Photoperiodic time measurement in the spider mite Tetranychus urticae: A novel concept

PHOTOPERIODIC MITE

Laboratoq

TIME MEASUREMENT IN THE SPIDER TETRANYCHUS URTICAE: A NOVEL CONCEPT

M. VAZ NUNES and A. VE~KMAN of Experimental Entomology. University of Amsterdam. Kruislaan 202 1098 SM Amsterdam. The Netherlands

Ahstract To explain photoperiodic induction of dlapause in the spider mite T~,trtrn!clnr.\ IWII~~LW a ncv. theoretical model was developed which took into account both the hourglass and rhythmic clcmcnts shown to be present in the photoperIodic reaction of these mites. It is emphasized that photoperiodx Induction is the result of time measurement as well as the summation and integration of a numhcr of the hypothesis that the photoperiodic clock itself is based on one or more circadian oscillators. Het-c :i direrent approach has been chosen as regards the role of the circadian system in photoperiodlsm: the possibility. previously put forward by other authors. that some aspect of the photoperiodic induction mechanism other than the clock is controlled by the circadian system was investigated by assuming a circadian influence on the photoperiodic counter mechanism. The derivation of this ‘hourglass timer txillator counter‘ model of photoperiodic induction in T. WI~L’LW is described and its operation demonstr,\ted on the basis of a number of diel and nondiel photoperiods. with and without light interruptions. Kc,\. Cliwd tmtc\-.- Photoperiodlsm,

diapause.

circadian

rhythm\.

theoretical

model. spider

mites

SAUNUERS. 1975. 1978a, 1979). double oscillators (TYSHCHENKO. 1966: PITTENDRIGH. 1972. 1981: A GREATvariety of theoretical models have been proSAUNDERS. 1974: BECK, 1974a.b, 1980) and the composed to explain photoperiodic time measurement in bined operation of an hourglass and an oscillator insects and mites. but essentially these models differ in (HAMNER, 1969: TR~MAX. 1971). However. with few only two criteria. The first is whether time measureexceptions these models have not been elaborated far ment is executed by an hourglass type mechanism or enough to allow predictions to be made of the photoin any conceivable light/dark response by an oscillatory type mechanism, and the second is periodic whether the mechanism consists of one system or of regime or for different species of insects and mites. For instance. the newly developed version of PITTFNtwo component systems. In single systems light has to IIRIGH’S (I981 ) internal coincidence model does not coincide with a specific light-sensitive phase or point express clearly which phase relationships between of time of the time measuring mechanism for inducpacemaker and slave oscillator will result in diapause tion to take place; for this kind of interaction between induction and which phase relationships will lead to light and the internal timing mechanism the name ‘external coincidence’ was coined by PITTENDRIGH continuous development. As a consequence +plication of this model to specific experimental results. (1972). Double mechanisms are conceived to work e.g. night interruption experiments with spider mites. according to ‘internal coincidence’. as this concept is not yet feasible. was named by PITTENDRIGH( 1972). In internal coinciSo far we have tried to explain photoperiodic time dence induction depends solely on the interaction measurement in the spider mite Trfrc~~l&t.s ~rrric~cc~ and ‘or internal relationship of both systems constitutby applying several of the most explicit modsls of ing the time measuring mechanism. An important diftime measurement. ;ts developed for ferencc between external and internal coincidence is photoperiodic certain insects. to our results with mites. The ‘Dual found in the way light interacts with the mechanism: System Theory’, developed by Beck ( 1974a.b. 1980) to in internal coincidence light has only a single function timing in the moth O\rriukl (entrainment of the constituent systems), whereas in explain photoperiodic external coincidence it has two (entrainment and rulhilulia. proved to be inadequate for T. ~rric~trc,.even in regimes based on a 24 hr period (VAT N~,\rrs and Induction) (PITTENDRIGH. 1972; SAUNDERS. 1978b). VEERMAS. 1979a.b). The external coincidence model. Based on the above criteria five classes of models elaborated by SAUNDERS (1975. 1978a. 1979) to for photoperiodic time measurement are conceivable account for photoperiodic time measurement in the and all five theoretical possibilities have been flesh-fly Sarcophnya ary~ro~tornu. proved to be suitexplored to a greater or less extent by various able to explain the results of a number of experiments authors: a single hourglass (LEES. 1973. 1981). double hourglasses (BONNEMAISON.1968. 1970. 1978: TAKEDA, in both diel and nondiel light/dark cycles with 71 urticar, but failed to explain the results obtained in cer1978; VAZ NUNES and VEERMAN, 1979a.b). a single and in a vo-called tain ‘skeleton’ photoperiods oscillator (BUNNING. 1936; PITTENDRIGH. 1966; INTRODUCTION

1042

M. VAZ NUNES and A. VEERMAN

T-experiment (VAZ NUNES and VEERMAN, 1982). Furthermore. the latter model could be applied relatively successfuiiy only if some auxiliary device was incorporated which took account of the summation of photoperiodic information. but which showed definite hourglass properties. In view of the fact that none of the existing models of photoperiodic time measurement was able to explain every aspect of photoperiodic timing in T. urtiau. we chose to develop a new model which would take into account both the rhythmic (VEERMANand VAZ NLJNES,1980) and hourglass (VAZ NUNES and VEEKMAN.1982) properties indicated to be involved in photoperiodic induction in these mites. For the development of our concept of photoperiodic time measurement in T. rtrticar two points were of the utmost importance: first. the realization that photoperiodic induction is the result of two interrelated processes, namely time measurement and the summation and integration of successive photoperiodic cycles and. secondly. a reconsideration of the role of the circadian system in photoperiodic induction. Although it has been accepted for some time that the summation of photoperiodic information forms an integral part of the induction mechanism [the concept of a ‘photoperiodic counter’ (SAUNDERS. 1976b. 1981a) or ‘memory link’ (TYSHCHENKO,1977)]. few models of photoperiodic time measurement incorporated a counter mechanism. However. since the contribution of the clock and the counter cannot be determined separately but only the integrated final result is measured in the form of a percentage diapause. in our opinion any model of photoperiodic induction should account for time measurement as well as summation and integration of photoperiodic cycles. Especially in experiments using extended nights and in experiments performed at different temperatures with the same test object, the outcome may be influenced strongly by the operation of the photoperiodic counter. We. therefore. considered it justifiable to give equal weight to separate clock and counter mechanisms in our new model. Involvement of the circadian system in photoperiodic induction has been demonstrated unequivocally in so-called resonance experiments for four species of insects (SAUNDERS,1973. 1974; THIELE, 1977a; CLARET et a/., 1981) and for a mite (VEERMANand VAZ NUNES, 1980). The same technique failed to demonstrate any influence of the circadian system on the photoperiodic reaction of seven insect species (ADKISSON, 1964. 1966; PETERSONand HAMMER,1968; LEES, 1973; SKOPIK and BOWEN, 1976; TAKEDA and MASAKI, 1976; THIELE, 197713; TAKEDA. 1978). The finding of circadian variations in a photoperiodic response is commonly interpreted in terms of B~~NNING’S (1936) hypothesis, which states that photoperiodic time measurement is a function of the circadian system. However, a positive resonance effect does not irrefutably demonstrate that the photoperiodic clock itself consists of one or more circadian oscillators, but merely indicates a circadian influence on some part of the complex photoperiodic induction mechanism. It is quite conceivable that some aspect other than the clock is influenced by the circadian system, e.g. one or more of the steps involved in the further processing of the ‘output’ of the clock, or. stated otherwise. the photoperiodic

counter mechanism. In fact, this possibility has already been put forward by PITTENDRICH(1972) who emphasized that “the performance of the system will be a function of its proximity to resonance, no matter how the photoperiodic time measurement is made”. Or, in SAUNDERS’(1981 b) words. it is probable that the internal temporal disorder generated in cycles whose periodicities are far from the natural circadian period (T) affects the way in which physiological functions. including time measurement. are discharged. It is exactly this idea which we have explored in a new model for T. t~rticu~. According to this model, photoperiodic time measurement is executed by a single hourglass mechanism. not unlike the one proposed by LEES (1973. 1981) for photoperiodic induction in the aphid Mc,goirrn ric’iue: a separate mechanism which accounts for the summation of photoperiodic information is subjected to the influence of a circadian oscillation. The latter is to a great extent comparable with the photoperiodic oscillator on which SAUNDERS (1978a, 1979) based his external coincidence model for S. urg~~rostotnc~, as far as its kinetics are concerned. The model has been worked out in a mathematical form as we feel that a coherent explanation of all results obtained in photoperiodic experiments. as well as predictions of the photoperiodic response for highly diverse light/dark cycles, is best provided for by a set of rules which have been described unambiguously. In this paper, the derivation of this ‘hourglass timer-oscillator counter’ model of photoperiodic induction in T. urricue is described and its operation demonstrated on the basis of a number of diel and nondiel photoperiods, with and without light interruptions. MATERIALS

