped with some small deviations. Perhaps the peaks are broadened by thermal variation or imprecise determination of onset of estrus. 5.1.6.
Events
in lives of religious
leaders
A list of 23 notable events in the lives of religious leaders gave 12 successes and 11 failures. That is, such “events” (divine vision, left home seeking truth, entered politics, crucifixion, vision of God, new religion conceived, etc.) are not biological events in the sense used herein, and the series does not apply. 5.1.7.
Distribution
of gestation
range
as percent
of mean
A study of the frequency distribution of the quotients of ranges to rneans has led to some important results. The data shown in Table 7 are for gestation periods. The list shown in Table 7, which is equivalent to a histogram, shows 9 peaks, each close to an integer multiple of 4.72%. That is, range is quantized. All data were obtained from Asdell [16], and they are all gestation data. This list is the clearest evidence for the existence of multimodal event ages. The slight displacements of some actual peaks from theoretical peaks are ascribed to inconsistent lopping off of tails in frequency distributions to get published ranges. One can get a fair estimate of the number 1.0472 by using the peak locations in the table. For example, the last peak appears to be at 43%. Dividing by 9 (it is the gth peak) and by lOO%, one obtains 431900 = .0478, whence one has for the spacing constant the value 1.0478, which is quite close to 1.0472. This result is important in that it affords a totally independent “ballpark” check of the approximate magnitude of the constant “1.0472” gotten from gestation data per se by regression. This observation should still any doubts that 1.0472 is approximately the best fitting value of the spacing constant.
A. B. CLYMER
190
Table 7.
I
7-7.99
2
8-8.99
6
9-9.99
3
10-10.99
3
11-11.99
3
12-12.99
0
13-13.99
6
14-14.99
3
15-15.99
4
16-16.99
1
17-17.99
1
18-18.99
3
19-19.99
0
28-28.99
1
*Both actual and theoretical
2
peak.
Actual peak 2 x 4.72 = 9.44
Theoretical
peak
Actual peak 13
x
4.72 = 14.16 1Theoretical
4 x 4.72 = 18.88
16 x 4.72 = 28.32
peak
Peak*
1
Peak*
I
Timetable
of Life
191
5.1.8. Opening and closing eyelids The eyelids of embryos of certain animals change state between open and closed at fairly predictable
post-fertilization
ages, as shown in Table 8. Table 8.
Species
Reported
Eyelid Event
NearyLfvent
% Error
S or F
Age Opossum
Close
12.25 d
12.07 d
+1.47
F
Ezat
Close
18
18.29
-1.61
F
Swine Guinea Die: Opossum
Close
1
Ooen
50 I
Open
59*
50.44 I
62*
57.93
-.88 1 -1-1.85
1 I
s F
63.52
-2.39
F
Opossum
Open
72
72.95
-1.32
F
Man
Close
70
69.66
+.49
S
Sheep
Open
84
83.78
+.26
Swine
Open
90
91.87
-2.08
1
F
Man
Open
139.1
1 +.64
I
S
I
140
I
S
*These two data are from [41]; all others are from (221. Note the large inconsistency
in “opossum open” data.
The results are S = 9 and F = 6, or 60% success. Part of the trouble is that all data are reported in integer days, a bad habit in pediatrics and development books. The resulting roundoff drives the percent success closer to 50% (purely random). 5.1.9. Red Howler Monkey gestation The Red Howler Monkey gestation data make an interesting case for analysis. the data published by Crockett and Sekulic [42]
Table 9 shows
Table 9.
The author’s int.erpretation is that the 6 animals were in two different event age subspecies: five at or near 192.2 days event age and between event ages 183.5 days and 192.2 days. Thus, the event age series seems to be very helpful in analyzing reported data.
A. B. CLYMER
192
5.1.10.
Viral
events
The author has found only very few viral timing data [43], which are shown in Table 10. Table 10. Event
Reported Time
DNA enters cell Replication
Near~~~vent
S or F
say. time zero
of DNA
I
5min
1 4.954min
Start of synthesis of head and tail proteins
8 min
7.857 min
I )
F
Completed
13min
I 13.05 min
I
S
virus
s
I
These data are too few to allow a conclusion to be drawn, but more data should be sought. 5.1.11.
Scientific
contributions
Table 11 shows some data for the ages at which some great scientists made their contribution. Table 11.
Table 11 is continued on the next page.
Timetable
of Life
193
Table 11. continued.
% Error
S,F
1P. Curie 1Joliet-Curie 1H. Lorentz
R.A. Millikan
-0.42
1C.V.
S
-0.04
s
-1.38
F
+1.5
F
-1.83
F
f0.92
s
-0.75
s
-1.14
s
C. J. Davisson
+1.39
F
G.P. Thompsor
+2.26
F
+1.09
s
-0.73
s
-1.83
F
J. Chadwick
R. Descartes
In Table
11, there are 48 successes
more significant contribution
and 23 failures,
is that scientific
The statistical
or 68% success.
were given to trying to identify
was made, using several sources.
The implication event ages.
if more attention
creativity
significance
mean, for this to be a firm conclusion;
The table
the exact month
would
be
when each
Too many of the data are reported as integer years. is made possible
is not high enough, it is only an indication.
by substance
release events at
being only three sigmas
from the
A. B. CLYMER
194
5.1.12.
Menarche
and menopause
Menarche is an event which is quite variable in its age of occurrence. Historically, it has shown a steady and substantial decline with time by three years in 200 years. This relationship might be due to the increase in the warmth of clothing, housing, schools, etc., over the past couple of centuries. At a given time, there is about a 5-year range of ages of occurrence of menarche. This range spans several event ages: 9.966, 10.867, 11.811, 12.800, 13.835, 14.919 years. No data have been found by the author which would indicate the presence of any peaks in the frequency distribution. Weight is a factor, probably through its thermal effect. Menopause has an unusually wide range of occurrence, hence, event ages. The author has found no presentation of data that resolve the supposed peaks. 5.1.13.
Chambered
nautilus
A study by N. Landman was reported in 1988 in which radioactivity measurements were made of the ages of the chambers of a fully grown chambered nautilus [44]. These data are quite well fitted by the event age list. The given facts were: “. . . the nautilus hatched in 1957 with seven chambers and added eight more in the course of the next year. Over the next decade the animal formed new chambers at a diminishing rate: the last fully sealed chamber took seven months to form and was completed in 1968, a year before the animal was netted . . . The shell has 31 chambers in all.” In order to match these observations, the series must be fitted to the given data to get the overall-best-fitting by choosing an event age when the first chamber is started. The choice made was to start the first chamber at event age 1.993 months (i = 23). The other choice that had to be made was the number of event ages per chamber built. The best fit was to take every third event age as the start of a new chamber. Then, having thus fixed two parameters, all other information about the building process can be read from the event age list, as shown in Table 12. The agreement between the predictions of the series with the reported data is within one digit (month or chamber) in each case. Perhaps the differences can be ascribed to experimental error and temperature variation, The agreement is good enough to support the statement that the growth of the chambered nautilus is an exponential function, as in the formula and as asserted by Landman and Cochran [45]. The chambered nautilus provides the only good example available now of a lifelong longitudinal verification of the series. It would be promising and worthwhile to seek and analyze similar data for other creatures having periodic structures. One question remaining is whether no building takes place after the second and third event age of a set of three, the only building occurring after the first event age and until the second event age of the set. 5.1.14.
White
and black children’s
development
Geber [46] has presented data for the postnatal behavioral development of black and white children (see Table 13). The result is only 33% successes. Perhaps this indicates that the “events” are really interevent stages rather than events. 5.1.15.
The central
nervous
system
The brain, like any other organ, has its events in the development process. Some of these are to apply “insulation” to “wiring” already in place, in order to start it operating. Growth of new neurons is confined to prenatal development.
Timetable
of Life
Table 12.
Table 13.
M’3! 19:6-8-N
195
A. B. CLYMER
196
One technique for observing present, the research permits a be compared with the formula. growth processes in certain age
newly functioning areas of the brain is with an EEG [47]. At resolution of time only to integer years, so their findings cannot However, it has been shown already that there are well defined ranges.
Functionally the brain contains hierarchies of sensory, multisensory and abstract pattern recognizers, each of which puts out a signal when it recognizes something in its category. For example, a frog recognizes a fly in motion nearby. Each pattern recognition unit consists of several inputs conveying signals indicating whether elements of the pattern are present, and an output signal when enough key inputs are present to indicate the whole pattern. The brain contains also hierarchies of pattern generators, each of which elaborates an abstract or general command into individual muscle action instructions. At the top is a command such as “Get that fly,” and the lower pattern generators convert this command into detailed instructions to tongue muscles [48]. It is postulated that these capabilities first appear at event ages. They might be a necessary condition for the physical and behavioral changes noted in Section 5.1.2. If such patterns are built-in before birth or the final metamorphosis, they can be used as a basis for constructive behavior, such as building a web or nest, learning a mating dance or song, etc. This might be the basis of instinct: genetically produced blueprints for key tasks. Similarly, such a system can be the basis for a simple organism simulator. 5.1.16.
Other bodies of data
It is known that many species from butterflies to lobsters to fish to birds to land mammals to whales migrate. Most of the data are quite nonquantitative, speaking in terms of a month by name but with no dates given. The author has been unable to collect enough good migration data to permit an analysis. There seem to be wide ranges of migration dates for a particular species. The range might be due to thermal variance or multimodal event spectra. There is one paper on the “migration” of toads in Wales [49]. It is about male and female toads going to the nearest pond for mating. Due to the frequent occurrence of deterrence from cold weather, which reduces drastically the daily attendance at a pond, and due to the small resolution of published data graphs, one cannot analyze the available data very well. However, the author thinks he can see evidence of a trimodal attendance spectrum, which suggests the possibility of multimodality. Bird migration is better documented. They have an event which produces “flight frenzy” or restlessness which is neuromuscular excitation for flight. It stops at the end point age of migration [50]. The distribution of migration arrival times is quite broad for most bird species. Perhaps the explanation is related to there being different generations or ages in a flight season of a species, or different points of origin being at different distances away from the destination. Bird molting is also under the control of an inner timer. Butterflies migrate also. However, the cycle is not performed by any one generation; several generations of monarch are involved in one round trip (511. Each of these generations has a different set of event times appropriate to its role in the migration cycle. Another category of events for which mainly inadequate data are available is mammalian prenatal development. It is the custom in this field to report all events to the nearest integer day, but such data are not desirable for testing the series of event ages given by the formula. Perhaps in the future these data will be obtained and reported in decimal days, or at least integer days and hours. Child behavior development is another field with excessively crude event ages reported. Although the data of Piaget (Section 5.1.2) appear to be marginally successful, it must be borne in mind that the reported data are ranges in years expressed in small integers. The data reported by Geber [46], Section 5.1.14 herein, suffer from the same defect, but they too seem to succeed.
Timetable of Life
197
In this field, also, it would be desirable to strive for more precision in measurement and reporting of event ages. One interesting observation [l] is that the formula has very surprising success in its fit to the series of times obtained by multiplying or dividing 24 hrs by 2, successively. There are 18 octaves of success in this run. The success is due to the proximity of 1.0472 to the 15th root of two. Cell cycle times give a fair body of data [52]. A sample of 25 kinds of cells gave 68% successes, which is statistically significant at the 3% level [l]. Cell mitosis data given in [l] have 83% successes, which is significant at the 1% level. A body of 94 mammalian prenatal events gave 65 successes, a result which is significant at the 2% level. A table of single cells and early stages of sea urchins, nematodes, mice and frogs [2], is significantly fitted by the formula at the 4% level. 5.2. Goodness 5.2.1. Error
and Significance of Fits
distribution
The differences between published and nearest calculated event ages are the errors of fit. For gestation data their frequency distribution is well enough described by a bell-shaped curve. See Table 14. Its standard deviation (sigma) is a factor of about 1.012. The fact that the errors are distributed like a bell-shaped curve is suggestive that they are random in magnitude and distributed in a Gaussian manner. Really the distribution is lognormal, but it is so narrow that a Gaussian distribution is a good approximation. Table 14.
This error distribution is nearly Gaussian, indicating that the errors are random, approximately. The peak is at zero error. The fact that there is no substantial offset of the peak from zero indicates that there is no constant error offset. The positive tail shows a small rise at the end, which could be a folding back of the tail in the next error class. This long tail would be consistent with the lognormal identification of the distribution. A well-intentioned reviewer of [53] noticed that some of the small integer numbers are fitted by the series better than would be expected from chance. On this basis, he extrapolated to the fallacious conclusion that the series worked only because of this arithmetical coincidence. On that basis, the paper was rejected. It is time to set the record straight. It is true that the first eight integer months are successes [l], regardless of what event might occur then. It is easy to delete such data in the interest of reducing statistical bias. On the other hand, integer days from one to 70 score only 40% success. The same is true of small integer hours, the first ten of which score 80% successes, regardless of event, but the success rate drops off to the expected level (50%) above the first 25 integer hours. Integer weeks also are biased, the first ten giving 80% success and the second ten giving 70% success.
A. B. CLYMER
198
To test the overall importance of the foregoing small integer problems, the author reran the gestation data analysis, deleting all integer hours up to 24, all integer days up to 21, all integer weeks up to 20, and all integer months up to 12. The result was 76% at low event ages and 58% at high event ages, very similar to the results with the small integer data included. 5.2.2.
Measures
of likelihood
of fit by chance
The errors of the calculated event ages relative to published values can be expressed in terms of success or failure to lie within 1.18% of the closest event age. Successes and failures are equally likely a priori. Therefore, successes (or failures) amounting to 70% or more of a large set of data being tested would be surprising, much more surprising than one might suppose. The diagram in Figure 1 (Section 5.1.1) shows how “success” and “failure” are defined. The formula for the number of standard deviations from the mean is No. of sigmas = ,prob.
deviation (as a fraction) x N f o success x prob. of failure x N]i/z’
where N is the number of cases. One can calculate the probability that exactly z of n trials of flipping a coin will be heads (or in evaluating event age data that there will be z successes) from the following formula: I
P(?
n, 4) =
qnz!(n 7L - z)! ’
where q is the probability of a head (l/2). To calculate the probability that z or more trials will be successful, one must repeat the calculation for 2, z + 1, zr+ 2, etc. up to z = n, then sum the results. 5.2.3.
