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A statistically oriented approach for teaching principles of paleontology
Computers & Geosciences,Vol. 2, pp. 33-40. Pergamon Press, 1976. Printed in Great Britain
A STATISTICALLY ORIENTED APPROACH FOR TEACHING PRINCIPLES OF PALEONTOLOGY JAMES C. BROWER Departmentof Geology,SyracuseUniversity,Syracuse,NY 13210,U.S.A.
(Received31 December1975) Abstract--Researchprojects that are oriented statisticallyare highlyeffectivefor teachingpaleontologicalprinciples. The exercisesdevelopedat SyracuseUniversityover the past severalyears are outlinedbrieflyand one is annotatedin detail. Students respondfavorably toward the projects and most individualsbelieve that the projects comprisemore creative and demanding,and better learning experiences than conventionallaboratory exercises.
Key Words: CAI, Classification,Cluster analysis, Ammonities, Cretaceous, Evolution, Numerical taxonomy, Paleontology.
INTRODUCTION
and the complexity of the exercise, the papers range from several pages to about 20 pages in length. In effect the students are required to design and carry out research projects that are similar to those done by many professional paleontologists. The projects are:
For several years computer-based laboratory exercises have been used in the beginning paleontology course at Syracuse University. The students mostly consist of junior and senior undergraduates with a smattering of first-year graduate students. Although a few individuals may be familiar with computers and basic statistics, the average person has no prior preparation in these fields. The required text for the course is the book by Raup and Stanley (1971) entitled "Principles of Paleontology" and the exercises are oriented toward paleontological principles. Somewhat similar projects were outlined by Osborne (1969) and Rodriguez and Malone (1974) whereas Dodd and Immega (1974) and Wright (1972) employed simulations to model biological processes such as natural selection for paleontology students.
(1) Paleoecology One possible study involves a Silurian eurypterid assemblage dominated by Eurypterus remipes remipes (DeKay). The students work out molt stages and determine mortality and survivorship rates which then are compared with similar data for its distant relative, the extant Limulus. The living habits and functional morphology and nature of the depositional environment also are reconstructed for the eurypterid. An alternate project deals with a series of fossil assemblages from the Middle Devonian. Here, assemblages and their component species are analyzed by simple techniques of numerical taxonomy.
THE APPROACH
The exercises actually are research projects which are initiated in the scheduled laboratories and completed outside of class. The purpose of the projects is to acquaint the students with major problems in paleontology and how these may be studied by means of statistics. Each project lasts two to three weeks. Several lectures are devoted to the aspect of paleontology, such as the species concept, to be researched. One or more statistical or mathematical methods pertinent to the problem also are annotated. The basic flowchart is simple and direct. In the first laboratory, the students are shown groups of specimens to be studied and the problem to be attacked is outlined. The material is examined and a set of measurements is devised to express the sizes and shapes involved. The measures are generally made and preliminary readings finished during the first week. The computer programming and programs needed for the project are covered in the second laboratory along with a general outline as to the report for the project. The remainder of the time is spent processing data, analyzing the computer output, and writing a paper discussing the data and interpreting the results. Although small groups of students pool their efforts to do the "dirty work" such as making the measurements, each individual must prepare a separate report. Depending on the student
(2) Ontogeny Relative growth sequences of several fossil invertebrates are studied by means of correlation coefficients and the simple allometric equation. The relationships between size and shape changes are stressed, and the equation data are interpreted in terms of functional morphology. Two projects on ontogeny relative to time also are available, one based on growth lines in corals and the other on pelecypods. (3) Species concept Species are treated in the context of interbreeding or potentially interbreeding populations in which the distribution of characters within and between samples is both pertinent and subject to statistical analysis and inference. Inasmuch as statistical inference is a difficult concept for most paleontologists, two exercises are devoted to this subject. In the first project, three samples are given, two of which are conspecific whereas the third belongs to a separate species. The data are analyzed by the one-way analysis of variance or a Students-t test to determine the equality of the means of the samples. In this situation, the students are able to compare results for 33
34
JAMES C. BROWER
samples which overlap greatly with results for samples showing little or no overlap. In the second species problem, the students are presented samples containing two closely related species as collected from the field. They are told to segregate the different species and test the differences statistically. In this situation, the differences are size related. These are tested by comparing slopes or equation values of several regression lines. Typically the species are selected to show progressive ontogenetic divergence, that is the young specimens are relatively similar but the forms diverge as the animals grew older. This illustrates one type of relationship between ontogeny and phylogeny. (4) Biostratigraphy One biostratigraphy project is based on several local stratigraphic sections in the Middle Devonian. Relative biostratigraphic values are calculated for the species in the two sections; these express the amount of "biostratigraphic information" conveyed by the presence of a particular species. Some taxa are more useful for correlation than others. The sections then are correlated based on the forms with the highest relative biostratigraphic values. Another problem defines morphoclines in ostracods in two stratigraphic sections which are matched subsequently by cross-correlating the morphoclines.
yields instant answers. APL is a high-level language with great power for manipulating matrices and vectors. Students with little or no experience with computers can be taught quickly a few basics which allow them to solve meaningful and reasonably complex problems after only several hours of instruction. APL is suitable for gradual learning--a bit at a time. Some of the programs for the exercises are written by the students, whereas others are provided by the instructor or taken from one of several APL statistical packages. The concepts behind the selection of the statistics are as follows. We attempt to apply basic univariate and bivariate statistics. Some multivariate techniques are involved, but these are restricted to simple types of numerical taxonomy. Most students do not have a working knowledge of matrix algebra. Consequently, algorithms requiring sophisticated matrix operations such as extraction of eigenvalues and eigenvectors or matrix inversion are avoided. Incidentally, if computers are not available, most of the techniques are simple enough so that the statistics can be obtained on a desk or pocket calculator for moderate-sized sets of data. Computers aid greatly but are not strictly necessary for the teaching of quantitative paleontology. AMMONITE PROJECT
Initial steps (5) Evolution The evolution project will be annotated later in this paper as an example of the approach. Suites of different fossils are used for each project. For example, evolutionary lineages have been analyzed in the Ordovician trilobite Cryptolithus, Cretaceous hoplitid ammonites, Paleozoic atrypid brachiopods, and Mesozoic pterodactyls. Ontogenies of various groups have been investigated including eurypterids, blastoids, crinoids, trilobites, ostracods, foraminifers, brachiopods, and pelecypods. The programming language for the course consists of APL which has several advantages for instruction purposes. It is a terminal-based interactive language which
However, the proof of the pudding lies in the eating and not in the recipe. Consequently it seems appropriate to turn to an example to display the virtues of this computerbased and project-oriented approach to instruction in paleontology. The project on ammonite evolution will be discussed which will illustrate the approach, methods, and results obtained by the class. Prior to beginning the study, several lectures have been given on numerical taxonomy as well as on the determination of lineages, that is lines of ancestry and descent, and reconstruction of evolutionary trends. The material consists of 11 samples of hoplitid ammonites from the Albian and Campanian of England (Table 1). The samples were collected by the late L. W. Ploger
Table 1. Listof samplesfor hoplitidammonites Species
Pseudosonneratia
Number ot speclmens in sample
Horizon
praedentata
Casey
Middle Albian, base of mammillatum zone 19
p. crassa Casey
Middle Albian, center of ma~millatum zone
p. crassa Casey
Middle Albian, top of mammillatum zone
Euhoplites truncatus Spath
Middle Albian,
zone 5
11
E. truncatus Spath
Middle Albian,
Zone 7
13