AND

METHODS

Origin and history of the strain of spider mites of T. urticur used in the experiments have been described before (VAZ NUNES and VEERMAN, 1979a). The mites are reared in the laboratory on bean plants (Pl~~eolu.s tdguris) under long-day illumination (LD 17:7). For the experiments mites were kept on detached leaf cultures of beans. Criteria for diapause in T. urticae have been described previously (VEERMAN.1977). Experimental cultures were exposed during the entire postembryonic development of the mites to a variety of light regimes at 19 k O.S~C in 26 light-proof wooden cabinets placed in an environmental chamber. Air of constant temperature and humidity was forced through the cabinets by means of small electric fans. Each cabinet was equipped with two daylight fluorescent tubes of 8 W. separated from the working space of the cabinet by a plexiglass screen and controlled by a Sodeco timer which is part of a time-programming installation capable of automatically generating all die1 and nondiel two- or fourcomponent light/dark cycles desired. Light intensity at the level of the mites varied from 500 to 700 lux. Approximately 250 mites were used in each photoperiodic treatment. The term photoperiod is used to denote the complete cycle of light and dark, the constituting phases of light and darkness being referred to as photophase

Photoperiodic

and scotophase. respectively. The following tions will be used throughout this paper: DD. LL. LD. 7.

T Zt. Ct.

Y. PRC.

abbrevia-

continuous darkness; continuous light; light/dark cycle (e.g. LD 12:12 is a cycle of 12 hr of light and I2 hr of darkness); period of the unentrained (i.e. free-running) circadian oscillation or pacemaker (hr): period of Zeitgebrr (experimental LD cycle) (hr). Zeitgeber time (hr): circadian time. A time scale measured in hours (Ct 00 Ct 24) covering one full circadian period. Ct I2 is defined arbitrarily as that phase of the oscillation at the end of a I2 hr light period when in steady-state entrainment to LD 13:12 (PITTEUDRIGH. 1965; SAt’UDI.KS. 1978X 1979): the phase relationship or phase angle between the circadian rhythm and the photoperiod: phase response curve

L,. D,. L2. Dz signify the successive photophases and scotophases of a ‘skeleton’ photoperiod.

RESL:LTS

As attempts to apply models based on one as well as two oscillators had failed as an explanation of photoperiodic time measurement in T. urficue (VAI Nr-ul-s and V~ERMAK. 1979a.b. 1982). we decided to work out another possibi!ity. first mentioned by PITTKUDRIGH(1972) and called a ‘resonance’ model by SAIINDERS(1978a). in which it is recognized that circadian organization is not necessarily involved in photoperiodic time measurement /UJYSP. According to PIN-IIYDRIGH (1972) the success with which photoperiodic induction is effected will be maximal when the circadian system as a whole is at ‘resonance’ with its environmental driving light cycle, and minimal when firr from ‘resonance’. no matter how the actual time measurement is performed (i.e. by circadian oscillations or by an hourglass). An elaboration of the way in which the circadian system might conceivably influence the ‘expression‘ of photoperiodic induction without being involved in time measurement itself will bc given in the next section. If it is assumed that the circadian system is not involved in photoperiodic time measurement, the obvious choice of a clock mechanism is an hourglass, which would account for the hourglass properties observed in the photoperiodic reaction of T. wricue. As the double hourglass mechanism we developed previously appeared to be rather complex (VAT NtlNEs and VEERMAN.1979a.b). we explored the possibility of designing a single hourglass timer, which preferably should possess the main characteristics of the only hourglass mechanism developed to a great extent, namely the one proposed by LEES (1973. 1981) for time measurement in M. vi&w. These main characteristics are the following: (I) Time measurement is largely a function of the scotophase; the hourglass measures a critical nightlength. which is characteristic of the species or population. (2) Light interruptions

timing

in mites

IO‘!?

applied early in the scotophase cause a reversal or ‘resetting’ of the timing mechanism to its starting position. (3) Later light interruptions do not reverse the dark reaction but end the process of time measurement by measuring either a ‘long’ or a ‘short’ night. i.e. longer or shorter than the critical nightlength. (4) In between the stages sensitive to early or late light breaks is a zone which is apparently refractory to light. (5) The function of the main photophase is to end the process of time measurement in the same manner as described for late night interruptions. and to ‘turn over’ the hourglass. thus preparing the system for the measurement of the next scotophase. For the expression of these characteristics in a formal model a number of empirical formulae were developed which describe the kinetics of the hourglass mechanism in successive light and dark phases. The hourglass wnill be called H; the numerical values which express the state of H at any moment are plotted on a linear scale from 0 to 100. All values which H can attain are expressed as a percentage maximum. The characteristics of this hourglass mechanism are summarized in Table I and are discussed below. When starting in the light at the minimum value of H = 1.0. H will be built up to a maximum value H,.. which is somewhat lower than the maximum value the system may attain in darkness (H,). HI,has arbitrarily been set at 100; the value for H,,was taken to be 80. This phase of building up in the light or ‘lightincrease’ has a duration of 4 hr (Fig. 1). When the maximum value HL has been reached H will remain inactive until the onset of darkness. At lights-off. H will start to increase further. until the maximum value Hu has been attained in slightly over 7 hr. according to ‘dark-increase’ kinetics (Fig. 1). As soon as the value of HI,has been reached a rapid ‘dark-decrease’ will begin. resulting in a value of H = I.0 after about 4.5 hr (Fig. 2). If darkness lasts still longer H will continue to decrease very slowly until in about 6 hr a value of H = 0.001 has been reached. after which H starts to increase rather slowly again (‘spontaneous dark-increase’. Fig. 3). Lights-on causes the system to switch to Iightdecrease’ kinetics if. at the moment of lights-on. H was following ‘dark-decrease’ kinetics or if H > H, (Figs I and 3). If at lights-on H is increasing but below HL. the system will switch to ‘light-increase’ kinetics (Figs 3. 4 and 5). If darkness intervenes with ‘light-decrease’ kinetics the system is forced to switch to ‘dark-decrease’ if H < H,. and to ‘dark-increase’ if H 2 If, at the moment of lights-off (Fig. 3). If H is in its stage of ‘light-increase’ at lights-off. the system switches to ‘dark-increase’ (Figs 4 and 5). Nightlength measurement is accomplished by the hourglass when a specific value of H (H*)is reached during a decreasing phase of the system. If H* falls in the dark the scotophase is measured to be a long night: if H* falls in the light the preceding scotophase is measured to be a short night (Figs 1 and 3). The operation of this hourglass for photoperiodic time measurement in T. wticut’ will be elucidated with some examples in a later section; in the next sections we will first consider the ‘resonance’ effect of the circadian system on photoperiodic induction and the summation of photoperiodic information.

M. VAT N~INES and A. VEERMAN

I044 Table

I. Summary

of the characteristics

of the hourglass H. executing in Tctrcctl~~cln~.\urtiuc

Stage Light-increase

time measurement

Characteristicr I. 2. 3.