Testing
for bias
Since most of the gestation data in hand are from [16], and since most of the data of all kinds are gestation data, it would be a prudent statistical check on Asdell as a source to incorporate the gestation data from Asdell into two subsets that might be chosen as follows [54]: 1. The first and second halves of the book, or 2. Odd and even chapter numbers, or 3. Draw chapter numbers out of a hat to insert into two other hats. 5.2.4.
Gestation
fit error
vs. age
The errors of fit for gestation periods of mammals are found to be 83% for animals with short gestation periods (up to 24 days) and 60% for animals with the longest gestation periods. It is believed that the difference is due to the fact that the longer period is more likely to include major temperature variations, which disturb gestation periods as they do all other event ages. The longer period brings in wider deviations from normal temperature. 5.2.5.
Overall
goodness
of fit
To obtain an overall measure of fit of all data to the series, one could find the total numbers of successes and failures, then divide successes by total and multiply by 100%. This is done below. Table 15 is a collection of all of the fitting results obtained by the author as of 1986 [l]. To add the data found meanwhile would not make a significant difference in outcome. Note from the table that the overall success rate of 922 events is 70%. This is far higher a result than is reasonably likely by chance. It is 12.4 standard deviations from the mean. The gestation data by themselves give 9.88 standard deviations from the mean. The implication is that there is indeed a regularity in nature which is very similar to the formula or series.
Timetable of Life
199
Table 15. Body of Data
References
Mammalian gestation
(
672
1
69
1 See Appendix A, Table Al
Bird incubation Deriods
1
14
1
64
I 1551
Reptile incubation or gestation periods Insect metamorphosis Development of Rana pipiens, 18’C Biological rhythms T4 virus building
10
80
[551
9
89
[55-571
23
65
7
100
Various 117,431
1581
1
100
24
83
P71
4
75
156,591
Mammalian prenatal events
94
69
[I71
Mammalian eyelid opening or closing
13
69
[I71
Cell cycle times of normal and cancer cells
25
68
[521
9
77
I601
20
90
[26,61,62]
122
70
Cell mitosis Start of synthesis of a compound
Slime mold stage start times Events in fertilized ova All of above events including 650 successes
Considering that the empirical formula was fitted only to gestation data, it is remarkable that it then fits also such a wide variety of other event data.
6. MULTIMODALITY 6.1. Distribution
of Range/Mean
Data
The gestation data include many figures given as ranges of values. Interestingly, the ranges divided by the means tend to cluster strongly around small integers multiplied by 0.0472, as portrayed by the frequency distribution, Table 7. This can be interpreted to mean that different species can have different numbers of event ages for gestation. For example, a species, having a range that just includes three successive event ages for a particular event, will contain individuals with various ones of the three event ages. The reported range will be about 3 x 0.0472 = 0.1416 multiplied by the mean. A species can have as many as 8 or 9 event ages per event.
6.2. Other
Evidence
of Multimodality
In some cases, the literature provides gestation data for each of a substantial number of organisms. In such a case, a frequency distribution can be plotted. It will be easy then to see that reported event data usually cluster around two or more event ages. The peaks are not necessarily of equal height; they usually have a bell-shaped envelope over the peaks. Asdell [16] gives no direct data for multimodality of gestation ages. However, he states that the guinea pig has a bimodal distribution of estrous cycle periods (peaks at 16 and 17 days). Hence, one should be alert for multimodality of all events in all species, with the expectation that most will show it. 6.3. Significance
of Multimodality
If an event has a multimodal event age distribution for a particular species, the implication is that the species has two or more subspecies differing at least in this respect. These subspecies have different timetables. Geographical samples of organisms could have differing frequency distributions of event ages. These data could be useful in finding the geographical origins of individual organisms. Perhaps the greatest significance of multimodality of event times is that it gives a species more options (subspecies), enabling a better chance of survival of some subspecies.
200
A. B. CLYMER
7. THE MOLECULE-BUILDING 7.1. Description
PROCESS
of the Process
A conjectured concept of the process of timing is that each of a set of neighboring cells builds a certain type of molecule over a period of time which might range from seconds to years. When the molecule is completed in all cells simultaneously, it produces an event having physiological or anatomical consequences. The building process can take a long time because the molecule is built one unit at a time in series, in contrast to most organic chemical building processes that are distributed, parallel, and are expedited by an enzyme. The building is imagined to consist of moving one unit along the molecule by thermal impacts from one end to the other, where it is then attached. The “molecule” is believed to be mRNA. The fixed end is believed to be attached to a gene on a chromosome. As the molecule gets longer, new units take longer to be installed. Addition of deuterium oxide to the fluid in the nucleus also makes the process take longer, indicating that water has a role in the process dynamics. stochastic simulation of this construction process would be interesting. A further stochastic
A
process can be operating.
If a unit is being moved along by cilia-like molecular extensions, there might be circumstances when the advancement of the unit does not occur. It could be as if the unit took 19 steps forward and one step nowhere, thus adding 5% to the duration of the assembly of the unit. Consider the probability of a unit making it all the way through a gauntlet in which at each step there is a probability of failure to advance. Then the probability of completion of the total trip is the product of the probabilities of making it through each step. As more steps are added, the probability of completion in a fixed time decreases. The probability of completion in a longer time increases. That is, the longer the trip, the slower the progress. This effect could make the time of completion of a molecule a nonlinear function of molecule length. The foregoing description is not all new; see, e.g., [63]. It is now recognized that, in Drosophila and E. coli at least, the length of time until expression of a gene is determined by the time of transcription. The mRNA building process is capable of being simulated, even if somewhat speculatively. In [l] the process was erroneously described as being analogous to the tiltboard game Pigs in Clover. In this game, all balls are to be rolled into holes in the board and kept there. However, this is a parallel process, which is known to go quickly, whereas mRNA building is believed to be a serial building process, one unit at a time. The roles of temperature in the mRNA building process are not fully understood by the author. It will be clear, however, that increase of temperature would speed up thermal agitation that is moving units. But also increase of temperature could thwart the desired movement by changing the mix of molecular modes being excited. 7,2. Derivation of the Formula The process described in Section 7.1 can be modeled to yield a formula for the time required to assemble a molecule having a given number of units. Consider the trip required of a unit to add one unit to a molecule already existing. The time is proportional to the number of units to be traversed from one end to the other, i.e., to the molecule size. However, there is an additional time required, because some of the steps were not traversed on the first try, and they must be repeated. Moreover, not all of those repeated will be successful the second time. Thus, a series of contributions to time taken is obtained:
tj(l + k + k2 + k3 +e +.),
Timetable of Life
of size j and k is the fraction
where tj is the time to traverse
a molecule
try. However,
in parentheses
the sum of terms
vice versa). Now it will be clear that the post-fertilization
201
to be repeated
on each
is, say, (1 + e), where e can be found from k (or age at which a molecule
of size j + 1 is completed
is: A~+I = Aj(l + e).
I
This is the desired recursion formula. All other forms of the formula follow from it. It is known, empirically, that e = .0472. It is simple to calculate k if it is noted that the series 1 + Ic + k2 + k3 + . . . is merely the reciprocal of 1 - k. Then,
&=l+e, which is readily particular step.
solved to give k = .04507. This is the fraction of units that must repeat a All steps are essentially alike, so k and e are constants over all species and
events. The effect of temperature upon k or e is not easy to determine. Likewise, it is not obvious how to determine the effect of deuterium in the water, except that it increases the masses of the water molecules enough to have a surprisingly large effect upon time of assembly. 7.3.
Some Questions
The foregoing theory is so incomplete and uncertain that numerous questions arise. One would wish to know the roles of the DNA in the chromosomes, of the genes, of the mRNA, and of the ribosomes. Probably the process is somewhat as described for bacteria by Hendricks [64]: like circumferential bands on an earthworm, puffs appear on chromosomes for production of mRNA by activation of a particular gene, and the mRNA causes a ribosome to build a polypeptide chain (protein), which, along with other identical protein molecules from other cells, helps to cause an event. Presumably, it is the building of the mRNA which is of concern in Sections 7.1 and 7.2. Does an enzyme do the reading of the gene, causing the assembly of an appropriate unit on the end of the mRNA being built there by moving along the axis of the mRNA to the end? What tells an mRNA molecule that it is completed and may go on its way? What could go wrong to let another unit build on at the end? Is it an error in the DNA which then produces a longer mRNA molecule? Does it matter which ribosome the mRNA finds first, or will any one do? Presumably, any will do. What decides between a single event and a biorhythm? That is, what makes mRNA or a ribosome stop directing the manufacture of a protein ? Is the decision made at the gene or at the ribosome? What can start a biorhythm at a time other than the event age equal to the biorhythm period? An example would be menarche, starting not until the second decade but having a periodicity of a lunar month. How can mRNA building survive cell division? How can mutations of mRNA be passed on to the next generation, if at all? Is it possible that low frequency electromagnetic waves (e.g., at or below powerline frequencies) can cause bending resonance and fracture of mRNA molecules, later producing wrong proteins and wrong processes in cells?
8. BIORHYTHMS 8.1. Postulated
Production of Biorhythms
Theories of biorhythm production have been incomplete and vague. For example, a reviewer of [50] refers to “. . . our almost complete ignorance of the physiological processes involved in generating circannual rhythmicity.”
A. B. CLYMER
202
The genes were implicated by Feldman [65]: “. . . the clock mechanism is somehow encoded in the genes.” Direct association of a biorhythm with regulation of protein synthesis is pointed out in a review of [66]: “Recent experiments . . . indicate that biological rhythms may arise directly from the regulatory mechanisms of protein synthesis.” As mentioned in the Introduction, the theory in Section 7 leads to the concept that a biorhythm is produced if the molecule building process does not stop when a molecule (protein, i.e., hormone, enzyme, etc.) is completed and released, so that the process can be repeated over and over synchronously in some set of cells. associated with the first building.
The period of the resulting biorhythm is the event age
However, it is not a new idea that repeated rebuilding of a molecule accounts for biorhythms. Johnson and Hastings [19] make the following statement citing basic references: “. . . many models of the clock’s biochemistry have been proposed that variously involve sequential gene transcription, membrane properties, ion transport, mitochondrial oxidative phosphorylation, cyclic nucleotide levels, messenger RNA production, or translation on 80s ribosomes.” Also “. . . a particular messenger RNA transcribed from the gene locus undergoes a 15-fold oscillation in its amount during the circadian cycle,” and “Perhaps this oscillating RNA is involved in coupling genetic information to overt rhythmicity.” Another source on the repetition of mRNA building to get a biorhythm is [67]. Some biorhythms, such as the human female’s monthly period, occur at an age which is different from the period. This might be called two events in series: menarche, then the period. The author has not given much attention to series events, because it has seemed as if an all-parallel model accounted for events well enough. However, it might turn out that some of the errors in the application of the formula are due to series events being analyzed as if parallel. The only data found in the literature on this question relate to the slime mold [SO], in which most but not all event producing processes are in parallel. It would appear, then, that greater attention should be paid to series events in all species. There has been some confusion of terminology in the science of biorhythms. The term “biological clock” implies to the author a continuously interrogable reckoning of time. The term “timer” is less ambitious, being applied to a particular tick of time (an event age). The term “oscillator” is most appropriate when the waveform of a biorhythm is sinusoidal. A timer resulting in a switchlike action or a pulse can maintain an oscillation with a sinusoidal waveform in a second order system. For each case of oscillation, the second order system must be identified. 8.2. Biorhythm
Periods
on Event
Age List
Several of the event ages are significantly close to the periods of known biorhythms. One is 24.01 hours (the circadian rhythm which approximates most closely one day). Another is the next larger event age, which is observed as the circadian rhythm in humans, namely, 25.15 hrs. One year is represented as 366.5 days. A lunar month appears as 27.695 days. A week is the event age at 6.9424 days. From these remarkable matches, it might be concluded that the parameters of the formula evolved to give the formula these properties. Thus, it appears to be promising to check any other known biorhythm periods for any species against event ages in the list. This is done to some extent in Table 16. Another possible check is to test an absurdly chosen astronomical cycle time against the series. For example, the period of Venus as seen from the earth is 583.923 d, according to Feynman [68]. The nearest event age is 581.2d, giving an error of only +0.47%, which is a success. Since it is inconceivable that Venus could have any biological influence on earth, the agreement must be regarded as a meaningless coincidence.
Timetable of Life
203
Table 16. Some biorhythm periods compared with event ages.
Rhythm of body
Javanese human
This agreement is remarkable (3.9 sigmas from the expected value that the successes are due to chance). There have been hundreds of investigations of the effects of various light-dark schedules upon the timing of biorhythms. The phenomenon is well established, but theory is sparse. It is not apparent to the author how the theory herein can be extended to account for these light exposure test results. NOTE ADDED IN PROOF. It appears that not only normal but also mutant organisms have biological rhythms whose periods are event ages, as shown in Table 16. An example is Drosophila, which has a mutant perS with 19 hr period (cf. 19.07 hrs) and a mutant per’ with 29 hr period (cf. 28.88 hrs). See [75].
204
A. B. CLYMER
9. SYNCHRONIZATIONS 9.1.
With
Calendar
and Seasons
One of the properties of the list of event ages is that it has a tendency for certain dates to be listed for a run of years, give or take a few days [3]. Hence, these ages can be selected to make a certain event occur at nearly the same time every year for some number of years. See Section 3.5. It is almost as if there were a circannual rhythm producing the event. However, this is not necessarily the case, because there are some events which use some but not all of these event ages. Examples might be black bear, lion or shark mating, which is skipped every other year [76,77], humpback whale which calves at two to four year intervals [78], or African elephant, which has a calf every third or fourth year. Of course, it might be a rhythm with a two year period. As a result of such cases there arises a question of the occurrence of such rhythms versus absolute timing. It is difficult to tell which occurs in many cases. It would be necessary to obtain a large body of precise data in order to choose between the two possible theories in particular
cases.
There is an overall pattern of the event ages which seem to repeat from year to year. There are streaks of such ages. Most of the streaks are short, but a few run to 10 or more years. The irregularities of these streaks constitute a signature which could enable a meaningful check of observed data against an absolute timing hypothesis. 9.2. With
Solar Days
and Lunar Months
The same pattern shows up when one works with lunar months or solar days as units for the event age list. It works because one lunar month, one solar day, and one solar year are all in the list of event ages (a surprising coincidence). One is led to speculate that the constants in the formula defining the event age series were “selected” over evolution to include these event ages. To have its event ages synchronized with lunar months guarantees synchronization with tides, which are essential mechanisms for many organisms. Other organisms exploit the phases of the moon per se for the light conditions provided. 9.3.
