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ABSTRACT
ASTOGENY AND INTRACLONAL VARIABILITY OF AN

ORDOVICIAN BRYOZOAN COLONY:
FOURIER SHAPE ANALYSIS

BY

Dale Aaron Delmet

The shape variation of zooecial cross sections
within a clone of zooids contains information regarding
the factors which controlled colony growth and development
in bryozoans. Exact characterization of the two dimen-
sional shapes by means of Fourier harmonic spectra enables
the partitioning of the effects due to ontogeny, astogeny,
environment, and genetics. Triangular shapes associated
with monticules indicate significant differences in the
number or development of budding centers within a growth
layer. The gross zooecial shape changes within a thin
section demonstrate the function of the monticule as a
budding center. Variation in the number of shapes with
inflecting acanthopores from area to area within a growth
level and from one growth level to another reflects en-

vironmental differences deve10ped over the colony surface

Dale Aaron Delmet

as well as changes with time or growth of the colony. The
central tendencies of the eighth and sixth harmonics re-
main relatively constant throughout the colony, indicating
that the degree of packing and the finer details of the
zooecial margin are strictly controlled by the genome and

therefore may be evolutionarily significant.

ASTOGENY AND INTRACLONAL VARIABILITY OF AN
ORDOVICIAN BRYOZOAN COLONY:

FOURIER SHAPE ANALYSIS

BY

Dale Aaron Delmet

A THESIS

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

MASTER OF SCIENCE

College of Natural Science
Department of Geology

1972

ACKNOWLEDGMENTS

I thank Robert L. Anstey for his help in this
research. I also thank Robert E. Ehrlich, J. Alan Holman,
and Sam B. Upchurch for their helpful criticisms of the

thesis.

ii

TABLE

LIST OF TABLES . . . . . .

LIST OF FIGURES. . . . . .

INTRODUCTION . . . . . .
PREVIOUS WORK. . . . . . .
METHOD . . . . . . . .

RESULTS 0 O O O O O O 0
Gross Zooecial Form. .
Intracolony Variation.

CONCLUSIONS. . . . . . . .

LIST OF REFERENCES . . . .
APPENDICES . . . . . . .
A. FOURIER AMPLITUDES
Entire zoarium

Lateral variation
Vertical variation

OF CONTENTS

B. FRIEDMAN TEST RESULTS.

iii

Page

iv

10
12
l8
18
32

50

52
56

56

104

LIST OF TABLES

Table Page

1. Recent terminology describing shapes of

zooecial margins . . . . . . . . . . . . . . 8

2. Rank and probability of each harmonic number
as calculated by the Friedman test . . . . . 45

iv

Figure

10.

11.

LIST OF FIGURES

Pathways of components making up the cross
sectional shape of a chamber margin . . .

Views of the zoarium, MSU 1001. . . . . . .
Amplitude spectra of the four cardinal
packing shapes, illustrating bryozoan

ontogeny. . . . . . . . . . . . . . . . .

Line drawings of the shapes described by
spectra in Figure 3 . . . . . . . . . . .

Tangential section showing the packing
gradient. . . . . . . . . . . . . . . . .

Photomicrographs of thin sections . . . . .

Variation of the third harmonic from core
to core and layer to layer. . . . . . . .

Line drawings of shapes illustrating
variations in the third harmonic. . . . .

Variation of the ninth harmonic from core
to core and layer to layer. . . . . . . .

Line drawings of shapes illustrating
variations in the ninth harmonic. . . . .

The harmonic spectrum for the entire colony

Page

l3

19

21

23

29

34

36

39

41

47

INTRODUCTION

To test hypotheses concerning the phylogeny and
paleoecology of any fossil group, paleontologists must
make effective use of the elements of skeletal morphology,
both as taxonomic characters and as functional adaptations
to environmental conditions. Two problems exist: 1) to
characterize morphological features effectively, and 2) to
determine how much of the observed variability reflects
growth, polymorphism, sex, nonmutational environmental
response, and genetic control. This study concerns the
characterization and partitioning of the variability in
morphological characteristics within the skeletal deposit
of a single bryozoan colony. The accomplishment of these
goals involves the use of the harmonic coefficients of
the Fourier series as shape descriptors.

Colonial organisms alone in the fossil record pro-
vide identifiable genetic response. Bryozoans were se-
lected for paleogenetic study because of their (1) clo-

nality; (2) importance in the Phanerozoic fossil record;

 

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and (3) evolutionary position at the divergence of the
protostome and deuterostome lineages.

A bryozoan colony, a clone of zooids generated by
asexual budding, consists of diploid individuals geneti-
cally identical to the ancestrula (first zooid). The
colony studied secreted a massive hemispherical zoarium
with numerous repetitive laminar growth zones. Succession
of growth zones involves cessation of colony growth and
later regeneration by the budding of new zooids on the
dormant colony surface. In the zoarium studied, each new
set of zooids occupied a successively greater surface area,
thereby generating a hemispherical zoarium. Cessation of
growth probably involved periodic influx of sediment or
perhaps periods of extreme environmental conditions causing
polypide degeneration and the formation of brown bodies.
When favorable conditions returned a new layer of zooids
budded from the epithelial cells covering the top of the
skeletal deposit.

Although the genetic makeup of each individual is
identical throughout a colony, phenetic characteristics
may vary widely. Tavener—Smith (1966) showed that intra-
colony variation in fenestrate bryozoans was significantly

less than intercolony variation and suggested that mean

values be used to compare colonies quantitatively, because
intrazoarial means would display only minimal variation.
Oliver (1968) concluded that mutations within a colony,
resulting in phenetic variation, could take place. However,
he considered such mutations exceptional; in laboratory
studies members of a clone can be considered identical for
all practical purposes.

