QUANTIFICATION OF THE CEPHALOPOD
SUTURE PATTERN

By

Douglas John Canfield

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of
MASTER OF SCIENCE

Department of Geology
1977

ABSTRACT

QUANTIFICATION OF THE CEPHALOPOD
SUTURE PATTERN
By
Douglas John Canfield

The Fourier series exactly describes the shape of ceph-
alopod suture patterns in the subclasses Nautiloidea, Bac-
tritoidea, and in four of the eight orders of the Ammonoidea,
but can not presently describe complex ammonitoid sutures.
The Fourier method allows the calculation and graphical dis-
play of the mean sutural patterns of the subclasses and
orders studied, and exactly quantifies the morphological dif-
ferences between groups. Discriminant analysis provides sig-
nificant differentiation of the four ammonoid orders using
only the Fourier harmonic amplitudes of the sutures. Discrim-
inant analysis also reveals significant and otherwise undect-
able differences between the two symmetric halves of sutures

in Acanthoclymenia neapolitana, and thereby measures the non-

 

genetic norm of recation in that species. Specific harmonic

amplitudes increase monotonically in the ontobeny of Koenenites

 

cooperi as well as in the phylogeny of four genera of the
family Gephuroceratidae, with the result that the ontogenetic
and phylogenetic scaling factors are statistically identical,
confirming on a quantitative basis the assumption of recapi-

tulatory evolution in this lineage.

TABLE OF CONTENTS

Acknowledgments .
List of Tables.
List of Figures
Introduction.
Methods
Results
Summary and Conclusions
List of References.
Appendix A .

B .

C
D .
E
F

Page

ii

iv

13
44
46
48
51
52
57
61
64

ACKNOWLEDGEMENTS

I wish to thank Dr. Robert L. Anstey for his advice and
guidance throughout this project. The helpful criticisms of
Dr. Duncan Sibley and Dr. John Wilband are also greatly
appreciated. Special thanks are given to Mitch Roth and
Lloyd Lerew for their assistance with understanding mathe-

matical, computational and philosophical problems.

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

LIST OF TABLES

Values of the Coefficient of Variation (CV)
for six replications of Koenenites cogperi
and seven replications of Goniatites
choctawensis

 

 

 

Mean values for the Coefficient of Variability
computed for the taxonmic hierarchy.

Summary of Discriminant Analysis of data from
sutures in the Orders Anarcestinda, Clymeniida,
Goniatitida, and Ceratitida. . . . . .

Summary of Discriminate Analysis of data from
Acanthoclymenia neapolitana. Perfect discrim~
ination between left and fight suture halves in
both juvenile and adult sutures demonstrates
presence of nongenetic influences on suture
shape.

 

Rankings of the harmonic amplitudes within

each harmonic frequency for six suture patterns

in the ontogenetic series of Koenenites cooperi

The increase in rank sums withvage isia response
to a general increase in signal with age

 

Coefficient of Variation of the harmonic
amplitudes, computed from the phylogentic series
in the Family Gephuroceratidae and the onto-
genetic series in Koenenites cooperi

 

Significant Correlation Coefficients (R) of
variables from the study of ontogeny in
Koenenites cooperi. Significance level is a=.05
and a=.OI—suturavaariables are HARM l to HARM
20 and HZERO. Aperatural variables are AHARMl
AHARM 20 and SIZE.

 

Varimax rotated factor matrix after rotation
with Kaiser normalization, computed from six
sutures and aperature shapes in the ontogenetic
series of Koenenites cooperi. AGE is the number
of volutions of the conch, SIZE is the log of
the mean radius of the aperature, HARM 1 through

 

ii

PAGE

14

15

23

24

28

32

TABLE 8 con't - HARM 20 are log transforms of sutural
harmonic amplitudes, AHARM 1 through AHARM 20
are log transforms of aperatural Fourier harmonic
amplitudes and HARMZERO is the zeroth harmonic
amplitude of suture shape . . . . . . . . . . . . 37

TABLE 9: Significant Correlation Coefficients (R) of
variables from the study of phylogeny in the
Family Gephuroceratidae at a=. 05 and a=. Ol.
SEQ is the log transform of the suture' 3
position in the phylogenetic series. HARM 1
through HARM 20 are log transforms of the Fourier
harmonic amplitudes . . . . . . . . . . . . . . . 39

TABLE 10: Varimax rotated factor matrix after rotation
with Kaiser normalization, computed form the
four sutures representing a phylogeneitc series
in the Family Gephuroceratidae. SEQ is the log
of the suture's position in the series, HARM 1
through HARM 20 are log transforms of Fourier
harmonic amplitudes, and HARMZERO is the zeroth
harmonic amplitude. . . . . . . . . . . . . . . . 40

iii

FIGURE

FIGURE

FIGURE

FIGURE

. FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

10:

LIST OF FIGURES

Variation in results, due to methods in six
replications on the suture of Koenenites

cooperi . . . . . .

Variation in results, due to methods, in
seven replications on the suture of
Goniatites choctawensis

 

 

Mean power spectra of Subclass Ammonoidea (A)
and Subclass Nautiloidea (N). .

Mean sutures of Subclasses Nautiloidea (A)
and Ammonoidea (B) and a graphic display of
the difference between them (C). . . .

Power spectra of the mean suture patterns of
Ammonoid Orders Anarcestida, Clymeniida,
Goniatitida, and Cerititida . . . . . .

Mean sutures of Orders Anarcestinda (A) and
Clymeniida (B) and a graphic display of the
difference between them (C) . . .

Mean sutures of Orders Goniatitida (A) and
Cerititida (B) and a graphic display of the
difference between them (C) .

Mean power spectra of left and right juvenile
and adult sutures of Acanthoclymenia
neapolitana .

 

 

Power spectra of the ontogenetic series of
sutures in Koenenites cooperi .

 

Power spectra of the four sutres in the
phylogenetic series in the Family Gephurocera-
tidae. SEQ 1 = E, stainbrooki, SEQ 3 = M.
sinuosum, SEQ 4 = K. cooperi, SEQ S = T
EeyserIingi . . T . . . . . . . .

 

 

iv

PAGE
11

12

17
'18
19
20
21

25

27

29

FIGURE 11:

FIGURE 12:

FIGURE 13:

PAGE

Contributions of harmonic frequencies seven

and eighteen to the fit of the approximations

of Koenenites cooperi at 0.5 volutions (A), 5.5
volutions (B) and a graphic display of differ-

ence between them,(C). . . . . 41

 

Relationship between the log transforms of
harmonic amplitudes seven and eighteen in the
ontogenetic series in E. cooperi . . . . . . . . 42

Relationship between the log transforms of

harmonic amplitudes seven and eighteen in the
phylogenetic series in the Family

Gephuroceratidae . . . . . . . . . . . . . . . . 43

INTRODUCTION

The importance of cephalopods in stratigraphy has long
been recognized. The suture has been a primary character
for the classification of these molluscs. In paleontology,
cephalopod sutures have provided some of the classic examples
of evolution by recapitulation and paedomorphosis (Tasch,

p. 389, 1973).

This study provides a preliminary evaluation of the use-
fulness of Fourier analysis of suture patterns with respect
to the higher taxonomy of the shelled cephalopods, their non-
genetic norm of reaction, and their growth, development and
phylogenesis.

In his discussion of leaf outlines, D'Arcy Thompson
(1917) used the metaphor of a Fourier series to explain var-
iations in form as the superposition of sinusoidal closed
form waves of varying period and amplitude upon one another.
He implied that plant morphogenesis and phylogeny took place
as Fourier analogs. The same point could possibley be made
for the ammonoid suture in paleontology, which could represent
the morphogenetic superposition of sinusoidal wave forms of
different amplitude and harmonic order. Because biological
growth and development commonly reflect natural periodic
functions, the optimal curve-fitting and filtering of many
biological forms will very likely be based on the Fourier

series.

Vicencio (1973) in an unpublished study attempted to use
Fourier shape analysis to describe sutures. This was only a
small aspect of a much larger study, and was incompletely
developed. Fourier analysis has been successfully used to
study the human face (Lu, 1965), the shapes of ostracodes
(Younker, 1971; Kaesler and Waters, 1972; Ewald, 1975),
pelecypods (Gevirtz, 1976), bryozoans (Delmet and Anstey,
1974; Anstey, Pachut and Prezbindowski, 1976), trilobites
(Tuckey, 1975), blastoids (Waters, 1977), miospores (Chris-
topher and Waters, 1974), and viruses (Crowther and Amos,
1971). The optimality of the Fourier basis of plane closed
curve description has been demonstrated by Zahn and Roskies
(1972).

All of the above studies, with the exception of Vicencio,
were based on nonsinusoidal closed forms (i.e. complete closed
curves in polar coordinates). Ammonoid sutures are natural
sinusoidal curves to which the application of the Fourier
series should be particulary effective.

