SEXUAL DIMORPHISM IN THE DEVONIAN TRILOBITE
PHACOPS RANiA

Thesis for the Degree of M. S.
MICHIGAN STATE UNIVERSITY
MICHAEL TUCKEY
19-75

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ABSTRACT
SEXUAL DIMORPHISM IN THE DEVONIAN TRILOBITE
PHACOPS RANA

BY

Michael Tuckey

Quantitative analysis of the cephalons of the Devonian

trilobites Phacops rana milleri and Phacops rana crassituber~

 

 

culata from the Silica shale, Sylvania, Ohio, reveal signi-
ficant morphological differences between the two subspecies,
and dimorphism within each of the two subspecies character-
ized by variation in glabellar and cephalic shape. The
dimorphism is interpreted to be sexual in nature with the
females having relatively longer and narrower glabellas and
cephalons and the males having relatively shorter and wider

glabellas and cephalons.

SEXUAL DIMORPHISM IN THE DEVONIAN TRILOBITE

PHACOPS RANA

 

BY

Michael Tuckey

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Geology

1975

ACKNOWLEDGMENTS

I would like to thank Robert Kesling of the Museum of
Paleontology, University of Michigan, and Larry Magrum for
—allowing me to use their specimens in this study. I would
also like to thank Merritt Enterprises for use of their
electronic digitizer. Finally, I would like to thank Alan
Holman and Auriel Cross for constructive criticism of the
manuscript, and Robert Anstey for the large part he played

in the planning and the actual carrying out of this endeavor.

ii

INTRODUCTION

METHOD .

ONTOGENY

SUBSPECIFIC DIFFERENCES

SEXUAL DIMORPHISM

CONCLUSION

BIBLIOGRAPHY

APPENDIX

TABLE OF CONTENTS

iii

Page

19
22
36
38

40

LIST OF TABLES

Table Page
1 Eleven potentially sexually dimorphic indicator
variables. . . . . . . . . . . . . . . . . . . . 6
2 List of morphological characters measured. x

and y coordinates refer to points in Figure 1.
HA indicates Fourier harmonic amplitude. PA
indicates Fourier harmonic phase angle . . . . . 8

3 Principal components analysis results for first
five factors. Variable numbers correspond to
variables in Table 2. x deleted variable . . . ll

4 Discriminant function results for ontogenetic
clusters in P. rana milleri. Specimen numbers
below 300 are from U of M collection. Specimen
numbers above 300 are from Magrum collection . . l3

 

5 DisCriminant function results for ontogenetic
clusters in g. rana crassituberculata. Specimen
numbers below 300 are from U of M collection.
Specimen numbers above 300 are from Magrum
collection . . . . . . . . . . . . . . . . . . . l4

 

6 Discriminant function results for subspecific
clusters in P. rana. Specimen numbers below
300 are fromFU of M collection. Specimen numbers
above 300 are from Magrum collection . . . . . . 20

7 Discriminant function results for sexually dimor-
phic clusters in g. rana milleri. Specimen
numbers below 300 are from U of M collection.
Specimen numbers above 300 are from Magrum
collection . . . . . . . . . . . . . . . . . . . 27

 

8 Discriminant function results for sexually
dimorphic clusters in g. rana crassituberculata.
Specimen numbers below 300 are from U of M collec-
tion. Specimen numbers above 300 are from Magrum
collection . . . . . . . . . . . . . . . . . . . 28

 

iv

Figure

LIST OF FIGURES

Page
Locations of the 18 key points . . . . . . . . 4

Computer drawn histograms revealing ontogenetic
distributions of P. rana milleri and P. rana
crassituberculata in variables; x10, x13, x14,

x15 and x18 . . . . . . . . . . . . . . 9

 

 

 

Graph of mean radius against variable x for
g. rana milleri. Measurements are in mieli—
meters 0 O O O O O O O O O O O O O O O O O O

 

. 15

Graph of mean radius against variable x for

P. rana crassituberculata. Measurement are

'I" r I

in milIimeters . . . . . . . . . . . . . . . . l7

 

Computer drawn histograms revealing sexually
dimorphic distributions of g. rana milleri in
variables; glabellar shape, cephalic shape,

and Fourier harmonic amplitudes 4, 7, 10, 16

and 20 . . . . . . . . . . . . . . . . . . . . 23

 

Computer drawn histograms revealing sexually
dimorphic distributions of g. rana crassituber-
culata in variables; glabellar shape, cephalic
shape, and Fourier harmonic amplitudes 4, 7, 10,

16 and 20 . . . . . . . . . . . . . . . . . . 25

 

Extreme males and females of g. rana milleri and

P. rana crassituberculata. Milleri male =

Epecimen no. 322, milleri female = specimen

no. 338, crassituberculata male = specimen no.