Maximum value in light is H,,= 80 If H = H,, H stays inactive until the onset of darkness Onset of darkness

causes switch to dark-mcrease

.4 = (80 - H,,bH" 15 79):

Cl= 2.1x

Maximum value in darkness is If, = IO0 If N = 100. kinetics switch to dark-decrease Light interruption LXUSL’Sswitch to light decrease Light interruption cat~srs switch to light-increase Kinetics: ff, = H, + ct

Dark-increase

If,2 70 If, < 70 Dark-decrease 1. 3.

if H 2 H, if H < H,

C’, = 2.7x (‘2 = ‘I.90

kinetics switch to spontaneous dark increase If H = H,,,,. Light interruption causes switch to light-decrease Kinetics: H, = Hormd'

H ml,, = 0.001; SpoiGaneous dark-increase

photoperiodic

tl = I .U

I.

If $ (sGf) = 0.8. H stays inactive

2. 3.

Lights-on Kinetics:

until lights-on

causes switch to light-increase

H, = .s,r

5 = 8.5 Light-decrease

I.

2. 3 i:

If H f 1.0, kinetics Dark Interruption Dark interruption Kinetics: N,= If H is decreasing

switch to light-increase causes switch to dark-increase causes switch to dark-decrease

If H is increasing

at lights-on:

if H 2 H, if H < H,

Hoe-"“ at lights-on:

.Y = 1.4 !’ = 2.0 .x = fc;H,, - I',

L'= w,ff,, - :, H, 5 H, 5 H,,, --)i = I (H,,,= 97) H ,<,% < H, < Hhlyh - i = 2 W,,,, = 94) ff,

+[=.I

2 Hh,yh

i I 7

;

'1, 0.01’ 0 0.015x

I',

w,

0.964 -0.00016 I .4X35

0 3.074 0

z, _ 2.4 280.X i - 8.0

H* = 6.08. Ho is the value of H at the onset of each stage. H, is the value of H, t hr later.

If it is assumed that it is not the clock which is under control of the circadian system but some other aspect of the induction mechanism, the most obvious possibility to look into is that the circadian system somehow affects the photoperiodic counter. As already mentioned in the Introduction, it is conceivable that, even if the animals experience a sufficient number of long nights during their sensitive stages, diapause induction will prevail only if during the inductive period the circadian system is ‘in resonance’

with the external light/dark cycle. The simplest approach to this question is to consider a single well defined circadian oscillator, whose resetting behaviour can be studied in widely divergent photoperiodic regimes. The theoretical circadian oscillator which was derived previously for T. urticae in order to test the external coincidence model in these mites (VAZ NUNS and VEERMAN,1982), could well serve this purpose. The phase resetting curves for light pulses of 1 and 2 hr (see VAZ NUNW and VEERMAN.1982. Fig. 1) were

Photoperiodic

timing

I

0 12

8 21 8

12

16

20

2& 12

h ct

Fig. I. Kinetics of the hourglass H. executing photoperiodic time measurement in T~trr~~clnts rrrricuc. in the phatoperiod LD 16:X. Circadian phases at lights-off and lights-on of the oscillator involved in the summation of photnpcriodic cycles. in the same photoperiodic regime. arc’ recorded along the abscissa (Ct). For further cxplanation see text.

Fig. 7. Kmetics of the hourglass H. executing photoperiodic time mcasuremcnt in Tetrtrr~~~lnr.s wtictrc, in the photopcriod LD X: 16. Circadian phases at lights-off and lights-on of the oscillator- Involved in the summation of photoperwdic cycles. In the same photoperiodic regime. arc recorded along the abscissa (0). Fur further explanation see text

100

80

1 4 t----’

H

IO45

in mites

used to compute the phase resetting data for other pulse durations. Computations were performed following the transformation method of JOHNSSON and KARLSSON (1973, which has recently been extended by VA% NIINES (1981) to be applicable to both ‘strong’ and ‘weak’ resetting stimuli. Phase resetting data of the oscillator for various pulse durations are shown in Table 2. The period T of the unentrained circadian oscillator is 19.5 hr (cf. VAZ NCINES and VEERMAN. 1987). The phase resetting data so obtained may be used to compute the phase relationships between the circadian oscillation and any conceivable light/dark regime by applying the extended transformation method. Examples of how these computations are performed have been given by SAUNDERS(1978aL The question to be answered next is: when is the oscillation assumed to be ‘in resonance’ with the external light/dark cycle’? If we want to investigate how the circadian oscillation may influence the process of induction. the terms ‘in resonance’ and ‘far from resonance’ are too ill-defined to be useful. For instance. in skeleton photoperiods in which the total length of the cycle is held constant (e.g. symmetrical and asymmetrical skeleton photoperiods based on a cycle length of 24 hr) the ratio T. T remains unchanged and the oscillator might be interpreted to be ‘in resonante’ sith the light/dark cycle. However. in the skeleton photoperiods mentioned the phase relationship Y between the oscillator and the photoperiod will change as a function of the time of night at which the light pulse is applied. Therefore. what is needed is not a calculation of whether T is close to r (or modulo 5). but a definition of those phase relationships which are considered to be ‘correct’ (i.e. not impairing induction) and those which are not. A rather simple solution was found b, looking at the circadian times at which lights-on occurs in various photoperiodic regimes. In complete 24.hl photoperiods with a diapause promoting long night. lights-on occurs during the ‘subjective day’ (Ct 00 c‘t I?). whereas in short-night photoperiods lights-on occurx during the ‘subjective night’ (Ct 12-Ct 23). If we took at a resonance experiment performed with 7: ~tic’trc,. in which a constant photophase of R hr was combined with scotophases varying bctwccrl 3 and

t

601

31 c--

q-p_

0 8 L-___ 12 16 9 11 6 Fig. 3. Kinetics

the photoperiod the summation

of the

. II-

16

.‘:

3.’

411

51,

L8 2.’

k.+

ii

11'

II

hourglass H. executing photoperiodic time measurement in T~rur~~~h~rs wticwt’. in LD I I :4: I :4X. Circadian phases at lights-off and lights-oo of the oscillator involved in of photoperiodic cycles. m the same photoperiodic regime. are recorded along the abscissa (Ct). For further explanation bee text.

1046

M. VAZ NLINESand A. VEEKMAN 100

4

80

H 60 LOi 1

20

1 * 0

8

16

12

24 --175 123

32

LO

18

56 226

64

h

12

ct

Fig. 4. Kinetics of the hourglass H. executing photoperiodic time measurement in Terru~~~chu.sltrticur. in the photoperiod LD 11: 24: 1: 28. Circadian phases at lights-off and lights-on of the oscillator involved in the summation

of photoperiodic cycles, in the same photoperiodic regime. abscissa (Ct). For further explanation see text.

84 hr (VAZ NUNES and VEERMAN,1982), no diapause is observed with scotophases of 24-28. 44-48 and 6G68 hr. although these scotophases are all ‘long’ nights. The similarity between these photoperiodic regimes and ‘natural’ short-night photoperiods is that lights-on occurs during the subjective night of a circadian oscillation which apparently interferes with the photoperiodic reaction. This coincidence of light and the subjective night might be interpreted as inhibiting the induction of diapause. Therefore the phase relationship between oscillator and photoperiod will be defined as ‘incorrect’ if lights-on happens to fall between about Ct 12 and Ct 24. 3. The photoperiodic

counter

The importance of the summation of photoperiodic information in successive cycles during the sensitive period for the final result of the induction process. in mites as well as in insects, has been discussed before (VAZ NUNES and VEERMAN, 1982). The photoperiodic counter in T. urticue is conceived to be a mechanism which adds up how many times H* falls in the dark or in the light during the sensitive period of 11 days

are

recorded

along

the

(264 hr) of these mites. This results in an ‘induction sum’. called S, which is defined as the number of coincidences of H* with darkness less the number of coincidences of H* with light. measured during the sensitive period. The induction sum is comparable with the ‘number of inductive events’, which has been used before for the summation of photoperiodic cycles as part of the external coincidence model (SAUNDERS, 1975; VAZ NUNES and VEERMAN. 1982). Also the threshold values of S are the same as those calculated for the number of inductive events in T. urticae. and are based on the fact that a minimal number of two to three long nights are already sufficient in T. urtiur to induce between 50 and loo”,, diapause (V~FRMAN, 1977). The threshold values of S are the following: loo”,, diapause is predicted if the value of S is found to be 3.1 or above: no diapause will be induced if S is 2.7 or less. If the calculations of S produce a value between 2.7 and 3.1. the predicted diapause incidence is taken to be 50”,,. In the previous section the concept was developed that in certain photoperiodic regimes diapause induction might be inhibited because of an ‘incorrect’ phase

80

H 60

0

22

a

‘3 L 24 237 22

32 ~ ,_LO 23.7 22

k8

56 2fiT2

6L

72 h 23iF2ct

Fig. 5. Kinetics of the hourglass H, executing photoperiodic time measurement in T&ur~~&u.s urticur. in the photoperiod LD 1: 17.5. Circadian phases at lights-off and lights-on of the oscillator involved in the summation of photoperiodic cycles, in the same photoperiodic regime. are recorded along the abscissa (Ctl. For further explanation see text.

