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This is to certify that the

thesis entitled

MARINE BIOSPHERE DIVERSITY THROUGH TIME:
PROVINCIALITY, GLOBAL SHELF AREA,
AND SEDIMENT SURVIVORSHIP

presented by

Constance Carolyn Eicher

has been accepted towards fulfillment
of the requirements for

M.S. degree in BBQ [99!

 

Major professor ‘

Date _Au9_._ll;l91§_

0-7639

 

MARINE BIOSPHERE DIVERSITY THROUGH TIME: PROVINCIALITY,
GLOBAL SHELF AREA, AND SEDIMENT SURVIVORSHIP

by

Constance Carolyn Eicher

A THESIS

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

MASTER OF SCIENCE

Department of Geology

l978

ABSTRACT

MARINE BIOSPHERE DIVERSITY THROUGH TIME: PROVINCIALITY,
GLOBAL SHELF AREA, AND SEDIMENT SURVIVORSHIP

By

Constance Carolyn Eicher

Provinciality, climatic gradations, shelf area variation, species
packing, continental fragmentation, sediment survivorship, and sto-
chastic variation are included in a comprehensive computer model that
simulates an actual and a preserved species diversity pattern through
600 million years of time. Results show that the number of continents
in the system is the dominant controlling factor. Actual species
diversity varies greatly through time. Preserved diversities always
increase dramatically from the beginning to the end of the simulations,
are highly biased and mask actual variation in the older parts of these
generated records. No global equilibrium number of actual species is
apparent, but the average number of species per continent is approxi-
mately constant through time. No chronologic increase in the number of
species per community occurs in the model, but a steady increase appears
in the number of preserved species per community. In addition, the
number of species per community is significantly correlated with global

species diversity.

Chapter
I
II
III
IV

VI
VII
VIII
IX

Appendix

TABLE OF CONTENTS

INTRODUCTION
PREVIOUS WORK
DISCUSSION

MODEL OVERVIEW
STOCHASTIC VARIABLES
MODEL SACRIFICES

THE SIMULATION
RESULTS

CONCLUSIONS

REFERENCES

ii

Page

l2
15
l7
l9
3O
48
51
72

Table

LIST OF TABLES

A list of the basic assumptions used in the model.

List of fundamental deterministic and stochastic
variables.

Correlation coefficients among six variables in
six randomly varied simulations.

iii

Page
l3

16

28

Figures

1

LIST OF FIGURES

Plots of number of continents (heavy line) and actual
global species diversity (light line) in six randomly
varied simulations, numbered in the same order as in

Table 3.

Plots of number of provinces (heavy line) and actual
global species diversity (light line) in six randomly
varied simulations, numbered in the same order as in
Table 3.

Plots of global shelf area (heavy line) and actual
global species diversity (light line) in six randomly
varied simulations, numbered in the same order as in
Table 3.

Plots of preserved (light line) and actual global
species diversity (heavy line) in six randomly varied

simulations, numbered in the same order as in Table 3.

Plots of preserved (heavy line) and actual number of
species per community (light line) in six randomly
varied simulations, numbered in the same order as

in Table 3.

Mean number of species per continent in six randomly

varied simulations, numbered in the same order as in
Table 3.

iv

Page

32

35

37

4l

44

47

CHAPTER I

INTRODUCTION

An ongoing paleontological controversy revolves around the
pattern of marine species diversity through time. At present, two
major models are employed to analyse recorded diversity observations.
One model depicts the observed diversity pattern as essentially real
(Valentine, Foin, and Peart, l978); it holds that the diversity levels
reach a peak in the present because of increased number of provinces
(Valentine, l970; 1972; l973) and increased species packing (Bambach,
1977). A second model depicts the observed species diversity pattern
as an artifact of the fossil record and not necessarily a real pattern;
instead species diversity rose to essentially present levels in the
Early Cambrian and remained approximately constant after reaching that
level (Raup, l972; l976 a,b; Schopf, l974; Simberloff, 1974; l976, and
May, 1974).