403, crassituberculata female = specimen no.

428 . . . . . . . . . . . . . . . . . . . . . 32

 

 

 

The eight "average" trilobites . . . ... . . . 34

INTRODUCTION

Sexual dimorphism has been recognized as an important
problem in paleontology, and among trilobites it has been
commonly inferred. Morphological variations in the cephalon,
glabella, libriginae, occipital ring, eye, genal area,
pygidium, ornamentation, and hypostome, among others have
been attributed to sexual dimorphism in several trilobite
species by many authors [Lochman and Hu, 1959, 1962; Hu,
1964, 1971; Wittington, 1963, 1965; Selwood, 1965; Selwood
and Burton, 1969; Clarkson, 1966, 1969; Webby, 1973). Often
the problem of sexual dimorphism is intertwined with the
problem of speciation, or subspeciation, as in this study
where it is difficult to tell whether the two groups are
different taxa or sexual dimorphs.

The trilobite species Phacops rana [Green, 1832] has

 

been divided into several subspecies, two of which, E.

rana milleri [Steward, 1927] and P. rana crassituberculata

 

[Stumm, 1953] are morphologically similar and occur together
in the Silica Shale (Devonian) at Sylvania, Ohio. The main
morphological difference between the two subspecies is in
eye structure, with g. r. milleri having more lenses, and a
less highly inflated interlensar schlera. Because of their
close morphological similarity, and mutual occurence in

the Silica Shale, Clarkson [1966] has suggested that the

1

two subspecies may be sexual dimorphs. Eldredge [1971] has
argued against sexual dimorphism, stating that E. 5. milleri

and g. E; crassituberculata are usually not found together at

 

the same locality (Table 7, Eldredge, 1971). Even within the
Silica Shale itself, although P. r. milleri and g. E- crassi-

tuberculata are occasionally found together in the same beds,

 

in general, the beds contain only one of the two subspecies,
or an overwhelming majority of one of the subspecies over the
other [Ehlers, Stumm and Kesling, 1951]. This has also been
confirmed through personal communication with Larry Magrum, a
hobbyist who has done extensive collecting at the Medusa
Portland Cement quarry at Sylvania (1.5 miles north of Silica,
SE 1/4, Section 7, T9S, R6E). Furthermore, "the eyes of all
small post-larval instars of 2. gang collected from the Silica
shale appear to be of the milleri variety" [Eldredge, 1971].
It is also possible that environmental differences play a part
in the distribution of the two subspecies, as g. g. milleri

is generally found in more argillaceous rocks, while 2. 5.

crassituberculata is usually found in more calcareous rocks.

 

This study is designed to clarify the relationship
between the two subspecies through extensive quantitative

analysis of the cephalons of specimens of g. rana milleri and

 

P. rana crassituberculata from the Silica Shale at Sylvania.

 

Through mathematical techniques including principal components
analysis, clustering, and use of the discriminant function,
morphological differences both within and between the two

subspecies will be analyzed to attempt to find discrete

clusters of individuals and thus shed light on the problem

of whether P. rana milleri and P. rana crassituberculata are

 

 

sexual dimorphs, and also to investigate the possibility of

sexual dimorphism within the two subspecies.