A bryozoan colony makes possible partitioning of
the variability of morphological characters. Genetics,
growth, and mechanistic (nonmutational) response to the
environment represent different pathways leading to the
observed shape (Figure l).

Nonmutational environmental stresses account for
a considerable portion of the variability both within and
between colonies. External factors can cause changes in
an organism within the limits of its genetic potential.
Beyond these limits the organism either dies, migrates, or
develops mutations. The organism's response lies within
fixed genetic bounds, but the environment controls the
extent to which a morphological character varies. Micro-
environmental stresses around a zooid, including relation-
ships to neighboring zooids, and location with respect to

water flow and agitation, food supply and waste materials,

make contributions to the total phenetic shape. Environ-
mental pressures in the micro habitat directly affect a
zooid's shape, without straining its genetic potential or
altering its growth pattern. Thus, some shape variation
results from the environmental "bypass" pathway, and does
not involve the genome directly (Figure l).

A second major cause of shape variability lies in
the organism's genome. The genetics influence colony
growth by controlling the limits of gross morphological
change. Also, the genetics control the developments of
the zooecial microstructure, including such anatomical
features as the characteristics of muscle attachments,
opercula, spines, fulcra, and communication pores.

The phenetic shape of a zooid changes with colony
growth (astogeny), which responds to environmental stresses
within fixed genetic limits. Schopf (1969) and Lagaiij
and Gautier (1965) have demonstrated the effect of environ—
mental factors on gross colony form in cheilostomes. The
colony's growth response to major environmental factors
also affects the shapes of the zooids. Thus, the phenetic
shape of a zooid results from the interaction of several
biological factors; the partitioning of these factors can
explain the variety of shapes observed within a single

colony.

 

PHENETIC

SHAPE

 

Fig. l.--Pathways of components making up the
Cross sectional shape of a chamber margin. Environment
has the greatest effect on the phenetic shape by affecting
all of the other components and the actual shape itself.
Genatics of the organism is the next most important com-
Ponent because it directs everything associated with the
organism except the environment. The growth of the
organism has the least effect because it is affected by
all of the other components shaping the zooecium.

 

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Anthozoans represent the only other fossil group
that exhibits similar growth and development, and in which
Umzsame phenetic pathways can be conveniently partitioned.
Ekyozoans presumably represent a higher evolutionary stage,
because they are true coelomates and intermediate to the
pmotostome and deuterostome lineages. Thus, they display
greater complexities both in development and anatomy than
corals. No other organic groups provide such well pre-
served clones in the fossil record.

To explain the distribution of shapes within a
bryozoan colony, the clonal phenome must be partitioned
according to the pathways indicated (Figure 1). Thus,
shape components can be divided into three groups:
lJ characters which remain constant throughout the colony,
Emimarily controlled by the genetic makeup of the organ-
isms; 2) characters that vary with the age of the zooid
(Ontogeny) and characters that vary vertically from growth
Zone to growth zone, but do not vary laterally over the
<xflony surface (astogeny); 3) characters that vary later-
allY On the colony surface, within or between specific
aStOgenetic levels, which reflect variation due to condi-
tions external to the colony, such as the direction or

lntensity of water movement.

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Phenetic characters that are generally constant
with respect to positional, ontogenetic, and astogenetic
locations within the colony belong to group 1. Characters
which show vertical variability at a single positional
location, either within or between laminar growth zones,
belong to group 2; those which show strong positional
variation within or between specific growth levels belong
to group 3.

Shape descriptions from the recent literature do
not characterize bryozoan chamber shapes to any greater
degree than that obtained from the use of simple geometric
terms (Table 1). Measurements commonly used in bryozoan
taxonomy include the longest diameter of the chamber open-
ing, or the total number of zooecia per unit distance or
unit area. However, these quantities measure size rather
than shape. Ross (1969) measured the length of both the
major and minor axis of zooecial and "mesozooecial" open-
ingS, but did not calculate any ratio between the two
values. Anstey and Perry (1969, 1970) calculated the ratio
0f zooecial diameter or zooecia per unit area to other
morphological variables, thus, providing a shape index.
Ratios of counts or measurements provide a shape index

that can be used in comparisons within and between

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TABLE 1.--Recent terminology describing shapes of zooecial

 

 

 

margins.
Boardman gtg:::: Cuffey in:::Zy McKinney
(1960) (1964) (1967) (1970) (1971)

Circular X X X X X
Subrounded X X X X
Elliptical X X X X
Elongate X X X
Triangular X X

Square X X X

Rhombic X X X

Regular X X X X X

polygons
Irregular X X X X X

polygons

 

colonies. Such indices, however, describe only a small
part of the gross zooecial shape. A considerable degree
of shape variability is still possible for any fixed ratio.
Small scale variations or fine sculpturing of the zooecial
margin are not measured at all. Underwood (1970, p. 228)
has listed other shape indices including both simple ra-
tios or complex combinations of form factors.

The Fourier method (Ehrlich and Weinberg, 1970)
measures the shape of a closed curve to any desired degree
of precision. This method has considerable potential for
analyzing the shapes of many organic structures dealt with
in paleontology. The Fourier method has three advantages
over other methods of shape measurement: 1) any degree of
detail can be characterized, 2) an amplitude spectrum and
its associated phase angles are unique for each different
shape, and 3) the effects of different phenetic pathways
can be separated among a collection of independent vari-
ables. The Fourier method provides, therefore, the most
effective means available of describing and comparing the

shapes of skeletal structures.