Coefficients of variation (standard deviations divided
by their means) are routinely used in biometry to compare
the relative ariability of different measurements. Examina-
tion of suture patterns from the widest possible taxonomic
range makes it possible to calculate coefficients of variation
of Fourier harmonic amplitudes at several heirarchical levels.
It is then possible to compare quantitatively the degree of
taxonomic variation in all of the Fourier wave forms filtered

from the actual sutures. The Fourier series has the unique

property of allowing the calculation of an exact mean suture
pattern for any taxonomic group, or the construction of an
exact intermediate suture pattern between any two "end mem-
bers".

The norm of reaction is a measure of the nongenetic, or
ecophenotypic aspects of morphology. Because cephalopod
sutures are bilaterally symmetrical about the mid-dorsum,
available complete suture patterns provide estimations of the
norm of reaction. The filtering capabilities of the Fourier
series allow the subtraction of the asymmetry from the ob-
served suture pattern, and the residual series can be used to
reconstruct a more ”ideal" suture pattern than that actually
produced by nature.

Heterochrony implies that phylogenetic differentiation
took place by extension or reduction of the development path-
ways followed in ontogeny. The study of heterochrony in
suture patterns has previously been graphic rather than quan-
titative, and direct measurement of scaling factors has not
been possible. The amplitudes of some Fourier wave forms
vary monotonically in both ontogenetic and phylogenetic se-
quences. These amplitudes can be used to calculate scaling
factors directly and to test the assumptions of heterochrony

in the taxa studied.

METHODS

Suture shape can be estimated as Y being a fuction of X

by a Fourier series. The general form of the Fourier equation

is co co
f(x) = C0 + Z CNCOSZnNX/T + 2: SNsinZnNX/T (1)
N=1 N=1

where T equals the range of the approximation, or the period
of f(x).
CO can be found by integrating both sides of (l) to
obtain: t + T
c - UT 05 f d (2)
0- to (x) x
Multiplying (l) by cosZnNX/T or sinZan/T and integrat-

ing finds CN and SN respectively.

to + T

CN = 2/T t5 f(x) c032nNX/T dx (3)
O
to + T

SN = 2/T 6; f(x) sinZnNX/T dx (4)
O

A set of data points (Xi, Yi) is approximated by a
Fourier series by determing f(x) by linear interpolation over
the data and solving for the Fourier coefficients in the for-
mulas (2), (3), and (4).

Thus, if the n data points are ordered such that X1<X2<

..<Xn, let f(x) = fi(x), xingXi+1 where
Y.-

E 1 Y
1“) " )‘q-x

 

 

i + 1 )x+ "(1+1+ Y1 + XiYi + 1

1 + 1 Xi‘xi + 1

XiEXEXi + 1 (5)
or E1 (X) = a1 X + b1 (6)

When fi(x) is substituted into (2)

x2 x
_ 1 ‘
cO — 21—11—371 5 fl(x)dx +5 f2(x)dx+...+
X1 2

Xn (7)

‘5 fn—l (X)dx
X

n-l
Integrating the functions fl"'fn yields

n-l
a.
- 2
C =l/(X-X) E ——1-(x. _ 2 _
o n 1 L=1 2 1+1 xi) + bi(xi+l x ) (8)

Similarily, for CN and SN

 

 

2 2 NXd
CN = x -x1 2: I (ai x + bi) cos J—T—l,N=1,2,3... (9)
n j=1 Ki
n-l X +1
3 == 2 ' j
N Xn-X1 (a. X + bi) sin ZnNde’N=l,2,3...(lO)
i=1 xi 1 _"T—

Integrating, these become

 

 

b ZnNX ZnNX
+.—£ sin +1 - s1n ——T——
nN
a.T ZnNX. ZnNX
1 1+1 _ . 1
+ 3:2gz- cos ——T———— cos T (11)

n

SN =

 

6
a. ZnNX . ZHNX.
_1 1+1 _ 1

b. ZuNX.+1 ZHNXi

1 1.
-— cos -—«———— - 05
"N T C T

a. ‘ 2nNX. 2nNX.
1 . 1+1 . 1
+ 2:7—7- Sln ———T_—_ - Sln T (12)

-1
i=1

 

 

Equations (8), (11) and (12) were coded into program
FOURIER (Appendix A) and used to compute Fourier approxi-
mations of suture shape. Harmonic amplitudes (AN) and phase

angles (Th!) are calculated by the formulae:

AN = CN + N

= 4:311
@N TAN CN

Published suture diagrams were the source of all data
(Apendix B). Diagrams were photographically enlarged and then
digitized on a set of cartesian coordinates. Each suture
pattern was situated to have the venter lie along the abcissa
The origin was at the point at which the suture pattern and
venter cross. Forty to one hundred X, Y coordinates of points
on the suture pattern were recorded, starting at the origin
and finishing with the point at which the suture intersected
the mid—dorsum. Points were selected at regular intervals,

with exceptions for inclusion of finer details which would

otherwise have been smoothed over by linear interpolation
over the sampling interval. Two methods of treating this
data were then compared.

The first or "half suture" method shifted the orienta-
tion of the suture pattern with respect to the coordinate
system so that both the first and last data points had a
Y-values were multiplied by the same normalization constant in
order to maintain scale relationships. The Fourier series
approximation was then computed over the 0.0 to Zn interval.

The second method takes advantage of the bilateral sym-
metry of the suture patterns by constructing a mirror image
from the mid-dorsum on around to the venter. This "complete
suture" is then normalized, as before, to range from 0.0 to
217 fromventer to venter. The Fourier series approximation is
then calculated over this interval.

A data set consisting of 126 suture patterns was used for
comparative evaluation of the two methods. For each method,
twenty harmonic amplitudes and twenty phase angles were com-
puted from each suture pattern. Data sets of less than forty
one data points were eliminated from analysis because of the
Nyquist frequency limitations (Davis, 1973, p. 266). Because
each harmonic amplitude was computed from the residual signal
(that not accounted for by the previous harmonics), all har-
monics are orthogonal. The contribution of each harmonic to
the approximation of the original data by the Fourier series
was first delineated by computing its root mean square error,

as defined by the formula:

8

 

N
RMS 21 (Yj Yj) IN 1
J=

where N is the number of data points, Yj is the Y—value of the

jth data point and int the approximation of the Y—value of
the jth data point.

A
Yj is computed by the formula:

F
{Y} = A0 + 8 (Ai sin (i Xj +§i)
i=1
where A0 is the value of the zeroth harmonic amplitude, Ai is
the vaule of the ith harmonic amplitude, and fig is the phase
angle of the ith harmonic, and F is the highest harmonic
frequency calculated.

Significance testing was carried out using an analysis of
variance design associated with Snedecor's F-test (Mendenhall,
1968, p. 174-181). Although data points were not necessarily
spaced at equal intervals, which is necessary for .a rigorous
test of significance, their close approximation to equal in-
tervals still allows the use of the significance test as an
accurate estimate of true significance (Gevirtz, 1976).

Subroutine FTEST (Appendix A) was used to compute both
the root mean square error and the F-statistics. It was found
with both methods that all twenty harmonics contributed sign-
ificant (o = .05) shape information.

It was also found that with the computation of twenty

harmonic amplitudes, the complete suture method was able to

reduce root mean square error to less than an arbitrary value
of 0.05 in 80% of the cases (101 out of 126); whereas the
half suture method could achieve this level of accuracy in
only 75% of the cases (95 out of 126).

The complete suture method also concentrates more in-
formation in the harmonic amplitudes. Because a suture pat-
tern is bilaterally symmetrical, the coefficients of the sine
terms in the Fourier equation take on a value of zero (Lu,
1965). Consequently, the Fourier series becomes a cosine
series and the phase angles only have values of plus or minus
ninety degrees.

A further advantage of the full suture method over the
half suture method lies in the assumption of a repeating signal
inherent in a Fourier series approximation (Davis, p. 256-272).
A suture pattern repeats itself by virtue of its continuity
around the conch from the venter to the mid-dorsum and back
to the original point, the venter. The half suture method
ignores the assumption of a repeating signal. It also changes
the function by rotating the orientation of the sutures on the
coordinate system, so it can not lend itself to representation
of the morphogenesis of the sutures as well as the complete
suture method. Therfore, only the results of the complete
suture method have been presented in this paper.

It should be also be noted that the results obtained from
the complete suture method agree with those reported by Vicencio
(1973). This includes his observation that Schindewolf's
phylogenetic scheem (1954) of trilobate, quadrilobate and qui-

nquilobate primary sutures correspond with large contributions

10

to the fit of the Fourier series approximation by the fourth,
sixth and eighth harmonics, respectively.