METHO D

This study is based on 99 specimens, 40 of which are

P. rana milleri and 59 of which are P. rana crassituberculata.

 

 

All of the specimens represent the holaspid stage of growth.
Thirty specimens were obtained from the Museum of Paleontology,
University of Michigan, and the remaining 69 specimens were
obtained from the collection of Larry Magrum of Toledo, Ohio.
The specimens were photographed and the photographic negatives
were mounted in slide mounts. By means of an overhead pro-
jector, the cephalons were magnified four times and measure-
ments were recorded from the drawings of the projected images.
Because many of the trilobites used in this study were in an
enrolled or incomplete state, only the cephalons were used.
Eldredge [1971] listed a number of measurements he made
on trilobite cephalons in his study. It was found that if
the locations of 18 key points on one side of the trilobite
cephalon were known, most of Eldredge's measurements could be
duplicated. These 18 key points (Figure l) were then marked
on one side of each drawing, either on the right side or left
side, depending on which half was more clearly delineated.
Drawings on which the 18 points were marked on the left side

were reversed to their mirror image to correspond to the right

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7
12 8
13
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17 18 10
3 2

Corner of genal angle

Corner of occipital ring

Intersection of vertical axis and rear of occipital ring
Intersection of vertical axis and occipital furrow
Intersection of vertical axis and glabellar furrow
Intersection of vertical axis and front of glabellar
Intersection of axial furrow and cephalic margin
Lower front corner of eye

Point on lower eye margin extended farthest to right
Upper rear corner of eye

Point on upper eye margin extended farthest to right
Upper front corner of eye

Intersection of axial and palpebral furrows

Point on palpebral furrow extended farthest to right
Rear edge of axial furrow

Front corner of glabellar lobe

Rear corner of glabellar lobe

Front corner of occipital ring

Figure 1. Locations of the 18 key points.

half of the cephalon. The coordinates of the 18 points were
then plotted, with respect to a common zero point, by means
of an electronic digitizer and then punched on computer cards,
with a x and y cordinate for each point, thus providing 36
coordinate values.

Fourier analysis, a mathematical technique to describe
shape quantitatively, has begun to be used in geology, notably
by Ehrlich and Weinberg [1970] and their students to measure
the shape of sand grains, and Anstey and Delmet [1972; 1973]
in measuring the shapes of bryozoan zooecia. In this study,

29 Fourier harmonics were calculated to describe the shape of
each cephalon. This was done by plotting the coordinates of

60 equiangular points on the outline of each cephalon by means
of the electronic digitizer, and having them punched on com—
puter cards. The harmonic coefficients were then calculated
by means of the Fourier analysis computer program devised by
Ehrlich and Weinberg. Along with the harmonic amplitudes,

were calculated 29 harmonic phase angles, measuring the orien-
tation of the individual harmonics with respect to the cephalon,
and the normalized roughness coefficient [Ehrlich and Weinberg,
1970], measuring the total Fourier deviation from a circle,

and the mean radius for each shape.

Based on cases of sexual dimorphism described in the
literature, eleven potentially sexually dimorphic indicator
variables were determined and defined by use of the coordinates

of the 18 key points (Table l). Twenty of the phase angles

 

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were then deemed insignificant because of inordinately high
or low values of their vector sums in the sample [Christopher
and Waters, 1974], and dropped from use, and seven of the 36
point coordinates were also dropped because five of them lay
on the axis and had zero values in all specimens, and two

of them were duplicated by the sexually dimorphic indicator
variables. It was decided that each of the 29 remaining x
and y coordinates be used as an independent variable so that
point locations along the width and length of the cephalon
could be defined separately. This left a total of 78

variables (Table 2).
ONTOGENY

Computer drawn histograms (Figure 2) revealed many
clearly and slightly bimodal distributions present among
several of the variables. It was found that the variables

x and the mean radius formed clusters

10' x13' X14' X15' x18'
in each of the two subspecies, in which large trilobites were
grouped into one cluster and small trilobites were grouped
into the other cluster. In SPSS principal components
analysis with varimax rotation [Nie, Bent and Hull, 1970],
the variables all had extremely high scores on factor one
(Table 3), which is interpreted to be the size of growth
factor, because the mean radius, a measure of absolute size,
expressed its greatest degree of variation along this axis.

It is therefore assumed that the bimodality present among

those variables is of an ontogenetic nature forming clusters

Table 2.

List of morphological characters measured. x and

y coordinates refer to points in Figure 1. HA

indicates Fourier harmonic amplitude.

Fourier harmonic phase angle.

PA indicates

 

 

11.
12.

13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.