P REV I OUS WORK

Two previous studies have applied the Fourier
method to the study of organic shapes (Younker, 1971;
Kaesler and Waters, 1972). Both described ostracode
carapaces and concluded that the technique could be used
for taxonomic purposes. Younker employed the technique
to demonstrate sexual dimorphism, and employed both Chi-
squared and discriminant analysis in studying the har-
monic spectra. Both studies dealt with solitary organisms,
and therefore lacked the control necessary to partition
effects due to the different phenetic pathways.

Intracolony variation in bryozoans has not previ—
ously been described in any great detail. Cumings (1904)
examined the primary budding stages of a colony and delin-
eated the changes occurring during the early part of
astogeny. Cumings (1912) also worked out in detail the
early astogenetic development of several genera. Stach
(1935) reported considerable intracolony variation in
cheilostomes. Boardman (1954) studied the axial ratio
within ramose colonies, and found that it changed

10

ll

astogenetically and should not be used in taxonomy. Perry
and Hattin (1958) examined astogenetic changes in several
quantitative characters of fistuliporoid cystoporates.
Oliver (1968) compared intraclonal variation in corals to
that in ectoprocts. Review papers that have discussed
intracolonial variability in bryozoans include Tavener-
Smith (1966), Boardman and Cheetham (1969), Boardman,
Cheetham, and Cook (1970) and Boardman (1971). Anstey
and Delmet (in press) have used the Fourier method to
demonstrate genetic, astogenetic, and environmental re-
sponses of phenetic characters in explaining intracolony
variation.

Previous studies of intracolony variation have
generally reported variation within only a small portion
of the surface of a colony, but with the exception of
Perry and Hattin (1958), have not examined variation at
different positions on the colony surface or at different

growth levels.

METHOD

Maximization of astogenetic and microenvironmental
variability was achieved by studying the largest fossil
zoarium available. The zoarium selected (Figure 2) be-
longing to Amplexopora filiasa (D'Orbigny) (Cumings, 1908,
p. 765), has the approximate dimensions 20 cm by 16 cm by
7 to 8 cm. Field work and limited museum surveys did not
yield any larger specimens. The specimen's age is Late
Ordovician, from the "Corryville" portion of the Dillsboro
Formation (Cincinnati Group), north central Kentucky. The
specimen was collected from the rubbly weathering facies
exposed in the long series of road cuts on U.S. highway 42
(where the road ascends the west bluff of the Little Ken-
tucky River Valley), 2.3 miles east of Bedford (Trimble
County).

The upper surfaces appear extensively bored by
epizoans, but not the lower surface of the zoarium. Be-
cause none of the borings are associated with any skeletal
modifications in their immediate neighborhood (Figure 2F),
the borings are most likely postmortem, and the zooids were

12

13

Fig. 2.--Views of the zoarium, MSU 1001. A) top
view; B) tOp view showing the locations of the cores re-
moved for sampling; core 1 at left, core 2 at right,
core 3 at center, core 4 at top; C) bottom View; D) pol-
ished section through the zoarium illustrating the
repetitive growth zones, numbered 1-17, and the eroded
edges; E) longitudinal section showing growth levels,
monticules, and borings, magnification 5 X, MSU 1001;

F) tangential section showing circular borings and the
absence of any structures indicating that the zooids
were alive at the time of penetration, magnification
10 X, MSU 1001-414.

 

15

not affected by the boring organisms during life. The
borings are circular in cross section, and are morpholog-
ically similar to those described by Richards and Shabica
(1969), who ascribed them to the work of polychaete
annelids. The colonial deposit also shows signs of post-
mortem abrasion, indicated by the absence of the outer
edges of some of the upper growth layers (Figure 2D).

Thin sections were cut from 2.5 cm diameter cores
taken vertically at four locations within the zoarium,
which were chosen to exhibit lateral variation (Figure 2B).
Three cores were taken near the perimeter of the zoarium,
and one in the center. The central core cuts vertically
through the largest number of repetitive growth zones.
The three dimensional geometry of the growth zones was
examined by cutting the specimen in half and then in
quarters. The sequence of growth zones can be seen in a
polished section (Figure 2D) and in a large longitudinal
section (Figure 2E). Each core was cut in half and thin
sections were cut from different growth zones within each
core.

Variation within each growth zone was normalized
by cutting each section from the distalmost portion of

each zone. Brown spherical bodies, most numerous at the

16

top of each growth zone, are abundant in each thin section.
These brown bodies probably represent polypide degeneration
associated with the end of each growth sequence. Sections
were cut to include the largest number of brown bodies and
to avoid elongation of shapes caused by misorientation.
Twenty tangential sections were cut, four to six from each
core, and two longitudinal sections.

Photographic prints of each thin section were pre-
pared to aid in sample selection. A Cartesian grid system
was superimposed on each print and from it two points were
chosen using a random numbers table. The points were then
connected with a straight line and the first twenty entire
zooecia intersected by the line were sampled for each thin
section. A total of 400 shapes were sampled from the
specimen, 20 from each of 20 sections.

Each zooecium to be used was projected to about
ten cm in diameter onto a screen, on which the shape was
visually centered and traced onto a starburst pattern com-
posed of 48 rays spaced at equal angles of 7.5 degrees.