E. opalinus Spath
Middle Albian,
zone 8
1
E. lautus
Middle Albian,
Zone 7
6
Middle Albian,
Zone 5
10
Middle Albian,
zone 7
21
(Sowerby)
Anahoplites planus I~" planus
(Mantell)
(Mantell)
Douvilleiceras mammillatum (Schlotheim) vat. aequlnodum (Quenstedt) i~ayleites baylei
(Collignon)
Middle Albian, mammillatum zone Campanian
1
35
A statisticallyorientedapproachfor teachingprinciplesof paleontology from the "Gault" near Folkestone in the 1930's. Ploger approximately keyed the samples into the horizons outlined by Spath (1923-1943, p. 1-5, 669-682). It must be noted that this class project is not a definitive study on hoplitid ammonites. Only a small number of taxa, stratigraphic horizons, and characters are included. Strictly speaking, the results are only valid for the samples examined by the students although they may be applicable generally to hoplitids and other ammonities. The conclusions by the students based on numerical taxonomy are essentially the same as the qualitative phylogenies presented by Spath (1923-1943, p. 685-699). However, the students have no access to this part of Spath's work. The students are advised to consult several basic paleontology texts on ammonite morphology and they are instructed to identify the species involved using monographs on ammonites by Spath (1923-1943, p. 1-311) and Casey (1960-1966) and the Treatise volume on ammonites (Arkell and others, 1957). The literature on ammonites is typological in which minor variants are described as belonging to different species or genera. Consequently the students experience the "trials and tribulations" of dealing with this type of taxonomy. This makes a distinct imprint on the brighter students; perhaps, taxonomic practices will improve if such individuals cgntinue on in paleontology. It is notable that the samples are placed generally in the same genera; however, species assignments have differed greatly through the years. This partially reflects a lack of student expertise, but the state of ammonite taxonomy is also a contributing factor. The samples are compared and contrasted with respect to homologous characters. The lineages mostly consist of closely related genera and species in which there are no problems in determining homologies. If desired, less closely allied forms with more subtle homologies could be treated. In such a study, the search for homology could be quantified, perhaps by the methods outlined by Jardine (1967, 1969). A set of measurements is devised to assess the similarities and differences between the samples. The specimens consist of partial conchs where only the juvenile part of the shell is preserved so that the size of specimens has no significance. Therefore the data should be as independent of size and measurement units as possible. It is the shapes of the shells that are of interest-not the sizes. Usually, this problem is solved by determining ratios that directly portray the desired shapes. Each
5
INVOLUTE
EVOLUTE
EXPANSION FATNESS
I
I I
I,
>I
4 INDEX = 2 / 3
INDEX = 1 / 3
INDEX = 4 / 5
Figure 1. Sketches showing measurements for first three characters in hoplitids. sample is represented by a single suite of measurements. In this situation, six variables were determined for the 11 samples. The evolute-involute index, the expansion index, and the fatness index are illustrated in Figure 1. The ornamentation was coded as follows. Nature of venter: 0.0 = undifferentiated from side of shell, 0.33 = faint ridge present so that the ribs become lower along the venter, 0.67=flat venter, and 1.0=strongly depressed and ditched venter. Nature of ribs: 0.0 = smooth, 0.33 = short ribs only seen near venter, 0.67 = complete fine ribs, and 1.0 = complete heavy ribs. Nature of nodes: 0.0 = nodes absent, 0.33 = nodes present along venter, 0.67 = small nodes present along venter and inner part of whorl, and 1.0 = strong nodes present along venter and inner part of whorl. The data are listed in Table 2, whereas some specimens are illustrated in Figure 2.
Numerical taxonomy of samples The data are analyzed by numerical taxonomy. The students are referred to Sneath and Sokal (1973), Sokal and Sneath (1963) and Davis (1973) for general discussions of numerical taxonomy. The initial data matrix is set up with the samples or species in the columns and the characters or variables in the rows (Table 2). The data are first standardized by characters so that each character contributes equally to the matrix of similarity coefficients determined in the next step. For small data sets such as this one, each character is standardized so that it ranges from 0.0 to 1.0. The class is given the formula listed here and instructed to write an APL function to compute the standardized data. This is good practice in programming
Table2. Originaldatamatrixfor hoplitids
o
~
~volute°involute index "" ~xpansion index
0,65
0.73
0,59
0.58
0,56
0.70
0,78
0.73
0.76
0.73
0.911
0.61
0.69
0.71
0,71
0.68
O;6q
0.62
0.65
0.6q
0.66
0.61
Patness
0.55
0.60
0.27
0.36
0.41
0.59
O.ql
0.62
0.37
0.3q
0.27
~ype of v e n t e r
0.0
0.0
0.33
0.33
0.33
1.0
1.0
1.0
1.0
0.67
0.67
type of ribs
1.0
0.67
1.0
1.0
1.0
1.0
1.0
1.0
0.67
0.33
0.33
~ype of nodes
0.0
0.0
0.0
0.0
0.0
0.67
0.67
1.0
0.33
0.0
0.0
index
36
JAMES C. BROWER
Douvilleiceras
mammillatum
Bayleites
baylei
Euhoplites
lautus
Anahoplites
Euhoplites
truncatus
Euhoplites
opalinus
/
( ~
Pseudosonneratia praedentata
planus
~
Pseudosonneratia
crassa
Figure 2. Sketches of hoplitids. All specimens are housed in paleontology collection at Syracuse University. Dou~Ueiceras mammillatUm (Schlotheim) var. aequinodum (Quenstedt), Middle Albian, rnammillatum zone, x 1.1. Bayleites baylei (Collignon),Campanian, × 3.4. Euhoplites lautus (Sowerby), Middle Albian, Zone 7, side view x 1.8, end view x 3.2. Anahoplites planus (Mantell), Middle Albian, Zone 7, x 2.0. Euhoplites truncatus Spath, Middle Albian, Zone 7, x 1.4. E. opalinus Spath, Middle Albian, Zone 8, x 1.3. Pseudosonneratia praedentata Casey, Middle Albian, base of marnmillatum zone, x 2.1. P. crassa Casey, MiddleAlbian, middle of mammillatum zone, x 2.4. and can be done easily--thanks to the high level of the APL language. v..- X,j-X~ "'~ -
i=ith
character,
X~,~, - X~,w"
j---jth
sample,
Xj~=maximtim
value of ith character, X~m~,=minimum value of ith character, Y~j = transformed value of X~. After standardizing the data, a matrix of similarity coefficients is determined for the samples. The students normally choose one or two similarity coefficients from the taxonomic or Euclidean distance, Manhattan distance, or correlation coefficients of the Pearson product moment
37
A statisticallyorientedapproachfor teachingprinciplesof paleontology
one crude method of ordination. As in the similarity matrix, all three techniques display nearly identical structure in the data. Students generally prefer the Prim or minimum distance networks because they seem to enjoy the idea of applying an algorithm which has been used for minimizing the length of telephone lines to working out phylogenies in fossils (Fig. 3). These Prim networks provide a simple introduction to cladistics. Single-linkage cluster analysis is similar to Prim networks. The ordination method borrows from Wagner trees. In the first step, the two or three most dissimilar samples are selected. These are used as axes for plotting all the samples. The most similar species lie closest together on the plot (Fig. 4). Although simple and somewhat crude, this technique serves as a primer to the use and interpretation of ordination. During some years, the students were required to determine the Prim network and the ordinations by hand; in other years programs were furnished but the data had to be plotted by hand. The reader will note the common denominator between the techniques--all are computationally simple and easily visualized by students
type. Programs are available for all coefficients except for the Manhattan distances which must be written by the students. The formulae for the distances are listed here. Manhattan distance
D,~ --- ~i = lI Y , , - Y,~I Taxonomic distance
j = jth sample, k = kth sample, i = ith character, p = number of characters. In the ammonite project, all three similarity coefficients yield almost identical results. All three coefficients share one major common feature---correlations between the characters are ignored. Consequently, some redundant information is included in the similarity matrix. Some numerical taxonomists condemn this practice. However, the writer believes that most character correlations are geometrically, functionally, and biologically meaningful. If this approach is valid, such information is germane and can reasonably be incorporated into a similarity matrix. If desired, such redundant information can be eliminated by calculating a similarity matrix based on Mablanobis D 2 or some other coefficient which scales the distances inversely with respect to the correlations between the characters. One last comment is that the Manhattan distance is easily calculated by hand--all that is required is simple subtraction and addition. The taxonomic distance matrix for the ammonites is presented in Table 3. In general, the matrix is arranged so that the most closely allied taxa are grouped in adjacent columns and rows. After forming the matrix of taxonomic distances, the next step is to extract the main similarities from the matrix. Several algorithms are made available to the class ranging from the brute-force scheme of direct inspection to Prim networks or single-linkage cluster analysis and