The sutures of the ammonitoid ammonites are too complex
to be studied directly by Fourier analysis. The lobules and
folioles which create the intricate nature of the suture pat-
terns cause the functions describing them to be multivalued.
The Fourier series cannot deal with this problem (Ehrlich and
Weinberg, 1970). Many of the ceratitic and goniatitic sutures
also exhibit this degree of complexity. A possible solution
to this problem, not examined in this study, would be the use
of an iterative curve smoothing algorithm. Vicincio (1973)
attempted such analysis, but found it not particulary useful
for extremely complex sutures. However, for sutures such as

those in Schistoceras missouriense, which only have a few

 

multivalued points along the ordinate, such a procedure could
be used. The number of iterations required to make the curve
suitable for Fourier analysis should be retained as an addi-
tional variable measuring complexity. A table of ammonoid
taxa which have been studied is included in Appendix C.

In order to evaluate the reproducibility of results by
this method, multiple data sets were generated form two suture

drawings, one of Koenenites cooperi and one of Goniatites

 

 

choctawensis. The data sets were processed, and results were

 

compared by graphical display (Figures 1 and 2) and by compu-

ting the coefficients of variation:

CVn = 100.0 (on/um)

FIGURE 1:

11

Variation in results, due to methods
in six replications on the suture of
Koenenites cogperi.

 

 

11a

—N

mu

hf

mwmzaz >uzmaauz... u H zozmc:
a

an.

a.»

«—

FD

 

 

 

 

 

 

 

 

J 4 32..."-
25...?
a...“ .3.
2.2+
«Sum.
23.0. .53.?
a
‘ +000.Ne
. \_
\ \.
J 1. S34...
. x
x \c/ _
2, , 2-
.L \I. as
.\
‘, Jog-u!
, ,\ .58....
$8.?

 

 

 

3001114118 OINOHUUH 001

12

FIGURE 2: Variation in results, due to methods,
in seven replications on the suture
of Goniatites choctawensis.

mwmtaz >uzwncm¢m uuzozmmz

 

12a

 

 

 

 

 

 

 

 

S m. 2 Z a .. u n .
0 a J. x 0 .1 T 0 log...
5 2...... .0.
a 25.. I... 8.”
_ 2.3. .0. Ho
3 35.. .x.
.j 25.. ..T
\ 1 «23.0. Sana-
. , $3.0.
a
foaa.m-
.92.“-
\/ / / +61?
,_ V //.r 63;..-
\ /
t c .. ,2 62.. T
x.) . my
\\./ . J.
. /. .lfifl . ,
. .. 1%... T
/
.\.
.2. T

 

.00...

BOOIITJHU OINOHBUH 001

13

where n is the harmonic frequency number, 0 is the standard
deviation and u is the mean.

The graphs of the harmonic amplitudes vs. the harmonic
frequency number (power spectra) of the six repitions of E;
cooperi (Figure 1) show a large variation of the harmonic
amplitudes at harmonic frequencies eleven and fourteen, The
coefficient of variation has maxima of 66.64 and 69.83 at
these respective frequencies (Table 1). The seven replica-

tions of g. choctawnsis (Figure 2) and E. cooper (Figure l)

 

is that relative variations increases greatly as the harmonic
amplitude drops below 10-2. This threshold level can be
lowered by reducing random noise due to methods. More accur-
ate digitizing equipment (accuracy greater than .025 in.) or
greater enlargment of suture patterns (larger than 8 X 10
photographs) can increase the signal strength with respect to

noise.

RESULTS

A data set of 140 sutures was analyzed and the mean harm-
onic amplitudes were calculated for the portion of the tax-
onomic hierarchy sampled (Appendix D). In order to compare
the degree of taxonomic variation in the Fourier was forms,
the coefficients of variation (CVn) was also computed for
taxonomically hiearchical levels (Appendix E). Table 2 gives
the mean coefficients of variability within hierarchical
levels. Harmonic frequency four shows a relatively constant

CV, with a minimum of 38.21 and a maximum of 45.19. The second

TABLE 1: Values of the Coefficient of Variation (CV) for
six replications of Koenenites cgpperi and seven
replications of Goniatites choctawensis.

 

 

HARMONIC FREQUENCY COEFFICIENT 0F VARIATION
K. cooperi g. choctawensis
l 2.46 4.51
2 2.78 4.53
3 3.26 7.60
4 2.61 21.28
5 1.99 70.09
6 3.15 1.15
7 6.42 3.90
8 1.33 46.07
9 4.17 20.92
10 4.54 4.04
11 66.64 1.99
12 16.36 4.42
13 4.30 15.78
14 69.83 5.82
15 13.77 13.69
16 8.68 124.66
17 16.09 4.88
18 8.04 15.26
19 37.38 8.03
20 32.87 20.31

14

TABLE 2: Mean values for the Coefficient of Variability
computed for the taxonomic hierarchy.

gégggglg GENERA FAMILIES SUPERFAMILIES ORDERS

 

l 46.74 45.79 31.23 20.30
2 41.30 42.94 35.86 35.57
3 42.19 60.73 52.01 41.08
4 39.70 44.26 38.21 45.19
5 57.37 56.35 37.21 55.11
6 32.02 32.84 48.83 50.60
7 44.85 38.33 47.61 52.76
8 28.70 65.84 43.29 53.92
9 36.27 40.94 45.49 63.33
10 43.40 46.78 54.75 48.26
11 35.74 67.27 46.55 53.96
12 48.37 61.85 27.53 55.59
13 51.81 59.39 45.42 65.94
14 56.64 49.45 47.19 59.01
15 42.29 54.16 35.04 62.79
16 43.04 47.64 51.07 58.16
17 44.21 35.02 64.74 72.05
18 40.30 45.76 52.90 59.58
19 42.61 38.42 44.35 52.93
20 54.93 44.49 36.39 59.91

15

16

harmonic also has a constant CV, ranging from 35.57 to 42 94.
Table 2 shows that all harmonic frequencies (1-20) contribute
shape information at all levels in the taxonomic hierarchy.

The complexity of a suture pattern can be roughly quan—
tified as the number of harmonic frequencies required to reduce
root mean square error to 0.05 or less. The average number to
reduce RMS to 0.05 or less is seven for the nautiloids and
eleven for the ammonoids. Those ammonoid approximations which
could not reduce RMS to 0.05 were not included in the computa-
tion of this average.

Sixteen harmonics were the maximum number required to
reduce RMS to 0.05 or less in the nautiloids. The ammonoids
differ form the nautiloids primarily in the increased signal
of the higher order harmonics (Figures 3 and 4). This is an
expected result of the ammonoids' increase in sutural complex-
ity by the addition of lateral lobes, which are not found in
the nautiloids.

The mean power spectrum of the Subclass Ammonoidea was
computed from the four power spectra shown in Figure 5. These
are the mean harmonic amplitudes of the Orders Anarcestida,
Clymeniida, Goniatitida and Cerititida. The mean suture pat-
terns which these power spectra represent were redrawn by
FORTRAN program FILTER (Appendix F) and are presented in
Figures 6 and 7). Discrimminant analysis (Nie, et al., 1975,
p. 434-467) was performed using these four Orders as the clas—

sification categories. Only nine individuals out of 129 were

17

FIGURE 3: Mean power spectra of Subclass Ammonoidea
(A) and Subclass Nautiloidea (N).

mumzaz >uzmaowmm u~zozm¢z
a. S m. 2. Sr a .. m m .

 

17a

 

P
4

db

~m.~n

<>
4P

4

by
q

4»
1

 

c101
z.mY
quuduJ .émn.~-

 

 

 

.6mfl.un

 

.6mo.~u

.ého.¢l

: {OnF-ul

16mm._|

lémn.—I

.énN.—I

.bbo.—t

 

 

 

um.l

3001116148 DINOHBUH N83“ 001

18

FIGURE 4: Mean sutures of Subclasses Nautiloidea
(A) and Ammonoidea (B) and a graphic

display of the difference between them
(C).

19

FIGURE 5: Power spectra of the mean suture patterns
of Ammonoid Orders Anarcestida, Clymen—
iida, Goniatitida, and Cerititida.

19a

”N

mum—.52 >ozmzau¢m u H 202mm:

 

 

 

 

 

2. 2. 3. 2. .2. _ o. p. u. a. 8.»
2.5.. o
5:28 1T
.... 65.5 a ‘ 8S-
Bugs... 9
a. .. 99“..
.68.“-
0‘)??- u..-
/ a... ‘ .. .4»
I R) \nf ...B ...... & \... I
., .93 a, \ i... ‘0: .. o... I .000. u...
.. . no. ‘8’ co

 

 

 

 

 

.uoo.u

301.! 1JHU 3 I NONHUH 001

20

FIGURE 6: Mean sutures of Orders Anarcestinda (A)
and Clymeniida (B) and a graphic display
of the difference between them (C).

21.

FIGURE 7: Mean sutures of Orders Goniatitida (A)
and Cerititida (B) and a graphic display
of the difference between them (C).

22

misclassified (Table 3). This result is significant at a =
.01 withX2 = 318.35. The sensitivity of Fourier shape anal—
ysis to genetic differences at high taxonomic levels is dem-
onstrated by the above results.