The intersection of the shape trace and the rays gave 48
peripheral points to represent each shape, thereby per-
mitting calculation of a maximum of 24 harmonic coefficients.

The peripheral points were then automatically digitized in

17

Cartesian coordinates from each tracing, and punched on
80-column Hollerith cards.

The harmonic coefficients were calculated by the
Fourier program written by Bernhard Weinberg of Michigan
State University, using a CDC 6500 computer. The program
converted the peripheral data to polar coordinates cal-
culated around the center of gravity of each shape, and
calculated the first 20 harmonic coefficients. Descriptive
statistics were also calculated for each harmonic for each
thin section, core, growth zone, and for the entire colony

(Appendix A).

 

‘.

._.
‘»

RESULTS
Gross Zooecial Form

Fourier amplitude spectra within thin sections of
Amplexopora filiasa suggest that gross zooecial shapes
fall into four cardinal groups: elongate or triangular,
quadrate, pentagonal, and hexagonal. These groups have,
respectively high (1) second or third, (2) fourth,
(3) fifth, and (4) sixth harmonic coefficients (Figures
3, 4). All shapes within a thin section (MSU 1001-204)
were thus classified, by looking at the maximum harmonic
coefficient (Figure 5). These gross shapes were generally
associated with particular neighborhoods within the tan-
gential section. These areas include (1) monticules (clus-
tered megazooecia, which are elongate and triangular),
(2) the aureole surrounding each monticule (quadrate and
pentagonal zooecia), and (3) the intermonticular areas
(pentagonal and hexagonal zooecia) (Figure 4). The inter—
pretation of these shape changes depends upon the ideas of
Thompson (1969, p. 107) who showed that as circular
cylinders become more tightly packed, they approach or

18

19

Fig. 3.-—Amplitude spectra of the four cardinal
packing shapes, illustrating bryozoan ontogeny. Solid
rhomb, monticular zooecia; open rhomb, quadrate zooecia;
triangle, pentagonal zooecia; and semicircle, hexagonal
zooecia. H.N. and H.A. refer to harmonic number and
harmonic amplitude, respectively. The graph is plotted
on three-cycle semilog paper.

20

 

 

 

 

LO—

0.] r

.< .I

.002

21

Fig. 4.--Line drawings of the shapes described by
spectra in Figure 3. A) monticular zooecium; B) quadrate
zooecium near monticule; C) pentagonal and D) hexagonal
zooecia from the intermonticular area. Each shape is
magnified 350 X.

 

 

 

 

23

Fig. 5.--Tangential section showing the packing
gradient. A) Section without shading.

 

25

Fig. 5.--Tangential section showing the packing
gradient. B) Section showing ontogenetic stages indicated
by shading: The monticules (lightly shaded areas) have
the lowest packing; around the monticules are quadrate
zooecia (intermediate shading) and pentagonal zooecia
(darkest shading); the intermonticular zooecia (white
areas) occupy the zones of closest packing. Magnifica-
tion 25 X, MSU 1001-204.

 

 

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27

become hexagonal prisms. Raup (1968, p. 50) proposed that
echinoid plate shapes resulted from close packing of the
growing plates. The size and the position of each plate
depend on its relationship to surrounding plates.

In the zoarium studied, zooecial cross sections
generally become more hexagonal away from the monticular
center, and become most densely packed in the intermonti-
cular areas. Monticular zooecia are more nearly circular
but some are triangular (wedge shaped) or almost square.
The wedge shapes fill up areas of poor packing in the
monticules. Thompson (Ibid.) showed that anthozoan cham-
bers have a more circular cross sectional shape when iso-
lated. However, monticular zooecia are not isolated and
do not display the polygonal shapes expected from packed
cylinders. Therefore, the monticules must represent ex-
pansion points or regions of newly budded zooecia. The
monticular zooids occupy a slightly raised area on the
colony surface, an upwelling caused by the need to expand
laterally. Sections through the monticule cut the raised
zooecia obliquely, making their shapes elongate (high
second harmonic). The upwelling allows greater isolation
of zooids than that found elsewhere on the colony surface.

Therefore monticular shapes are not consistent with the

_—;—#
m

[‘1

28

model of closest hexagonal packing. The monticule is the
area of newly arising tubes, as can be seen in longitud-
inal section (Figures 2B, 6B).

In the longitudinal sections containing monticules,
new buds are not attached to a preexisting tube but arise
from the point at which two zooecia diverge equally. These
new zooecia do not bud from a neighboring zooid but prob-
ably arise from the covering epithelium as an invagination
of the hypostegal coelom. The new zooids initially have
circular cross sections in the areas of loosely packed
zooecia. As each bud grows it encounters at least three
neighboring zooids, making it wedge shaped or cuneiform
(high third harmonic). As the tube shifts away from the
zone of budding (monticule) it encounters more neighbors;
four neighbors induce a quadrate shape; five, pentagonal;
and six, hexagonal. When it has gained six neighbors and
six sides, the neighborhood has reached an equilibrium
condition of closest packing so that the addition of any
new sides would create a need for space filling structures.
The zoarium studied has no zooecia with more than six
sides. The same ontogenetic progression is illustrated

by the genus Rhombotrypa, in which the endozonal zooecia

 

are quadrate and progressively become more polygonal in

29

Fig. 6.--Photomicrographs of thin sections. A) Tan-
gential section with numerous monticules, magnification
15 X, MSU 1001-204. B) Longitudinal section showing the
orientation of the monticules with respect to the neighbor-
ing zooecia and the budding pattern within the monticules,
magnification 5 X, MSU 1001.