E. t runcatus ~k.
A planus (Zone 7) Oouvi,leiceras
~.~.~
E. opalinus ?
~ h ~ /
E. truncatus
A. planus / ( Z o n e S )
" ~ Z o n e
5)
,
~-
E, lautuS
a•ites P. Cr assa " ~ (Upper)
crassa " " - ~ idd I e)
R praedentata
Figure3. Prim networkfor hoplitids.
Table3. Taxonomicdistancematrixfor hoplitids
,
m
n:l
elo
mo
~
m
~
tQ
*~l
*:L
o:l
,~l
r~t
'-;I
~l
,~t
dl~
0.0
0.15
0.22
0.19
0.15
0.21
0.22
0.25
0.22
0.21
0.2d
0.15
0.0
0.19
0.16
0.10,
0.22
0.25
0,25
0.22
0.18
0.2
0.22
0.19
0.0
0.04
0.08
0.25
0.24
0,28
0.20
0.17
0.2
0.19
0.16
0.00,
0.0
0.05
0.23
0.23
0.26
0.19
0.16
0.2
0.15
0.14
0.08
0.05
0.0
0,20
0.21
0.24
0.18
0.16
0.2!
0.21
0.22
0.25
0.23
0.20
0.0
0.09
0.06
0.13
0.21
0.2!
0.22
0.25
0.24
0,23
0.21
0.09
0.0
0.13
0.09
0.18
0.11
0.25
0.25
0,28
0.26
0.2~.
0.07
0.13
0.0
0.17
0.25
0.29
0.22
0.22
0.20
0.19
0.18
0.13
0.09
0.17
0.0
0.10
0.1~
0.21
0.18
0.17
0.16
0.16
0.21
0.18
0.25
0.10
0.0
0.12
0-2 o,
0.25
0.26
0.26
0.25
0.25
0.19
0.29
0.1o,
0.12
0.0
JAMES C. BROWER
38
opalinus c c
Douvilleiceras P. crassa (Middlel • E truncatus l~crassa (Upper)o " " oR p r a e d e n t a t a (Zone 51
= °~ 2 E
Ba ~leites
I E t runcatus
(Zo,e 7)
• E. lautus • A. planus
(zo.e 5)
.1
~5 , 0
A. pla nus
~
.
, (zoo~ 7)
.
Distance
from
.3 E. o p a l i n u s
Figure4. Ordinationdiagramfor hoplitids. with little or no training in statistics or mathematics. Some students, blessed with a working knowledge of matrix algebra, prefer to extract the main similarities by principal components, principal coordinates, or some other method based on eigenvalues and eigenvectors.
The lineage Before discussing the ammonite lineage, a note on the reconstruction of lineages is necessary. The view presented or imposed on the students (depending on personal philosophy) is that the most closely allied organisms are those most similar with respect to homologous characters. This can be ascertained from the statistics. However, before these data can be structured into a phylogeny or line of ancestry and descent, the stratigraphic and biogeographic relationships must be considered. After all, geologically older species are ancestral to younger ones and not the other way around. Similarly, the proposed biogeographic migrations, if any, within the lineage must
be reasonable and plausible. Any proposed lineage must be consistent with the known stratigraphic and biogeographic relations. In fact, a lineage could not be determined for the hoplitid ammonites without superposition because primitive characters could not be conclusively separated from advanced ones. For a contrary view, the reader is referred to Schaeffer, Hecht, and Eldredge (1972). At any rate, the philosophy followed here is that stratigraphy constitutes the yardstick for phylogeny. Figure 5 portrays the most likely lineage for the samples studied. The lineage consists of four main segments. The species of Pseudosonneratia provide the ancestral stock. About the time of the Upper mammillatum zone, this line split into two segments, one of which includes Anahoplites planus whereas the three species of Euhoplites are grouped in the other. Douoilleiceras mammillatum seems to represent an offshoot from Pseudosonneratia. Among the studied forms, Bayleites baylei is closest to Douvil-
leiceras mammillatum. Relationships between characters The correlations between the characters are shown in Table 4 and these are summarized by the single-linkage cluster analysis of the absolute values of the correlation coefficients in Figure 6. Only three correlation coefficients are significantly different from nil at the 5 percent risk level. The degree of whorl overlap (evolute-involute index) is correlated inversely with the amount of whorl expansion (expansion index, r = -0.68). The whorls of the more involute forms overlap greatly and the whorls expand rapidly whereas the evolute conchs, in which the whorls are almost fully visible, are characterized by slow expansion of the whorls. The evolute-involute index is negatively correlated with the nature of the ribs (r = -0.67). Involute forms generally lack ribs but these are present in evolute species. The nature of the venter is positively associated with the presence of nodes (r =
ites
CAMPANIAN
Z <
'-J
ZONE
8
ZONE
7
ZONE
6
ZONE
5
~
UPPER
~"'
MIDDLE
F. opalinus
E.lautus/ E. truncatuS
T
E. truncatus
\/
A'Ianus
A. planus
p. c r o s s o
T
P. c r a s s a
Figure5. Line of ancestry and descent for hoplitids.