Photoperiodic Table

2. Resetting

Circadtan time before pulse

timing in mites

of the circadian oscillator involved In the summation cycles in Tetranychus urticue Pulse duration (hr) 4 5 6 X 9 Circadtan time (0) after pulse

1

Z

3

1.7 3.4

4.1 4.8

5.5 6.1

6.7 7.4

8.0 8.5

9.0 9.5

10.6 II.0

4.4 5.3 6.3 7.3

5.7 6.6 7.6 8.5

7.0 7.8 8.7 9.5

x.2 x.9 9.6 IO.3

9.’ 9.8 10.5

10.0 10.6 II.1

1I.4

04 05 06

07 OH

8.7 9.0

9.7 9.9

10.1 10.7

IO.8 II.3

II.0 11.5

9.9 10.8 II.6 11.0 11.9 11.6 I I.’

10.6 II.4 11.9 12.0 12.0 11.9 Il.8

11.3 11.9 12.0 12.0 13.0 12.0 12.0

11.7 12.0 12.0 12.0 I’.0 12.0 12.0

Il.1 II.7 13.3 16.0 20.0 ‘3.8 I.1

11.7 11.7 11.9 12.2 7.0 2.1 2.7

11.9 11.9 Il.0 17.0 8.2 3.5 4.1

1.8 2.’

3.2 3.6

4.6 5.0

01

02 03

09 IO I1 I7 I? I4 IS I6

I7 IX I9 ‘0 71 2 13

‘4.00

of photoperiodic

IO

II

2 17

II.3 II.6

11.9 12.0

12.0 12.0

I’.0 12.0

I I.7 Il.9

II.9 12.0 I’.0

12.0 12.0 12.0

12.0 12.0 12.0

I’.0 12.0 12.0

II.6 11.x

12.0 17.0

17.0 12.0

17.0 12.0

12.0 12.0

I’.0 IX

II.8 11.9 12.0 12.0 12.0 17.0 I’.0 11.0

II.9 12.0 11.0 11.0 12.0 12.0 12.0 12.0

I’.0 11.0 12.0 12.0 12.0 12.0 I’.0 12.0

11.0 12.0 12.0 17.0 12.1) 11.0 12.0 12.0

12.0 17.0 12.0 12.0 12.0 12.0 12.0 12.0

12.0 12.0 12.0 12.0 12.0 I?.0 12.0 12.0

I’.0 12.0 I’.0 12.0 12.0 12.0 12.0 12.0

12.0 12.0 12.0 12.0 9.2 4.9 5.4

12.0 12.0 12.0 12.0 10.0 6.7 6.X

I’.0 12.0 12.0 12.0 l0.S 7.5 x.0

12.0 12.0 12.0 12.0 11.x 9.6 9.9

12.0 12.0 12.0 12.0 12.0 10.4

11.0 IL.0 I’.0 12.0 I 2.0 I I.1

12.0 12.0 I’.0 12.0 I~.0 I I.9

I’.0 12.0 12.0 ILO 12.0 12.0

10.7

1 I.1

II.9

12.0

5.9 6.3

7.1 7.6

x.4 x.7

IO.’ IO.4

II.0 I I.1

I I.6 II.7

12.0 12.0

12.0 12.0

The phase (circadian time) of the oscillator after the light pulse aa a function of it\ phase at the beginning of the pulse. Resettmg data computed from the resetting curves published previously (VAZ NI’NES and VEERMAN. 10X1).

relationship between a circadian oscillation. involved in photoperiodic induction. and the photoperiod. In other words, although in certain light/dark regimes the ‘output’ of the hourglass timer, accumulated by the photoperiodic counter as the induction sum S. would be expected to result in diapause induction (S > 2.7). the incidence of diapause in these regimes is diminished or even abolished as a consequence of the fact that light is falling on the wrong phases (the subjective night) of a circadian oscillation which somchow interferes with the further processing of the output of the clock. The inhibition exerted by the circadian oscillation may be expressed as an ‘inhibitory force’. g. Because of this inhibitory force the induction sum S will be reduced to S, = S - gS (0 5 g 5 I). If the phase relationship between oscillator and photoperiod is ‘correct’, g = 0 and no inhibition is found. However. even with an ‘incorrect’ Y no inhibition will occur if the induction sum S is high enough; as it is easy to check, this will be the cast when s 1 ?.I;(1 - g). In some photoperiodic regimes lights-on occurs one or more times both during the subjective day and the subjective night (e.g. in certain skeleton photoperiods and during ‘transient’ cycles which may occur before the oscillator has reached a steady-state). In these cases inhibition will result if the number of ‘incorrect’ Y’s (Z Y,) is equal to or larger than the number of ‘corr-ect’ Ys (IX YJ which occur during the sensitive period of the mites. It appeared that the inhibitory force is not equally strong in all photoperiodic regimes for which inhi-

bition was expected to take place: this might be explained by the fact that the sensitivity to light is not equal during the entire subjective night. For those regimes where IL Yi 2 IL Yc the value of (1 was found to be a function of the phase (Ct) of the oscillation at the moment of lights-on and lights-off. If in these regimes lights-on occurs between Ct 14.5 and Ct 0.4 and lights-off between Ct I 1.8 and Ct 12.2. ‘I/ m these regimes is ‘strongly incorrect’ (Y,,). If lights-on occurs between Ct 11.3 and Ct 14.5. or lights-of does not fall between Ct I I.8 and Ct 12.2. Y IS ‘weakly incorrect’ (Yi,). From the number of ‘strongly’ and ‘weakly’ incorrect phase relationships measured during the entire sensitive period a weak (~1= 0.501 or strong (gg= 0.70) inhibitory force could be calculated: fat X Y,,, > 32 YL, the inhibitory force is called weak, and for Z Yi, j 2X Y,, the inhibitory force is called strong. In addition. if day and night are completely reversed with respect to the circadian oscillation, i.e. if the subjective day falls entirely in darkness and lights-on occurs during the succeeding subjective night. the inhibition appeared to bc somewhat stronger than expected according to the above calculations; in these cases a small correction was neccssary in the form of an increase of the value of 6, with -1”(1. With all elements which according to the model participate in photoperiodic induction defined (an hourglass clock. a photoperiodic counter. and a circadian oscillation which in certain phase relationships with the photoperiod impairs induction to a greater or less extent). we may now consider the operation of

1048

M.