The ability to filter nongenetic effects from the mor-
phologic information, leaving only genetically regulated
shape information, is of great importance to the studies of
taxonomy, ontogeny, and phylogeny. The data set included only
two complete suture patterns suitable for examing both halves.
Both suture patterns were of Acanthoclymenia neapolitana, at
2% volutions of the conch and at maturity.

Each suture half was processed eight to ten times.
Discriminant analysis was perfomred upon the harmonic ampli-
tudes and 100% correct classification (1:2 = 105.00) was achie-
ved (Table 4). The significant differences between left and
right suture halves are summarized in the mean power spectra
of these sutures (Figure 8) These differences are not dis—
cernible in visual inspection of the suture patterns.

The ontogenetic sequences of sutre patterns of Adrianites

 

dunbari, Agatherisis uralicum and Koenenites cooperi (taken

 

 

from Arkell, et al., 1957) were studied. Suture patterns
which were too complex for analysis i.e., those which requre
a double valued function) were omitted. Sutural complexity,
as measured by the number of harmonics required to reduce RMS
to 0.05 or less, increased with age in each of the three
sequences. Because of the elimination of the complex mature
sutures of A. dunbari and A. Uralicum, further study of

ontogeny was limited to E. cooperi.

23

 

N .00. No.0 No.0 No.0
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N0.N No.00 No.0 N .0
0.. 0.N0 0.0 0.0 om 00N0N00N000

No.0 No.0 No.0N N .mm
0.0 0.0 0.0. 0.0 m. moaacmENH0

No.0 N0.N No.0 NN.mo
0.0 0.. 0.N o..0 00 mocaommoumca

aoHeHeammo aoHeaHzoo <0HHzmzwao <02H00000<z< mmmao mzaz

aHmmmmozmz 00000 omeoHommo 00 2 00000 gaseoa

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muopuo osu cw mousuam Eoum pump mo mammamc< unmaNEwuomwa mo >umaapm ”m mum<H

24

No 00. Nouo Noflo Nouo

 

 

o m o o o c o o a HADQ<-M
x .o No.ooa No.0 N .o
0.0 o.m 0.0 0.0 m Hana<nq
w .0 No.0 No.ooa N .o
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N .0 No.0 No.0 No.ooa
0.0 0.0 0.0 o.m m quzm>Dhuq
HADQ¢-M HADQ<uq quzm>Dw-m quzm>Dhuq mmm<o mz<z
mHzmmmmzmz msomu QmHoHQmMm no 2 msomc A<DHU<
.momnm ouaudm co
mp6CopHm:N owuocomcoc mo monomohd moumuumcoEop moususm Dappm paw mHNCo>Dm
Loom Cm mo>Hm£ ousudm unwwu paw umoa coo3uon cowumcwswuomwp uoowuom
.mcmufiaommoc mNcoENHoonucmo< Scum pump mo mHm>Hmc< oumcfiawuomwn mo humeadm no mqm<H

25

FIGURE 8: Mean power spectra of left and right
juvenile and adult sutures of
Acanthoclymenia neapolitana.

 

253.

—N

mwmzzz >uzu3awxm uuzo:mc:

 

 

 
         

 

0. 2 0. 2 z 0 .. 0 n .
. .. x .1 0 v x . 0 180.0-
000.00.. 0.
e 230...?
... N522... .0. 1.8.0-
.. . :32... .0.
.. 0.9....

 

 

 

 

 

 

 

 

 

 

 

300111JUU JINOHUUH NUBH 001

26

Figure 9 is the power spectra of the harmonic amplitudes
of the six sutures in the ontogenetic series of M. cooperi as
reported by Miller (1938). Growth and development is re-
flected in the power spectra as a slow broadening and migra—
tion of the first peak of the series to higher order harmonic
frequencies. Each successive approximation (i.e., suture)
tends to be of a higher overall power spectrum than the pre-
vious one. This visual observation is supported by ranking
the approximation at each frequency and summing the ranks
over the approximations (Table 5). The above observation
fit Miller's description of the ontogeny as proceeding by
the subdivision of lobes and increase in size.

A phylogenetic sequence of sutures proposed by Miller
(Arkell, et al. p. 134, 1957) for the Family Gephuroceratidae
was studied in the same manner as the ontogeny of sutures in

M. cooperi. The sequence consisted of Ponticeras aquabilis,

 

Manticoceras simulator, Manticoceras sinuosum, Koenenenites

 

 

 

cooperi and Timanites keyserlingi. The complete sutures

 

of M. simulator was not available in the literature and could

 

not be included. The same problem forced substitution of

Ponticeras stainbrooki for E. aequabilis.

 

 

P. stainbrooki, which has the most simple suture, forming
only four distinct lobes (Arkell et al., p. 135, 1957), has
a peak in its power spectrum (Figure 10) at the fourth harm-

onic frequency and then drops for the higher order frequencies.

 

M. sinuosum, M. cooperi and T. keyserlingi should then be ex-

pected to have peaks at frequencies six, eight and ten,

27

FIGURE 9: Power spectra of the ontogenetic series
of sutures in Koenenites cooperi.

 

 

27%:

 

 

 

 

 

X INCA
l 0025
I ma

 

 

\
”NH”
MK!

a mu:
-+-mna

 

 

 

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300111JHU N83" 001

21

10

HRRHONIC FREQUENCY NUHBER

 

TABLE 5: Rankings of the harmonic amplitudes within each
harmonic frequency for six suture patterns in the
ontogenetic series of Koenenites cooperi. The
increase in rank sums with age is a response to a
general increase in signal with age.

 

VOLUTION OF CONCH
0.5 1.5 2.5 3.5 4.5 5.5

HARMONIC NUMBER RANKINGS OF HARMONIC AMPLITUDES

l 5 4 l 2 3 6
2 3 l 2 5 6 4
3 2 l 3 5 6 4
4 l 3 6 4 5 2
5 3 4 2 5 l 6
6 2 l 3 4 6 5
7 l 3 2 4 5 6
8 l 2 4 5 3 6
9 3 2 l 4 6 r
10 l 2 3 4 5 6
ll 2 3 4 5 6 l
12 l 3 2 4 6 5
l3 2 3 l 4 5 6
l4 2 4 l 6 5 3
15 l 3 2 5 6 4
l6 1 2 3 4 5 6
l7 1 3 4 5 2 6
l8 1 2 4 3 5 6
l9 1 2 4 3 5 6

20 .1__ _2_ _4_ .1 a... _5__
Ranking Sums 35 50 56 87 95 97

28

FIGURE 10:

29

Power sectra of the four sutures in the
phylogenetic series in the Family
Gephuroceratidae. SEQl = P.

SEQ3
SE05

M.
:.

sinuosum, SEQ4 =_M.
keyserlingi

stainbrooki
9.992221.

29a

21

 

 

 

“33'." 5> “F:

“3:132:90

17

  
   
   
  
  

'18

 

13

l
V

'11

HRRHON IC FREQUENCY NUHBER

 

 

 

 

 

 

 

 

300.111.1118 N83“ 0

30

corresponding to their respective number of lobes (Arkell et
al., p. 135, 1957). M. sinuosum and M. cooperi do have high
values where expected, but these are not their maximua T.

keyserlingi has a relatively low value for its tenth harmonic

 

amplitude. These anomolies are considered to be the results
of combinations of lower order frequencies making good approx-
imations to the fit of the data, leaving less residual signal
to be accounted for by the higher order frequencies. The
asymmetric, non-regular (variable frequency) nature of the

lobes of I. keyserlingi can be better approximated by the

 

combination of two signals, the fourth and the seventh harm-
onic frequencies, than by the tenth frequency.

A measure of the similarity of the sutures within a group-
ing can be made by calculating the normalized roughness co-

efficient (RC) of each suture pattern.

 

fi

20
J. 25 Z (Aij/ A1)

i=1

RC

where Aij is the harmonic amplitude of the ith frequency in
the jth suture, and Xi is the mean harmonic amplitude of the
ith frequency.

A set of identical sutures should all have values of RC
equal to 10 or 3.1623. The phylogenetic sequence has value

of RC ranging from 2.9135 for I. keyserlingi to 4.7666 for M.

 

sinuosum. The ontogenetic sequence ranges from 1.6082 at the
earliest suture to 7.4351 at the adult suture. This indicates
that the sutures of the phylogenetic series are less differ-

ent from each other than those of the ontogenetic series.

31

The sources of the variation can be determined by ex-
amining the coefficients of variability for the two sequences
(Table 6). The phylogenetic sequence only has two values of
CV greater than 100 (harmonics twelve, thirteen). Other
sources of variation are, in descending order, harmonics six,
fourteen, sixteen, eleven, and one. The ontogenetic sequence
has six harmonics with coefficients of variability greater
than 100. Only harmonics one, two, four, six, twelve, four-
teen and sixteen have lower values of CV in the ontogenetic
sequence than in the phylogenetic sequence. The extremely
low values of CV for harmonics two and four in the ontogenetic
series indicate that these harmonic frequencies are relatively
independent of development, and reflect a basic sutural form
that does not vary with growth.