Douvillelceras
A statisticallyorientedapproachfor teachingprinciplesof paleontology MAGNLrUDE OF C O R R E L A T I O N COEFFICIENT
__
i
--
i
i EVOLUTE-INVOLUTE
EXPANSION
t
-
-
TYPE O [
~
INDEX
INDEX
RIBS
TYPE OF NODES
TYPE OF VENTER
FATNESS
INDEX
Figure 6. Singleqinkage cluster analysis for magnitudes of correlationcoefficientsof hoplitidcharacters. Table4. Correlationmatrixbetweencharacters
I .0 -0.68
-0.68
-0.07
0.~7
I .0
-0.6"~
0.211
-0.17
-0.38
0.23
-0.32
-0.17
1.0
-0.03
0.39
0.B1
0.~7
-0.38
-0.03
I .0
-0.07
0.78
-0.67
0.23
0.39
-0.07
I .0
0.37
0.37
I .0
-0.07
0.2I~
-0.32
0.5"I
0.78
0.78). Nodes are usually not observed in taxa with simple venters, but forms with ditches along the venter may have nodes. The fatness index is more or less independent of the other variables.
Evolutionary trends and functional morphology The evolution of hoplitids is interpreted as adaptative for several reasons. The lineage consisted of large populations in which small coefficients of natural selection would have provided efficient vectors of evolution. Also the evolutionary trends can be interpreted logically in terms of adaptation. As a guide to the living habits and functional morphology of ammonites, the students are advised to consult a basic paleontology text and the "Treatise" volumes on ammonites (Arkell and others, 1957) and nautiloids (Teichert and others, 1964). Aside from those, the students are left to their own devices. Most individuals manage to "discover" the works by Raup (1967), Kummel and Lloyd (1955), and Trueman (1941) which aid in interpretation. The ancestral stock, Pseudosonneratia, is interpreted as a generalized group of ammonites, which probably was adapted to a combination of active swimming, drifting over a particular habitat, and resting on the bottom. The main line of descent from Pseudosonneratia seen in the studied samples comprises the various species of Euhoplites. In terms of conch shape, these forms are fatter, somewhat more involute, and possess whorls that expand at a slightly faster rate. However, the most striking changes are in the nodes and the venter part of the
39
shell. The euhoplitids developed strongly ditched venters, heavier ribs in most forms, and more or less strong nodes along the venter and inner parts of the whorls. The fatter, more nodose, and more heavily ribbed shells of the euhoplitids suggest a high amount of frictional drag which may have been correlated with a shift to a less active way of life. Possibly the euhoplitids were primarily drifters which were sluggish swimmers and the animals may have spent an appreciable amount of time resting, crawling or foraging on the bottom. The ribs and nodes may have served as camouflage which functioned to break the silhouette of the shell as do the color bands of the living Nautilus. The venter nodes perhaps stabilized the shell when resting or crawling on the seafloor. The ditched venter might reflect some change in the siphon. The main line of eupholitids included Euhoplites truncatus. The two descendent species diverged. E. opalinus retained the shell shape of its ancestor but accentuated the ribs and nodes. On the other hand, E. lautus formed a more slender shell with less prominent ribs and nodes. The anahoplitids deviated from the ancestral stock in several respects. The shell became more involute whereas the whorls expanded more rapidly. This probably dictated increased separation of the centers of gravity and buoyancy which should have augmented the stability of the shell while swimming or floating. The two samples of Anahoplites planus also are characterized by compressed conchs of slender and graceful profile. The ribs are almost completely obsolete, being only represented by small riblets located near the flat venter. The anahoplitids probably were specialized for a more actively swimming mode of life that that of the ancestral Pseudosonneratia or contemporary species of Euhoplites. This is suggested by the wide displacement of the centers of gravity and buoyancy and the resultant high degree of shell stability in conjunction with the slender, involute, and almost smooth conch which must have been subject to low drag. Most students believe that Douvilleiceras is most similar to Pseudosonneratia. The main difference comprises the fatter shell of Douvilleiceras. Bayleites may be allied remotely to Douvilleiceras from which it was derived by the development of finer ribs. The douvilleiceratidbayleitid line possibly represented another adaptation to less active living habits than seen in Pseudosonneratia. SUMMARY
The research project that is oriented statistically has proven an effective vehicle for teaching brinciples of paleontology. The students must design and carry out studies which are comparable to those done by some professional paleontologists. In order that the projects can be completed in several weeks, small- to moderatesized data sets with consistent and fairly simple structure are necessary. Under these ground rules, reasonable results can be obtained by the students. These exercises produce several useful byproducts aside from knowledge of paleontological principles. These include some degree of competence in simple statistics and increased familiarity with the fossil groups studied in the projects. For example, it is difficult to interpret an ontogenetic sequence of brachiopods without some general acquaintance with
40 these dents more more
JAMESC. BROWER animals. Lastly but by no means least, many stufeel that projects of this sort are more creative, demanding, and better learning experiences than conventional laboratory exercises.
REFERENCES
Arkel], W. J., and others, 1975, Cephalopoda, Ammonoidea, in Treatise on invertebrate paleontology, Part L: Geol. Soc. America and Univ. Kansas Press, 490 p. Casey, R., 1960-1966, A monograph of the Ammonoidea of the Lower Greensand: Palaeontographical Soc. Monograph, 582 p. Davis, J. C., 1973, Statistics and data analysis in geology: John Wiley & Sons, Inc., New York, 550 p. Dodd, J. R., and Immega, N. T., 1974,The portable computer as a teaching aid: examples from a geobiology course: Jour. Geol. Educ., v. 22, No. 5, p. 209-214. Jardine, N., 1967, The concept of homology in biology: British Jour. Philosophy of Science, v. 18, p. 125-139. Jardine, N., 1969, The observational and theoretical components of homology: a study based on the morphology of the dermal skull-roofs of rhipidistian fishes: Biol. Jour. Lima. Soc., v. l, p. 327-361. Kummel, B., and Lloyd, R. M., 1955, Experiments on relative streamlining of coiled cephalopod shells: Jour. Paleontogy, v. 29, no. l, p. 159-170.
Osborne, R. H., 1969, Undergraduate instruction in geomathematics: Jour. Geol. Educ., v. 17, no. 4, p. 9, 120-124. Raup, D. M., 1967, Geometric analysis of shell coiling: coiling in ammonoids: Jour. Paleontotogy, v. 41, no. 1, p. 43-65. Raup, D. M., and Stanley, S. M., 1971, Principles of paleontology: W. H. Freeman and Co., San Francisco, 388 p. Rodriguez, J., and Malone, P. C., 1974, Computer-oriented exercises in undergraduate paleontology: Jour. Geol. Educ., v. 22, no. 3, p. ll2-114. Schaeffer, B., Hecht, M. K., and Eldredge, N., 1972, Phylogeny and paleontology, in Evolutionary biology, v. 6: AppletonCentury-Crofts, New York, p. 31--46. Sneath, P. H. A., and Sokal, R. R., 1973, Numerical taxonomy-the principles and practice of numerical classification: W. H. Freeman and Co., San Francisco, 573 p. Sokal, R. R., and Sneath, P. H. A., 1963, Principles of numerical taxonomy: W. H. Freeman and Co., San Francisco, 359 p. Spath, L. F., 1923-1943, A monograph on the Ammonoidea of the Ganlt: Palaeontogruphical Soc. Monograph, 787 p. Teichert, C., and others, 1964, Cephalopoda, Nautilnidea, in Treatise on invertebrate paleontology, Part K: Geol. Soc. America and Univ. Kansas Press, 519 p. Trueman, A. E., 1941, The ammonite body chamber with special reference to the buoyancy and mode of life of the living ammonite: Geol. Soc. London Quart. Jour., v. 96, p. 339-383. Wright, R. C., 1972, Evol 1--a computer based natural selection game: Jour. Geol. Educ., v. 20, no. 2, p. 75--77.