VAZ NUNES and A. VEERMAN

0

0

4

8

12

16 hours

20 of

24

llghf

Fig. 6. Observed (closed circles) and predicted (open circles) incidences of diapause in Tetran~x+~us wticw in a series of 24 hr photoperiods composed of different duratlons of light and dark (photoperiodic response curve).

the complete photoperiods.

model

in various

die1 and

4. Operation of the ‘hourglass timer-oscillator model ,ftir T. urticae

nondiel counter’

As shown in Fig. 6 the model outlined in the previous sections is capable of generating the complete photoperiodic response curve of T. urticae. Model dynamics for a long-day (LD 16:8) and a short-day (LD 8:16) regime are shown in Figs 1 and 2. respectively. In LD 16:8 (Fig. 1) H* falls in the light in all photoperiodic cycles during the sensitive period of the mites; this results in S = - 11.0 and the prediction is for non-diapause in this regime. In LD 8:16 (Fig. 2) H* coincides with darkness in every cycle, which results in S = 11.0. Moreover. light occurs only during the subjective day, so no inhibition is expected on account of the circadian system. Therefore the prediction in this regime is for full diapause to occur. In all other short-day regimes similar model dynamics are observed. although in ultra-short days (L < 4 hr) H*

is reached at a later time, reckoning from ‘dusk’. as the photophase is too short for the light-increase of H to be completed in the light. At the onset of darkness, therefore, H is less than 80 and more time is needed for H to reach the maximum value H,; consequently H* will also fall at a later time. In continuous light (LL) H remains at its maximum value in the light (HL = 80). and no coincidences of H* with either light or dark will occur. Therefore, S = 0 and O”,, diapause is predicted by the model. Also in continuous darkness (DD) the prediction is for non-diapause, since H* occurs only once. coinciding with the dark. which results in S = 1.0. LD 14:lO. the critical photoperiod, presents a special case. In this regime H* coincides exactly with lights-on, which makes it uncertain whether H* is measured as a coincidence with darkness or with light. In this case we assume that half the population of mites measures H* as falling in darkness and the other half as falling in light. The latter half of the population. therefore, will not enter diapause. As lights-on occurs at Ct 0.3 in the photoperiod LD 14: 10, Y is incorrect and y = 0.70. However, all mites that belong to that half of the population which measure LD 14: 10 as a long-night regime are destined to dlapause. since S, = 11 - 0.70 x 11 = 3.30. which is above the threshold of 3.10. For the population as a whole therefore the prediction is for SO”,, diapause to occur in LD 14:lO. In a previous paper a resonance experiment was published with a fixed photophase of 8 hr and a variable scotophase ranging over 4 to 84 hr (VAZ NUNIS and VEERMAN. 1982). In Fig. 7 another resonance experiment performed with T. urticar is shown, in which a photophase of only 2 hr is combined with scotophases which vary between 2 and 84 hr. The results are in some respects different from those of the resonance experiments with a photophase of 8 hr. Here five resonance peaks are observed, four of which arc rather large. recurring at about 30 hr intervals. and one small peak occurring at night lengths of only 46 hr. Notwithstanding the surprising number of peaks, the model-predicted responses show a good agreement with the experimental results: all five peaks are expected according to the model (Fig. 7).

Observed (closed circles) and predicted (open circles) incidenccs of diapause in Tctrur~ych in a resonance experiment consisting of cycles of 2 hr of light and (abscissa) different durations of darkness.

Photoperiodic In order to understand how these model predictions were obtained the operation of the model will be elucidated for some specific photoperiodic regimes. For instance, in the regime LD 2:36 seven long-night cycles are experienced by the mites during the sensitive period of 11 days. resulting in an induction sum of S = 7. Since Y appears to be correct, the prediction ia for lOO”,, diapause in this regime (Fig. 7). In LD 2:44. on the other hand, lights-on falls at 18.1 Ct(l2 + r.24 x 44) = Ct(12 + 1.23 x 44) = ct and lights-off at Ct 11.9. Accordingly Y is ‘strongly’ incorrect and g = 0.70. In this regime the induction sum S = 5.7 and consequently S, = 1.7, which means that no diapause is expected according to the model (Fig. 7). The small ‘additional’ peak of diapause incidence found with scotophases of 4 and 6 hr is difficult to explain on the basis of the external coincidence model. since in these regimes (LD 2:4 and LD 2:6) no photo-inducible phase. $i. occurs at all and consequently no diapause would be expected (cf. VAX Nr UFS and VEERMAN. 1982). However. according to the ‘hourglass timer-oscillator counter’ model in LD 2:4 H* recurs once in every three cycles. coinciding with darkness. This results in an induction sum S of 14.7. As the phase relationship between the circadian oscillator and the photoperiod is ‘strongly’ incorrect in this regime. the reduced induction sum becomes: S, = 14.7 - 0.7 x 14.7 = 4.4. which is above the threshold of 3.1 and thus results in a prediction of 100”,, diapause. On the other hand, in the regime LD 2: X H* recurs once in every two cycles and falls in the light. thus resulting in a prediction of non-diapause (Fig. 7). In Fig. 8 the model-predicted and experimentally observed incidences of diapause are shown for nightinterruption experiments in which a 1 hr light break ‘scans’ through the night of an LD 12:52 photoperiod (D, + Dz = 52 hr). In the uninterrupted photoperiod LD I’:52 about 90”,, of the mites enter diapause. Three peaks of sensitivity to the light breaks appear in the extended night: one at Zt 14-16, a second at Zt 36 and a third at Zt 56. The peak intervals of about 20 hr agree well with the distance found between successive resonance peaks in T. urticae, demonstrated in resonance experiments with constant photophases of 7 and X hr (Fig. 7. and VAL NUNES and VEERMAK. 19X3) and corroborate the evidence that the circadian sq\tem is involved in photoperiodic induction in these mites. The predicted diapause incidence in the uninterrupted photoperiod LD 12:52 is loo”.: the induction sum S = 4.1 and Y for this regime is ‘correct’. For an esplanation of the peaks of sensitivity to the light breaks the model dynamics are shown for two Iregimes. one with a light interruption in the early night at the position of the first peak (Fig. 3). and the other with the light interruption near the middle of the night. at the position of the second peak (Fig. 4). The regime shown in Fig. 3 is L,D,L,D, 1 I :4: I :4X. At the end of L,, the main photophase. H is at its maximum value in the light, HL. At lights-off ff starts to increase, according to dark-increase kinctics. attaining a value of H = 91.1 after 4 hr of darkIWSS. The light interruption then causes the hourglass

timing

I049

in mites

to switch to light-decrease kinetics (Fig. 3: see also Table 1). For H = 91.1, the light-decrease constants Y and J are: z = 0.012 x 91.1 - 0.964 = 0.13 and \’ = 0 x 91.1 - (-2.4) = 2.4. After the 1 hr light Interruption. according to light-decrease kinetics, H = H e-‘.l = 91 le-” - 91.1em”.‘3 - X0.. therefoie, at tOheend of the light pulse H will restart following dark-increase kinetics and will continue to follow dark kinetics until the end of Dz (cf. Fig. 3). At the start of the next L,. the value of H = 46 and, as H is increasing, lights-on causes a switch to light-increase kinetics. which are completed after about 2 hr Until the onset of the next D,. H will remain inactive at its maximum value H,_,According to these kinetics. as shown in Fig. 3. H* falls in the dark, which gives for the induction sum S a value of 4.1. In Fig. 3 also the phase relationship between the circadian oscillation and the photoperiodic regime is shown. which appears to be ‘incorrect’. From the circadian phases (Ct) at lights-on and lights-off of both the main phothat tophase and the light pulse it follows x YiW = x Y,, and therefore the ‘inhibitory force’ of the oscillator is strong: g = 0.70. Consequently the reduced induction sum is S, = 1.2 and the prediction in this regime is for non-diapause to occur (cf. Fig. X). Figure 4 shows the kinetics of the hourglass timer for a light pulse at hour 24 in an extended night of 52 hr: the photoperiodic regime shown is L,D,L2D2 11:24:1:28. At the end of the 24 hr scotophase. D,. H is in the stage of spontaneous dark-increase. and lights-on causes a switch to light-increase. At the end of the light pulse H is still increasing and will switch to dark-increase until H, = 100 has been reached and dark-decrease kinetics take over. Spontaneous darkincrease starts 11.5 hr later and is terminated by the onset of L,. In the light H is built up again to the maximum value of H in the light, H, = X0. According to the kinetics shown in Fig. 4 in this regime H* falls in D, as well as in D2. Consequently. as II* occurs twice in every 64 hr cycle. the induction sum S = X.25, However. the inhibition exerted bv the circadian ohcillation is again strong in this regime. as can be seen from the circadian phases at lights-on and lights-off of the oscillation shown in Fig. 4. The reduced induction sum then becomes S, = 8.25 - 0.70 Y 13.25= 7.5.