 

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31

the exozone (Cuffey and Perry, 1964). The ancestrula and
protoecium of all bryozoans are circular in cross section,
because no neighbors are yet available to produce any
packing.

In A. filiasa the monticules are themselves ar-
ranged hexagonally (Figure 6A), so that all of the monti-
cules are equidistant. The same pattern is strikingly

demonstrated by the genus Hexagonella in which ridges form

 

around a hexagonal area of the colony surface, the center
of which is occupied by a monticule (Bassler, 1953, p. 87,
Figure 52). These ridges probably developed in response
to the packing gradients exerted by the six neighboring
monticules. In the genus Constellaria the monticules
commonly have six radiating arms, giving each a hexagonal

shape. Hexagonella, Constellaria, and Amplexopora filiasa

 

 

all display hexagonal arrangements of monticules.

Zooecial packing probably does not increase in a
completely radial fashion away from the monticule. Zooecia
pushed outward from a budding center in a radial pattern
would either have (1) to enlarge their cross sectional
area as they are forced away from the center to occupy
PIOgressively more space as the circumference expands, or

(2) to secrete space filling structures to fill the gaps

32

left by zooecia which did not enlarge. Zooecia in A,
filiasa neither become larger away from the monticule,

nor do space-filling structures appear (Figure 5). There-
fore, packing does not increase radially, but must de-
velop in a different manner. One possibility is that the
tubes are pushed away from the monticule along a line
tangential to it, if the monticule is round, or parallel
to a side if the monticule is polygonal. In A. filiasa
many quadrate and pentagonal zooecia form a double linear
series, the central boundary of which is a straight line
(Figures 5, 6A), many of which are tangential to a monti-
cular margin. Perhaps zooids shift away from the monticule
along tangential zones, the positions of which could shift

as packing increases locally.

Intracolony Variation

To test for shape differences from one core to
another within a layer (growth zone) and for differences
between layers within a core, the nonparametric Friedman
two-way analysis of variance by ranks (Siegel, 1956) was
used. Only the three layers represented in all four cores

(six, ten, and twelve) were used in this test providing

33

12 samples of 20 shapes each. The median values for each
harmonic in each thin section were ranked in order within
each core and layer. The null hypothesis was that there
were no significant differences in the shapes (desoribed
by the harmonic coefficients) from area to area within a
layer and from layer to layer within a core. The test
statistic, x:, was calculated for each harmonic within
cores and layers, and the associated probability of each
was determined. The results of the Friedman test indicate
that from core to core the third and the ninth harmonics
are significant at the 0.10 level and from layer to layer
only the ninth harmonic is significant (Appendix B).

The third harmonic's association with the wedge
shaped zooecia in the monticule and its significant vari—
ability from core to core within a layer indicate that
different amounts of budding take place from area to area
within a layer (Figures 7, 8). This variability results
from differences in environmental stresses, such as water
direction, agitation, or nutrition. The third harmonic,
therefore, represents a nonmutational environmental re-
sponse. The lateral and vertical variation of the ninth
harmonic results from different numbers of inflecting

acanthopores, which can be recognized as circular

34

Fig. 7.--Variation of the third harmonic from core
to core and from layer to layer. Circles, layer six; stars,
layer ten; triangles, layer twelve. H.A., harmonic ampli-
tude multiplied by 100. Cores numbered as in Figure 28.

A.

"a

10—

9—J

 

 

36

Fig. 8.--Line drawings of shapes illustrating
variations in the third harmonic. A), B), C) Shapes with
maximum third harmonic. D), E), F) Shapes with minimum
third harmonic. Each shape is magnified 350 X.

38

invaginations of the zooecial margin (Figures 9, 10).
Those zooecia with very low harmonic amplitudes for both
the third and ninth harmonic are remarkably hexagonal
(Figures 8, 10). This indicates that inflecting acantho-
pores are generally absent in the tightly packed inter-
monticular regions and are more abundant towards the
budding centers.

The ninth harmonic varies laterally over the colony
surface, and thus represents a nonmutational environmental
response. The ninth is the only harmonic that shows sig-
nificant variation between growth zones. Only the ninth
harmonic, therefore, shows astogenetic change. Because
the ninth harmonic does not vary by the same amount or in
the same direction in all of the cores, but fluctuates
nonsystematically, its changes cannot be a function of
colony growth. Rather the vertical variation must also
represent nonmutational response to changing environmental
conditions, as does the lateral variation of the ninth
harmonic. The ninth measures the development of inflect-
ing acanthopores. Acanthopores represent solid calcite
spines that projected above the colony surface during life.
As acanthopores become larger in diameter, they project

more into the interior of the zooecium, forming

39

Fig. 9.--Variation of the ninth harmonic from core
to core and from layer to layer. Circles, layer six;
stars, layer ten; triangles, layer twelve. H.A., harmonic
amplitude multiplied by 1000. Cores numbered as in
Figure 28.

H. A.

69'—

64-—

59~

54m

49-:

44-“

39-:

 

4O

 

34

d—4

41

Fig. lO.--Line drawings of shapes illustrating
variations in the ninth harmonic. A), B), C) Shapes with
maximum ninth harmonic. D), E), F), Shapes with minimum
ninth harmonic. Each shape is magnified 350 X.