A STATISTICALLY ORIENTED APPROACH FOR TEACHING PRINCIPLES OF PALEONTOLOGY JAMES C. BROWER Departmentof Geology,SyracuseUniversity,Syracuse,NY 13210,U.S.A.
(Received31 December1975) Abstract--Researchprojects that are oriented statisticallyare highlyeffectivefor teachingpaleontologicalprinciples. The exercisesdevelopedat SyracuseUniversityover the past severalyears are outlinedbrieflyand one is annotatedin detail. Students respondfavorably toward the projects and most individualsbelieve that the projects comprisemore creative and demanding,and better learning experiences than conventionallaboratory exercises.
Key Words: CAI, Classification,Cluster analysis, Ammonities, Cretaceous, Evolution, Numerical taxonomy, Paleontology.
INTRODUCTION
and the complexity of the exercise, the papers range from several pages to about 20 pages in length. In effect the students are required to design and carry out research projects that are similar to those done by many professional paleontologists. The projects are:
For several years computer-based laboratory exercises have been used in the beginning paleontology course at Syracuse University. The students mostly consist of junior and senior undergraduates with a smattering of first-year graduate students. Although a few individuals may be familiar with computers and basic statistics, the average person has no prior preparation in these fields. The required text for the course is the book by Raup and Stanley (1971) entitled "Principles of Paleontology" and the exercises are oriented toward paleontological principles. Somewhat similar projects were outlined by Osborne (1969) and Rodriguez and Malone (1974) whereas Dodd and Immega (1974) and Wright (1972) employed simulations to model biological processes such as natural selection for paleontology students.
(1) Paleoecology One possible study involves a Silurian eurypterid assemblage dominated by Eurypterus remipes remipes (DeKay). The students work out molt stages and determine mortality and survivorship rates which then are compared with similar data for its distant relative, the extant Limulus. The living habits and functional morphology and nature of the depositional environment also are reconstructed for the eurypterid. An alternate project deals with a series of fossil assemblages from the Middle Devonian. Here, assemblages and their component species are analyzed by simple techniques of numerical taxonomy.
THE APPROACH
The exercises actually are research projects which are initiated in the scheduled laboratories and completed outside of class. The purpose of the projects is to acquaint the students with major problems in paleontology and how these may be studied by means of statistics. Each project lasts two to three weeks. Several lectures are devoted to the aspect of paleontology, such as the species concept, to be researched. One or more statistical or mathematical methods pertinent to the problem also are annotated. The basic flowchart is simple and direct. In the first laboratory, the students are shown groups of specimens to be studied and the problem to be attacked is outlined. The material is examined and a set of measurements is devised to express the sizes and shapes involved. The measures are generally made and preliminary readings finished during the first week. The computer programming and programs needed for the project are covered in the second laboratory along with a general outline as to the report for the project. The remainder of the time is spent processing data, analyzing the computer output, and writing a paper discussing the data and interpreting the results. Although small groups of students pool their efforts to do the "dirty work" such as making the measurements, each individual must prepare a separate report. Depending on the student
(2) Ontogeny Relative growth sequences of several fossil invertebrates are studied by means of correlation coefficients and the simple allometric equation. The relationships between size and shape changes are stressed, and the equation data are interpreted in terms of functional morphology. Two projects on ontogeny relative to time also are available, one based on growth lines in corals and the other on pelecypods. (3) Species concept Species are treated in the context of interbreeding or potentially interbreeding populations in which the distribution of characters within and between samples is both pertinent and subject to statistical analysis and inference. Inasmuch as statistical inference is a difficult concept for most paleontologists, two exercises are devoted to this subject. In the first project, three samples are given, two of which are conspecific whereas the third belongs to a separate species. The data are analyzed by the one-way analysis of variance or a Students-t test to determine the equality of the means of the samples. In this situation, the students are able to compare results for 33
34
JAMES C. BROWER
samples which overlap greatly with results for samples showing little or no overlap. In the second species problem, the students are presented samples containing two closely related species as collected from the field. They are told to segregate the different species and test the differences statistically. In this situation, the differences are size related. These are tested by comparing slopes or equation values of several regression lines. Typically the species are selected to show progressive ontogenetic divergence, that is the young specimens are relatively similar but the forms diverge as the animals grew older. This illustrates one type of relationship between ontogeny and phylogeny. (4) Biostratigraphy One biostratigraphy project is based on several local stratigraphic sections in the Middle Devonian. Relative biostratigraphic values are calculated for the species in the two sections; these express the amount of "biostratigraphic information" conveyed by the presence of a particular species. Some taxa are more useful for correlation than others. The sections then are correlated based on the forms with the highest relative biostratigraphic values. Another problem defines morphoclines in ostracods in two stratigraphic sections which are matched subsequently by cross-correlating the morphoclines.
yields instant answers. APL is a high-level language with great power for manipulating matrices and vectors. Students with little or no experience with computers can be taught quickly a few basics which allow them to solve meaningful and reasonably complex problems after only several hours of instruction. APL is suitable for gradual learning--a bit at a time. Some of the programs for the exercises are written by the students, whereas others are provided by the instructor or taken from one of several APL statistical packages. The concepts behind the selection of the statistics are as follows. We attempt to apply basic univariate and bivariate statistics. Some multivariate techniques are involved, but these are restricted to simple types of numerical taxonomy. Most students do not have a working knowledge of matrix algebra. Consequently, algorithms requiring sophisticated matrix operations such as extraction of eigenvalues and eigenvectors or matrix inversion are avoided. Incidentally, if computers are not available, most of the techniques are simple enough so that the statistics can be obtained on a desk or pocket calculator for moderate-sized sets of data. Computers aid greatly but are not strictly necessary for the teaching of quantitative paleontology. AMMONITE PROJECT
Initial steps (5) Evolution The evolution project will be annotated later in this paper as an example of the approach. Suites of different fossils are used for each project. For example, evolutionary lineages have been analyzed in the Ordovician trilobite Cryptolithus, Cretaceous hoplitid ammonites, Paleozoic atrypid brachiopods, and Mesozoic pterodactyls. Ontogenies of various groups have been investigated including eurypterids, blastoids, crinoids, trilobites, ostracods, foraminifers, brachiopods, and pelecypods. The programming language for the course consists of APL which has several advantages for instruction purposes. It is a terminal-based interactive language which
However, the proof of the pudding lies in the eating and not in the recipe. Consequently it seems appropriate to turn to an example to display the virtues of this computerbased and project-oriented approach to instruction in paleontology. The project on ammonite evolution will be discussed which will illustrate the approach, methods, and results obtained by the class. Prior to beginning the study, several lectures have been given on numerical taxonomy as well as on the determination of lineages, that is lines of ancestry and descent, and reconstruction of evolutionary trends. The material consists of 11 samples of hoplitid ammonites from the Albian and Campanian of England (Table 1). The samples were collected by the late L. W. Ploger
Table 1. Listof samplesfor hoplitidammonites Species
Pseudosonneratia
Number ot speclmens in sample
Horizon
praedentata
Casey
Middle Albian, base of mammillatum zone 19
p. crassa Casey
Middle Albian, center of ma~millatum zone
p. crassa Casey
Middle Albian, top of mammillatum zone
Euhoplites truncatus Spath
Middle Albian,
zone 5
11
E. truncatus Spath
Middle Albian,
Zone 7
13
E. opalinus Spath
Middle Albian,
zone 8
1
E. lautus
Middle Albian,
Zone 7
6
Middle Albian,
Zone 5
10