:i

LOi

r----e 0

12

20

28

f

i

36

f!

/”

L-

time at nlghtbreak

52

60 lh#

Fig. 8. Obsewed (closed circles) and predicted (open circles) incidences of diapause in Tctrurtyclnr l(rtI(tw 111 a series of night-interruption experiments in which the scotophase of the photoperiod LD 11:52 IS syrematically interrupted with light pulses of I hr duration.

M. VAL NUNH and A. VEERMAN

1050

which is below the threshold for diapause induction (cf. Fig. 8). Although according to the model the first and the last peak are determined partially also by the activity of the hourglass. the central peak of sensitivity to light interruptions in an extended night of 52 hr is only the result of an inhibition of the ‘expression’ of diapause induction exerted by a circadian oscillation with a natural period 5 of 19.5 hr. In a previous paper a so-called T-experiment has been described for T. urticur. consisting of 1 hr pulses of light in a cycle of LD 1:17.5 (T = 18.5 hr) with the first pulse of the train starting at different circadian phases (VAZ NUNES and VEEKMAN, 1982). According to the external coincidence model diapause induction was expected to be a function of the number of transient cycles executed by the oscillator before a steadystate was reached. The photo-inducible phase 4i was calculated to fall in the light when the oscillator would be in steady-state; during the transient cycles. however, $i would fall in the dark. Therefore, a high incidence of diapause was expected with a large number of transients and a low incidence when steady-state was reached after only a few transient cycles (Fig. 9). The same experimental design has been applied to S. u~g~rostorna by SA~INDERS(19791, who considered this experiment to be a crucial test of the external coincidence model. The predictions proved to be consistent with experimental results obtained with S. ctr:y~~~stomu (SAUNDERS, 1979). but in T. wtiML’ the predictions were not in accordance with experimental results: diapause incidence was found to be between 95 and loo”,,, regardless of the number of transients experienced by the mites (Fig. 9 and VAZ NCNES and VEERMAN. 1982). Although the results of this T-experiment performed with T. ur.fic’c~ could not be explained in terms of the external coincidence

100

11

1

a 11 e

1142

6 5 3 1

3

5

n

4020-

-7

16

p-7

18

20 22 -n Ct at 1st light pulse

Fig. 9. lncidences of diapause in Terrun~chrs wt ic,cw exposed to the photoperiod LD 1:17.5, with the 1 hr light pulse starting at different circadian phases (Ct). n. number of transient cycles required to bring the circadian oscillator to steady-state entrainment: l -m -0. observed incidences of diapause; O-0. diapause incidences predicted on the basis of the ‘hourglass timer oscillator counter’ model; A---A. diapause incidences predicted on the basis of the external coincidence model. For further explanation see text.

model. they are consistent with the ‘hourglass timeroscillator counter’ model, as the model dynamics shown in Fig. 5 may demonstrate. In Fig. 5 the model dynamics of both the hourglass and the oscillator are shown for the photoperiod LD 1: 17.5. One steady-state cycle of the hourglass comprises three cycles of LD 1:17.5; during these three cycles H* occurs twice. coinciding with darkness. Therefore, the induction sum S in this regime is calculated to be 9.5. If the first light pulse starts at Ct 23.7, the circadian oscillator immediately attains a steady-state phase relationship to the photoperiodic cycle (Fig. 5). According to the circadian time at lights-on and lights-off, Y in this regime is ‘weakly’ incorrect. resulting in a weak inhibitory force of f = 0.50. Consequently the reduced induction sum IS S, = 9.5 - 0.50 x 9.5 = 4.8. which is above the threshold for IOO”,, diapause induction. This means that even if the circadian oscillation attains steadystate instantaneously. a steady-state in which the phase relationship between oscillator and photoperiod is ‘incorrect’ and results in the maximal amount of inhibition which may be attained in this regime, still according to the ‘hourglass timer-oscillator counter’ model the prediction is for loo”,, diapause. which is in accordance with the experimental results obtained with T. ~ticar (Fig. 9). DISCUSSION Since the remark

made by HILLMAN in 1976 that literature than that on the relationship between circadian rhythmicity and photoperiodism further exploration of this relationship has not solved the issue. Although finding a circadian variation in a photoperiodic reaction may be interpreted in support of BIINNING’S (1936) hypothesis, which states that photoperiodic time measurement is made by reference to the circadian system, it may also be explained in a different way. as we have demonstrated in this paper by elaborating PITTENIIRIGH’S (1972) ‘resonance’ model. In this concept, which we named an ‘hourglass timerPoscillator counter’ model. time measurement is not a function of the circadian system. but is executed by a single hourglass mechanism. The influence of the circadian systcm is restricted to an inhibition of photoperiodic induction which becomes apparent only in certain ‘forbidden’ phase relationships between a circadian oscillation and the photoperiod. This inhibition could be visualized most easily as a partial or complete destruction of the product of photoperiodic time measurement during its accumulation and integration by a photoperiodic counter mechanism. The amount of ‘product’ remaining at the end of the sensitive period is decisive for the direction development will take in each individual animal: either continuous development or diapause. This model. which incorporates an explanation of photoperiodic time measurement and of the summation of photoperiodic information as well as an explanation of the influence of the circadian system on photoperiodic induction. proved to be consistent with experimental results in T. urficcrr in widely divergent photoperiodic regimes, like resonance experiments and night interruption experiments. as shown in Figs 68. Also the result of a there

is no

more

confusing

Photoperiodic

T-experiment performed with T. urticae could be explained on the basis of the ‘hourglass timer-oscillator counter’ model (cf. Fig. 9). Our interpretation of the role of the circadian systern in photoperiodism finds support in the results of photoperiodic experiments with various organisms. As early as 1959 NANDA and HAMNER explained the effect of the endogenous rhythm affecting the photoperiodic response of the short-day plant Glycine ma.~ as an inhibition of flower bud initiation; according to these authors flowering in this plant is the net result of the balance between a flowering stimulus, accumulated during successive inductive cycles. and a rhythmical process which was thought to be inhibitory in nature. This hypothesis provided an elegant explanation for experiments with G. mux in which the accumulation of photoperiodic information in 24- and 36-hr cycles was compared. A maximum of flower bud initiation was found in plants receiving 7 cycles of LD 8:16 (T = 24 hr). whereas plants receiving 7 cycles of LD 8: 28 (T = 36 hr) hardly formed any flower buds. However. increasing the number of LD X:X cycles resulted in a maximal amount of flower bud initiation. whereas increasing the number of noninductive short-night cycles (T = 24 hr) did not result in the formation of any flower buds, which showed that the 36-hr cycles are not non-inductive. Comparable results were obtained by SAUYDERS (1973) in resonance experiments with S. argqyxronlcc. Increasing the number of photoperiodic cycles experienced by the tlv larvae by lowering the temperature resulted in an Increase of diapause induction up to IW,, in all cycles with scotophases longer than about 9.5 hr (the critical nightlength). but no increase occurred in short-night cycles. These results, like those for Gl~~c,ir~.are most easily explained by assuming that: (I) nightlength is measured to be longer or shorter than some critical value: (3) this information is accumulated in successive cycles. up to a threshold value and (3) the information may or may not be partially destroyed because of the inhibitory influence exerted in some photoperiodic regimes by the circadian system. The concept we developed in this paper would find strong support if it were possible to separate photoperiodic time measurement from circadian rhythmicity in one and the same organism. One example to this elTect may be found in the work of O~TA and Tsc D/.~XI (lY79). who demonstrated that elimination of the circadian rhythm of flower production in Lertwtr Hihhu by the addition of chemicals to the growth medium of the plants left the measurement of the critical nightlength unimpaired. These authors concluded that the circadian oscillator only modulates Rower production but is not related to the critical daylength measurement. According lo PI.T’TF.NDRIC;H (1972) photoperiodic induction would depend on the circadian system as a whole being in resonance with the environmental light,dark cycle. Our model is a simplification of this concept in so far as we studied the behaviour of only one well defined circadian oscillator, describing its e&ct on the photoperiodic reaction in terms of the coincidence or non-coincidence of light with the subjective night (Ct 12-0 24) of the oscillation. The results obtained with this rather simple concept