Glabellar length
Glabellar width
Librigineal length
Genal prolongation
Occipital ring length
Occipital ring length
width

Cephalic length
Cephalic width
Glabellar shape
Cephalic shape
Palpebral lobe position

 

27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.

41-67.

68.
69.

70.
71.
72.
73.
74.
75.
76.
77.
78.

HA 2 - 28
Mean radius

Normalized roughness

coefficient

PA
PA
PA
PA
PA
PA
PA
PA
PA

4

7

11
12
14
15
17
18
21

 

Figure 2. Computer drawn histograms revealing ontogenetic
distributions of g. rana milleri and P. rana
cra531tuberculata 1n variables; x10, x13, x14,
X15' and X18

 

 

 

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12

of young and old individuals. As to why there seem to be
clusters of old and young, rather than a gradient between the
two, could be explained either by a biased sample, or by the
fact that during growth, trilobites go through a series of
molt stages, with discrete jumps from one size to the next.
It is possible that a sample may contain a high relative
proportion of one or two different instars due to differen—
tial preservation, differential collection, or if a large
number of trilobites tend to die during the same molt states.
In 3. E' milleri, which had 21 older individuals and
19 younger ones, use of the discriminant function using the
above variables, confirmed the validity of the ontogenetic

clustering (Table 4). In E. r. crassituberculata, which had

 

36 older trilobites and 23 younger ones, the discriminant
function reclassified two individuals into the opposite
group (Table 5).

Graphs, plotting the mean radius against size of the
individual variables show that increase of the individual vari-
ables proceeds in a linear fashion with respect to overall
growth, and if the overall size, as indicated by the mean
radius, is taken to be correlated to a certain extent with
age, then the growth of the individual variables has pro-
ceeded in a linear fashion throughout ontogeny. Only the

graph of variable x is shown (Figures 3 and 4) as the others

10

show the same results and are redundant.

Table 4.

clusters in P.

13

rana milleri.

 

below 300 are from U of M collection.
numbers above 300 are from Magrum collection.

Discriminant function results for ontogenetic
Specimen numbers

Specimen

 

 

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336
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clusters in P.

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Discriminant function results for ontogenetic
rana crassituberculata.

Specimen

 

numbers belofi 300 are from U of M collection.
Specimen numbers above 300 are from Magrum

collection.

 

 

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YOUNG

 

15

 

Figure 3. Graph of mean radius against variable x for
E. rana milleri. Measurements are in milli-
meters.

0 = young females
4 = young males

0 = old females

4| = old males

l6

 

 

O
tfl

IN‘Z I‘D-DUO

35

40

30

17

Figure 4. Graph of mean radius against variable x 0 for
P. rana crassituberculata. Measurements are

in millimeters.

 

young females
young males
old females
old males

4
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SUBSPECIFIC DIFFERENCES

Eldredge [1971] has rejected Clarkson's [1966] idea
with the statement, "Sexual dimorphism must also be rejected
in view of the stratigraphic and geographic distributions of
the two variants. The precise nature of the relationship

between milleri and crassituberculata seems an insoluble

 

problem with the given data as the correct explanation appears
to lie in the realm of population genetics. Perhaps the
ontogeny of the eye was flexible and capable of reaction to
the peculiar environmental conditions obtaining at a given
place at a given time. Alternately, a more strictly geneti-
cally based adaptation to local environments may underlie

the distributions of the two variants."

The quantitative measurements of the morphology of the
cephalon taken in this study clarify the relationship between
the two subspecies. Sixty-seven variables (the 78 listed in
Table 2 minus the nine phase angles, the occipital ring
length, and the libriginial length) were used in a discrimin-
ant analysis to distinguish the two subspecies. The dis-
criminant function successfully separated the two subspecies,
misclassifying only one specimen (Table 6). Use of fewer
than 67 variables produced a greater degree of.misclassifi—
cation; this indicates that the difference between the two
subspecies are an overall effect of a large number of mor-
phological differences. The fact that the subspecies differ

significantly in a large number of morphologic characteristics

20

Table 6. Discriminant function results for subspecific
clusters in g. rana. Specimen numbers below 300
are from U of M collection. Specimen numbers
above 300 are from Magrum collection.

 

 

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Table 6 .

Continued.