With
Mate
It might be the case for some species that a pair must be synchronized in order to reproduce. Synchronization of the entire species would insure this condition. Another possibility is that a sperm might have to be synchronized with an ovum in order to achieve fertilization. This condition could be met by providing a large number of sperm running on variously shifted timers, so that the ovum could make a selection on the basis of timing. 9.4.
Between
Generations
If the time of year (or lunar month or day) of mating by parents is the fertilization time of the offspring (no storage of sperm), their sets of timers can be synchronized to the calendar year (or lunar month or day). If mating is an event having an event age tied indirectly to the calendar, such as by being repeated every year or twice a year, then so will the timetable of the offspring be tied to the calendar (including eventually the dates of mating). Then each generation will follow the calendar (apparently). Such relationships between generations can give rise to subspecies which mate at different times of year and have other events at different sets of event ages. 9.5. Within
Ecosystems
It is crucial for the stability and well-being of an ecosystem to maintain its system of event age timetables. If a prey species stops appearing at the time and place it is needed by a predator species, the predators will suffer, perhaps fatally. This result, in turn, could affect another species adversely, such as a plant to be pollinated.
Timetable of Life
205
One of the mechanisms that exist potentially for the disruption of ecosystems is climatic drift. As physical conditions (particularly temperature) shift within an ecosystem, its event ages, as observed, change also, possibly altering the functional relationships among species. Still more important is the impact on an ecosystem when some of its species are wiped out by an unusual temperature change. The young are especially vulnerable. The cause of death might be the consequence of a developmental event prevented by temperature from ever occurring. Even quite a modest temperature change in the environment of a young organism or egg can have fatal results, as shown by the data in Section 4.1. One can imagine the demise of the dinosaurs as having been perhaps due to this danger. Considering this thermal sensitivity, it is remarkable that nearly 1% of the species that ever existed still do. Organisms that have thermal homeostasis are able to cope better against environmental temperature shifts. However, this advantage is lacking before the thermal homeostatic system develops in the adult organism. Organisms living in shallow fresh water have only a temporary protection against a temperature change in the air because of the finite thermal capacity of the water. The same is true of organisms living in the shallow or upper water of an ocean. The shapes, sizes and locations of the curves of event age vs. temperature could conceivably have evolved somewhat to be wider and shallower, if that is physicochemically possible.
10. QUANTIZATION 10.1.
Quantized
Growth
A growth process takes place between two event ages corresponding to the growth start and stop events. The growth rate might be constant, if the process were driven by release of a growth stimulator at a constant rate. If the growth stimulating substance is released by the very cells that are being created in the growth process, then the growth would be exponential, i.e., progressively faster. If the growth is at a constant rate, say for simplicity, then the resulting final magnitude of some characteristic dimension will be directly proportional to the time period between events. The event integers j at the beginning and end of the growth period may be thought of as quantum numbers that characterize the growth process. To specify these quantum numbers amounts to specifying the two event ages and, hence, their difference. Another possible pattern of a local growth is in the form of a pulse (brief and intense), as was recently regrated for lengths of babies [6]. This growth would be caused by a pulse of a growth promoting substance at an event age, according to the theory herein. 10.2.
Dimension
Spectra
Since most events have multimodal occurrence times (see Section 6), it follows that a growth process in a species can result in different quantized lengths in different individual organisms. One then has a spectrum of possible dimensions, each with its own amplitude representing relative frequency of occurrence.
11. EVOLUTION 11.1. 11.1.1.
The
Trend
Subspecies
in Event differing
Times
in Evolution
in event
ages
Subspecies differing in event ages are important in evolution. They may be portrayed for an event by a spectrum of event ages. Typically, this spectrum consists of several peaks, each at an event age, the event ages being consecutive. Each peak may be thought of as a subspecies. The envelope (curve tangent to the tops of the peaks) is a bell-shaped curve. This picture plays a prominent part in the process of evolution.
A. B. CLYMER
206
11.1.2.
Marching of event age subspecies sets
A bell-shaped spectrum of subspecies is not a stable configuration. Indeed, it has a standard dynamics. Normally, the subspecies at the highest event age has advantages over the other species by virtue of its larger size, due to longer periods of growth. Accordingly, the later peak will usually grow at the expense of the other peaks. The same is true of the second peak; it will grow at the expense of earlier peaks. The result is that the envelope glides smoothly to higher ages, enclosing a gradually changing set of event ages, since subspecies will be dropped off by extinction at the early end and added by mutation at the high age end. The progression of sizes with time in evolution can reach remarkable extremes of size. Examples are giraffe legs and necks, dinosaurs, whales, mammoths, etc. Since a doubling in event ages takes 15 event age intervals, several doublings of size are understandable and credible over the eons of evolution. 11.1.3.
Dwarf species
It is not necessarily true that marching of the envelope will be to higher ages. There can be local climatic and ecosystem conditions which favor a smaller body. In such a case, one observes a marching to lower ages, producing smaller species, such as human dwarfs or pygmies. If the smaller body size is compatible with long-enduring physical conditions, the dwarf species can optimize (find the best set of event quantum numbers j, one per event per species) and become stable (no longer evolving). If the envelope drift to lower ages is too slow to keep up with a shift in climate or other physical conditions, a species can become extinct. The degeneration of a species can be accelerated by an abnormal temperature over a long period. Likewise, a species can become extinct by not being able to move its envelope to higher ages fast enough. 11.1.4.
Multimodality
of different events
In the foregoing material, there are discussions of a subspecies comprised of individuals having the same event age for a particular event. However, there can also be subspecies defined in terms of the event ages of all of their events. It is unknown what correlations there might be in nature concerning the various event ages for a pair of events in one species, for example. One might expect to find an individual using consistently a high or a low event age for every event, if each event were a growth trigger or stopper. 11.1.5.
Speed of evolution of a species vs. multimodality
It has been observed by the author that the rate of evolution of a primate species, which correlates with its position in the tree (fastest for those farther out from the trunk), correlates also with its degree of multimodality of gestation period. Then one could generalize to the hypothesis that the rate of evolution of any species correlates with the degree of multimodality of its event ages for any of its events. A special case, yet obeying the principle, would be a species no longer evolving and having only one event age per event. One possible explanation of the general correlation would be that a rapidly evolving species, with its envelope rapidly moving to higher ages, would not have time to lose its peaks at lower ages at that same rate, making the envelope span more event ages. In fact, the same could be true of a species whose envelope is moving rapidly to lower ages during some unusual circumstances of long duration. The process of delaying an event to the next later (occasionally earlier) event age, or the evolutionary change in the timing of developmental events, is called heterochrony [63,79-851. The work of Matsuda [83] is said, by McCune [83], to be a “gold mine of examples of heterochrony.”
Timetable of Life
207
NOTE ADDED IN PROOF. See also [86]. According to Marx [79], “There is a great deal of evidence indicating that new species often emerge because the timing of some developmental events is altered so that they occur earlier or later with respect to other events than they normally would. This proposed mode of evolution is called heterochrony.” Likewise, Vermeij [81] says that “. . . shifts in the timing of developmental events have been frequent in the history of life . . .” Studies of Drosophila and E. coli have shown that ‘L.. . delays in gene expression are determined by the length of time required to transcribe the gene itself . . .” [63]. In the terminology of the present paper, a “delay in gene expression” is an “event age.” The mechanism of the molecular events that cause heterochrony Perhaps the mechanism described in Section 7.1 is involved.
11.2.
Evolution
11.2.1.
of Timer
Mutations
are not understood
[63,80].
Molecules
of timer
molecules
The process of evolution on a molecular scale can be viewed in part in terms of the progressive change by mutations of event-causing molecules. A timer molecule, if it were to mutate, could do so by adding a unit building block on its end. With the molecule now taking longer to build, an organism larger in some respect might result, giving it advantages. Thus, competition would usually favor mutations of timer molecules to make them longer.
11.2.2.
Environmental
constraints
on timer
evolution
Winter presents problems to many species. Generally, with exceptions, a species avoids trying to rear its young from a start in winter. Therefore, a mutation of event age extending birth too close to winter could be unsuccessful. A trend to age, could be For example, cold problem
increase event supported by young born in in the species’
ages, while blocked by disadvantages of increasing a particular event getting around the blockage, such as by migration, hibernation, etc. a place where winter is warm, thanks to migration, would avoid the original winter location.
More generally, one would expect to find examples problems.
of many
“ingenious”
solutions
to evolution
blockage
11.2.3.
Some
unanswered
questions
The author has no insight into the process of timer molecule be passed along to offspring.
11.3. 11.3.1.
Transients Effects
and
Evolution
of an ecosystem
mutation
or how a mutation
might
in an Ecosystem upon
development
The successful development of individuals of a particular species requires favorable interaction with many other species in an ecosystem. For example, other species are required as food, for pollination in some cases, and for other services. Likewise, the species is itself used less often by other species as food if there are related species present as alternative foods. In addition, the physical conditions are affected by other species, enabling enjoyment of favorable environment for development. Thus, trees provide shelter against the sun and wind.
A. B. CLYMER
208
11.3.2.
Stability
of an ecosystem
Stability of an ecosystem overall tends to stabilize the event age spectra of species living there, and the reverse is also true. A diversified ecosystem is knitted by a network of interactions among species. For example, a migrating bird species passing through an ecosystem can take as food the eggs of horseshoe crabs being laid at that time. Also hatches of several insect species in succession in a river provide more and better diet for the fish and young of birds. Also, a temporary loss of one food source can be compensated by another food source. By use of niches by species, many more species can be fitted into an ecosystem, increasing its variety and stability. Niches reduce competition among species, providing a better living for all. The local ecosystem forms an important part of the environment of a species. As such, the environment can help to shape the course of the evolution of a species. 11.4.
Quantization
in Evolution
It has been shown in Section 10 that one obtains a spectrum of a dimension for a multimodal species as a result of growth in development. These spectra shift to ever increasing ages and dimensions in evolution as a result of mutations in event ages. Conversely, going back in time, as in paleobioscience, one finds spectra shifted to ever shorter event ages and dimensions. For example, given an ancient bone fossil, one could use such spectra, together with a knowledge of event ages of a species versus evolutionary time, as an aid to dating of the bone. A case in point would be to make careful measurements of the dimensions (lengths, radii, etc.) of the beaks of Darwin’s finches as they are today. One would expect to find the frequency distributions quantized.
12. CONCLUSIONS 12.1.
Conclusions
Regarding
Life Science
The conclusions of this paper deal mostly with matters in life science. The most important are the following: 1. Development is marked by events that start or stop processes. The processes in development are localized and of discrete duration, with overlapping in time. Growth is intermittent in any location. All events are revealed by sudden changes in the concentration of some substance somewhere in the organism. Life consists of the consequences of a precisely timed series of biological events. 2. Events occur at one of the post-fertilization ages given by the geometric series in which each event age is 1.0472 times the age at the last previous event. One day is very close to being a member of the series. So are most biorhythm periods. Since there are about three hundred event ages in the range of concern, whereas there are millions of species, each with thousands of events, the series permits remarkable condensation of data. Another fascinating property of the series is that the spacings of the logarithms of the event ages are all identical, i.e., a linear series. Some events are exceptions. For example, plant seeds germinate in response to physical criteria, not timing. 3. Building of the mRNA molecules that achieve event timing is believed to take place on DNA, unit by unit, i.e., on the chromosomes of any cell. The resulting mRNA molecule moves to a ribosome to direct the start and stop of the building of a protein which participates in the new process. Building of the mRNA would be the time-taking step, the others being relatively fast. The foregoing building process is sufficient as a model from which to derive the geometric series of event ages. 4. The geometric series of event ages is considered to have been sufficiently well established against published data herein that it can be used to identify suspicious (possibly erroneous) data. The frequency distribution of errors of fit is Gaussian. Such a pattern could result
Timetable of Life
from temperature
209
variation, improper data processing, etc. Data newly being found in the
literature are members of the same statistical
family that was fitted; error magnitudes and
distributions are similar. 5. Most events occur for a particular species at two or more consecutive event ages. It has been concluded that one should expect to find growth to be quantized, i.e., clustering around certain values. This distribution would result from multiplying a constant growth rate by the difference of the starting and stopping event ages. If the event ages are multimodal, then so will be the resulting growth dimension. The same would be true of migration distance, duration of hibernation, etc. 6. Most biorhythms are shown herein to have periods that closely match event ages. This agreement is explained by assuming that the molecule building for one event age can be merely repeated over and over to produce a biorhythm. 7. Event ages as observed are affected significantly by temperature change. The curve is a hyperbola with an asymptote at each of two critical temperatures at which event ages becomes infinite. Since the asymptotes are not very far apart, a small temperature shift can greatly delay or prevent a vital event from occurring. 8. Evolution could be modeled in some respects as a flea or frog race: an ensemble of racers intermittently jumping to the next higher event age in a stochastic manner. These event age changes would be caused by mutations of mRNA by one unit each time. A species that is evolving rapidly would have a large number of event ages per event, say 8 or 9. This relationship is true for primates, at least. 9. If the event age formula and series survive evaluation by others, they will introduce a new requirement for precision in measurement and reporting of event age data. 10. The biological time of each organism is mathematically structured. 12.2.
Conclusions
Regarding
Medicine
The availability of patient event timetables and improved means for locally causing events that do not occur naturally should result in improved monitoring and management of child and adult development. Similar timetables for other species should permit the same developmental management to be applied in veterinary medicine, zoo management, etc. In general medicine and medical research, it would be desirable to have event age data for malaria parasites, nucleus-invading organisms, various cancer cells, mental illnesses that have any temporal causation, etc. Timetables would be useful also in determining an appropriate time for administration of a drug whose effect depends sharply upon patient age. Physicians and life scientists have always held a deep respect for the system and beauty in organisms. The system aspect is now enhanced by the inclusion of simple mathematics with general scope of application. In general, it is understood that medical applications emerge from advances in the life sciences. Thus, one could expect progress in medicine from the advances in chrontogenetic science postulated in Section 12.1. 12.3.
Conclusions
Regarding
Planet
Management
It has been shown that major losses of life can result from modest changes in atmospheric temperature. Eggs and young are particularly vulnerable. Surely this problem of potential species and ecosystem extinctions deserves massive research. The postulated cause is the impact of temperature change upon the age of occurrence of one or more events. Beings who would presume to manage entire ecosystems and planets must know much about timing in the lives of organisms.
A. B. CLYMER
210
12.4.