Log transforms of the harmonic amplitudes form the suture
patterns of the ontogenetic series were submitted to prin-
cipal components factor analysis (Nye, et al., p. 468-514,
1970). The number of volutions of the conch at each suture
was included as a variable representing age. Also included
were log transforms of the size of the aperature and twenty
harmonic amplitudes computed in closed form (Ehrlich and Wein-
berh, 1970; Ewald, 1975; Anstey, Pachut and Prezbindowski,
1976) from the shape of the aperature at the respective number
of volutions.

The matrix of correlations, output as a preliminary re-
sult, shows significant (a = .05) correlations of age with

size, sutural harmonic frequencies zero, six, seven, ten,

TABLE 6: Coefficients of Variation of the harmonic
amplitudes, computed from the phylogentic series
in the Family Gephuroceratidae and the onto-
genetic series in Koenenites cooperi.

 

 

 

HARMONIC NUMBER COEFFICIENT OF VARIATION
Phylogeny Ontogeny
l 80.14 76.61
2 67.25 32.53
3 56.67 61.68
4 52.41 39.45
5 64.15 114.58
6 95.35 68.16
7 52.95 78.82
8 70.77 84.23
9 51.54 76.68
10 76.93 113.23
11 80.68 123.17
12 104.56 67.60
13 113.84 153.60
14 88.63 66.56
15 43.61 93.68
16 87.28 65.48
17 46.38 117.06
18 55.36 119.19
19 62.38 71.61
20 52.28 81.46

32

33

twelve, sixteen, eighteen, twenty and aperatural harmonic
frequencie four (Table 7). All of these variables load
most heavily on the first principal component (Table 8) or
the general growth factor (Gould, 1966).

Principal components analysis of the phylogenetic se-
quence was performed using a dummy ”SEQ" variable coded as
the log of the suture's position in the series. As before,
log transforms of the harmonic amplitudes were used. No
aperatural shapes were available for the study. Only har-
monic frequencies seven, eighteen and twenty were signifi-
cantly (a = .05) correlated with "SEQ" (Table 9). These four
variables all loaded most highly on Factor two (Table 10).

The correlation of harmonic frequencies seven and eigh-
teen with age in both the ontogenetic and the phyloeneetic
series is an interesting point. The seventh harmonic is re-
sponsible, in part, for the presence of lateral lobes. The
eighteenth harmonic frequency is equivalent to eighteen evenly
spaces lobes. Alone, its effect can only be in small scale
sculpturing of the suture patterns. However, the high levels
of correlation imply an interaction of the two variables.

The results of this interaction is demonstrated by Figure 11,
which shows the actual contribution of harmonic frequencies
seven and eighteen to the approximation of the earliest and

adult sutures of M. cooperi.

The log transformation of the two harmonic amplitudes
were plotted against each other and regression lines were com-
puted (Figures 12 and 13) for the ontogenetic and phylogenetic

data. The slopes of the regression lines are 0.593 for the

TABLE 7: Significant Correlation Coefficients (R) of

variables from the study of ontogeny in Koenenites

 

cooperi. Significance level is a=.05 and a=.01(*)
Sutural variables are HARM l to HARM 20 and HZERO.
Aperatural variables are AHARM 1 to AHARM 20 and

SIZE.

AGE SIZE
Size .97982* HARM 6 .82005
HARM 6 .88217 HARM 7 .97274*
HARM 7 .85522 HARM 8 .89910
HARM 10 .86423* HARM 9 .98817*
HARM 12 .81744 HARM 16 .95864*
HARM 16 .99448* HARM 17 .88508
HARM 18 .95072* HARM 18 .95433*
HARM 20 .85268 AHARM 2 -.82488
AHARM 4 .87485 AHARM 4 .83539
HZERO .84909

HARM 1 HARM 2
AHARM 1 -.95539* HARM 3 .94236*
AHARM 8 -.92109*
AHARM 9 -.95587*
AHARM 12 -.94688*
AHARM 13 -.83069 HARM 3
AHARM 17 -.90256
AHARM 18 -.85346 HARM 15 .88907

HARM 4 HARM 5
AHARM 3 .92283* HARM 17 .86010
AHARM 7 .99258* AHARM 2 -.92246
AHARM 11 .95408*
AHARM 16 .91773*
HZERO .85889

HARM 6 HARM 7
HARM 7 .81684 HARM 8 .86530
HARM 10 .86140 HARM 10 .95855
HARM 12 .82726 HARM 13 .89130
HARM 16 .86628 HARM 16 .94243*
HARM 18 .86439 HARM 17 .82926
HARM 20 .81644 HARM 18 .89193

34

TABLE 7 cont.

HARM 8
HARM 10 .82804
HARM 16 .85520
HARM 17 .95015*
HARM 18 .81873
HARM 19 .82126
HZERO .83168
HARM 10
HARM 16 .93151*
HARM 17 .85613
HARM 18 .95146*
AHARM 2 -.83102
HARM 12
HARM 15 .87466
HARM 16 .84243
AHARM 16 .83725
HARM 16
HARM 18 .92970*
HARM 20 .87048
AHARM 3 .84199
AHARM 4 .88852
AHARM 16 .86241
HZERO .89209
HARM 18
HARM 20 .88226
AHARM 4 .83301
AHARM 10 -.84336

35

HARM
HARM

AHARM
AHARM
AHARM
AHARM

HARM
AHARM
HZERO

HARM
AHARM

AHARM
AHARM
AHARM
HZERO

HARM 9
13 .88184
14 .87175
HARM 11
1 .83761
5 -.90542
12 .88750
17 .87568
HARM 15
16 .83718
16 .82249
.89209
HARM 17
19 .86686
2 -.85699
HARM 20
3 .88562
4 .91223
16 .82590
.82147

TABLE 7 cont.

AHARM 1

AHARM 8 .95857*

AHARM 9 .90245

AHARM 12 .97886*

AHARM 13 .89945

AHARM 17 .96507*

AHARM 18 .95515*

AHARM 19 .87201
AHARM 4

AHARM 13 .83189

HZERO .91379
AHARM 7

AHARM 11 .91470

AHARM 16 .93642*

HZERO .90564
AHARM 9

AHARM 12 .86207

AHARM 17 .84155
AHARM 12

AHARM 13 .87988

AHARM 17 .95505*

AHARM 18 .89848
AHARM 16

HZERO .92995*
AHARM 18

AHARM 19 .95388*

36

AHARM

AHARM 4
AHARM 7
AHARM 13
AHARM l6
HZERO

AHARM
AHARM 15

AHARM

AHARM 9
AHARM 12
AHARM 13
AHARM 17
AHARM 18
AHARM l9

AHARM
AHARM 16

AHARM

AHARM l7
AHARM 18
AHARM 19
HZERO

AHARM

AHARM 18
AHARM 19

.88997
.95938
.87177
.95328*
.96608*

.88451

.93093
.88597
.81726
.88752
.93639*
.92850*

11
.81148

13

.91031
.94541*
.84781
.82988

17

.93180*
.85166

37

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38

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TABLE 9:

Significant Correlation Coefficients (R) of
variables from the study of phylogeny in the
Family Gephuroceratidae at u=.05 and u=.01(*).
SEQ is the log transform of the suture's

position in the phylogenetic series.

HARM 1

through HARM 20 are log transforms of the
Fourier harmonic amplitudes.

HARM
HARM
HARM

HARM
HARM

HARM
HARM

HARM

HARM

HARM
HARM

HARM

HZERO

HZERO

HARM

SEQ
7

18

20

HARM
10
18

HARM
18 -

HARM
12
16

HARM
18

HARM

l9 -.

HARM
18

HARM

16
19 -

20

.99742*
.95574
.96331

1

.98079
.96335

4

.97937

6

.99829*
.96995

7

.95070

9
98345

10

.96978

12

.97012
.95463

14

.95408
.99793*

17

.96656

18

.97393

TABLE 10: Varimax rotated factor matrix after rotation with
Kaiser normalization, computed from the four
sutures representing a phylogenetic series in the
Family Gephuroceratidae. SEQ is the log of the
suture's position in the series, HARM 1 through
HARM 20 are log transforms of Fourier harmonic
amplitudes, and HARMZERO is the zeroth harmonic
amplitude.