21

 

 

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22

combined with the fact that they are rarely found at the same
locality does not support Clarkson's hypothesis of sexual
dimorphism. Rather, the data suggest that their recognition
as subspecies is tentatively valid, until more is known about
the population genetics of these animals. Despite Eldredge's
observation concerning eye pattern, the two subspecies are
sufficiently distinct at the Sylvania locality to represent

two phenetically differentiated populations.
SEXUAL DIMORPHI SM

Histograms and cluster analysis of the milleri and

crassituberculata populations reveal another set of clearly

 

and slightly dimorphic clusters within each of the two sub-
species (Figures 5 and 6). This dimorphism is expressed by
glabellar shape, cephalic shape, and the amplitudes of the
Fourier harmonics 4, 7, 10, 16 and 20. Individuals with

high values for glabellar shape, cephalic shape, and harmonic
16, and low values for harmonics 4, 7, 10 and 20 form one
cluster (cluster A), and individuals with low values for
glabellar shape, cephalic shape, and harmonic 16, and high
values for harmonics 4, 7, 10, and 20 form the other cluster

(cluster B). In crassituberculata, there were 36 trilobites

 

in cluster A and 23 trilobites in cluster B. In milleri,
there were 23 trilobites in cluster A and 17 in cluster B.
Use of the discriminant function confirms the validity of
dimorphic clusters within both the milleri and crassituber—

culata groups (Tables 7 and 8). In principal components

 

23

Figure 5. Computer drawn histograms revealing sexually
dimorphic distributions of g. rana milleri in
variables; glabellar shape, cephalic shape, and
Fourier harmonic amplitudes 4, 7, 10, 16 and 20.

 

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25

Figure 6. Computer drawn histograms revealing sexually

dimorphic distributions of B. rana crassituber-
culata in variables; glabellar shape, cephalic

shape, and Fourier harmonic amplitudes 4, 7, 10,
16 and 20.

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26

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27

Table 7. Discriminant function results for sexually dimor-
phic clusters in g. rana milleri. Specimen numbers
below 300 are from U of M collection. Specimen
numbers above 300 are from Magrum collection.

 

 

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Table 8.

28

clusters in P.

tion.

Discriminant;functitulresults for sexually dimorphic
rana crassituberculata.

_ Specimen
numbers below 300 are from U of M collection.
,Specimen numbers above 300 are from Magrum

collec-

 

 

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29

analysis, the variables denoting this bimodality scored high
values on factor three and low values on factor one, the size
or growth factor (Table 3). Thus these variables depict a
bimodality that is independent of ontogeny, but instead
depicts various aspects of cephalic and glabellar shape.

Sexual dimorphism is often expressed by shape differ-
ences in many animals, including trilobites. Hu [1971]
found dimorphism in the glabellas and cephalons of 9 species
of trilobites, and attributed it to sexual differences. In
E species, Hu described the female as having a longer and
narrower glabella than the male; in one species, the female
was described as having a narrower and more conical glabella;
in one species, the female was described as having both a
longer and narrower glabella and cephalon; and in one species,
the female was described as having a more elongate cranidum.
As rationale for these sexual designations, Hu states, "It
is the assumption here that the most abundantly represented
specimens were males, either having relatively small bodies
without special prosopon, or large bodies with strongly
modifying prosopon. The less numerous females are large-
bodied without special prosopon or small-bodied with slightly
modifying prosopon. These morphologic and sexual ratio
differences seem to correlate with sexual dimorphism in
Recent Arthropoda, such as Insecta, Crustacea, and Merosto-
mata" [Hu, 1971].

The dimorphism found in E. r. milleri and E. r.

crassituberculata is similar to that found by Hu, in that

30

the individuals in cluster A have relatively longer and
narrower glabellas and cephalons than the individuals in
cluster B. The individuals in cluster A also had a greater
degree of l6—rayed symmetry in their cephalic shape, but a
lesser degree of 4, 7, 10 and 20-rayed symmetry, than the
individuals in cluster B, as expressed by the bimodality in
the Fourier harmonics. Based on similarities with Hu's study,
I attribute the dimorphism to be of a sexual nature, with
cluster A being the females and cluster B being the males.
A possible discrepancy in this judgment is that in each of
the subspecies, the females outnumber the males (36 to 23