Some
Remaining
Questions
Of the many questions remaining, the following are especially interesting: 1. Does the event age list apply in any way to bacteria, viruses, cancer cells, plants, etc.? 2. Are the mRNA and/or protein molecules, that are presumed here to be responsible for events and event ages, quantized in molecular weight, as might be suggested by the findings of Savageau as reported by Lewin [87]? 3. Is the molecule building process described in Section 7 a valid theory? observed, or observed not to occur?
Can any of it be
4. Why do some mutations of mRNA molecules produce no change in the resulting events while others do?
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.
27. 28. 29. 30. 31.
A.B. Clymer, Simulations of the timing of nature, In Proc. Sot. for Comp. Simulation Conf. on Simulations at the Frontier of Science, pp. 3-22, SCS, San Diego, CA, (1986). A.B. Clymer, The precise timing of events in disease and development, In Proc. SCS Summer Computer SimzLlation ConJ., San Diego, CA, pp. 42&430, Sot. for Comp. Simulation, (1987). A.B. Clymer, Patterns of timing in living systems, In Proc. SCS Simulators Conf., San Diego, CA, SCS, (1988). S.J. Gould, Bully for Brontosaurus, W.W. Norton, New York, (1991). S. Au&ad, On the nature of aging, Nut. Hist. 2, 25-56 (1992). M. Lampl, J.D. Veldhuis and M.L. Johnson, Science (October 1992). Witschi, In Biology Data Book, (Edited by Altman and Dittmer), Fed. of Amer. Sot. on Expl. Biol., Washington, DC, (1964). Streeter, Biology Data Book, (Edited by Altman and Dittmer), Fed. of Amer. Sot. on Expl. Biol., Washington, DC, (1964). R. O’Rahilly and E. Gardner, Acta Anat. 104, 122-133 (1979). A. Delaney, (personal communication), (1986). J. Brooks-Gunn, Antecedents and consequences of variations in girls’ maturational timing, J. Adolescent Health Care 9, 365-373 (1988). A.A.B. Pritsker, Papers, Experiences, Perspectives, Systems Publ. Corp., W. Lafayette, IN, (1990). C.F.A. Moorees, Variability of dental and facial development, In The Biology of Human Variation, Annals of the NY Academy of Sciences, (Edited by J. Brozek), Volume 134, pp. 846-857, (1966). D.A. Nelson, Life history and environmental requirements of loggerhead sea turtles, Technical Report EL-86-2, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS, (1986). S.B. Hrdy, Daughters or sons, Nat. Hist., 63-83 (1988). S. A. Asdell, Patterns of Mammalian Reproduction, Cornell Univ. Press, Ithica, NY, (1964). Altman and Dittmer, Editors, Biology Data Book, Fed. Amer. Sot. on Expl. Biol., Washington, DC, (1964). P. A. Racey, Environmental factors affecting the length of gestation in mammals, In Environmental Factors in Mammal Reproduction, pp. 199-213, Univ. Park Press, Baltimore, MD, (1981). C.H. Johnson and J.W. Hastings, The elusive mechanism of the circannual clock, Amer. Sci. 74, 29-36 (1986). King and Mitchell, Breeding primates in zoos, In Comparative Primate Biology, Vol. 2B, Behavior, Cognition and Motivation, pp. 219-261, A.R. Liss, New York, (1986). K.A. Fagerstone, The annual cycle of Wyoming ground squirrels in Colorado, J. Mamm. 69,678-687 (1988). Altman and Dittmer, Editors, Growth, Including Reproduction and Morphological Development, FASEB, Washington, DC, (1962). L.S. Earley, On the rebound, Nat. Parks, 35-38 (1992). T. Verde, Mothers in waiting, Nat. Wildlije 30, 16-20 (1992). M. Sandell, Stop-and-go stoats, Nat. Hist. 97, 55-65 (1988). M. Kirschner et al., Initiation of the cell cycle and establishment of bilateral symmetry in xenopus eggs, In The Cell Surface: Mediators of Developmental Processes, (Edited by Subtelny and Weasells), pp. 187-216, Academic Press, New York, (1980). M.J. Whitaker and R.A. Steinhardt, Ionic regulation of egg activation, Q. Rev. of Biophys. 15, 593-666 (1982). P.H. Harvey and T.H. Clutton-Brock, Life history variation in primates, Evol. 39, 559-581 (1985). C.G. Hartman, The irregularity of the menstrual cycle, In Science and the Safe Period, R.E. Krieger Publ. Co., Huntington, NY, (1972). Arey, Developmental Anatomy, Sixth Edition, Saunders, Philadelphia, (1956). J. Hemingway, Despite long odds, mighty herds still plunge across the Serengeti, Smithsonian 17, 50-61 (1987).
Timetable 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48.
49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62.
63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80.
of Life
211
G.W. Asher, Oestrus cycle and breeding season of farmed fallow deer, Dana dama, J. Repro. Fert. 75, 521-529 (1985). J.D. Curlewis, Estrous cycles and the breeding season of the Pere David’s deer hind, J. Repro. Fed. 82, 119-126 (1988). D.G. Kleiman, Maternal behavior of the Green Acouchi (Myoprocta prathi Pocock), A South American caviomorph rodent, Behavior 43, 44-84 (1972). E. Linden, Bonobos, Nat. Geogr., 46-53 (March 1992). Van Horn, Valerio et al. Hampton and Hampton. Lorenz. Dixson. Glander. Tobach, Aronson and Shaw, Editors, The Biopsychology of Development, Academic Press, NY, (1971). C.M. Crockett and R. Sekulic, Gestation length in Red Howler Monkeys, Amer. J. Primatology 3, 291-294 (1982). W.B. Wood and R.S. Edgar, Building a bacterial virus, Sci. Amer. 217, 60-74 (1967). J.H., The Nautilus and the born, Sci. Amer., 22-23 (January 1988). N.H. Landman and J.K. Cochran, Growth and longevity of Nautilus, In Nautilus, (Edited by N.H. Landman and W.B. Saunders), (1989). M. Geber, The psychomotor development of African children in the first year and the influence of maternal behavior, J. Sot. Psych. 47 (1958). R.W. Thatcher, R.A. Walker and S. Giudice, Human cerebral hemispheres develop at different rates and ages, Science 236, 1110-1123 (1987). A.B. Clymer, Roles of simulation in the application of expert systems in emergency management operations, In Proc. First Symposium in the Application of Expert Systems in Emergency Management Operations, FEMA/NBS, Washington, DC, (1985). F.M. Slater, S.P. Gittins and J.D. Harrison, The timing and duration of the breeding migration of the common toad (Bufo bufo) at the Llandrindod Wells Lake, Mid-Wales, Br. J. Herpetology 6, 424-426 (1985). E. Gwinner, Internal rhythms, bird migration, Sci. Amer. 254, 84-92 (1988). L.P. Brower, A place in the sun, Animal Kingdom 91 (4), 42-51 (1988). R. Baserga, Multiplication and Division in Mammalian Cells, Marcel Dekker, New York, (1976). A.B. Clymer, Development: A timed series of molecular events, Science (submitted 1967, in review by author). J.H.S. Bradley, (personal communication), (1986). Diagram group, Comparisons, St. Martin’s Press, New York, (1980). F.C. Kafatos and N. Feder, Cytodifferentiation during insect metamorphosis, the galea of silkmoths, Science 161, 470-472 (1968). W.J. Gehring, The molecular basis of development, Sci. Amer. 253, 152B-162 (October 1985). S.B. Oppenheimer and R.L.C. Chao, Atlas of Embryonic Development, Allyn and Bacon, Boston, (1944). J.D. Wilson, F.W. George and J.E. Griffin, The hormonal control of sexual development, Science 211, 1278-1284 (1981). D.R. Soll, Timers in developing systems, Science 203, 841-849 (1979). M. Poenie et al., Changes of free calcium levels with stages of the cell division cycle, Nature 315, 147-149 (1985). R.P. Elinson, The amphibian egg cortex in fertilization and early development, In The Cell Surface: Mediator of Development Processes, (Edited by Subtelny and Wessells), pp. 217-234, Academic Press, New York, (1980). C.S. Thummel, Mechanisms of transcriptional timing in Drosophila, Science 255, 39-40 (1992). S.B. Hendricks, Metabolic control of timing, Science 141, 21-27 (1963). J.F. Feldman, Genetic approaches to circadian clocks, Ann. rev., Plant Physiol. 33, 583-608 (1982). B.C. Goodwin, Temporal Organization in Cells. A Dynamic Theory of Cellular Control Processes, Academic Press, London, (1963). C.F. Ehret and E. Trucco, J. Theor. Biol. 15, 240 (1967). R.F. Feynman, Surely You’re Jo&g, Mr. Feynman, Norton, New York, (1985). Suter and Rawson. Living Clocks. Boslough. Zernbavel. Martin and Menacker. Klevecz. J.S. Takahashi, Circadian clock genes are ticking, Science 258, 238-239 (October 9, 1992). P. McConnell, Bears . in New Jersey.?, New Jersey Outdoors, 3-5 (1987). P.E. Ross, Man bites shark, Sci. Amer., 31 (1990). T. Bedell, There’s a whale, there’s a whale, Skylines, 17-20, 32-33 (September 1986). J.L. Marx, Clues to developmental timing, Science 226, 425-426 (1984). J.L. Marx, Evolution’s link to development explored, Science 240, 880-882 (1988).
MCM 19:6-8-O
212 81. 82. 83. 84. 85. 86. 87. 88. 89. 90.
91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103.
A. B. CLYMER G.J. Vermeij, Review of Evolutionary IPrends, (Edited by K.J. McNamara, Univ. of Arizona Press, Tucson, 1990), Science 251, 1374-1375 (1991). P. Mabee, Review of The Evolution of Ontogeny, (Edited by M.L. McKinney and K.J. McNamara, Plenum, New York, 1991), Science 254, 874-875 (1991). A.R. McCune, Review of Animal Evolution in Changing Environments, (Edited by R. Matsuda, Wiley-Interscience, New York, 1987), Science, 300-301 (1988). J. Hanken, Development and evolution in amphibians, Amer. Sci. 77, 336-343 (1989). D.A. Powers, Fish as model systems, Science 246, 352-358 (1989). D.L. Slocum, Review of Developmental Patterning of the Verterbrate Limb, (Edited by Hinchliffe, Hurle, and Summerbell, Plenum, New York, 1991), Science 257, 1570-1571 (September 11, 1992). R. Lewin, Unexpected size pattern in bacterial proteins, Science 232, 825-826 (1986). S.J. Gould, Justice Scalia’s misunderstanding, Nat. Hi&., 14-21 (1987). A.B. Clymer, Dear John (letter), Simulation, v-vii (1967). A.B. Clymer, Development: A timed series of molecular events, Submitted to T. Theor. Biol., March 1968, rejected (author’s paper A.B. Clymer, The regularity of the timing of developmental events, submitted BS an abstract to the 31th ACEMB, October 1978, also was rejected). S.J. Gould, Nat. Hist. 20 (February 1984). J. Bronowski, The educated man in 1984, Science 123, 710 (1956). A.G. Thorne and M.H. Wolpoff, The multiregional evolution of humans, Sci. Amer., 76-83 (April 1992). F. Crick, Lessons from biology, Nat. Hi&., 32-39 (November 1988). S.J. Gould, Letter, Science 232, 439 (1986). Adams, Smithsonian horizons, Smithsonian (issue unknown). G. Lakoff, What Categories Reveal about the Mind, Univ. of Chicago Press; L.H. Brody, Lib. J. 78 (1987). A.B. Clymer, A model of abuse, In Proc. Conf. on Emergency Planning, Society for Computer Simulation, San Diego, CA, pp. 54-60, (1987). R.L. Armstrong, Review of Theories of the Earth and Universe, (Edited by S.W. Carey, Stanford Univ. Press, 1988), Amer. Sci. 77, 382-384 (1989). Sir J.A. Thomson, The Great Biologists, Books for Libraries Press, Freeport, New York, (1932). W. Bagehot, Physics and Politics, Knopf, New York, (1948). U. Windhorst, How brainlike is the spinal cord 7, In Studies of Brain l%nction, p. 15, Springer-Verlag, (1988). J.H.M. Thornley and I.R. Johnson, Plant and Crop Modelling, Clarendon Press, Oxford, (1990).
Timetable
of Life
213
APPENDIX A GESTATION DATA Table Al.
Comparision
of event times with reported gestation periods.
*These are events ages
closest to published gestation data. l*S = Success, F = Failure (see Section 5.1.1).
Species Name
* Refs
-
111 - 121
13741
[51 El 171 172’1
[71 - [71 - 171 I71 -IT -IT PI [71
“402 hrs with 14 month-old”
-VT [71 Tr 171 171 - 171 171
20.05d
(Dipodomys merriami Mearns)
17.00d and 23.00d
cf 23.03d
S
Hamster
“20 to 22 days” = 20.00d to 22.00d
cf 20.05dz cf 21.99d
S S
tvery unlikely spread. SAlso, expect peak at 21.00d.
-FT (71
A. B. CLYMER
214 Table Al.
Continued.
Comparision
of event times with reported gestation
periods.
‘These
are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
First Species Name
Event
Published
Interpretation
Gestation
and
Data
Comments*
Time Common
Applicable
Name
(Latin Name)
to Species
S,F Refs **
20.05d
(
cf 20.05d
F
19.15d
<
cf 19.15dt cf 21.00d
20.05d
(
-S -S -F -S -S -S S s
20.05d 20.05d 19.15d
= 20.50d to 21.00d
( Micro&
oeconomus Pallas)l “20 to 21 20.00d to 1“20 to 21 ( :erbil, I= 20.00d __IG. simoni Lataste) [ “19 to 22 E3onbieda
days” = 21:OOd days, usually 20” to 21.00d days, usually 20”
= 19.00d to 22.00d 20.05d 20.05d 21.00d 20.05d 21.00d 21.00d 21.00d 21.00d 20.00d
F‘ersian house mouse Elouse mouse (wild), Mus musculus L.) i Dasyurinae Dasyurops naculatus Kerr) I :ommon shrew, _( Soricidae sorez Araneusl ( :lider -1 Sorex fumeus Miller) Sihort-tailed shrew EIarvest mouse, .I R. montanus) ‘ygmy mouse,
“20 days” = 20.00d “20.24& 0.12 days” = 20.24d “3 wks” = 21.00d “20 days” = 20.00d
cf cf cf cf cf cf cf
20.05d 21.00d 20.05d 21.00d 20.05d 21.00d 19.15d
:f 21.00d and 21.99dz cf 20.05d cf 20.05d cf 21.00d cf 20.05d
“3 weeks” = 21.00d “3 weeks or less” = 21.00d “5 lay betw. 21 and 23 days” I= 21.00d to 23.00d ( “21 days” = 21.00d
j “20 days” = 20.00d
cf 21.00d cf 21.00d cf 21. OOd cf 23.03d* cf 21.00d cf 21.00d
21.00d 21.00d
.L (
21.00d
21.99d 21.00d 21.00d 21.00d 21.99d
-
S
s s s-S S -
S
(” ? J
cf 21.00d
s
cf 21.00d
s
I
cf cf cf cf
(
= 21.00d to 22.00d
piorway rat .( albino, laboratory) Jorway rat .; albino, laboratory) E3lack rat EIormouse, .( M. avellanarius L.) IIormouse, ( E. auercinus L.1
1Also, expect
pea at
20.05d
IExpect peak at 20.05d and 21.00d ‘Expect peak at 21.99d too.