VARIABLE FACTOR l FACTOR 2 FACTOR 3

SEQ .46889 .84657 -.25708

HARM 1 .80022 .59156 .09034

HARM 2 .01218 -.46439 .87535

HARM 3 .19196 -.87878 .42148

HARM 4 .77523 -.56903 .27186

HARM 5 .35566 - 31327 .86779

HARM 6 .96505 .21535 -.15494

HARM 7 .44470 .87560 -.19579

HARM 8 .23334 .91280 .31783

HARM 9 .96230 -.22026 -.15694

HARM 10 .66822 .73571 .10482

HARM 11 .08710 -.96333 -.23045

HARM 12 .97243 .16059 -.l7435

HARM 13 .23329 .22795 .93484

HARM 14 .51499 .01546 -.85997

HARM 15 .16449 -.97662 .09033

HARM 16 .88527 .25251 -.38537

HARM 17 .58465 .26344 .76419

HARM 18 .69944 .70027 -.l3667

HARM 19 .99434 .09952 .02443

HARM 20 .64945 .67044 -.35770

HARMZERO .56325 .01434 .82892

40

FIGURE 11:

41

Contributions of harmonic frequencies
seven and eighteen to the fit of the
approximations of Koenenites cooperi
at 0.5 volutions (A), 5.5 volutions
(B) and a graphic display of the dif-
ference between them (C).

41a

 

 

 

 

 

 

 

 

 

 

FIGURE 12:

42

Relationship between the log transforms
of harmonic amplitudes seven and eigh-
teen in the ontogenetic series in M.

cooperi.

42a

 

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.
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80...- 8...... 08.0.. Sons.

80. an
p
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80. an
F
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80. .1

i083:

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L HUSH ‘300111JHU N83" 001

43

FIGURE 13: Relationship between the log transforms
of harmonic amplitudes seven and eigh-
teen in the phylogenetic series in the
Family Gephuroceratidae.

43a

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L HHUH '300111JHU NUBH 001

44

ontogentic sequence and 0.505 for the phylogenetic sequence.
This difference is slight enough to show that the two har-
monics maintain a constant relationship through the changes
of ontogeny and that this relationship is held constant across
the changes of the specific phylogenetic sequence postulated
by Miller. The constant relationship demonstrates, on a
quantitative level, the assumption of heterochrony (in this

example, recapitulation) in the cephalopods analyzed.

SUMMARY AND CONCLUSIONS

A wide taxonomic range of cephalopod suture patterns have
been studied by means of the Fourier series. Coefficients of
variation and mean suture patterns have been computed. The
filtering capability of the Fourier series allows the quanti-
tative comparison of these meansuture patterns, at any level
in the taxonomic heirarchy. This same filtering capability
permits a measure of a suture's nongenetic norm or reaction.
Measurements show that subtle differences exist between the

left and right suture halves of Acanthoclymenia negpolitana

 

at both 2% volutions of the conch and at maturity.

The relationship between harmonic frequency seven and
harmonic frequency eighteen is monotonic for both an onto-
genetic and a phylogenetic sequence in the family Gephuro-
ceratidae. The linear relationships were calculated directly
from the log transformation of the harmonic amplitudes and
found to be almost identical. Heterochrony (recapitulation)

is there fore demonstrated on a quantitative level for

45

Koenenites cooperi and three other genera to which it is

 

closely related. The correlation of aperatural shape var-
iables, generaged by Fourier analysis, with those of sutural
shape through development in M. cooperi implies a functional
relationship between specific aspects of aperature and suture
morphology.

The power of Fourier analysis in the sutdy of the ceph-
alopod suture is unprecedented. Taxonomy, nongenetic norm
of reaction, heterochrony, and functional morphology of
cephalopod sutures can be studied quantitatively by means of

Fourier analysis.

LIST OF REFERENCES

Anstey, R.L., J.F. Pachut, and D.R. Prezbindowki, Morphogenetic

gradients in Paleozoic bryozoan colonies: Paleobiology,
V. 2, No. 2, p. 131-146.

Arkell, W.J., et al., 1957, Treatise on Invertebrate Paleon-

tology: part L, Mollusca 4, University Kansas Press,
490 p.

Christopher, R.A., and J.A. Waters, 1974, Fourier series as a

quantitative descriptor of miospore shape: Jour. Paleon-
tology. V. 48, No. 4, p. 697-709.

Crowther, R.A., and L.A. Amos, 1971, Harmonic analysis of

electron microscope images with rotation symmetry: J.
Mol. Biol., V. 60, No. 1, p. 123-130.

Davis, J.C., 1973, Statistics and data analysis in geology:
John Wiley and Sons, Inc., New York, 550 p.

Delmet, D.A., and R.L. Anstey, Fourier analysis of morpholog-
ical plasticity within an Ordovician bryozoan colony:
Jour. Paleontology, V. 48, No. 2, p. 217-226.

Ehrlich, R. and B Weinberg, 1970, An exact method for charac-

terization of grain shape: J. Sed. Petrology, V. 40,
No. l, p. 205-212.

Ewald, F.C., 1975, Feasibility of completely automated micro-
fossil identification in petroleum exploration: Mich.
State University, MS Thesis, 68 p.

Gevirtz, J.L., 1976, Fourier analysis of Bivalue Outlines:
Implications on evolution and autec010gy: Math. Geol.,
V. 8, No. 2, p. 151-163.

Gould, S.J., 1966, Allometry and size in ontogeny and phylogeny:
Biol. Rev., V. 41, No. 4, p. 587-640.

Kaesler, R. and Waters, J.A., 1972, Fourier analysis of the
Ostracode margin: Geol. Soc. Amer. Bull., V. 83, No 4,
p. 1169-1178.

Lu, K.H., 1965, Harmonic analysis of the human face: Bio-
metrics, V. 21, No. 2, p. 491-505.

I

46

47

Mendenhall, W., 1968, Introduction to linear models and the
design and analysis of experiments: Wadsworth Publishing
Co., Inc., Belmont, CA, 465 p.

Miller, A.K., 1938, Devonian ammonoids of America: Geol. Soc.
Amer. Spec. Paper 14, 262 p.

Nie, N.H., C.H. Hull, J.G. Jenkins, K. Steinbrenner, and
D.H. Bent, 1975, Statistical package for the social
sciences: McGraw-Hill Book Co., Inc., New York, 675 p.

Oxnard, C., 1973, Form and pattern in Human evolution: some
mathematical physical, and engineering approaches: Univ.
Chicago Press, 218 p.

Schindewolf, O.H., 1954, On development, evolution and term-
inology of the ammonoid suture line: Harvard Univ. Mus.
Comp. 2001., Bull. 112, No. 3, p.217-237.

Tasch, P., 1973, Paleobiology of the invertibrates, data re-
trieval from the fossil record: John Wiley and Sons,
Inc., New York, 946 p.

Thompson, D.W., 1917, On growth and form: Cambridge University
Press.

Tuckey, M., 1975, Sexual dimorphism in the Devonian trilobite
Phacops rana: Mich. State University, MS Thesis, 90 p.

Vicencio, R., 1973, Models for the morphology and morphogensis
of the ammonoid shell: McMaster Univeristy, Ph. D.
Dissertation, 116 p.

Waters, J.A., 1977, Quantification of shape by use of Fourier
analysis: The Mississippian Blastoid genus Pentremites:
Paleobiology, V. 3, No. 3, p. 288-299.

Younker, J.K., 1971, Evaluation of the utility of two-dimen-
sional Fourier shape analysis for the sutdy of ostracode
carapaces: Michigan State University, MS Thesis, 62 p.

Zahn, C.T., and R.Z.Roskies, 1972, Fourier descriptors for

plane closed curves: IEEE Trans. on Computers C-21,
No. 3. p. 269-282.

APPENDIX A

48

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APPENDIX B

APPENDIX B

Sources of Suture Diagrams

Arkell, W.J., et al., 1957, Treatise on Invertebrate Paleontol-
ogy, part L, Mollusca 4, University Kansas Press, 490 p.

Miller, A.K., 1947, Tertiary Nautiloids of the Americas, Geol.
Soc. Amer., Mem. 23, 234 p.

Miller, A.K. and w.M., Furnish, 1940, Permian Ammonoids of the
Guadalupe mountain region and adjacent areas, Geol. Soc.
Amer., Spec. paper 26, 242 p.

Petersen, M.S., 1975, Upper Devonian (Famennian) ammonoids
from the Canning Basin, western Australia, Paleontologi-
cal Society, Mem. 8, 55p.

Teichert, C., et al., 1964, Treatise on Invertebrate Paleon-
tology, part K, Mollusca 3, University Kansas Press, 519 p.