in crassituberculata and 23 to 17 in milleri). However,

 

judging by the fact that the samples were not random, the
sexual ratio may not be too applicable. In terms of actual
quantitative shape differences in the glabellas and cephalons,
the morphologic differences involved here are subtle. The
extreme cases can easily be visually differentiated as being
male or female, but with many of the average and gradational
individuals it is difficult to determine the sex on a visual
basis alone. Figure 7 shows an example of the extreme male
and female types of each subspecies. By summing up the
coordinates of the 18 points and averaging them out for the
group, eight "average" trilobites, each representing its own
group, were determined and reconstructed. The eight "average"
trilobites are, the average younger milleri female, the
average younger milleri male, the average older milleri

female, the average older milleri male, the average younger

31

crassituberculata female, the average younger crassituber-

 

 

 

culata male, the average older crassituberculata female, and

the average older crassituberculata male (Figure 8). These

 

"average" trilobites then, give an indication of the mean
differences between sexes throughout ontogeny within both
subspecies, and as Figure 8 indicates, the younger individ-
uals of each sex are quite similar, while the mature indi-
viduals are more clearly sexually dimorphic. This, along
with Eldredge's statement about the eyes of all small post-
larval instars being of the milleri variety, indicates that,
just as in many other animals, the differences between males
and females, as well as possible genetic differences, become
more pronounced as they reach maturity. A possible explanation
as to why sexual dimorphism seems to manifest itself in
cephalic and glabellar shape is found in the Treatise on
Invertebrate Paleontology, "Barrande, in 1872, described and

illustrated a specimen of Barrandia crassa from the Middle

 

Ordovician of Bohemia bearing a mall of tiny ovoid bodies
located below the integument of the frontal glabellar lobe.
The bodies were regarded as eggs still in place in ovaries
below the cephalic exoskeleton." If Barrande's interpreta-
tion is correct, the glabellas of the females may be longer
and narrower than the glabellas of the males in order to

provide space for the ovaries contained within.

Figure 7.

32

Extreme males and females of E. rana milleri and B.
rana crassituberculata. Milleri male = specimen no.
322, milleri female = specimen no. 338, crassituber-

 

 

culatafimale = specimen no. 403, crassituberculata

female = specimen no. 428.

33

 

 

P1

 

 

 

 

34

Figure 8. The eight "average" trilobites.

36
CONCLUSION

The trilobites examined in this study were found to
contain four natural clusters in each of the two subspecies.
Two of the clusters were ontogenetic, consisting of clusters
of younger and older individuals based on size differences.
The variables which were found to be most useful in determin-
ing the ontogenetic clusters were the mean radius, and the x
coordinates of the points 10, l3, 14, 15 and 18 on the ce-
phalon. Graphs of mean radius, which could be taken as an
indication of age, against size, revealed that growth pro-
ceeded at a constant rate rather than exponentially.

The second two clusters were independent of the first,
and were determined by the glabellar shape, cephalic shape,
and Fourier harmonics 4, 7, 10, 16 and 20. These variables
are expressive of cephalic and glabellar shape, and one
cluster consisted of trilobites with longer and narrower
glabellas and cephalons, and the other cluster consisted of
trilobites with shorter and wider glabellas and cephalons.
These two clusters have been judged to be sexually dimorphic
clusters, and, in accordance with previous work done by Hu,
the individuals with longer and narrower glabellas and cepha-
lons were judged to be females. The two subspecies, g. £222

milleri and g. rana crassituberculata, were found to be

 

morphologically distinct, and differed from each other by a
large number of characters other than eye structure. This

tentatively confirms the idea that milleri and crassituberculata

37

are valid subspecies, although their differences might be
ecophenotypic responses to specific local environments

represented as a depositional mosaic in the Sylvania area.

BIBLIOGRAPHY

BIBLIOGRAPHY

Anstey, R. L., and Delmet, D. A.: Genetic Meaning of Zooecial
Chamber Shapes in Fossil Bryozoans. Science, 177,
1000-1002, 1972.

Anstey, R. L., and Delmet, D. A.: Fourier Analysis of Zooecial
Shapes in Fossil Tubular Bryozoans, G. S. A. Bu11.;
84m 1753-1763, 1973.