Middle Albian,
zone 7
21
(Sowerby)
Anahoplites planus I~" planus
(Mantell)
(Mantell)
Douvilleiceras mammillatum (Schlotheim) vat. aequlnodum (Quenstedt) i~ayleites baylei
(Collignon)
Middle Albian, mammillatum zone Campanian
1
35
A statisticallyorientedapproachfor teachingprinciplesof paleontology from the "Gault" near Folkestone in the 1930's. Ploger approximately keyed the samples into the horizons outlined by Spath (1923-1943, p. 1-5, 669-682). It must be noted that this class project is not a definitive study on hoplitid ammonites. Only a small number of taxa, stratigraphic horizons, and characters are included. Strictly speaking, the results are only valid for the samples examined by the students although they may be applicable generally to hoplitids and other ammonities. The conclusions by the students based on numerical taxonomy are essentially the same as the qualitative phylogenies presented by Spath (1923-1943, p. 685-699). However, the students have no access to this part of Spath's work. The students are advised to consult several basic paleontology texts on ammonite morphology and they are instructed to identify the species involved using monographs on ammonites by Spath (1923-1943, p. 1-311) and Casey (1960-1966) and the Treatise volume on ammonites (Arkell and others, 1957). The literature on ammonites is typological in which minor variants are described as belonging to different species or genera. Consequently the students experience the "trials and tribulations" of dealing with this type of taxonomy. This makes a distinct imprint on the brighter students; perhaps, taxonomic practices will improve if such individuals cgntinue on in paleontology. It is notable that the samples are placed generally in the same genera; however, species assignments have differed greatly through the years. This partially reflects a lack of student expertise, but the state of ammonite taxonomy is also a contributing factor. The samples are compared and contrasted with respect to homologous characters. The lineages mostly consist of closely related genera and species in which there are no problems in determining homologies. If desired, less closely allied forms with more subtle homologies could be treated. In such a study, the search for homology could be quantified, perhaps by the methods outlined by Jardine (1967, 1969). A set of measurements is devised to assess the similarities and differences between the samples. The specimens consist of partial conchs where only the juvenile part of the shell is preserved so that the size of specimens has no significance. Therefore the data should be as independent of size and measurement units as possible. It is the shapes of the shells that are of interest-not the sizes. Usually, this problem is solved by determining ratios that directly portray the desired shapes. Each
5
INVOLUTE
EVOLUTE
EXPANSION FATNESS
I
I I
I,
>I
4 INDEX = 2 / 3
INDEX = 1 / 3
INDEX = 4 / 5
Figure 1. Sketches showing measurements for first three characters in hoplitids. sample is represented by a single suite of measurements. In this situation, six variables were determined for the 11 samples. The evolute-involute index, the expansion index, and the fatness index are illustrated in Figure 1. The ornamentation was coded as follows. Nature of venter: 0.0 = undifferentiated from side of shell, 0.33 = faint ridge present so that the ribs become lower along the venter, 0.67=flat venter, and 1.0=strongly depressed and ditched venter. Nature of ribs: 0.0 = smooth, 0.33 = short ribs only seen near venter, 0.67 = complete fine ribs, and 1.0 = complete heavy ribs. Nature of nodes: 0.0 = nodes absent, 0.33 = nodes present along venter, 0.67 = small nodes present along venter and inner part of whorl, and 1.0 = strong nodes present along venter and inner part of whorl. The data are listed in Table 2, whereas some specimens are illustrated in Figure 2.
Numerical taxonomy of samples The data are analyzed by numerical taxonomy. The students are referred to Sneath and Sokal (1973), Sokal and Sneath (1963) and Davis (1973) for general discussions of numerical taxonomy. The initial data matrix is set up with the samples or species in the columns and the characters or variables in the rows (Table 2). The data are first standardized by characters so that each character contributes equally to the matrix of similarity coefficients determined in the next step. For small data sets such as this one, each character is standardized so that it ranges from 0.0 to 1.0. The class is given the formula listed here and instructed to write an APL function to compute the standardized data. This is good practice in programming
Table2. Originaldatamatrixfor hoplitids
o
~
~volute°involute index "" ~xpansion index
0,65
0.73
0,59
0.58
0,56
0.70
0,78
0.73
0.76
0.73
0.911
0.61
0.69
0.71
0,71
0.68
O;6q
0.62
0.65
0.6q
0.66
0.61
Patness
0.55
0.60
0.27
0.36
0.41
0.59
O.ql
0.62
0.37
0.3q
0.27
~ype of v e n t e r
0.0
0.0
0.33
0.33
0.33
1.0
1.0
1.0
1.0
0.67
0.67
type of ribs
1.0
0.67
1.0
1.0
1.0
1.0
1.0
1.0
0.67
0.33
0.33
~ype of nodes
0.0
0.0
0.0
0.0
0.0
0.67
0.67
1.0
0.33
0.0
0.0
index
36
JAMES C. BROWER
Douvilleiceras
mammillatum
Bayleites
baylei
Euhoplites
lautus
Anahoplites
Euhoplites
truncatus
Euhoplites
opalinus
/
( ~
Pseudosonneratia praedentata
planus
~
Pseudosonneratia
crassa
Figure 2. Sketches of hoplitids. All specimens are housed in paleontology collection at Syracuse University. Dou~Ueiceras mammillatUm (Schlotheim) var. aequinodum (Quenstedt), Middle Albian, rnammillatum zone, x 1.1. Bayleites baylei (Collignon),Campanian, × 3.4. Euhoplites lautus (Sowerby), Middle Albian, Zone 7, side view x 1.8, end view x 3.2. Anahoplites planus (Mantell), Middle Albian, Zone 7, x 2.0. Euhoplites truncatus Spath, Middle Albian, Zone 7, x 1.4. E. opalinus Spath, Middle Albian, Zone 8, x 1.3. Pseudosonneratia praedentata Casey, Middle Albian, base of marnmillatum zone, x 2.1. P. crassa Casey, MiddleAlbian, middle of mammillatum zone, x 2.4. and can be done easily--thanks to the high level of the APL language. v..- X,j-X~ "'~ -
i=ith
character,
X~,~, - X~,w"
j---jth
sample,
Xj~=maximtim
value of ith character, X~m~,=minimum value of ith character, Y~j = transformed value of X~. After standardizing the data, a matrix of similarity coefficients is determined for the samples. The students normally choose one or two similarity coefficients from the taxonomic or Euclidean distance, Manhattan distance, or correlation coefficients of the Pearson product moment
37
A statisticallyorientedapproachfor teachingprinciplesof paleontology
one crude method of ordination. As in the similarity matrix, all three techniques display nearly identical structure in the data. Students generally prefer the Prim or minimum distance networks because they seem to enjoy the idea of applying an algorithm which has been used for minimizing the length of telephone lines to working out phylogenies in fossils (Fig. 3). These Prim networks provide a simple introduction to cladistics. Single-linkage cluster analysis is similar to Prim networks. The ordination method borrows from Wagner trees. In the first step, the two or three most dissimilar samples are selected. These are used as axes for plotting all the samples. The most similar species lie closest together on the plot (Fig. 4). Although simple and somewhat crude, this technique serves as a primer to the use and interpretation of ordination. During some years, the students were required to determine the Prim network and the ordinations by hand; in other years programs were furnished but the data had to be plotted by hand. The reader will note the common denominator between the techniques--all are computationally simple and easily visualized by students
type. Programs are available for all coefficients except for the Manhattan distances which must be written by the students. The formulae for the distances are listed here. Manhattan distance
D,~ --- ~i = lI Y , , - Y,~I Taxonomic distance
j = jth sample, k = kth sample, i = ith character, p = number of characters. In the ammonite project, all three similarity coefficients yield almost identical results. All three coefficients share one major common feature---correlations between the characters are ignored. Consequently, some redundant information is included in the similarity matrix. Some numerical taxonomists condemn this practice. However, the writer believes that most character correlations are geometrically, functionally, and biologically meaningful. If this approach is valid, such information is germane and can reasonably be incorporated into a similarity matrix. If desired, such redundant information can be eliminated by calculating a similarity matrix based on Mablanobis D 2 or some other coefficient which scales the distances inversely with respect to the correlations between the characters. One last comment is that the Manhattan distance is easily calculated by hand--all that is required is simple subtraction and addition. The taxonomic distance matrix for the ammonites is presented in Table 3. In general, the matrix is arranged so that the most closely allied taxa are grouped in adjacent columns and rows. After forming the matrix of taxonomic distances, the next step is to extract the main similarities from the matrix. Several algorithms are made available to the class ranging from the brute-force scheme of direct inspection to Prim networks or single-linkage cluster analysis and