APPENDIX C

APPENDIX C

Taxonomy of Ammonoids Studied

Subclass Ammonoidea
Order Anarcestida
Superfamily Anarcestaceae
Family Mimoceratidae
Subfamily Mimoceratinae
Genus Gyroceratites

species gracilis

 

Family Agoniatitidae
Genus Agoniaties

 

species vanuxemi

species costulatus

 

Family Anarcestidae
Subfamily Anarcestinae
Genus Anarcestes

 

species lateseptatus

 

Genus Subanarcestes

 

species macrocephalus

 

Genus Werneroceras

 

species ruppanchensis

 

species plebeiforme

 

Superfamily Prolobitaceae
Family Prolobitidae
Subfamily Prolobitinae

Genus Prolobitcs

 

species delphinus

 

52

53

Superfamily Pharcicerataceae
Family Gephuroceratidae
Genus Manticoceras

 

species sinuosum
Genus Ponticeras

 

species aequabilis

 

Genus Koenenites

species cooperi

Genus Timanites

 

 

species keyserlingi

 

Order Clymeniida
Superfamily Gonioclymeniaceae
Family Acanthoclymeniidae
Genus Acanthoclymenia

 

species neopolitana

 

Superfamily Clymeniaceae
Family Clymeniidae
Genus Platyclymenia

 

species annulata
Genus species americana

 

species polypleura

 

Order Goniatitida
Superfamily Cheilocerataceae
Family Tornoceratidae
Genus Tornoceras

 

species crebriseptum

 

species delepinei

 

Family Cheiloceratidae
Subfamily Cheiloceratinae
Genus Cheiloceras
species schmidti
species ovatum
species angulatum

 

54

species enkebergense

 

Subfamily Raymondiceratinae

Genus Raymondiceras

species simplex

 

Subfamily Speradoceratinae
Genus Sporadoceras

 

species milleri

Subfamily Imitoceratinae

Genus Imitoceras

 

species rotatorium

 

Superfamily Agathicerataceae
Family Agathiceratidae
Genus Agathiceras

 

species uralicum

Superfamily Cyclolobaceae
Family Popanoceratidae
Subfamily Marathonitinae
Genus Peritrochia

 

species dieneri

Superfamily Goniatitaceae
Family Goniatitidae
Subfamily Goniatitnae
Genus Goniatites

 

species choctawensis

 

Genus Muensteroceras

 

species parallelum

 

Subfamily Girtyoceratinae
Genus Eumorphoceras

 

species bisulcatum

 

55

Family Neoicoceratidae
Genus Pseudoparalegoceras

 

species russiense

 

Genus Atsabites

 

species multiliratus

 

Family Schistoceratidae
Subfamily Schistoceratinae
Genus Paralegoceras

 

species iowense
Genus Diaboloceras

 

species varicostatum

 

Genus Winslowoceras

 

species henbesti

Superfamily Adrainitaceae
Family Adrianitidae
Subfamily Adrianitinae
Genus Adrianites
species dunbari
Genus Texoceras

 

species texanum
Subfamily Dunbaritinae
Genus Emilites
species inggrgus

Order Cerititida
Superfamily Otocerataceae
Family Xenodiscidae
Genus Xenodiscites

species waageni
Genus Xenaspis

species skinneri

 

species carbonaria

 

56

Genus Paraceltites

species elegans

species ornatus

 

species hoeferi

species altudensi

 

APPENDIX D

APPENDIX D

Mean Harmonic Amplitudes of the Taxonomic Hierarchy

Subclass Bactritoidea
Order Bactritida
Family Bictritidae

 

 

.02095 .32555 .02070 .01040 .04330 .01150 .02130 .00450 .01120 .00305
.00935 .00265 .00640 .00240 .00245 .00070 .00405 .00040 .00305 .00195
Genus Bactrites
.0234 .0280 .0228 .0167 .0239 .0045 .0079 .0020 .0052 .0001
.0060 .0030 .0042 .0009 .0007 .0008 .0030 .0007 .0024 .0001
Genus Lobobactrities
.0182 .3711 .0186 .0041 .0627 .0185 .0347 .0070 .0172 .0060
.0127 .0023 .0086 .0039 .0042 .0006 .0051 .0003 .0037 .0038
Subclass Nautiloidea
Order Nautilida
Superfamily Nautilaceae
.05106 .09448 .08412 .11349 .07427 .06311 .03092 .03661 .02606 .02124
.02187 .01156 .01988 .01398 .00786 .00936 .00671 .00652 .00398 .00311

Family Nautilidae

Genus Nautilus species pompilius

 

.07480
.00915

.04712
.02081

.07885
.00770

.00270
.0711

.17710
.00410

.04751
.01162

.03910
.00643

.00450
.03450

.13065
.00835

.08930 .04245 .01360 .02030
.00750 .00340 .00240 .00035

Family Hercoglossidae

.04583
.01160

.07132
.01133

.01850
.02640

.08622 .06632
.00573 .00467 .00352 .00302

.08717 .07846 .08613 .03662
.00790 .00879 .00863 .00199

Genus Hercgglossa
.14175

 

. 05500

Genus Aturoidea

 

57

.02565 .00220
.00015 .00175

.03354 .02610
.00249 .00289

.01477 .03080
.00463 .00235

.01850
.00240

.00884
.00150

.00718
.00289

species paucifex

.15030 .14680 .07740 .04910 .09520 .03590 .01380
.01850 .02170 .02450 .00330 .00110 .00750 .00030

.03280
.00010

.07414
.00435

.06190
.00260

.08453
.00295

58

Genus Cimonia

.04010
.00450

.()1510
.00330

.03520 .05430 .01890 .00890
.00500 .00320 .00000 .00280
Genus Deltoidonautilus

.07205 .06550 .07107 .02349 .01528
.00287 .00378 .00330 .00165 .00143

 

.07840
.00537

Family Aturiidae
Genus Aturia

.07588 .16400 .10190 .08960 .03583
.03970 .02655 .01138 .01705 .01778

.03125
.03565

.05883
.01895

Subclass Ammonoidea
Order Anarcerstida

.14496 .10793 .06543 .08882 .06464 .05544
.02262 .01919 .02774 .01292 .02331 .01125

.06117
.00918

Superfamily Anarcestaceae

.22808 .07480 .07541 .03812 .03812 .03677
.01206 .00986 .01067 .00861 .00786 .00670

.05883
.01432

.05065
.01693

.06138
.01687

.02476
.00685

.02018
.00152

.04988
.00730

.03219
.00658

.01534
.00538

.02220
.01087

.08849
.01334

.06580
.01874

.03740
.0067

.31423
.00800

.26273
.01602

.10728

Family Mimocertidae
Subfamily Mimoceratinae
Genus Gyroceratitites

speCIES gracilis

 

.01930 .00470 .03897 .02253 .02480 .01633 .01433

.00680 .00530 .00343 .00343 .00320 .00330 .00233

Family Agoniatitidae

.16612 .12352 .01078 .07081 .04357 .04184
.01341 .01124 .00124 .01210 .00903 .00975

.01772
.00728

Family Anarcestidae
Subfamily Anarcestinae

.03898 .09803 .04061 .02103 .04193 .01610

.01215 .00938 .01296 .01115 .00804 .00788 .00750

Superfamily Prolobitaceae

.1532
.0132

Family Prolobitidae
Subfamily Prolobitinae
Genus Prolobites

 

.01398
.00653

species délphinus

 

.0858
.0164

.0504
.0162

.1359
.0141

.1513
.0184

.0612
.0244

.0353
.0203

.0239
.0092

species vincenti

.01750
.00020

.00490
.00120

.00948
.00153

.03638
.00543

.02717
.00796

.01787
.00591

.01177
.00257

.02550
.00867

.01634
.00649

.0239
.0081

59

Superfamily Pharcicerataceae
Family Gephuroceratidae

.08729 .05360 .11310 .08559 .08504 .09459 .07916 .07359 .05732 .03973
.00653 .04259 .03362 .05226 .01174 .03768 .01084 .02739 .00516 .00986

Order Clymeniida

.07519 .09789 .07040 .15919 .07853 .07986 .05960 .04834 .02938 .02461
.02366 .01073 .01171 .00773 .01410 .00979 .00953 .00704 .00435 .00439

Superfamily Gonioclymeniaceae
Family Acanthoclymeniidae
Genus Acanthoclymenia
species neopolitana

.06323 .07938 .09539 .23029 .10228 .11569 .08164 .07589 .05083 .04378
.04164 .01792 .02063 .01287 .02559 .01800 .01711 .01222 .00740 .00804

 

 

Superfamily Clymeniaceae
Family Clymeniidae
Genus Platyclymenia

.08715 .11640 .04540 .07808 .05478 .04403 .03755 .02078 .00793 .00543
.00568 .00353 .00278 .00258 .00260 .00158 .00195 .00185 .00130 .00073

 

Order Goniatitida

.03871 .04289 .02517 .92292 .03185 .05728 .05515 .06996 .05550 .04199
.03116 .32443 .03544 .02540 .02239 .02777 .01906 .01946 .02441 .02443

Superfamily Cheilocerataceae

.04573 .07560 .03598 .03916 .07009 .07606 .02257 .05186 .02674 .03236
.03139 .04706 .00692 .02240 .01880 .01704 .00968 .02347 .00524 .01548

Family Tornoceratidae

.05127 .06311 .04165 .05246 .05829 .10137 .00520 .06616 .01634 .01654
.01326 .03505 .00346 .02600 .01174 .01321 .00254 .01914 .00192 .01319

Family Cheiloceratidae

.04018 .08809 .03031 .02585 .08189 .05075 .03993 .03756 .03713 .04817
.04951 .04647 .01037 .01879 .02585 .02087 .01681 .02779 .00855 .01776