“avg.. .21.8 days” = 21.80d
21.00d 21.00d 21.99d 21.99d
-
S -s -S S
“about 21 days” = 21.00d “21 days” = 21.00d “21 days” = 21.00d
cf 21.00d
s
cf 21.00d cf 21.00d
s s
“22 days” = 22.00d
cf 21.99d
s -
~ 171 171 171 [71 -
[71 [71
- 171 [71
S
sS
.( 21.00d 21.00d
-
cf 21.00d cf 21.00d
(
21.00d
sS
s s sS
( r~ F EEuropean field mouse,
21.00d 21.00d
S
1
.; 21.00d
s-
-
171 -
PO1 - [71 - [71 [71 [71 -
[71
-
[71 - [71 [71 Jl_ 171 [71 [71 - [71 171 [71 [71 - (71 [71 171
Timetable Table Al.
Continued.
Comparision
of Life
215
of event times with reported gestation
events ages closest to published gestation data. “S
periods.
*These are
= Success, F = Failure (see Section 5.1.1).
First Event
Species Name
Published
Time Applicable
Common Name
Gestation
to Species
(Latin Name)
Data
21.00d
klce rar
Refs.
“Variously given as 25 or from 21 to 24 days” = 21.00d, 24.00d, and 25.00d “21 to 24 days” = 21.00d to 24.00d “22.5 days”
21.99d 21.99d 21.99d 21.00d 23.03d 21.99d 23.03d 23.03d 21.00d 23.03d 21.03d 24.12d
bird, (N. persicus Blanford) Jird, (M. vinogmdovi Heptner) (Thallomys namaquensis A. Smith) (Rattus hawaiiensis Stone) Suslik, (Citellus Townsendii) Suslik, (Citellus Suslicus) Columbian ground squirrel (U.S.A. and Canada) Harvest mouse, (R. megalotis) White-footed mouse, (P. calif.) Cotton mouse Wood mouse Gerbil,
“22 days” “21.5 to 23 days” = 21.50d to 23.00d “may be 22 days or more” = 22.00d “not lees than 21 days” = 21.00d “at least 23 days” = 23.00d “22 to 26 days” = 22.0d to 26.00d “23 to 24 days, usually the latter” = 23.00d to 24.00d “23 to 24 days” = 23.00d to 24.00d “range 21 to 25 days” = 21.00d to 25.00d “22.9 days” = 22.90d “23.2 days” = 23.20d “about 24 days” I
cf 23.03d
I= 24.00d 23.03d 23.03d
23.03d
1(Citellus 1townsendii Bachman) 1(Rattus assimilis Gould)
1Multimammate
rat
“at least 23 days” I
I = 23.Orld 1“22 to 24 days, _
I
~-
---
with 22.8 the avg. and with 60% at 23 days” = 22.00d 1to 23.00d, 24.00d 1“23.1f.7 days” I= 23.10d
Possibly peak also at 21.99d and 23.03d. L TPossibly peak also at 21.99d and 23.03d. *Is 22.5d an average across a distribution from 22 to 23d? *Should show 3 peaks in between. *Should show 3 peaks in between. *Apparently peaks near 22, 23, and 24 days. OPerhaps peaks also at 21.99d and 24.12d.
I I I
1 S
216
A. B. CLYMER Table Al.
Continued.
Comparision of event times with reported gestation periods.
*These are
events ages closest to published gestation data. l*S = Success, F = Failure (see Section 5.1.1).
Common Name
IPerhaps *Perhaps *Perhaps *Possible *Possible OPerhaps OPerhaps
peaks also at 26.45d and 27.69d. peaks also at 26.45d, 27.69d and 29.00d. peaks also at 29.OOd and 30.37d. peak also at 30.37d. peak also at 30.37d. peaks also at 27.69, 29.00d, and 30.37d. peak at 31.80d too.
Timetable Table Al.
Continued.
Comparision
of Life
of event times with reported gestation periods.
events ages closest to published gestation data. “S
Common Name
(Mawnota
monax
mona
31.084~0.02 days, D = 0.83d,
Note broad distribution
covers 30.37d and 31.8Od.
SPerhaps distribution covers 31.8Od and 33.31d. *Perhaps peaks also at 29.OOd and 30.37d.
*These are
= Success, F = Failure (see Section 5.1.1).
218
A. B. CLYMER Table Al.
Continued.
Comparision
of event times with reported gestation
periods.
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
First Species Name
Event Time
Published
I nterpretation
Applicable
Common Name
Gestation
and
to Species
(Latin Name)
Data
Comments*
30.37d 30.37d 30.37d 30.37d 30.37d 30.37d 33.31d 30.37d
F‘rairle aog, _( Cynomys ludovicianus Ord) c California ground squirrel ( Citellus fulvus Lkhtenstein) EIastern chipmunk _L Eutamias quadrimaculatus Gray) F‘lying squirrel, (Glaucomys abrinus Shaw) mouse : &sshopper F‘ocket gopher
31.80d
5Vood rat, _( N. floridana Ord) VVood rat, _( N. fuscipes Baird) VVood rat,
30.37d 34.88d 34.88d
_L N. lepida Thomas) Iilound-tailed muskrat P E
31.8Od 33.31d
27.6Qd 38.25d 38.25d 34.88d 34.88d 36.52d 40.05d 38.25d 41.94d 41.94d 41.94d
40.05d 41.94d 38.25d 40.05d
C:ommon European mole S nowshoe hare Eiuropean red squirrel r )warf mongoose L,ittle northern chipmunk, Eutamias sibiricus Laxmann) _i Mystromys albicandatus A. Smith) Ebrush wallaby C:ray Kangaroo Rlat Kangaroo h4ole, (Mogera latouchei Thomas) J ack rabbit
F‘lying squirrel, _i Glaucomys sabrinus Shaw) \‘srying hare \‘olcano rabbit, diazi) _L Romerolagus Swamp rabbit
G ray squirrel _& ~&TIM griseus Ord) Perhaps peaks also at 31.80d and 33.31d. 43.92d 43.92d
SPossible peaks also at 33.31d and 34.88d. *Perhaps peaks also at 36.52 and 38.25d. *Perhaps peaks also at 36.52 and 38.25d. *Perhaps peaks at all three of these event ages.
“30 to 35 days”
cf 30.37d
W **
Refs
-
-
= 30.00d to 35.00d “probably 30 days” = 30.00d “about 1 month” = 30.42d
cf 34.88dt cf 30.37d cf 30.37d
-F -S -F S
“31 days” = 31.00d “31 days” = 31.00d “1 month” = 30.42d
cf 30.37d cf 30.37d cf 30.37d
F F s
“33 days” = 33.00d “30 days” = 30.00d “19 days”=19.00d “in captivity 32 days” = 32.00d “33 days” (2 cases) = 33.00d “32 to 36 days”
cf cf cf cf
-S -F -S S
= 32.00d to 36.00d “SC 30 days” = 30.00d
“about 4 wks” = 28.00d “38 days” = 38.00d “38 days” (1 case) = 38.00d “about 5 wks” = 35.00d “35 to 40 days” = 35.oOd to 4o.oOd “about 37 days” = 37.00d “40 days” = 40.00d “38 or 39 days” = 38.50d “probably 6 weeks”=42,00d “6 wks” = 42.00d “41 to 47 days. mean of 43” = 41.00d 43.00d 47.00d “40 days” = 40.00d “about 42 days” = 42.OOd “38 or 40 days”=38.00d (1 case in zoo) or 40.00d “39-40 days” = 39.50d (1 case) “44 days” = 44.00d “43 days or more” = 43.00d
33.31d 30.37d 19.15d 31.8Od
cf 33.31d cf 31.80d cf 36.52dJ cf 30.37d cf 34.88d cf 34.88d cf 40.05d cf 34.88d* cf 31.80d cf 31.80d cf 27.69d cf 38.25d cf 38.25d cf 34.88d cf 34.88d cf 40.05.d* cf 36.52.d cf 40.05d cf 38.25d cf 41.94d cf 41.94d rf 41.94d cf 43.92d cf 46.00d* cf 40.05d cf 41.94d cf 38.25d cf 40.05d
-
[71 [71 [71 (71 (71 [71 [71 [71 (71
S
-S -F -F S s-S S F s-S S s-S -S S F s s s s F F F s sS s F s F
171 [71 -[71 pl_ 171
(181 [71 [71 [71 [71 [71 -[71 -[71 -171 -[71 -[71 [71 [71 m P91 [71 -[71 -[71
Timetable Table Al.
Continued.
Comparision
of Life
219
of event times with reported gestation periods.
‘These
are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
First Species Name
Event
Interpretation
Time Common
Applicable to Species
American red squirrel Palm squirrel,
(finabulus pennanti Wrought07 Marmot, (Mannota bobak Mzlller) Pinon mouse African jerboa (Desmana moschata L.)
40.05d 40.05d 41.94d 46.00d I
40.05d
Himalayan marmot, (Marmoto bobak Mullerl
30.37d 41.94d 34.88d 50.44d 48.17d 50.44d 50.44d 55.31d
1Fox squirrel IGiant Rat European stoat, (h4ustela putorius eversmanni) a weasel, (M. sibirica Pallas) European badger Dwarf mongoose, (Helogale vet&a Thomas) Common European bat a bat, (Pipistrellus (Nyctalus) noctula Shreber) Fennec Bobcat Philippine tree shrew
x 50.44d 48.17d 55.31d 55.31d 55.31d 50.44d
** Data
, -‘about 40 days” = 40.00d “40 to 42 days” = 40.00d to 42.00d “about 40 days” = 40.00d “40 days” = 40.00d “42 days” = 42.00d “45 to 50 days”
English red fox European weasel Marbled polecat (Felis libyca Forster) (Felis bengalansis Kerr) Spiny Hedgehog tenrec, (Setijer setosus)
Possible peak also at 48.17d. Possible peak also at 48.17d. Possible peaks also at 55.32d and 57.93d.
Comments* cf cf cf cf
40.05d 40.05d 41.94d 40.05d
cf 40.05d cf 41.94d cf 46.00d
= 45.00d to 50.00d “about 40 days” = 40.00d
cf 50.44dt cf 40.05d
“about 44 days” = 44.00d “46 to 50 days”
cf 43.92d cf 46.00d
= 46.00d to 50.00d “42 days” = 42.00d
cf 50.44dT cf 41.94d cf 41.94d
“42 days with practically no variation” = 42.00d
I
46.00d 41.94d 40.05d
S,F ReE
Name
(Latin Name)
40.05d 40.05d
I
S s
171
171 S S
171
S S E S
[71 [71 [71
S
171
S
[71 171
s S S S
PI [71
“about 45 days” = 45.00d “42 days” = 42.00d “40 to 42 days” = 40.00d to 42.00d “about 30 days” = 30.00d
cf 46.00 cf 41.94d cf 40.05d cf 41.94d cf 30.37d
F S _s_ S
[71 [71 [71
F
[71
“6 wks” = 42.00d “about 5 wks” = 35.00d
cf 41.94d cf 41.94d
S S
[71 [71
“50 davs” = 50.00d “probably about 49 days” = 49.00d “2 case, 50 and 51 davs” = 50.50d
cf 50.44d cf 48.17d
S F
[71 [71
S S F S
171 [71 171
F S
171
F
[71
s_
[71
“approx. 56 days” = 56.00d “or < 50 days” = 50.00d “52 days” and “60 days” = 52.00d and 60.00d “49 to 55 days, with a
=
49.00d 52.00d 55.00d
cf 50.44d cf 50.44d cf 55.31d cf 50.44 cf 52.82d cf 60.66d* cf 48.17d cf 52.82d cf 55.31d cf 50.44d cf 52.83d cf 48.17d cf 55.31d cf 55.31d cf 55.31d cf 50.44d cf 52.82d cf 55.31d cf 55.31d cf 57.93d cf 60.66d
F S
S F F F F s
F S F S S
[71 [71 171 [71 WI
220
A. B. CLYMER Table Al.
Continued.
Comparision
of event times with reported gestation
events ages closest to published gestation data. “S
periods.
*These are
= Success, F = Failure (see Section 5.1.1).