E. t runcatus ~k.
A planus (Zone 7) Oouvi,leiceras
~.~.~
E. opalinus ?
~ h ~ /
E. truncatus
A. planus / ( Z o n e S )
" ~ Z o n e
5)
,
~-
E, lautuS
a•ites P. Cr assa " ~ (Upper)
crassa " " - ~ idd I e)
R praedentata
Figure3. Prim networkfor hoplitids.
Table3. Taxonomicdistancematrixfor hoplitids
,
m
n:l
elo
mo
~
m
~
tQ
*~l
*:L
o:l
,~l
r~t
'-;I
~l
,~t
dl~
0.0
0.15
0.22
0.19
0.15
0.21
0.22
0.25
0.22
0.21
0.2d
0.15
0.0
0.19
0.16
0.10,
0.22
0.25
0,25
0.22
0.18
0.2
0.22
0.19
0.0
0.04
0.08
0.25
0.24
0,28
0.20
0.17
0.2
0.19
0.16
0.00,
0.0
0.05
0.23
0.23
0.26
0.19
0.16
0.2
0.15
0.14
0.08
0.05
0.0
0,20
0.21
0.24
0.18
0.16
0.2!
0.21
0.22
0.25
0.23
0.20
0.0
0.09
0.06
0.13
0.21
0.2!
0.22
0.25
0.24
0,23
0.21
0.09
0.0
0.13
0.09
0.18
0.11
0.25
0.25
0,28
0.26
0.2~.
0.07
0.13
0.0
0.17
0.25
0.29
0.22
0.22
0.20
0.19
0.18
0.13
0.09
0.17
0.0
0.10
0.1~
0.21
0.18
0.17
0.16
0.16
0.21
0.18
0.25
0.10
0.0
0.12
0-2 o,
0.25
0.26
0.26
0.25
0.25
0.19
0.29
0.1o,
0.12
0.0
JAMES C. BROWER
38
opalinus c c
Douvilleiceras P. crassa (Middlel • E truncatus l~crassa (Upper)o " " oR p r a e d e n t a t a (Zone 51
= °~ 2 E
Ba ~leites
I E t runcatus
(Zo,e 7)
• E. lautus • A. planus
(zo.e 5)
.1
~5 , 0
A. pla nus
~
.
, (zoo~ 7)
.
Distance
from
.3 E. o p a l i n u s
Figure4. Ordinationdiagramfor hoplitids. with little or no training in statistics or mathematics. Some students, blessed with a working knowledge of matrix algebra, prefer to extract the main similarities by principal components, principal coordinates, or some other method based on eigenvalues and eigenvectors.
The lineage Before discussing the ammonite lineage, a note on the reconstruction of lineages is necessary. The view presented or imposed on the students (depending on personal philosophy) is that the most closely allied organisms are those most similar with respect to homologous characters. This can be ascertained from the statistics. However, before these data can be structured into a phylogeny or line of ancestry and descent, the stratigraphic and biogeographic relationships must be considered. After all, geologically older species are ancestral to younger ones and not the other way around. Similarly, the proposed biogeographic migrations, if any, within the lineage must
be reasonable and plausible. Any proposed lineage must be consistent with the known stratigraphic and biogeographic relations. In fact, a lineage could not be determined for the hoplitid ammonites without superposition because primitive characters could not be conclusively separated from advanced ones. For a contrary view, the reader is referred to Schaeffer, Hecht, and Eldredge (1972). At any rate, the philosophy followed here is that stratigraphy constitutes the yardstick for phylogeny. Figure 5 portrays the most likely lineage for the samples studied. The lineage consists of four main segments. The species of Pseudosonneratia provide the ancestral stock. About the time of the Upper mammillatum zone, this line split into two segments, one of which includes Anahoplites planus whereas the three species of Euhoplites are grouped in the other. Douoilleiceras mammillatum seems to represent an offshoot from Pseudosonneratia. Among the studied forms, Bayleites baylei is closest to Douvil-
leiceras mammillatum. Relationships between characters The correlations between the characters are shown in Table 4 and these are summarized by the single-linkage cluster analysis of the absolute values of the correlation coefficients in Figure 6. Only three correlation coefficients are significantly different from nil at the 5 percent risk level. The degree of whorl overlap (evolute-involute index) is correlated inversely with the amount of whorl expansion (expansion index, r = -0.68). The whorls of the more involute forms overlap greatly and the whorls expand rapidly whereas the evolute conchs, in which the whorls are almost fully visible, are characterized by slow expansion of the whorls. The evolute-involute index is negatively correlated with the nature of the ribs (r = -0.67). Involute forms generally lack ribs but these are present in evolute species. The nature of the venter is positively associated with the presence of nodes (r =
ites
CAMPANIAN
Z <
'-J
ZONE
8
ZONE
7
ZONE
6
ZONE
5
~
UPPER
~"'
MIDDLE
F. opalinus
E.lautus/ E. truncatuS
T
E. truncatus
\/
A'Ianus
A. planus
p. c r o s s o
T
P. c r a s s a
Figure5. Line of ancestry and descent for hoplitids.
Douvillelceras
A statisticallyorientedapproachfor teachingprinciplesof paleontology MAGNLrUDE OF C O R R E L A T I O N COEFFICIENT
__
i
--
i
i EVOLUTE-INVOLUTE
EXPANSION
t
-
-
TYPE O [
~
INDEX
INDEX
RIBS
TYPE OF NODES
TYPE OF VENTER
FATNESS
INDEX
Figure 6. Singleqinkage cluster analysis for magnitudes of correlationcoefficientsof hoplitidcharacters. Table4. Correlationmatrixbetweencharacters
I .0 -0.68
-0.68
-0.07
0.~7
I .0
-0.6"~
0.211
-0.17
-0.38
0.23
-0.32
-0.17
1.0
-0.03
0.39
0.B1
0.~7
-0.38
-0.03
I .0
-0.07
0.78
-0.67
0.23
0.39
-0.07
I .0
0.37
0.37
I .0
-0.07
0.2I~
-0.32
0.5"I
0.78
0.78). Nodes are usually not observed in taxa with simple venters, but forms with ditches along the venter may have nodes. The fatness index is more or less independent of the other variables.