Superfamily Cyclolobaceae
Family Popanoceratidae
Subfamily Marathonitinae
Genus Peritrochia
species dieneri

.0528 .0431 .0084 .0153 .0088 .0022 .0036 .0218 .0022 .0308
.0087 .0262 .0179 .0248 .0006 .0317 .0037 .0084 .0391 .0619

 

.0259
.0582

.04260
.02411

.0538
.0073

.04980
.04030

.02690
.03338

.02429
.01585

.02950
.0509

.02602
.03966

60

Superfamily Agathicerataceae
Family Agathiceratidae
Genus Agathiceras

 

species uralicum

.0415 .0331 .0055 .0079 .0773 .1007 .0666 .0507

.0039 .0346 .0212 .0142 .0257 .0013 .0170 .0163
Superfamily Goniatitaceae

.03331 .03034 .03783 .04595 .09347 .06182 .12305 .11161

.02986 .04467 .04217

.03708 .04229 .04404

.03594 .02970

Family Neoicoceratidae

.0284
.0365

.0072
.0553

.0335
.0844

.0216
.0405

.0485

.0835

.0176
.0295

.2346
.0384

.1672
.0241

Family Schitoceratidae
Subfamily Schistoceratinae

.02590 .05452 .03170 .03655 .08070 .11608 .10283 .14580
.02470 .05510 .03102 .04288 .03350 .06185 .05235 .03315

Superfamily Adrianitaceae

Family Adrianitidae

.01680 .02650 .03738 .08705 .08650
.01644 .04128 .02211 .03659 .01249

.02095 .01803
.02141 .07309

.08623
.03173

Subfamily Adrianitinae

.01189 .02035
.03582 .05197

.01090 .01630 .04715 .10529 .06959
.01947 .00735 .02012 .03957 .02237

.07425
.02475

Subfamil Dunbaritinae
y 0 O

Genus Emilites
*.
spec1es incertus

.0300
.0070

.0157
.0942

.0227
.0134

.0367
.0752

Order Cerititida

.0276

.0241

.0982
.0387

.0688
.0336

.1034
.0026

Superfamily Otocerataceae

Family Xenodiscidae

.04284 .06059 .04433 .08939

.18577

.10257 .08220 .06517

.02877 .02061 .01668 .03424 .01734 .01884 .01566 .01574

.0289
.0182

.05971
.00815

.0178
.0230

.13065
.02268

.05819
.00815

.09067
.01179

.0257
.0045

.02121
.00834

APPENDIX E

APPENDIX E

Coefficients of Variation of the Harmonic Amplitudes for
the Taxonomic Hierarchy.

Subclass Nautiloidea

35.25
49.59

66.39
140.10

22.27
12.64

60.98
65.74

Order Nautilida
Superfamily Nautilaceae

62.03 41.74 31.48 32.92 55.52 24.30

52.46

Family Hercoglossidae

62.25 63.

114.41 77.92 78.52 84.99 106.18 65.59

28.50

70.79 63.56 42.31 64.14 117.18 113.75

63 46.00 52.77 38.55 42.74 106.42

55.83

Genus Deltoidonautilus

 

65.45 43.69 40.32 66.49 9.03 21.75
66.10 71.11 59.86 82.78 18.18 51.52

Genus Hercoglossa

56.34 26.91 68.27 23.13 26.22
81.06 115.52 54.56 124.36 64.91

 

70.60
67.88

Subclass Ammonoidea

43.80
46.48

33.40
39.56

51.04
51.48

46.76
22.95

51.81 46.52 64.81 32.87 49.46
52.26 36.67 31.49 32.10 20.56

27.98
19.08
Order Anarcestida

49.30 23.36 33.18 55.78 35.86
62.48 53.91 64.07 31.61 52.32

31.87
34.58

Superfamily Pharcicerataceae
Family Gephuroceratidae

83.29 62.64 11.39 71.01 76.08 26.57
79.27 112.68 66.87 64.14 69.10 73.17

Superfamily Anarcestaceae

38.57 86.99 67.72 45.46 60.65 23.09
27.16 27.58 35.72 42.53 45.08 37.61

61

23.08
47.37

14.42
51.27

10.46
25.19

42.96
49.67

52.11
15.26

48.80
39.02

74.69
60.13

28.88
95.71

15.24
32.37

26.69
22.98

40.42
54.79

56.27
28.19

36.58
26.90

10.99
40.49

53.71
54.06

37.22
64.20

54.62
34.43

60.85
88.12

28.49
70.46

34.74
20.31

58.54
44.64

31.95
42.70

69.
41.

25.
69.

29.
23.

14.
26.

27

86.
16.

30.
55.

74.
99.

5.
55.

25
12

62
63

3O
50

.26
70.

77

97
87

.23
51.

56

.69
.51

54
09

77
91

80
39

77
85

62

Family Anarcestidae

47.99 102.55 34.32 12.83 44.52
11.18 42.14 16.32 19.19 8.46

36.52
19.97
Family Agoniatitidae

11.46 61.97 2.34 22.77
11.24 40.36 12.36 31.30

2.91
45.17

Genus Agoniatites

12.86 80.24 3.36 19.42
18.22 16.90 33.41 33.33

 

7.26
25.74

12.87
12.27

Order Clymeniida

15.12 58.65 44.34 35.33 58.08 59.26
54.82 79.26 28.26 89.96 90.86 88.61

Superfamily Clymeniaceae

Genus Platyclymenia

 

65.68 26.54 59.08 79.46 73.42 75.92
37.59 27.93 14.56 21.15 33.33 30.77

Order Goniatitida
42.49 41.24 58.05 74.23 57.86 67.14
49.46 64.65 34.70 67.06 31.30 92.98
Superfamily Adrianitaceae
Family Adrianitidae

12.90 35.12 38.49 26.15 20.96
28.89 18.47 82.19 9.00 8.16

43.
67.

23
30

.()9

7.68

70.
79.

48

49.

19.
79.

.10
.34

33
54

.45
.70

.47

54

54
18

53.

99.

26.
16.

48.
48.

13
16

32
50

26
40

1.18

5.

76

Subfamily Adrianitinae

72.48 44.04 68.71 79.64 77.04 58.80
76.33 8.91 64.63 50.29 87.29 40.53

Superfamily Goniatitiaceae

68.30
40.38

63.71 19.66 53.61 45.89 66.04
33.35 73.39 17.76 72.57 30.44
Family Goniatitidae

92.49 78.38 55.02 7.02 95.17
29.69 90.53 2.04 69.11 12.30

73.65
30.54

Subfamily Goniatitinae

9.25 78.52 22.02 .90 70.70
7.65 .32 74.25 2.24 13.77

29.10
37.47

39.99
.51

47.48
36.08

5.83
28.28

62.62
81.09

81.07
7.69

71.10
49.51

13.89
21.99

11.38
88.69

57.41
13.45

46.64
23.84

50.65
26.32

36.
18.

10.
22.

25.
.60

28

76.
81.

41.
58.

33.
78.

55.
44.

31.
10.

84
34

62.
.41

31

85.
.66

34

58
10

02
10

68

96
23

01
62

10
19

83
75

69
90

.46
.04

20

54

12.
57.

40.
76.

90.
72.

78.
17.

47.
25.

30.
31.

.77
.85

13
75

96
98

60
60

15
27

48
73

91
53

104.

112.

Family

9.25
7.65

1.81
5.76

2.10
37.47

Superfamily

15.76 33.98
49.96 16.10

16.
14.

52
01

Family

98.40 83.52
53.29 89.00

19.57

62

Subfamily Cheiloceratidae

41.58

49

101.77 28.91
13.82 69.16
Family

29.17 56.82
95.66 51.92

13.25
29.53

Order Cerititida
Superfamily
Family

84.48 48.15
50.71 32.95

39.61
46.23

18.66
12.70

30.53 52.95
47.35 67.24

63

Schistoceratidae

78.52 22.02 .90
.32 74.25 2.24

Cheilocerataceae

16.84 33.28 76.96
37.54 22.48 73.75

Cheiloceratinae

70.48 41.74 31.41
78.08 58.62 59.57

31.69 48.42 70.84
43.12 6.28 60.64

Tornoceratidae

42.13 32.12 63.46
39.95 57.23 35.83

Otocerataceae
Xenodiscidae

65.50 16.03 20.41
50.14 30.55 30.32

70.70
13.77

27.57
18.43

120.78

92.37

13.02
54.81

42.03
55.06

73.44
58.83

Genus Paraceltites

 

33.29 34.66 54.36
37.57 28.46 32.50

23.80
40.55

50.65
26.32

38.88
63.32

66.21
61.37

45.50
75.82

10.19
61.88

57.32
29.11

69.40
69.59

85

48

61.
90.

77.
57.

74.
.02

45

36
41

.54
24.

66

.88
14.

77

19
92

44
24

.80
.12

24

.40
.36

APPENDIX F

64

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