...-a

w..

ns~

s\~

._~

:—
.s s

 

 

43

invaginations in the cystid. The inflecting acanthopores
in this zoarium were generally associated with quadrate
shapes, indicating the association with the margin of the
monticule. They may have functioned as protective struc—
tures within and around the budding center, perhaps guard—
ing the newly budded zooecia from predators, encrustation
by larvae of other organisms, or larger sediment particles.
Ryland (1971, p. 117) and Tavener-Smith (1969, p. 96) have
suggested that acanthopores served either as protective
structures or as a means of supporting the cuticle and
eustegal cell layers of the colonial wall.

The degree of variability of both the third and
the ninth harmonics changes laterally over the colony sur-
face from core to core. The central core shows the lowest
amplitudes and the lowest variability in the ninth har-
monic (Figure 9), indicating that the colony center has
the smallest number of inflecting acanthopores and the
smallest degree of shape variation. The colony center
also has the highest sixth harmonic, indicating that pack-
ing is at a maximum and that the budding of new zooids is
minimal. The lowest layer tested (number six) shows con—
siderable differences in comparison to the higher layers

(ten and twelve) (Figures 7, 9). It is likely that

44

environmental conditions changed sufficiently from the
time that layer six was alive to the time of layers ten
and twelve to cause the observed differences.

Although only the third and ninth harmonics were
significant at the alpha level of 0.10, the other harmonics
show varying degrees of lateral and vertical changes
throughout the zoarium. Inasmuch as the alpha level is
arbitrarily chosen, the harmonics studies have been ranked
in order of the probabilities derived from the Friedman
test (Table 2). These probabilities reflect the relative
degree of vertical and lateral variability displayed by
each harmonic. Harmonics nine, seven, and eleven display
the greatest vertical variability throughout the zoarium.
All three of these reflect variations in the number of
inflecting acanthopores, and confirm the changes displayed
by the ninth harmonic. Harmonics nine, three, and five
display the greatest lateral variability throughout the
zoarium. All three of these are related to the packing
gradient, which displays considerable lateral variation
over the colony surface. Harmonics six, eight, and ten
display the least variability throughout the zoarium. The
sixth harmonic measures the number of mature zooids in

neighborhoods of equilibrium packing, which remains

45

TABLE 2.--Rank (R) and probability (p) of each harmonic
number (H.N.) as calculated by the Friedman
test; Column A, vertical variation; Column B,
lateral variation; Column C, reverse order and
inverse probability of average lateral and
vertical variation.

 

 

 

 

 

 

A B C
H.N.
R p R P R P
2 5 .653 7 .727 4 .310
3 8 .931 2 .054 7 .507
4 5 .653 4.5 .446 5 .450
5 5 .653 3 .148 9 .599
6 8 .931 9.5 .910 2 .079
7 2 .273 7 .727 6 .500
8 10 1.000 9.5 .910 1 .045
9 l .069 l .011 10 .960
10 8 .931 7 .727 3 .171

ll 3 .431 4.5 .446 8 .561

 

46

relatively constant throughout the colony. The eighth and
tenth harmonics represent finer sculpturing of the zooe-
cial margin that is independent of the number of acantho-
pores. Thus the eighth and tenth harmonics reflect
stricter genetic control, and may be of evolutionary im-
portance. The lower numbered harmonics (two through six)
reflect gross morphological changes that take place during
ontogeny. The higher order harmonics represent both non-
mutational response to the environment and control of the
shape by the genome within narrow limits. The seventh,
ninth, and eleventh belong to the former class, and the
eighth and the tenth to the latter.

The amplitude spectrum of the means and standard
deviations for each harmonic for the entire colony
(Figure 11) shows that the higher the harmonic number,
the lower the mean amplitude and the smaller the standard
deviation. Most of the shape information is removed by
the lower order harmonics, and each higher harmonic pro-
vides decreasing amounts of phenetic information. For
practical purposes the first 20 harmonics reveal all of
the shape information needed to solve evolutionary and

ecological problems in the bryozoans.

47

Fig. ll.--The harmonic spectrum for the entire
colony. Vertical bars represent one standard deviation
on each side of the mean for each of the twenty harmonic

numbers (H.N.). H.A., harmonic amplitude. The graph

was plotted on three—cycle semilog paper.

49

The coefficient of variability (CV = 100 s/Y;
3, standard deviation; x, mean) was calculated for the
first 20 harmonics for the entire colony (400 shapes,
Appendix A). This coefficient has commonly been used to
assess the genetic control of taxonomic characters: low
values indicate low variability and therefore control by
the genome within narrow limits. For harmonics two through
eleven, the CV's were ranked in order of increasing magni-
tude. This ranking should be comparable to the probability
ranking obtained above (Table 2, Column C), provided that
the means and standard deviations adequately describe the
form of the data distribution for each harmonic. Compar-
ison of the two rankings indicates that harmonics two,
four, six, seven, nine, and eleven have virtually iden-
tical rank in both listings, therefore, behaving as though
the parent distributions were normal. On the other hand,
harmonics three, five, eight, and ten, have considerably
different ranks in the two listings, and the use of the

CV to assess their variability would be misleading.

CONCLUSIONS

This study shows that Fourier analysis effectively
characterizes the cross sectional shapes of bryozoan

zooecia.

This method separated the total shape of each zooid
studied into multiple shape components. The value of

each component was then independently determined.

The phenetic shapes of the zooecia studied reflect
responses made by the organism to environmental

stresses, genetics, ontogeny, and astogeny.

Each shape component was assigned to varying degrees
of control by the genome of the organism, thereby

suggesting different taxonomic values.