First Species Name
Event Time
Common
Applicable to Species
Name
Published
Interpretation
Gestation
and
Data
Comments*
(Latin Name)
46.00
Tree shrew, (Tzlpaia glis belangeri)
60.66d
Northern coyote
60.66d
Wolf
47 days (4 cases) = 47.00d 48 days (1 case) = 48.00d 52 days (1 case) = 52.00d 54 days (2 cases) = 54.00d “59 to 63 days” “betw. 58 and 63 days” = 58.00d to 63.00d, “61.3 davs” = 61.30d.
cf cf cf cf
46.00d 48.17d 52.82d 52.82d
cf 57.93d cf 63.52d cf 60.66d
%F Hefs. **
F
[I91
s F F
s s s s s
WI [71
D51 [191 [71
F
s -S
= 60.00d to 63.00d, 60.66d
a wolf, (Canis a~rens L.) Stripe-sided jackal
57.93d 63.52d 57.93d
Pale bat Mouse lemur, (Microcebus murinus) Tree shrew, (npaia)
43.92d
60.00d 63.52d 60.00d
Indri Hairy armadillo Hair tree porcupine
63.52d 63.52d 60.66d
Dingo Gray fox Cape hunting dog
60.66d
Big-eared fox
n Dublin “60 to 63 = 60.00d “57 to 60 = 57.00d
Zoo 63d days” to 63.00d davs” to -6O.OOd
Raccoon, (PTOCyOT2
63.52d 63.52d 60.66d 60.66d
LOtOT)
Stone marten, Beech marten Striped skunk Skunk I
(L. maculicollis Lichtenstein)
IPerhaps peaks at 63.52d and 66.52d. [Perhaps peaks also at 63.52 and 66.52d.
cf cf cf cf
60.66d 63.52d 57.93d 60.66d
5 “43 davs” = 43.20d “45 days” = 45.00d “49 days” = 49.00d “49-51 days” = 49.00d to 51.00d “56 days” = 56.00d “60 days” = 60.00d “65 days” = 65.00d “60 to 70 days”
= 60.00d to 70.00d
63.52d
-
“63 days” = 63.00d “about 63 davs” = 63.00d “60 to 63 days” = 60.00d to 63.00d “80 days” = 80.00d “probably 60 to 70 days” = 60.00d to 70.00d “avg. 63 days” = 63.00d “64 days” = 64.00d “In India. 9 wks” = 63.00d
cf 45.996d cf 48.167d cf 50.44d cf cf cf cf
55.31d 60.66d 63.52d 60.66d
cf 69.66dt cf 63.52d cf 63.52d cf 60.66d cf 63.52d cf 80.00d cf 60.66d cf 69.66dr cf 63.52 cf 63.52 cf 63.52d
171 WI
S
s
[71
F
171
-S F F F F F s
[71 -IT
s s -
-VI
F S
[71
F [7) -5 [71 S
s -
-S S
[71 [71 171 PO1
-S S
[71
s -S
s -S
171
-
S
F -
F sS
g -m (71
Timetable Table Al.
Continued.
Comparision
of Life
221
of event times with reported gestation periods.
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
First Event Time
Published
Interpretation
Applicable
Common Name
Gestation
and
to Species
(Latin Name)
Data
Comments*
60.66d
(Felis chaus Gulders Taedt)
63.52d
(Felis yaguarondi Desmarest) Lynx, (Felis canadensis Kerr) Lynx,
60.66d 63.52d
)
(Felis lunx L.1 69.66d
Asiatic pipistrelle bat
ggE
S,F l
R.efs
*
“about 63 days” = 63.OOd “60 to 65 davs” = 60.00d to -65.00d “about 63 days” = 63.00d “cat in the wild 68 days” “about 2 months” = 60.87d “9 weeks” = 63.OOd “about 2 months”
= 60.87d
;I9 to 10 weeks” = 63.00d
1;o 70.00d “60 days” = 60.00d “about 70 days” = 70.00d “(litters of 6), 66.8 days” = 66.80d “about 67 to 68 days’ = 67.00d to 68.OOd “usually given as 61 to 63 days’ , = 61.00d to 63.00d “60 to 65 days” “70 “68 “71 “74 “75 “76 “67
days” days” days” days” days” days” to 77
(1 case) = 70.00d = 68.00d (1 case) = 71.00d (1 case) = 74 .OOd (2 cases) = 75.00d (2 cases) = 76.00d days”
[71
(71 (231 - 171 [71 WI
1241
= 67.00d to 77.00d “61 days” (1 case) = 61.00d “64 days” (1 case) = 64.00d “66 days” = 66.00d “63 days” = 63.00d “64 days” = 64.00d “63-70 days” = 63.00d to 7O.OOd
76.69d
1Coati
IPossible peak also at 66.52d. TPerhaps peaks also at 72.95d and 69.66d. *Possible peak also at 66.52d. *Perhaps a peak also at 80.00d.
“about 73 days” = 73.00d “about 11 to 12 weeks” = 77.00d to 84.OOd “77 days” = 77.00d
1251 I191 PI PI
222
A. B. CLYMER Table Al.
Continued.
Comparision
of event times with reported gestation
periods,
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
Common
105.5d 105.5d 105.5d
Name
African lion, (Panthera lea) Capybara, (Hydrochoeris isthmius Agouti
Goldman)
‘Perhaps a peak at 72.95d also. SPerhaps peak also at 96.20d. *Perhaps peaks also at 96.20d and 100.7d. *Possibly peaks also 96.20d and 100.7d. *Perhaps peak also at 110.5d. *2 or 3 peaks?
Gestation
“105 to 113 days” = 105.0d to 113.0d “104 and 111 days” = 104.Od and lll.Od “about 104 days” = 104.0d
cf cf cf cf cf
105.5d 110.5d 105.5d 110.5d 1055d
S F
[311
P S
[71
F
[71
Timetable Table Al.
Continued.
Comparision
of Life
of event times with reported gestation
223 periods.
‘These
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
Common
(Chinchilla
iPerhaps
Name
laniger)
peak also at 115.7d
Gestation
are
224
A. B. CLYMER Table Al.
Continued.
Comparision
of event times with reported gestation
periods.
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
Common
Name
= 158.0d to 175.Od
Perhaps 3 other peaks also. SPerhaps peak also at 145.7d. *Perhaps peak also at 145.7d. ‘Perhaps peak also at 145.7d. *Perhaps peaks also at 145.7d 152.6, 159.8d.
Timetable Table Al.
Continued.
Comparision
of Life
of event times with reported gestation periods.
events ages closest to published gestation data. “S
Species Name
Time Applicable to Species
Common
Name
(Latin Name)
Interpretation
Gestation
and
Data
Saiga Rocky Mountain goat Bar bari goat E. African dwarf goat
145.7d
Angora goat
“148.08 f
145.7d 152.6d 152.6d 152.6d 152.6d 145.7d 152.6d 159.8d 152.6d
Philippine EOat Jummaoari eoat Anglo-nubian goat Schwartzald goat (Callithriz argentata) (Cebuella pygmaea) Markhor Bharal Barbary sheep (So. Morocco) Dorset horn sheep Karakul sheep Rambouiilet sheep
‘<148.1 & .07 days” = 148.ld “150 days” = 150.0d “150.0 * .l days” = 150.0d “150.8 f .2 days” = 150.8d “154 days” = 154.0d “140-150 days” = 145.0d “about 153 days” = 153.0d “160 davs” = 160.0d “154 to 161 days” = 154.0d to 161.0d “144.1 days” = 144.ld “151.8 days” = 151.8d “143 to 159 days” = 143.0d to 159.0d “5 months” = 152.2d “about 150 davs” = 150.0d “156 days (2 &ass) = 156.0d
152.6d 152.6d 152.6d 152.6d 152.6d 159.8d 175.2d 145.7d 145.7d
159.8d 132.9d 145.7d
159.8d
Argali, Arkar Mouflon sheen Common marmoset, (Cullithrix jacchus) (Cullimico goeldii) Night monkey, (A&us trivergatus) Rhesus monkey, (Macaca radiata) Rhesus monkey, ‘Macaca silenus) sheep Hybrid marmoset, : C. penicillate, 7. jacchzls) saddle-back tamarin, ‘Saguinus fuscicollis) saddle-back tamarin, :Saguinus fuscicollis) Celebes black ape, :Cynopithecus 2. niger) Celebes black ape, 1Cynopithecus n. niger
7-r
Published
145.7d 145.7d 145.7d 145.7d
145.7d 152.6d 145.7d
*These are
= Success. F = Failure (see Section 5.1.1).
First Event
225
“145 days” = “147 davs” = “146 dais” = “146.5 days”
145.0d 147.0d 146.Od = 146.5d
.09 days” = 148.ld
“150-160 days” (‘150-153 days” = 151.5d “162 days” “173-183 days” =173.0 to 183.0d 148.9 days” ,145 days” (1 case) = 145.0d. 146 days” (1 cssej = 146.0d, 125 davs” = 125.0d.* 159 days” (1 case) = 159.0d 134-140 or more” = 134.0 to 140.0d 149 days” (1 case) = 149.0d, 157 days” (1 case) = 157.Od, ,163 days” (1 case) = 163.0d 160 to 165 days” = 160.0d to 165.0d
.Bimodal? SBimodal? lBimodal? lBimodai? *Perhaps peak also at 152.6d. *Third case anothor species? Third case seems doubful.
S,F Refs **
A. B. CLYMER
226 Table Al.
Continued.
Comparision
of event times with reported gestation
periods.
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
l:l Event
/
Applicable
SW=
Name
Common
Name
159.8d
Loris, (Loris tardigradus grandis)
152.6d 159.8d
Saki, (Pith&a) Rhesus monkey, (Macaca) Goat Ursine black-and-white colobus, (Colobus p. polykomos)
152.6d 145.7d
167.3d 139.ld
Indian langur Collared peccary, (Tayassu. tajaczl) Collared peccary, (Tayassu tajacu) a lemur, (Hapalemur griseus Link) Black lemur Slender loris Squirrel monkey,
145.7d 159.8d 152.6d 167.3d 167.3d
(Saimiri) 159.8d
Japanese monkey
1Crab-eating macaque
167.3d
Pig-tailed
152.6d
macaque
Bonnet macaque
152.6d
Sacred baboon
167.3d
Proboscis monkey, (Nasalis larva&s) Black bear
152.6d 220.7d
Grizzly bear, ( UTSUS howibilis Ord) 1
152.6d 159.8d
1Manatee 1Musk deer
fnterpretation
Gestation
and
Data
Comments*
(Latin Name)
to Species
159.8d
Published
(
“160-166 days” “166-169 days” “175 davs” “approx. 150 days” = 150.0d “162-164 days” =162.0d to 164.0d “150.8 days” “147 days” (1 case) = 147.0d “154 “169 “177 “178
days” days” days” da&
(1 (1 (1 (1
case) case) case) casej
= = = =
154.0d 169.0d 177.0d 178.0d
“168 days” = 168.0d “142 days” (1 case) = 142.0d “142-149 days” = 145.5d “160 days” = 160.0d “about 5 months” = 152.2d “171 days” = 171.0d “168-182 days” = 168.0d-182.0d
159.8d 167.3d 175.2d 152.0d 159.8d 167.3d 152.6d 145.7d 152.6d 167.3d 175.2d 175.2d 167.3d 139.ld
s s s
WI
F
[211 WI
F
[38) iI91
cf 145.7d
s
Kw
cf 159.8d
s
[71
cf 152.6d cf 167.3d cf 167.3d
s
cf cf cf cf cf cf cf cf cf cf cf cf cf cf
cf 183.5dT
“Mode 161.3 days” = 161.3d “5-6 months” = 152.2d and 182.6d 1“160 to 170 days” = 160.0d to l+O.Od “about 170 days” = 170.0d “171 days” (1 case) = 171.0d “153 days” (1 case) = 153.0d “166 days” (1 case) = 166.0d “169 days” (1 case) = 169.0d “range 154 to 183 days” =154.0d to 183.0d “about 166 days” = 166.0d
cf cf cf cf cf cf cf cf cf cf cf cf cf
(17 cases) “151 to 177 days” = 151.0d to 177.0d “spread evenly’ “216 days” (1 case) = 216.0d “245 days” (1 case) = 245.0d “258 davs” (1 case1 = 258.0d I -_I\-I “at least 152 days” = 152.0d 1“160 days” = 160.0d
cf 152.6d cf 175.2d* cf 220.7d cf 242.0d cf 253.4d* cf 152.6d cf 159.8
Possible peak also at 175.2d. $0 ne at 5 peaks? *Perhaps peak also at 159.8d. *Perhaps peaks also at 159.8d, 167.3d 175.2d. *Perhaps peak also 167.3d. *Perhaps peak also 231.ld.
S,F Refs. **
159.8dt 152.6d 183.5d 159.8d 167.3d 167.3d 167.3d l52..6d 167.3d 167.3d. 152.6d 183.5d’ 167.3d
F F
F
s
s S s
iI51 [191
F
s
F
s
s s s s
s F
F F S
--ST
s S s
Jl_ [71 WI [71
[71 [71 171
[71
s
7,211
s s
[71
F
(71
F -
F
s s-
[71 [71
Timetable Table Al.
Continued.
Comparision
of Life
227
of event times with reported gestation periods.
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
First Event
Published
Interpretation and
Time Applicable
Common Name
Gestation
to Species
(Latin Name)
Data
152.6d
“5 to 6 months”
152.6d
Blackbuck,
= 152.2d to 182.6d “5 to 6 months”
cf 183.5dt cf 152.6d
152.6d
Indian antelope (Gazelle dama Pallas)
= 152.2d to 182.8d “5 months” = 152.2d “158-166 days” = 158.0 to 166.Od “150 to 160 days” = 150.0d to 160.0d “165 to 170 days” = 167.5d “171 to 175 days” = 172.5d “170 to 174 days” = 172.0d “171 days” (1 case) = 171.0d “180 to 210 days” = 180.d to 21O.Od “6 months” = 182.6d “6 months” = 182.6d “6 months” = 182.6d “about 180 davs” = 180.0d “6 months” = 182.6d “6 months” = 182.6d
cf 182.5df cf 152.6d cf 159.8 cf 167.3d cf 152.6d cf 159.8d cf 167.3d
159.8d 152.6d
Talapoin, (Miopithecus Chamois
167.3d
Ibex
175.2d 175.2d 167.3d
Wart hog Dik-dik Impala
183.5d
Impala
183.5d 183.5d 183.5d 183.5d 183.5d 183.5d 175.2d 183.5d 183.5d 183.5d 192.ld 192.ld 183.5d 183.5d 183.5d 183.5d 167.3d 167.3d 192.ld 183.5d 192.2d 201.2d
talapoin)
Chiru. Tibetan antelooe Goral Tahr Bighorn 1Urial 1Howler monkey, (Alouatta) _ ) Mangabey, 1I\--Cercorebus1-, Weeping capuchin Squirrel monkey, Titi Chacma baboon, (Papio) Langur Giant anteater, Brazil Honey badger, Rate1 Hanglu, in Kashmir Hanglu Four-horned Antelope Springbok Hamadryss baboon Potto, (Lotis Perodicticus potto) (Genus Tar&s) Slow Lot%, 1(Nycticebus coucang) 1Grizzly bear,
( Ursus) 175.2d
1Slow Loris
I“174-175 days” = 174.5d
cf 175.2d cf 175.2d cf 167.3d cf 183.5d cf 210.7d. cf cf cf cf cf cf
183.5d 183.5d 183.5d 183.5d 183.5d 183.5d
cf 175.2d
I “about 6 months” = 182.6d “6 months” = 182.6d “184 to 193 days” =184.0d to 193.0d (14 cases) “196 days” (1 case) = 196.0d “190 days” = 190.0d “about 6 months” = 182.6d “6 months” = 182.6d “183 days” = (London Zoo) =183.0d “6 months” = 182.6d “about 171 days” = 171.0d “average 170 days” = 171.0d “193 days”
cf 183.5d cf 167.3d* cf 167.3d* cf 192.ld
“approx 6 months” = 182.6d “averaged 192.2 days”
cf 183.5d cf 192.2d
1“6.5-7 months” I= 197.8d-213.ld 1“174 days” = 174.0d
IPerhaps 3 other peaks in between. aPerhaps 3 other peaks in between. *Perhaps peak also at 192.ld and 201.2d. lBimodal? *Bimodal?