timing

in mites

1051

proved to be quite satisfactory for T. urtimr. indicating that the theoretical oscillator used in this model is either representative of the influence of the circadian system as a whole. or the induction process may be affected by a specific circadian oscillation whose kinetics match those of our theoretical oscillator. In fact, the idea of light having a specific effect when falling in the subjective night of a circadian oscillatron is strongly reminiscent of the original model of Bi’;hNING (1936) with a ‘photophil’ and ‘scotophil’ of I2 hr each. However. in Biinning’s views light falling in the ‘scotophil’ would measure a short night or long day. whereas in our concept it may impair the ‘expression’ of a photoperiodic response determined by a separate hourglass timer. A well known property of rhythmic phenomena is the fact that physiological processes are locked to certain circadian phases. It is quite conceivable. thercfore. that also in the case of photoperiodic induction one or more of the successive steps in the as yet unknown physiological process of induction are dominated by a circadian oscillation or subjected to the influence of the circadian system as a whole, resulting in impairment of the induction process if the wrong phase relationships prevail during the inductive period. Also a direct inhibitory efI’ect of light on certain physiological processes is not precluded. as has been shown by EDMUNDSet trl. (1979) for growth and transport processes in the yeast Srrc,c,h‘r,ortl!,~~,.\(,rsrvrisiuc. In natural photoperiods. however. the phase relationship between oscillator and photoperiod is correct in Inductive long-night cycles in % wtic,ac, and consequently the circadian system probably ha’r 110 substantial role in photoperiodic induction. apart from securing that the summation and integration of photoperiodic information occurs time]! during the night. As long as an) detailed knowledge of the ph!siology of the mechanism of photopcriodic time measurement is lacking. the kinetics of the hourglass timer developed for T. wticw are purely theoretical and comparisons with the kinetics of biochemical processes are irrelevant. The point we wanted to prove is that in principle a mechanism consisting of an hourglass timer. in combination with a simple counter mechanism. suffices to explain photoperiodic induction in 7. rrrtic,rrr. if a certain ‘resonance‘ effect 01 the circadian system is taken into account. 4t this moment the degree of complexity of the hourglass timer’s kinetics does not seem to be essential: 111this respect it is interesting to note that the hourglass model (without any interference of the circadian systern) is capable of explaining all results of photoperiodic experiments performed by Ltrt:~ (lY73) with .J1. rick. for which LI:HSdeveloped a non-mathematical hourglass model (LEES. 1973. 1981). Also In the case of RI. rick,. however. equally complex hourgla.ss kinetics proved to be necessary to explain the results obtained in greatly varying photoperiodic I-sglmeh (unpublished results). Moreover. from prelimmar\ trials to apply the ‘hourglass timer oscillator count&’ model to the results obtained in photoperiodic cxpcriments with insects. it appeared that the various parameters of the model may not be chosen at will: most of the parameter values depend on the values of c, and H*. of which cl may be dctermincd rather exactt)

M. VAZ NUNE~ and A. VEERMAN

1052

a grant to the first author from the Netherlands Organizfrom experiments with asymmetrical skeleton photoation for the Advancement of Pure Research (ZWO). periods. According to SAUNDERS(1979) the hourglass clock executing photoperiodic time measurement in M. REFERENCES rick might be regarded as a redundant oscillation, which is so rapidly ‘damped out’ in DD that it ADKISSON P. L. (1964) Action of the photoperiod in conrequires to be reset by the next main photophase after trolling insect diapausc. .4m. Nar. 98, 357-374. accomplishing only one night-measuring event. HowADKISSON P. L. (1966) Internal clocks and insect diapause. ever, there are some indications now that the photoScience 154, 234 241. receptors involved in photoperiodic induction are difBEACH R. F. and CRAIG G. B.. Jr. (1977) Night length ferent from those involved in the entrainment of circameasurements by the circadian clock controlling diapause induction in the mosquito Ardes utropalpar. J. dian rhythms in insects and mites: carotenoids have Insect P6ysiol. 23, 865-870. been found to be essential for the photoperiodic reacBECK S. D. (1974a) Photoperiodic determination of insect tion (TAKEDA. 1978; VEERMAN and HELLE. 1978; development and diapause. I. Oscillators. hourglasses VEERMAN.1980; VAN ZON et al., 1981). whereas flavins and a determination model. J. camp. Physiol. 90, are more likely candidates for the photoreceptor func275.-295. tion of circadian rhythms (KLEMM and NINNEMANN. BECK S. D. (1974b) Photoperiodic determination of insect 1976; NINNEMANN, 1980). It is not unlikely, therefore, development and diapause. II. The determination gate in that the mechanism of the photoperiodic clock is a theoretical model. J. camp. Ph!:sio/. 90, 297-310. BECK S. D. (1980) insect Photoprriodism, 2nd edition. Acaquite distinct from that of a circadian pacemaker. demic Press. New York. Experimental results suggesting hourglass timing BONNEMAISONL. (1968) Mode d‘action de la scotophase et are observed also in night interruption experiments de la photophase sur la production des gynopares ail&s performed with Pieris hrassicae (B~~NNING. 1969: de Dysaphis plantuginru Pass. (Homopt&es, Aphididae), CLARET et al., 1981; DUMORTIER and BRUNNARIUS, C.r. hebd. Sdanc. Acad. Sri.. Paris D267, 218-220. 1981). Two peaks of sensitivity to the light breaks BONNEMAISONL. (1970) Action de la photopCriode sur la were found in P. hrassicar when scotophases of up to production des gynopares ailees de Dysaphi.s plafaginva 40 hr in duration were scanned by light pulses of Pass. AIM Zool. Ecol. unit. 2. 523-554. either 30min or 2 hr. Characteristically the distance BONNEMAISON L. (1978) Action de I’obscuriti et de la lumiire sur I’induction de la diapause chez trois espices between the first peak in the night and lights-on and de Ltpidoptires. Z. angrtv. Enc. 86, 178-204. between lights-off and the second peak were constant B~~NNINC E. (1936) Die endogene Tagesrhythmik als in each experiment, regardless of cycle length. These Grundlage der photoperiodischen Reaktion. Brr. dt. hot. results may be interpreted without any constraint in Ges. 53. 596623. terms of an hourglass timer. Similarly the results of B~~NNINGE. (1969) Common features of photoperiodism in light break experiments performed by BEACH and plants and animals. Pho~ochem. Phtohiol. 9, 2 19-228. CRAIG (1977) with Ardes atropalpzrs. which also CLARET J.. DUMORT~ER B. and BRUNNARIUS J. (1981) Mise showed two peaks of sensitivity to the light breaks in en kvidence d’une composante circadienne dans I’horloge extended nights of 38 hr. do not form conclusive evibiologique de Pieris hrtrs.sicuc~ (Lepidoptera). lors de I’induction photopCriodique de la diapause. C.r. hchd. dence for the participation of the circadian system in Siam. ,4cad. Sci.. Paris C292. 427-430. photoperiodic induction in this species; like in Pirris DUMO~TIERB. and BRL~VNARIUS J. (1981) Involvement of these two peaks could easily be explained as a result the circadian system in photoperiodism and thermoperof hourglass time measurement. A circadian influence iodism in Pieris hssictrr (Lepidoptera). In Bwloyictrl is established convincingly only if scanning through Clock.\ in Seasvntrl Reproductiw Cycles (edited by Fat the night with a short light pulse reveals three peaks LCTTB. K. and D.E.). pp. 83-99. John Wright. Bristol. in extended nights of sufficient length, as the central EDMUNDS L. N.. Jr.. APTER R. 1.. ROSENTHAL P. J.. SHUN peak is unlikely to arise from a direct interaction W.-K. and WOOIIWARD J. R. (1979) Light effects in vcast: between the light pulse and the main photophase. persisting oscillations in cell division activity and amino acid I rampor [II cull ures of So~ihctrom?.~~,.s wrcv%& Thus far three peaks of light sensitivity in extended entrained hy light-dark cycles. P/rotoclw~~ Phvohiol. 30, nights have only been found in light break experi595-601. ments with Nasoniu ritripmnis (SAUNDERS, 1970), S. HAMNERW. M. (1969) Hour-glass dusk and rhythmic dawn arg!~ro.stoma (SAUNDERS. 1976a). and T. urticar, as timers control diapause in the codling moth. J. In.\cc/ shown in Fig. 8 of the present paper. However. an PI~~siol. 15. 1499- 1504. explanation of how these peaks are originated accordHILLMANW. S. (1976) Biological rhythms and phvsiologiing to the ‘hourglass timer-oscillator counter’ model. cal timing. .4. RN. Planr Pltysiol. i7, 159-179: _ as set forth in this paper. differs fundamentally from JOHNSSON A. and KAHLSSON H. G. (1972) The Dmwpiriia intepretations by other authors. using models based eclosion rhythm. the transformation method and the fixed point theorem. Department of Electrical Measureon an oscillator clock (cf. SAUNDERS, 1976b). ments, Lund Institute of Technology. Report No. 2.1972. In a following paper the ‘hourglass timer-oscillator 15 November. counter’ model will be applied to large series of night KLEMM E. and NINNEMANN H. (1976) Detailed action specinterruption experiments performed with T. wticar, trum for the delay shift in pupae emergence of Droxboth with die1 and nondiel light/dark cycles, as a phi/a p.srlrdooh.sc,ura. Photuchnn. Photobiol. 24, 369-37 I. further test of its validity as an explanation of photoLt:~s A. D. 119731 Photoperiodic time measurement in the periodic induction in spider mites. aphid Meyoura r,iciue. J. fuvrcr Phvsiol. 19. 2179 23 16.