Christopher, R. A., and Waters, J. A.: Fourier Series as a
Quantitative Description of Miospore Shape. Jour, Pal.,
‘ 48, 697-709, 1974.

Clarkson, E. N. K.: Schizochroal eyes and vision of some
Silurian Acastid trilobites. Paleontology, 9, 1-29,
1966.

Clarkson, E. N. K.: Dimorphism of the Eye in Weberides
shunnerensis. Sexual Dimorphism in FossII Metazoa,
Int. Union Geol. Sci. 1969.

 

 

 

Ehlers, G. M., Stumm, E. C. and Kesling, R. V.: Devonian
rocks of southeastern Michigan and northwestern Ohio.
Michigan Basin Geol. Soc. Annual Field Trip Guide, 30
pp., 1952.

Ehrlich, R. and Weinberg, B.: An exact method for character-
ization of grain shape. J. Sediment, Petrology, 40,
205-212. 1970.

Eldredge, N.: Morphology and Relationships of the Biospecies
Phacops rana (Green, 1832) and Phacops iowensis (Delo,
1935). U.S. Museum of Natural History Memoirs, 1971.

 

 

Green, J.: A monograph of the trilobites of North America.
Philadelphia, 93 pP-, 1832.

Hu, C. H.: The Ontogeny and Dimorphism of Wellaraspis Lata.
Jour. Pal., 38, 95-97, 1964.

 

Hu, C. H.: Ontogeny and Sexual Dimorphism of Lower Paleozoic
Trilobita. Paleont. Amer., 7, 28-155, 1971.

Lochman, C. and Wu, C. H.: A Ptychaspis from Idaho. Jour.
Pal., 33' 431—441, 19590

38

39

Lochman, C. and Hu, C. H.: An Aphelaspis Faunule from Logan
Montana, Jour. Pal. 36, 431-441, 1962.

 

Moore, R. C.: Treatise on Invertebrate Paleontology, Part 0,
Arthropoda, p. 101.

 

Nie, Bent, and Hull: SPSS Statistical Package for Social
Sciences, 1970.

 

Selwood, E. B.: British Devonian Dechenellid Trilobites.
Bull. Br. Mus. Nat. Hist., 10, 319-323, 1965.

Selwood, E. B. and Burton, C. J.: Possible Dimorphism in
Certain Devonian Phacopids. Sexual Dimorphism in
Fossil Metazoa. Int. Union Geol. Sci., 1969.

 

 

Stewart, G. A.: Fauna of the Silica Shale of Lucas County.
Geol. Surv. Ohio, Fourth Series, Bul., 32, 76pp., 1927.

Stumm, E. C.: Trilobites of the Devonian Traverse of Michi-
gan. Contrib. Mus. Paleont. Univ. Mich. vol 10, no. 6,
1953.

Webby, B. D.: Remopleurides and Other Upper Ordovician
Trilobites from New South Wales. Paleontology, 16,
445-475, 1973.

 

Whittington, H. B.: Ordovician Trilobites. Bul. Harv. Mus.
Comp. Zool., 1963.

Whittington, H. B.: Table Head Trilobites. Bull. Harv.
Mus. Comp. Zool., 1965.

APPENDIX

Data printed as follows:

Specimen
Specimen
Specimen

Specimen

Specimen

Specimen
Specimen

Speciman

NOS .
NOS.
NOS.

NOS 0

NOS .

Nos.
Nos.

NOS.

103-354
107-352
302-321
306-344

205-433

209-437
220-440
201-438

thI'U

I'U I'U [’6

APPENDIX

Specimen no.,

Eleven potentially dimorphic indi-
cator variables in same order as
in Table l,

Coordinates of the 18 key points,

Xl' yl' X2' Y2" ° "X18’ Y18'
Fourier Harmonic amplitudes 1-29,
Mean radius multiplied by 100,

The number 60 which was the number
of coordinate points taken to
determine the Fourier analysis,
Normalized roughness coefficient,
and phase angles 1-29.

B. rana milleri young females

 

P. rana milleri old females

 

P. rana milleri young males

 

P. rana milleri old males

 

rana crassituberculata young
emales

 

rana crassituberculata old females

 

 

rana crassituberculata young males

 

rana crassituberculata old males

 

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