The ontogeny of a single zooid reflects the changes
that take place after budding in a monticule, which
consists of gradual shape changes caused by increasing

packing.

50

10.

51

An increase in packing within this colony resulted in
a zooecium becoming more polygonal until a hexagonal

equilibrium shape was reached.

Monticular areas demonstrate the greatest variation in
shapes of individual tubes compared with other areas

within a single thin section.

The development of inflecting acanthopores causes the

most significant shape variation within the zoarium.

The number of protective structures (acanthopores) in-
creases vertically within a zoarium, and is associated
with the monticules. The younger the colony, the
greater the number of acanthopores required to protect
budding zooids until the colony is mature enough to
decelerate its asexual reproduction and devote maximum

effort to carrying on its other physiological processes.

The degree of budding varies widely over the surface of
the zoarium at any growth level. Budding is more ex-
tensive towards the periphery of any layer. Expansion
by budding is greater, therefore, towards the free
edges of the colony surface than it is in the center

where packing is greatest.

LIST OF REFERENCES

LIST OF REFERENCES

Anstey, R. L. & Delmet, D. A. 1972: Genetic meaning of
chamber shapes in fossil bryozoans: Fourier
analysis. In press.

Anstey, R. L. & Perry, T. G. 1969: Redescription of
cotypes of PeronOpora vera Ulrich, a Cincinnatian
(Late Ordovician) ectoproct species. Jour.
Paleont. 43, 245-251. Menasha, Wisconsin.

 

Anstey, R. L. & Perry, T. G. Biometric procedures in
taxonomic studies of Paleozoic bryozoans. Jour.
Paleont. 44, 383—398. Menasha, Wisconsin.

Bassler, R. S. 1953: Systematic descriptions. Treatise
on Invertebrate Paleontology, G, Bryozoa. 30—234.
Lawrence, Kansas.

Boardman, R. S. 1954: Morphologic variation and mode
of growth of Devonian Trepostomatous Bryozoa.
Science. 120, 322-323. Washington, D.C.

Boardman, R. S. 1960: Trepostomatous Bryozoa of the
Hamilton Group of New York State. U.S. Geol.
Survey Prof. Paper 340. 1-87. Washington, D.C.

Boardman, R. S. 1971: Mode of growth and functional
morphology of autozooids in some Recent and Paleo-
zoic tubular Bryozoa. Smithsonian Contributions
to Paleobiology. 8, 1-51. Washington, D.C.

Boardman, R. S. & Cheetham, A. H. 1969: Skeletal growth,
intracolony variation, and evolution in Bryozoa:
A review. Jour. Paleont. 43, 205-233. Menasha,
Wisconsin.

Boardman, R. S., Cheetham, A. H. & Cook, P. L. 1970:
Intracolony variation and the genus concept in
Bryozoa. Proc. North Amer. Paleontological Con-
vention, Part C. 294-320. Lawrence, Kansas.

52

53

Cuffey, R. J. 1967: Bryozoan Tabulipora carbonaria in
Wreford Megacyclothem (Lower Permian) of Kansas.
Univ. Kansas Paleontological Contributions. 1,
1-96. Lawrence, Kansas.

Cuffey, R. J. & Perry, T. G. 1964: Redescription of syn-
types of the bryozoan species Rhombotrypa quadrata
(Rominger). Contributions Museum of Paleontology,
Univ. Michigan. 19, 37-45. Ann Arbor, Michigan.

Cumings, E. R. 1904: Development of some Paleozoic
Bryozoa. Amer. Jour. Science. 17, 49-78. New
Haven, Connecticut.

Cumings, E. R. 1908: The stratigraphy and paleontology
of the Cincinnati Series of Indiana. Indiana Dept.
Geol. and Nat. Resources, 32nd Ann. Report. 605-
1189. Indianapolis, Indiana.

Cumings, E. R. 1912: Development and systematic position
of the Monticuliporoids. Bull. Geol. Soc. Amer.
23, 357-370. Washington, D.C.

Ehrlich, R. & Weinberg, B. 1970: An exact method for
characterization of grain shape. Jour. Sed. Petr.
40, 205-212. Menasha, Wisconsin.

Kaesler, R. L. & Waters, J. A. 1972: Fourier analysis of
the ostracode margin. Bull. Geol. Soc. Amer. 83,
1169-1178. Boulder, Colorado.

Lagaiij, R. & Gautier, Y. V. 1965: Bryozoan assemblages
from the marine sediments of the Rhone Delta,
France. Micropaleontology. 11, 39-58. New York.

McKinney, F. K. 1971: Trepostomatous Ectoprocta (Bryozoa)
from the Lower Chickamauga Group (Middle Ordovi-
cian), Wills Valley, Alabama. Bull. Amer. Paleont.
60, 195-337. Ithaca, New York.

Oliver, W. A. 1968: Some aspects of colony development
in corals. Jour. Paleont. Mem. II. 42, 16-34.
Menasha, Wisconsin.

54

Perry, T. G. & Hattin, D. E. 1958: Astogenetic study of
Fistuliporoid bryozoans. Jour. Paleont. 32,
1039-1050. Menasha, Wisconsin.

Raup, D. M. 1968: Theoretical morphology of echinoid
growth. Jour. Paleont. Mem. II. 42, 50-63.
Menasha, Wisconsin.

Richards, R. P. & Shabica, C. W. 1969: Cylindrical living
burrows in Ordovician Dalmanellid brachiopod beds.
Jour. Paleont. 43, 838-841. Menasha, Wisconsin.