KM 19:6-B-P
cf 152.6d
Kob
cf cf cf cf cf cf cf cf cf
183.5d 183.5d 183.5d 192.ld 192.ld 192.ld 183.5d 183.5d 183.5d
cf 201.2d cf 210.7d cf 175.2d
W Hefs. **
-
S
s
s S s -
-S -S -F S s F -F F F S s s s F S s -
171 (71 [71 WI 171 [71 [71 [71 [71 171 [71 [71 [71 [71 Jl_ Pll
S
WI
S
(71 [71 [71
s-
S s F
S
Jl_ [7) [71 (71 [71
-S -F -F S
[71 [71 [401 WI
ss-
ss s-
S
S
[211 [411
F
[71 Jl_
A. B. Table Al.
Continued.
Comparision
CLYMER
of event times with reported gestation
periods.
*These are
events ages closest to published gestation data. l*S = Success, F = Failure (see Section 5.1.1).
First Species Name
Event
Common
Applicable
Name
Interpretation
Gestation
and
Data
(Latin Name)
to Species 175.2d
Vervet monkey, (Cerco-pithecus Pygerythrzls)
183.5d
Vervet monkey,
183.5d 210.7d 210.7d 210.7d 210.7d 210.7d 210.7d 201.2d
220.7d
(Cerco-pithecus Pygerythru) Indian fruit bat (2 species) Barbary ape Grivet monkey Sloth bear Hvaena. in India 1Aardvark 1Asiatic two-horned rhinoceros Pygmy hippopotamus ,I
,
210.7d
Mandrill, (Mandrillus sphinx L.) Spotted deer, Chital
201.2d
Mule deer
201.2d
White tailed deer, Virginia deer Greater kudu Harnessed bushbok Bear, Dublin Zoo (Damaliscus Korriaum
210.7d 220.7d 210.7d 210.7d
242.0d 220.7d 210.7d 210.7d 210.7d 210.7d 242.0d 220.7d 23l.ld
,175 days” (1 case) = 175.0 ‘178 days” (1 case) = 178.0 ‘203 days” (1 case) = 203.0 ‘180-213 days” I 180.0 to 213.Od ,about 6 months” = :about 210 days” = about 7 months” = ,about 7 months” = ,7 months” = 213.ld ,about 7 months” = ,7 months” = 213.ld
Ringed seal Siamang, (Symphalangus syndactylus) Reindeer, (Rangifer tarandus) Steinbok Lechwe Porcuoine I Leooard seal ITree hyrax 1Rock dsssie
[Perhaps peak also at 192.ld and 201.2d. I FBimodaI. *Perhaps 3 peaks between. *Perhaps peak at 220.7d. * Bimodal? &Perhaps peak also at 210.7d.
S,F Refs. **
Comments*
182.6d 2lO.Od 213.ld 213.ld 213.ld
,201 to 210 days” = 201.0d to 210.0d ‘184 days.” ,230 days” :9-10 months” = !73.9d-304.4d ‘220 and 270 days” = 220.0d and 270.0d ,7 to 7.5 months” = 213.ld to 228.3d l99 to 207 days” =199.0d to 207.0d (5 cases) :197 to 222 days” =197.0d to 222.0d ‘about 214 days” = 214.0d
Ooilbv
T
Published
Time
‘214 to 225 days” = 219.5d ‘7 months” = 213.ld ‘about 214 days” = 214.0d ‘214 days” = 214.0d ‘7 months” = 213.ld ‘about 240 days” = 240.0d 10 births, London Zoo) ‘8 months” = 243.5d (223-239 days” : 223.0d-239.0d 7-8 months” : 213.1-243.5d 7 months” = 213.0d 7 months” = 213.0d 210 days” about 8 months” = 243.5d 225 days” = 225.0d 7.5 months” = 228.3d
cf 220.7d*
IS
Timetable Table Al.
Continued.
Comparision
of Life
229
of event times with reported gestation periods.
*These are
events ages closest to published gestation data. l*S = Success, F = Failure (see Section 5.1.1).
Common Name
= 225.0d to 257.0d
“255 days” = 225.0d
253.4d
Orangutan,
(Pongo)
242.0d 242.0d 253.4d
Serow Musk ox Wooly monkey, (Lagothiz cana Geofloy)
“249 days” = 249.0d “251 days” = 251.0d “255 days” = 255.0d 250 to ss many as 288 days* “8 months” = 243.5d “8 months” = 243.5d “8 months and 10 days” = 253.5d
._ Perhaps peaks at 220.7d and 231.ld also. IPerhaps peaks at 220.7d and 231.ld. *Perhaps peaks at 265.4, 277.7d.
cf cf cf cf cf cf
253.4d 253.4d 291.0d 242.0d 242.0d 253.4d
S F S
PI
E
;;
S
(71
230
A. B. CLYMER Table Al.
Continued.
Comparision
of event times with reported gestation
periods,
*These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
Common
Name
“8 to 9 months”
= 240.0d to 270.0d “9 to 10 months”
= 258.7d to 273.9d
“about 285 days” = 285.0d
Timetable of Life Table Al.
Continued.
Comparision of event times with reported gestation periods.
231 *These are
events ages closest to published gestation data. **S = Success, F = Failure (see Section 5.1.1).
Published Common Name
Perhaps peak also at 277.9 and 291.0 days.
Gestation
232
A. B. CLYMER Table Al.
Continued.
Comparision of event times with reported gestation periods.
*These are
events ages closest to published gestation data. “‘S = Success, F = Failure (see Section 5.1.1).
Published Common Name
Gestation
389.9 h 2.1 days”
Timetable of Life Table Al.
Continued.
Comparision
of event times with reported
events ages closest to published gestation data.
Common Name
“S
233 gestation
periods.
*These are
= Success, F = Failure (see Section 5.1.1).
Gestation
= 607.0d-641.Od “25 cases 17-24 months”
A considerable number of unselected gestation data have been collected in the large table above. These data include both published data and for each the nearest event age from the formula. By counting successes and failures, one would expect to find them nearly equal, as in the analogy of heads and tails of a coin. Quite surprisingly, however, the ratio of successes and failures is very highly improbable. For example, in the first 103 species in the table there are 85 successes and 18 failures, giving 83% success (versus the 50% expected a priori). This outcome is so improbable that it strongly supports the formula. The percentage success decreases slowly with increase of age of species, dropping to about 60% for the largest reported event ages. That is still remarkably improbable. The reason for the decrease is discussed in Section 5.2. It is problematical to determine how to deal with data given as a range. If the mean is used, then all ranges equivalent to even multiples of 1.0472 will automatically give a failure. On the other hand, if the ends of the range are used as two data, it is likely that each will be a success. The latter alternative was used. This might seem to be cheating by taking advantage of a hypothesis to improve the fit. However, if this method is not used, the difference in results is small enough to make the result still statistically astonishing. The following are references cited in Table Al.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
F. Sunquist, Of quells and quokkss, International Wildlife (July/Aug), 12-16 (1991). A.G. Lyne, Gestation period and birth in the marsupial Zsoodon macrourus, Austr. J. Zool. 22 (3), 303-309 (1974). Stodart (1966). Hughes (1962). Reynolds (1952). D. Ferrigno, The Virginia opossum, New Jersey Outdoors (May/June), 36-37 (1984). S.A. Asdell, Patterns of Mammalian Reproduction, Cornell Univ. Press, Ithaca, NY, (1964). M. Griffiths, The platypus, Sci. Amer. 258, 84-91 (1988). MacLusky and Naftolin. P. Vogel, Comparative investigations of the mode of ontogenesis of domestic soricidae, Rev. Sulsse Zool. 79 (4) 1201-1332 (1973). McAllen and Dickman (1986). HA. Griszell, A study of the southern woodchuck, Marmota monax monax, American Midland Natumlist 53 (2), 257-293 (1955). G.B. Sharman and P.E. Pilton, The life history and reproduction of the red kangaroo (Megaleia n&a), Proc. Zool. Sot. London 142 (Part l), 29-48 (January 1964). D.A. Conner, Life in a rockpile, Natural History (June), 51-59 (1983). Lush, Animal Breeding Plans, Collegiate Press, Ames, Iowa, (1937). D. Mackenzie and C. Shwarek, The Eastern Chipmonk, New Jersey Outdoors (Fall), 64 (1992).
234
A. B. CLYMER
17.
Hoogland, Infanticide in prairie dogs, lactating females kill offspring of close kin, Science 230, 1037ff (No_ vember 1985). B. Morris, Some observations on the breeding season of the hedgehog and the rearing and handling of the young, Proc. Zool. Sot. London 136, 201-206 (1961). J.J.C. Mallinson, Establishing mammal gestation periods at the Jersey Zoological Park, In International Zoo Yearbook, Husbandry, pp. 184-187, (1974). Marshall and Jolly. N.E. King and G. Mitchell, Breeding primates in zoos, In Comparative Primate Biology, Volume 2B, Behavior, Cognition and Motivation, pp. 219-261, A.R. Liss, New York, (1986). (unknown source). H. Ikeda, Old dogs, new treks, Natural History (August), 38-45 (1986). Wackemagel (1968). Eisenberg (1970). Goldman (1950). J. Scott, The leopard’s tale, SWARA 8 (6), 8-12 (1985). Baker (1984). C.P. Kofron, Seasonal reproduction of the springhare (Pedetes capensis) in Southeastern Zimbabwe, Afr. J. Ecol. 25, 185-194 (1987). San Diego Zoo signs. Bourliere (1967). P.G. Crawshaw, Top cat in a vast Brazilian marsh, Animal Kingdom (September/October), 12-19 (1987). Houston and Prestwich. Sign at the San Diego Wild Animal Park. P.L Krohn, The duration of pregnancy in rhesus monkeys Macaca mulatta, J. Zool. Sot. London 134, 595-599 (1960). Wolfe et al. (1972). Howard. Harms (1956). Sowls. Yerkes (1953). M.K. Izard, K.A. Weisenceel and R.L. Ange, Reproduction in the slow loris (Nycticebus coucang), Amer. J. Prim. 16, 331-339 (1988). Napier and Napier (1967). Gilbert, Some not-too-close encounters with a cactus that walks, Smithsonian 23, 56-67 (1992). Klingel, Sizing up a heavyweight, International Wildlife 21 (5), 4-10 (1991). C.W. Wemmer, Sociology and management, In The Biology and Management of an Extinct Species, Pere David’s Deer, (Edited by Beck and Wemmer), Noyes Publications, New Jersey, (1983). Bergernd (1983). Signs in San Diego Wild Animal Park, Columbus Zoo. unknown (1976). T. Bedell, There’s a whale, there’s a whale, Skylines, 32-33, 17-20 (September 1986). D.A. Glockner-Ferrari, Humpback whales, up close and personal, Animal Kingdom (November/December), 38-49 (1986). Tapir Res. Inst. (1971). T.V. Program. The Diagram Group, Comparisons, pp. 172-173, St. Martin’s Press, New York, (1980). Bronx Zoo sign. S.N. Austad, The adaptable opossum, Sci. Amer. 258 (2), 98-104 (February 1988).
18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.
APPENDIX B GLOSSARY Ambient temperature: Asymptote: Bimodal: Differential equation: Enthalpy: Envelope: Event : Event age: Failure:
the temperature in the vicinity of an object of concern. a vertical straight line at which a curve goes to infinity. a frequency distribution with two peaks. an equation in which the unknown appears in a rate of change term. the amount of heat in an object. a smooth curve which kisses a wiggly curve at several points. a sudden start or stop of some process involved in development or later life of an organism. the age, post-fertilization, at which an event can occur according to the formula or series. a reported age at which an event occurred which is more than 1.18% away from the nearest event age in the series.
Timetable of Life Frequency distribution: Geometric series: Histogram: Integer: Logarithmic mRNA:
time scale:
Molecule: Multimodality: Mutation: Mutation space: Quantum numbers:
Series: Simulation: Success: The formula: Thermal capacity: Timetable:
235
a graph, histogram or table showing how many items (e.g., species) there are in each class interval (e.g., range of ages). each member of the series is a certain constant times the immediate past member of the series. a stair-stepped plot of a frequency distribution using horizontal line segments between class boundaries. whole number. a scale on which logarithms of a variable are plotted. messenger ribonucleic acid, produced on a chromosome by a hypothetical slow process making it a timer, which directs the manufacture of a protein in a ribosome outside the nucleus of a cell. (as in “molecule building”) a linear molecule (mRNA), the completion of whose building constitutes a timing signal. the property of having several peaks in a frequency distribution. as used here, any change in a gene (mRNA) giving a new event age. a hypothetical space whose dimensions are all the parameters of possible mutations (one quantum number per gene?). integers associated with particular states of a system, such as possible orbits of an electron around an atom, or possible dimensions after growth of a particular tissue. a geometric series of event ages given by the formula. the process of solving a given mathematical model on a computer in a number of cases of concern. a reported age at which an event occurred which is closer than l.lS% to the nearest event age in the series. one of several equivalent forms of equation yielding the event ages, namely, Aj+l = l.O472Aj, or Aj = (l.O472)j, or 1ogAj = j log 1.0472. the amount of heat required to heat an object one degree. a table listing events and the time of occurrence of each.
APPENDIX C A LOOK BACK 1. INTRODUCTION The appendix is about the author’s struggle in the research and its “marketing.” The story is an account of one unaffiliated and unanointed man innocently bringing his work before his scientific peers in search of feedback, which is a highly discouraging process. He allowed himself to be silenced then for 19 years. That is cowardice. Then he wrote three papers in an attempt to attract attention. Nothing resulted. There followed several more years of quiet cowardice, then this paper. 2. HOW
IT GOT
STARTED
It is educational to look into how a research project got started. First it is desirable to get out of the way the mistaken idea that research proceeds from nothing by deliberate rational thought about what would be the best question to address. For example, John Wheeler has advised: “In any field, find the strangest thing, and then explore it.” Similarly, Steven Jay Gould has said: “You might almost define a good scientist as a person with the horse sense to discern the largest answerable question-and to shun useless issues t,hat sound bigger,” [88]. This ploy might be good, but it was not used in this case. So big a problem was not originally sought. In college, the author was urged to apply mathematics to biology as a part of his career. It was widely felt by mathematicians then that biology was ripe for “strengthening” by mathematics. At that time, the author made a mental note to try. In 1966, the author read a paper by Moorees [13] in which the use of the logarithm of conceptual age was mentioned as being a useful modified “time scale” variable for developmental data presentation. That could have started him to think in terms of events equally spaced on a logarithmic time scale, or the equivalent in terms of a geometric series in regular time.