LEESA. D. (1981) Action spectra for the photoperiodlc

.4c~no,clfdgu,r1m~.s-The authors would like to thank Mrs. C. KEMPERS-VAN R~ITHand Mr. G. VANDE BERC for technical

assistance.

The investigations

were supported

by

conof polymorphism in the aphid Mqmtrtr ricia,,. J. Insect Plsj~siol. 27, 761 771. NANDA K. K. and HAMNER K. C. (1959) Photoperiodic trol

Photoperiodic cycles of different

lengths in relation to flowering in Biloxi soybean (G/>,cin~, mu.x L.: Merr.). Plurzra 53, 45- 52. NfwNEhwsi-4 H. (1980) Blue light photoreceptors. BioSr+c~tct, 30. 16& I 70. OOTA Y. and TS~DZ~KI T. (1979) Evidence against involvement of circadian floral rhythm in the critical daylength measurement in Lrmntr yihh G3. Pltrnt Cdl Pk~siol. 20, 725 731. P~~I WIN D. M. and

control

of diapause

HAMNER W. M. (1968) Photoperiodic in the codling moth. J. Irlsc,cf Phy-

siol. 14, 519 5%. PIWI NDKIGH C. S. (1965) On the entrainment of a circadian rhythm

mechanism of the by light cycles. In <‘~r&irrrl C/OC,~.\ (edited by ASCHOFF J.). pp. 777-297. North-Holland, Amsterdam. PI I I I \I)KI~;H C. S. (1966) The circadian oscillation in Drorr~pllilu p.st,lrr/oohsc,lrrtr pupae: a model for the photoperlodic clock. %. Pfla,llt,,lp/l!,.sio/, 54, 775-307. PIT I I UDKIGH C. S. (lY72) Circadian surfaces and the diver-

sny of posslhle roles of circadian organization in photonerlodic induciion. Proc. nrrrn. ,Ic,rrt/. Sci.. I’.S.A. 69, !724 2737. P~rrf.\;f~fuc;f~ C. S. (1981) Circadian

organization and the photoperlodic phenomena. In Bioloqicrrl C/r~ck.\ in .&tl\ol;tl/ Rrprodwrirc C,w/rs (edited by FOLL~TT B. K. and D. E.I. pp. 1 35.John Wright. Bristol. SAI’\I)I.RS D. S. (1970) Circadian clocks in insect photoperlodism. S&nc~e 168, 601 -603. SAI,UI)IRS D. S. (1973) The photoperiodic clock in the tle&0y. .SII~~~,/~hqq~rtr,!/?‘,‘r,.\ror,~tr. J. Imrc’t. PIlxviol. 19, lull lY54. SAG VI)I KS D. S. (1974) Evidence for ‘dawn’ and ‘dusk’ oscilla~nr’r in the ,Vtrrottill photoperlodic clock. J. I~rrct P/I!,\iO/. 20. 77 X8. SAI SIIIRS D. S. (1975) ‘Skeleton’ photoperiods and the control of diapause and development in the flesh-fly. S~rrc.~~phu~quc~rg~rc~.\ror,~u.J. camp. P/q%ol. 97. 97--l 12. SAC WFRS D. S. (1976a) The circadian eclosion rhythm in S[r,cophuqu ~rrq.,“>.stornu: some comparisons with the photoperiodic clock. J. cornp. Physiol. 110, I I I- 133. SAI WIRS Il. S. (1976b) In\.uc,t C/&is. Pergamon Press. Ol;ford. SAG \DI KS D. S. (1978a) An experimental and theoretical analysis of photoperiodic induction in the flesh-fly. Sirr~~~pl~rr~q~~ mym~\fomu. J. ump. Pl~~siol. 124, 75-95. S.&I \I>I KS D. S. (197Xb) Internal and external coincidence and the apparent diversity of photoperiodic clocks in the insects. J. c’onlp. PI1~~siol.127, 197. ‘07. SAI UIXXS D. S. (1979) External coincidence and the photc>lnducihle phase in the Swcophugu photoperiodlc clock. J. c~orup. P/l wiol. 132, l79- 189. SAI YIII.RS D. S. (19Xla) Insect photoperiodismthe clock and the counter: a review. Physiol. Ent. 6, 99-I 16. SAI UDI.RS D. S. (19Xlb) Insect photoperiodism. In Htrndho116 t!f Br/ltrrior0/ Nru,ohioloq~. Vol. 4. Biologicul R/~~~ltrt~a (edited by AS~H~FF J.). pp. 411-447. Plenum Pres\, New York.

timing

in mites

1053

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TAREDA M. (1978) Photoperiodic time measurement and seasonal adaptation of the southwestern corn borer. Dirrtrueu qruntliosrllu Dyar (Lepidoptera: Pyralidae) Thesis. University of Missouri. Columbia. TAKEDA M. and MASA~I S. (1976) Photoperiodic control of larval developmen m Plotiiu ir~r~,r/~~r,~c~tul/~r. Pruc Jc>irlt 1 S. Juput~ Srmintrr on Stored Prod. Insc~ra. Manhattan.

Kansas. Kansas State University. pp. I X6-10 THIEL~ H. U. (1977a) Measurement of day-length

I. as ;L hasIs

for photoperiodism and annual pcrlodicity in the carabid beetle Ptc~rtr.srx~/ur.s niyrirti F. Orwhgiu 30. 33 I 34X. THff.I.1: H. U. (1977b) Differences in measurcmenl 01 daylength and photopcriodism in two stocks from subarctIc and temperate chmatcs in the carahid beetle f’rcrr~~ri~~/uc\ uiyritcr F. Ocw/o(qitr 30, 349- 365. TK~IMAU J. W. (lY71) The role of the braIn in the I.cdjsIs rhythm of silkmoths: comparison wnh the photopermdic termination of diapause. In Bloc~/tr~)nr,r,lctr~~ (edited by MENAKFR M.). pp. 4X3%504. National Academy of

Sciences. Washington. TYSHCHFNK~ V. P. (lY66) Two-oscdlatory

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VEERMAU A. (1980) Functional

involvement

of ca!-o~enolds

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