Ross, J. P. 1969: Champlainian (Ordovician) Ectoprocta
(Bryozoa), New York State, Part II. Jour. Paleont.
43, 257-284. Menasha, Wisconsin.

Ryland, J. S. 1970: Bryozoans. 175 pp. London.

Schopf, T. J. M. 1969: Paleoecology of ectoprocts
(bryozoans). Jour. Paleont. 43, 234-244.
Menasha, Wisconsin.

Siegel, S. 1956: Nonparametric Statistics for the Behav-
ioral Sciences. 301 pp. New York.

Stach, L. W. 1935: Growth variation in Bryozoa Cheilo-
stomata. Ann. Mag. Nat. Hist. 16, 645-647.

Tavener-Smith, R. 1966: The micrometric formula and the
classification of fenestrate cryptostomes. Palae—
ontology. 9, 413-425. London.

Tavener-Smith, R. 1969: Wall structure and acanthopores
in the bryozoan Leioclema asperum. Lethaia. 2,
89-97. Oslo.

 

Thompson, D'Arcy. 1969: On Growth and Form. 327 pp.
New York.

Underwood, E. E. 1970: Quantitative Stereology. 246 pp.
Reading, Massachusetts.

55

Utgaard, J. & Perry, T. G. 1964: Trepostomatous bryozoan
fauna of the upper part of the Whitewater Formation
(Cincinnatian) of Eastern Indiana and Western Ohio.
Indiana Dept. of Conservation, Geol. Sur. Bull.

33, 1-111. Bloomington, Indiana.

Younker, J. K. 1971: Evaluation of the utility of two—
dimensional Fourier shape analysis for the study
of ostracode carapaces. M.S. Thesis, Michigan
State University. 1-62. East Lansing, Michigan.

APPENDIX A

FOURIER AMPLITUDES

565

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N auntaz UHZOtacz
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78

um >huJHO¢H¢¢> no pzu~0nuuwoo on zo-¢n>mo o««oz¢hm
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a «wmzaz Gazetacx
no >hu4~0¢~¢¢> no hzuuoHuuwoo cu zo-¢~>wo ou<oz¢bm
to Malta 0. u34¢> bnmzwuz N u34¢> hwwaod can w02¢H¢<> 0N 24w: oo« munm wJatdm
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78

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APPENDIX B

FRIEDMAN TEST RESULTS

APPENDIX B

Tables of ranks of median values for hormonics 2 through

11 and calculations of Friedman test: R39 sum or ranks. r

I. Harmonic 2

 

Core: I
1 2 3 4 R3 23. L
6 .0898 .0657 .0720 .0883 9
Layers 10 .1010 .0533 .0656 .0665 6 1.5
12 .0608 .1021 .0730 .0865 9
Rj 9 6 6 9
13. 1.8
II. Harmonic 3
Cores
1 2 3 4 R3 7L";
6 .0665 .0512 .0349 .0605
layers 10 .0494 .0596 .0431 .0456 8 0.5
12 .0547 .0477 .0428 .0456 7
R3 11 9 3 7
Xi 7.0

104

III. Harmonic 4
1
6 .0412
Layers 10 .0319
12 .0326
6
R.
5
:zr
IV. Harmonic 5
1
6 .0274
Layers 10 .0197
12 .0290
R.
J 6
Ii
V. Harmonic 6
1
6 .0206
layers 10 .0168
12 .0133
7

.14 m
M“.

Cores

2
.0234

.0493
.0351

3.4

Cores

2
.0303
.0319
.0248

5.8

Cores

2
.0142
.0260
.0149

6

1.0

105

3
.0609
.0351

.0334
10

3
.0272
.0261
.0198

3

.0195
.0177
.0213

9

.0568 10
.0311 7 1.5

.0321 7

5

2

4 R3 ggr
.0330 10
.0287 7 1.5
.0303 7

ll

4 RJ 7:?
.0229 9
.0151 7 0.5
.0165 8

8

 

106

VI. Harmonic 7

Cores
1 2 3 4
6 .0105 .0122 .0117 .0156
Layers 10 .0066 .0098 .0097 .0080
12 .0135 .0084 .0096 .0090
Rj 6 7 7 10
if, 1.8
VII. Harmonic 8
Cores
1 2 3 4
6 .0083 .0097 .0084 .0086
Layers 10 .0088 .0093 .0088 .0072
12 .0085 .0082 .0094 .0084
Rj 7 9 8 6
7‘: 1.0
VIII. Harmonic 9
Cores
1 2 3 4
6 .0060 .0075 .0075 .0106
Layers 10 .0045 .0065 .0068 .0045
12 .0053 .0060 .0062 .0055
R3 3.5 8 11 7.5
7&2 8.5

2
113 1.1,
11
6 3.5
7

2
113 1r
8
8 0.0
8

2
Rj 7(r
12
6 6.0
6

 

107

IX. Harmonic 10

Cores
1 2 3 4 RJ :1:
6 .0038 .0044 .0074 .0055 8
Layers 10 .0047 .0038 .0045 .0060 9 0.5
12 .0041 .0048 .0040 .0042 7
R3 6 7 7 10
2
Ir 1.8
X. Harmonic 11
Cores
2
1 2 3 4 R3 IT
6 .0058 .0044 .0074 .0055 10
Layers 10 .0041 .0034 .0047 .0031 8 2.0
12 .0031 .0043 .0041 .0029 6
Rj 7 7 11 5
2
11, 5.4

 

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