A. B.
236
In January
CLYMER
1967, the author was entertaining the conceptual scheme of a log spiral with radial
lines every 36 degrees. Every turn of the spiral represented a doubling of age. The age increase between radial lines was a factor equal to the twelfth root of two. Every intersection of the spiral with a radial line stood for an event in the development of the individual whose life was thus charted. The author believed for a while that the events on a particular radial line were of the same type, in some undefined sense, but this frill was abandoned for lack of evidence. At this point, the author first went into print [89], using what few kinds of data he had found by then. The author was already pursuing science as defined by Pritsker [12]: “Science is nothing else than the search to discover unity in the wild variety of nature.. .” The next attempted paper was an article submitted to Science [53]. It was rejected. Then a paper was submitted to the Journal of Theoretical Biology [go]. It too was rejected. 3. THE RESEARCH 3.1.
Tools
Used
The author had a limited set of tools with which to work. He had the biological and medical literature, mathematical analytical tools, and a full set of conceptual schemes. He had no funding, no equipment, no laboratory or field skill or knowledge, no collaborators (all candidates ran, as from a leper), no biological knowledge (except from a high school course), no statistical expertise (except from one college course), and no connections. These limitations of tools naturally limited the types of research he could perform. Nevertheless, significant work was done, regardless of whether it all has merit. Thus, an amateur in biology, unequipped and unplaced for professional work, can do work deservingsome notice. 3.2.
The Roles of Luck
It is humbling to keep in mind that “Really sharp and noteworthy accomplishments require luck as well as hard work” (M. Freedman, U.S.C.). By pure luck, Asdell’s book full of gestation data had been published in 1964, just three years before the author needed those data. Those data were absolutely crucial, because the only other data on hand then were of little value [89]. There is perhaps an analogy with the excellent planetary measurements made by Tycho Brahe that enabled Johannes Kepler to discover and establish his laws. Similarly, by luck the author happened to see a tree diagram of the evolution of primates. That enabled him to make an easy test: did the number of event ages per event of a species correlate with the stated rate of evolution of that species? The answer was affirmative, thus suggesting a generalization to a hypothesis covering all species. By luck, the author had had graduate courses in molecular vibration and rotation. This background provided some of the concepts in the molecule building theory. By luck, the author had had a job (1942-1945) in which he was taught the skills of numerical differencing and smoothing. That is just what was needed in order to see the geometric series in the data. By luck, the author came across some data for the effect of temperature upon event ages. At first the only apparent relevance was to the errors in reported event age data, but eventually the greater importance of thermal effects was seen. 3.3. The Research Work The research work required a considerable amount of toil. Searches for data had to be performed, which required an enormous amount of reading in spite of some degree of computer automation of the task. Then the relevant material had to be copied and filed.
Timetable of Life
237
Given these hard-won data, it was necessary to analyze them. The purposes of the analyses were to detect error patterns, to compare event ages for related species, and to try to identify the series signal buried in the noise. Actually, the foregoing steps were organized into many successive campaigns with batches of data, going through the entire process for each batch. The author is able to agree heartily with Gould that “Scientific discovery. . . is a reciprocal interaction between a multifarious and confusing nature and a mind sufficiently receptive (as many are not) to extract a weak but sensible pattern from the prevailing noise.” The fact of the noise and the fact that the relationship was logarithmic together insured that the secret was kept from life scientists by nature. Occasional one-of-a-kind analyses were required. One was the listing (see Table 7) of the range-mean ratio of gestation data, which revealed the multiplicity of peaks in the frequency distribution for most species. Until then, the author had regarded the ranges of values as reflecting errors. What had seemed to be unforgivably large errors quickly became precise and meaningful structure! The given data suddenly improved greatly in apparent quality! Likewise, the errors of fit of the series to the reported event age data had to be calculated and a histogram prepared. This effort led to the conclusion that the errors are approximately Gaussian (actually lognormal because of the logarithmic time scale). The greatest task was preparing and maintaining the large table in Appendix A. Unfortunately, it could not previously be published because of its size. Therefore, the author agrees with Gould [91]: “Good science may require genius and imagination.. .but never forget that new conclusions are the fruit of hard empirical work as well.. .” Likewise, Newton is said to have discovered his revolutionary findings by thinking about them without ceasing. The author has had many such long periods caught up in questions. The intense emotions associated with creating a scientific theory are not qualitatively different from those of creating a work of art. Each is a network of problem solvings and tentative decisions. Throughout the work the author had to guard against unintentional fraud. It was easy to eschew creating or changing data, but it was difficult to remember to include bodies of data that did not agree very well with the hypothesis. Finally, by 1986 the author had enough courage, new data, and new ideas to make it desirable to publish. The publication of 1967, [89], had been highly preliminary; it was less than professional. It served no purpose but to establish priority for the format of the formula and for the concept of development. Three papers in three successive years were published [l-3]. Those papers were presented to and published by the Society for Computer Simulation, the author reasoning that his peers would be more receptive than the editors of Science. Wrong. There was a nearly total lack of persons in the audiences or among the readers who knew enough biology to understand the subject and enough system science to understand the presentation. The editor of this journal was one of the few. 4. THE
FINDINGS
In this section, the author offers some of his notions about the contribution. There are several possibly notable aspects of the series which resulted from the foregoing work: 1. It has the simplicity of a law that usually turns out to be necessary for success for a very general application. This simplicity applies to each form: the geometric series, the recursion formula, and the logarithmic equal-spacing form. 2. It introduces an unprecedented degree of precision into life science in dealing with time. 3. The series fits many important natural constants, such as: 24.01 hrs (one day), 6.9424 d (one week), 27.695 d (one lunar month), and 366.5 d (one solar year). It fits also many biorhythms (if not all). A two-parameter formula should not a priori fit so many points. Hence, these fits are quite surprising.
A. B. CLYMER
238
4. The series offers a remarkable condensation of the data of chrontology: event ages fit all events (thousands?)
a few hundred
in all species (millions), i.e., billions of species-event
combinations. 5. The errors of fit for all events-and species for which data were available are remarkably small, with some glaring exceptions. The fault seems usually to lie with the data more than with the formula for the event age series. 6. The series should be a nice help in simulating organisms. 7. According to Bronowski [92], “Science is . . . a way of giving order and therefore unity and intelligibility to the facts of nature.” The series is a candidate to be a part of this science. Given the series, it was humanly inevitable that questions would be asked which would produce the theory to explain the series. The author followed this road and then had another success experience with a theory. (At least it still looks like a success experience to the author.) The unlikelihood of all of this success has been pointed out by Ward: “. . .rarely, a scientist finds a brilliant answer to the very problem he set out to solve, and then further finds to his delight that that answer holds implications of deeper significance than the original problem seemed to suggest. That might be called serendipity in spades.” In the author’s case, there seems to have been a lot of “serendipity in spades,” if some of the hypotheses can be validated by other investigators. The theory, like the series, has many unusual aspects: 1. It sheds a new light on the processes of development, evolution, and life itself. 2. Far reaching, it relates many diverse areas. 3. It has the audacity to imply (by hypothesis) that a molecular stochastic process based on random thermal excitation can constitute a precise timer. 4. The theory contains some unifying conceptual frameworks such as species timetables, marching envelopes of event ages in evolution, the concept of the starting and stopping events of processes, synchronization and quantization. 5. The theory has enormous generality of scope, embracing all events over the lifetimes of all species (those having sexual reproduction at least). The theory also has aspects on levels ranging from molecular to global. The theory can be drawn as a network in which the pieces (hypotheses) of the theory are directly or indirectly connected. A question is whether these connections make the hypotheses any more validated than if they stood in isolation. 5. TESTS
OF THE WORK
The literature yields many criteria for a theory to be good, such as: 1. How much can it explain [93]? The theory herein seems to offer explanations over a wide range of questions. 2. How good are its predictions [94]? It is too early to answer this question. Only the author has tested it. A few predictions are stated herein. Crick’s statement is “A good theory makes not only predictions, but surprising predictions that then turn out to be true.” 3. Is the idea completely crazy (Bohr)? Some scientists are ready to pin this label on any theory that involves cycles, rhythms, overly simple mathematics, etc., but the idea of a universal list of event ages is completely crazy to almost anyone. Moreover, any chemical kineticist knows that biochemical reactions take place in milliseconds, not minutes to years, so the proposed molecule building process is completely crazy. 4. How many empirical investigations can it trigger [95]? The event ages of any event in any species can be determined by observation or experiment. Age relationships in an ecosystem can be studied. Quantization can be investigated in paleontology. The effects of temperature upon observed event ages can be determined.
Timetable of Life
239
5. Does it explain several large and independent classes of facts [96]? The formula accounts for the ages published for most of the thousand or so of observed events tested thus far. It had not been realized formerly that these large classes of facts (data) are in fact not independent but rather share membership in a smallish clan. The explanations of development and evolution afforded by the theory appear to be useful, although not complete explanations. The idea of multimodality of event ages has shed much light on the published data. 6. Has testing been done down to minute detail [97]? The most thorough testing done to date is Table Al in Appendix A. The results indicate beyond any doubt that gestation data are numerically accounted for by the formula herein. Additional testing is shown in the cameo studies in Section 5. 6. ACCEPTANCE
OF THE WORK
One should keep in mind the fact that “One of the great paradoxes of the history of technology is that the greatest progress often comes in unexpected ways.” Belief cannot be stretched in a continuous manner. It acts as if there were static friction in the system which must be overcome before there can be any change. A model of belief could be made by minor modification of the author’s model of abuse [98]. To the best of the author’s knowledge, none of the three papers [l-3] is referenced anywhere. Moreover, the author received very little informal feedback from any of the papers. The lack of wide interest in the author’s series kept him trapped in problems related to it. Had it been accepted early, he would have been free to look into entirely different problems. Thus, the need to keep trying to “sell” his earlier ideas motivated half-hearted intermittent further research on matters related to the original question, causing the author to do work he was less and less well fitted for, such as molecular biology or evolution, to try to bolster his earlier theory. It is difficult to say whether the course actually taken will prove to have been the best in the long run. The author has had the benefit of good advice regarding how to 2ake” the slings and arrows. Carey [99] urges the researcher to keep his hopes and expectations low: “. . .do not expect to be hailed as a hero when you make your great discovery. More likely you will be a ratbagmaybe failed by your examiners. Your statistics, or your observations, or your literature study, or something else will be patently deficient. Do not doubt that in our enlightened age the really important advances are and will be rejected more often than acclaimed.” Equally dire is the warning by Huang: “Once you let your idea out, it can go through several phases: First your idea is ignored; then people think it’s impossible; then impractical; then that it’s not really that original; and then that they have had that same idea themselves.” Similarly, as Arthur Koestler has pointed out, “The more original the discovery, the more obvious it seems afterwards.” In the same vein Sir Arthur Thomson has written [loo] “It seems to be a fact, though not a cheerful fact, that the recognition of a scientific conclusion depends very largely on the intellectual preparedness of the time.” Apparently the author has again been many years ahead, trying in vain to “sell” his ideas. It is the story of his life. Regardless of one’s understanding of these psychological aspects, however, lack of acceptance of one’s work is the cause of long and deep despair, as many scientists have attested. 7. THE
PAPER
IN THE AUTHOR’S
VIEW
In summary, attend the theory presented by Walter Bagenhot [loll: “One of the greatest pains to human nature is the pain of a new idea. It is, as common people say, so ‘upsetting’ it makes you think that, after all, your favourite notions may be wrong, your firmest beliefs ill-founded; it is certain that till now there was no place allotted in your mind to the new and startling inhabitant, and now that it has conquered an entrance, you do not at once see which of your old
240
A. B. CLYMER
ideas it will or will not turn out, with which of them it can be reconciled, and with which it is at essential enmity. Naturally, therefore, common men hate a new idea, and are disposed more or less to ill-treat the original man who brings it.” The ideal attitude is detachment. However, any author’s assessment of his own work is to be viewed with suspicion. The author’s view of the paper is of its contents and findings, which he has discussed in Section 5 of this Appendix. Of course he feels that it is transparently clear to the reader. However, he is aware of the truth in Windhorst’s [102] remarks: “When the great innovation appears, it will almost certainly be in a muddled, incomplete, and confusing form. To the discoverer himself it will be only half understood, to everybody else it will be a mystery.” 8. FURTHER
WORK
Much further work seems to the author to be highly desirable.
Some of the possible investiga-
tions are: 1. Analytical investigations, such as determination of the best-fitting constants for the formula by iterative least squares; simulations of many types. 2. Experiments with big samples, temperature control and other necessary refinements, blink comparators of images to seek the time something first appeared, etc. Challenge the formula with data that are much more precisely determined. 3. Checks of the data which the author has questioned or which have large errors; checks that the reader could make easily. 4. Searches for data for types of event not now analyzable. Get data capable of resolving multiple peaks in frequency distributions of observed event ages. 5. Extension of the work to earlier event times. 6. Extension of the work to species that do not use sexual reproduction. 7. Searches for the frequency distributions of event ages now given only as averages (means) or ranges. 8. More applications to medicine need to be conceived and pursued, including pediatrics, gerontology, and pharmacology, as well as general medicine and research in specialized topics. 9. Measurement of thermal effects upon crucial event ages of concern in connection with global warming. 10. Investigation of the limits of validity of the theory. 11. Spot-checks of the author’s work. 12. Use of advanced microscopy techniques to seek predicted behaviors on the molecular level. 13. Appendix A contains many criticisms, suggestions, and research ideas for others interested in gestation periods to investigate. 14. Get timing data for plant events. Standard texts, e.g., Thornley and Johnson [103], are not helpful for this work. Possibly there are significantly different temperatures for fastest growing of different plants, which would help florists and farmers. 15. See if it is possible to determine time of fertilization of a person or animal by noting the times of later events, enabling assignment to a specific event time subspecies. 16. New research never contemplated by the author (the most important of all, keeping in mind the advice to expect the unexpected).