Evolutionary trends and functional morphology The evolution of hoplitids is interpreted as adaptative for several reasons. The lineage consisted of large populations in which small coefficients of natural selection would have provided efficient vectors of evolution. Also the evolutionary trends can be interpreted logically in terms of adaptation. As a guide to the living habits and functional morphology of ammonites, the students are advised to consult a basic paleontology text and the "Treatise" volumes on ammonites (Arkell and others, 1957) and nautiloids (Teichert and others, 1964). Aside from those, the students are left to their own devices. Most individuals manage to "discover" the works by Raup (1967), Kummel and Lloyd (1955), and Trueman (1941) which aid in interpretation. The ancestral stock, Pseudosonneratia, is interpreted as a generalized group of ammonites, which probably was adapted to a combination of active swimming, drifting over a particular habitat, and resting on the bottom. The main line of descent from Pseudosonneratia seen in the studied samples comprises the various species of Euhoplites. In terms of conch shape, these forms are fatter, somewhat more involute, and possess whorls that expand at a slightly faster rate. However, the most striking changes are in the nodes and the venter part of the
39
shell. The euhoplitids developed strongly ditched venters, heavier ribs in most forms, and more or less strong nodes along the venter and inner parts of the whorls. The fatter, more nodose, and more heavily ribbed shells of the euhoplitids suggest a high amount of frictional drag which may have been correlated with a shift to a less active way of life. Possibly the euhoplitids were primarily drifters which were sluggish swimmers and the animals may have spent an appreciable amount of time resting, crawling or foraging on the bottom. The ribs and nodes may have served as camouflage which functioned to break the silhouette of the shell as do the color bands of the living Nautilus. The venter nodes perhaps stabilized the shell when resting or crawling on the seafloor. The ditched venter might reflect some change in the siphon. The main line of eupholitids included Euhoplites truncatus. The two descendent species diverged. E. opalinus retained the shell shape of its ancestor but accentuated the ribs and nodes. On the other hand, E. lautus formed a more slender shell with less prominent ribs and nodes. The anahoplitids deviated from the ancestral stock in several respects. The shell became more involute whereas the whorls expanded more rapidly. This probably dictated increased separation of the centers of gravity and buoyancy which should have augmented the stability of the shell while swimming or floating. The two samples of Anahoplites planus also are characterized by compressed conchs of slender and graceful profile. The ribs are almost completely obsolete, being only represented by small riblets located near the flat venter. The anahoplitids probably were specialized for a more actively swimming mode of life that that of the ancestral Pseudosonneratia or contemporary species of Euhoplites. This is suggested by the wide displacement of the centers of gravity and buoyancy and the resultant high degree of shell stability in conjunction with the slender, involute, and almost smooth conch which must have been subject to low drag. Most students believe that Douvilleiceras is most similar to Pseudosonneratia. The main difference comprises the fatter shell of Douvilleiceras. Bayleites may be allied remotely to Douvilleiceras from which it was derived by the development of finer ribs. The douvilleiceratidbayleitid line possibly represented another adaptation to less active living habits than seen in Pseudosonneratia. SUMMARY
The research project that is oriented statistically has proven an effective vehicle for teaching brinciples of paleontology. The students must design and carry out studies which are comparable to those done by some professional paleontologists. In order that the projects can be completed in several weeks, small- to moderatesized data sets with consistent and fairly simple structure are necessary. Under these ground rules, reasonable results can be obtained by the students. These exercises produce several useful byproducts aside from knowledge of paleontological principles. These include some degree of competence in simple statistics and increased familiarity with the fossil groups studied in the projects. For example, it is difficult to interpret an ontogenetic sequence of brachiopods without some general acquaintance with
40 these dents more more
JAMESC. BROWER animals. Lastly but by no means least, many stufeel that projects of this sort are more creative, demanding, and better learning experiences than conventional laboratory exercises.
REFERENCES
Arkel], W. J., and others, 1975, Cephalopoda, Ammonoidea, in Treatise on invertebrate paleontology, Part L: Geol. Soc. America and Univ. Kansas Press, 490 p. Casey, R., 1960-1966, A monograph of the Ammonoidea of the Lower Greensand: Palaeontographical Soc. Monograph, 582 p. Davis, J. C., 1973, Statistics and data analysis in geology: John Wiley & Sons, Inc., New York, 550 p. Dodd, J. R., and Immega, N. T., 1974,The portable computer as a teaching aid: examples from a geobiology course: Jour. Geol. Educ., v. 22, No. 5, p. 209-214. Jardine, N., 1967, The concept of homology in biology: British Jour. Philosophy of Science, v. 18, p. 125-139. Jardine, N., 1969, The observational and theoretical components of homology: a study based on the morphology of the dermal skull-roofs of rhipidistian fishes: Biol. Jour. Lima. Soc., v. l, p. 327-361. Kummel, B., and Lloyd, R. M., 1955, Experiments on relative streamlining of coiled cephalopod shells: Jour. Paleontogy, v. 29, no. l, p. 159-170.
Osborne, R. H., 1969, Undergraduate instruction in geomathematics: Jour. Geol. Educ., v. 17, no. 4, p. 9, 120-124. Raup, D. M., 1967, Geometric analysis of shell coiling: coiling in ammonoids: Jour. Paleontotogy, v. 41, no. 1, p. 43-65. Raup, D. M., and Stanley, S. M., 1971, Principles of paleontology: W. H. Freeman and Co., San Francisco, 388 p. Rodriguez, J., and Malone, P. C., 1974, Computer-oriented exercises in undergraduate paleontology: Jour. Geol. Educ., v. 22, no. 3, p. ll2-114. Schaeffer, B., Hecht, M. K., and Eldredge, N., 1972, Phylogeny and paleontology, in Evolutionary biology, v. 6: AppletonCentury-Crofts, New York, p. 31--46. Sneath, P. H. A., and Sokal, R. R., 1973, Numerical taxonomy-the principles and practice of numerical classification: W. H. Freeman and Co., San Francisco, 573 p. Sokal, R. R., and Sneath, P. H. A., 1963, Principles of numerical taxonomy: W. H. Freeman and Co., San Francisco, 359 p. Spath, L. F., 1923-1943, A monograph on the Ammonoidea of the Ganlt: Palaeontogruphical Soc. Monograph, 787 p. Teichert, C., and others, 1964, Cephalopoda, Nautilnidea, in Treatise on invertebrate paleontology, Part K: Geol. Soc. America and Univ. Kansas Press, 519 p. Trueman, A. E., 1941, The ammonite body chamber with special reference to the buoyancy and mode of life of the living ammonite: Geol. Soc. London Quart. Jour., v. 96, p. 339-383. Wright, R. C., 1972, Evol 1--a computer based natural selection game: Jour. Geol. Educ., v. 20, no. 2, p. 75--77.