In order to construct a comprehensive and effective explanation
of change in marine species diversity as many environmental and pres-
ervational factors as possible must be dealt with and incorporated
into a model. As can be seen in the ecological and paleontological
literature, numerous variables have been proposed as environmental
(Connrell and Orias, l964; Kormondy, 1969; Osman and Nhitlach, l978)
or preservational (Lasker, l978) factors that deterministically

control observed diversity patterns. These factors include

l

2
provinciality, climatic stability, number of climatic zones, species
packing, number of continents, continental position, stability of the
environment, resource abundance, niche size, province area, sea level
fluctuations, differential preservation, and rock survivorship. In
addition, the element of random chance should be included in the list
to avoid the pitfall of erecting a deterministic explanation where none
is justified and to search for statistical generalizations which could
have predictive value in the fossil record (Raup, 1977; Raup, et al.,
1973). Accordingly, all these factors (and probably more) acted upon
the diversity patterns seen in the fossil record.

In this paper, I combine many of these environmental and pres-
ervational factors into a synthetic model that uses a computer simu-
lation to examine possible species diversity patterns through time.
This simulation combines deterministic and stochastic features to
construct a complex earth system unlike previous studies which have
not included both deterministic and stochastic features in their
models. These previous studies also used only a few (one or two)
factors for constructing their systems.

This model examines generated species diversity patterns (actual
and preserved) to see if the number of species increases or remains
constant through time, and to explain what factors cause the generated
patterns. Previous works have generally limited their studies to the
fossil record and have based their conclusions strictly on that record.
These studies are limited by the biases in the same fossil record that
they are attempting to explain.

An objective look at possible actual diversity patterns that are
generated by a simulation and their biases in a preserved generated

record is necessary because it can provide a valuable insight and an

3
explanation that can help to interpret the complex fossil record. It
is my hope that this simulation provides such an explanation of the
observed fossil diversity pattern and sheds light on the debate of
whether the number of species is increasing or remaining constant

through time.

CHAPTER II

PREVIOUS WORK

Both Valentine (1970) and Raup (1972; 1976 a,b) agree that the
observed diversity in the Phanerozoic fossil record started at low
levels and generally increased through time to the present. Valentine
(1968, 1972, and 1973), however, has suggested major deterministic
causes for the changes in marine shelf diversity, emphasizing provin-
ciality. The provinciality concepts hold that assemblages of endemic
organisms are restricted by climatic and geomorphological boundaries
(deep ocean basins and continents). Valentine (1970; 1972; 1973) has
also suggested that the number of continents present at any time con-
trols diversity for various reasons. As the number of unconnected
continents increases (which can increase the number of provinces), the
global circulation of sea water is changed, lowering the number of
climatic zones present. The width of climatic zones increases and the
latitudinal thermal gradient is lowered, thus causing a decrease in
the global number of provinces. The number of continents present does
not always have the same effect on province number. When long conti-
nental margins are parallel to the climatic boundaries, the number of
provinces is low because climatic zones do not cut across the margins.
When long continental margins are perpendicular to climatic boundaries,
however, the number of provinces is high because climatic zones cut

across long margins.

5

Other authors have also suggested causes for the variation in the
pattern of observed species diversity. Shelf area availability is of
major importance in diversity control according to Schopf (1974),
Simberloff (1973; 1976) and Sepkoski (1976). According to these authors,
as shelf area increases, diversity increases (D=k AX, D is the diversity,
A is the available area, x and k are empirical constants). Many ecolo-
gists have supported this view for much smaller areas (Preston, 1960;

Mac Arthur, 1965; 1969). Schopf believes that shelf area availability
is related to sea level transgressions and regressions. These sea
level shifts are due to changes in the rate of sea floor spreading
(Windley, 1977; Bond, 1978; Raup and Stanley, 1978). As the rate of
spreading increases sea level rises and causes a transgression. As
spreading slows down or stops, sea level falls, causing a regression
and subsequent emergence of the continents. This correlation between
sea floor spreading and degree of continental submergence is known as
the Haug Effect (Raup and Stanley, 1978).

In addition to shelf area, Bambach (1977) offers no causes but

suggests that the number of individual species within communities has
increased through time, thus affecting the global diversity pattern.
In analysis of a separate problem, Raup (1972; 1976; 1976) and Raup and
Stanley (l978) contend that rock survivorship and fossil preservability
play major roles in producing the observed diversity pattern. Sepkoski
(l976) concurs, and relates observed diversity directly to rock volume
and habitat area (D=kAxVy, D is the diversity, A‘is the available area,
V is the rock volume, and x, y, and k are empirically derived constants).

The conclusions derived from the above considerations vary greatly,

but consist of two general types. One view presents the earth's biota

6
as an equilibrium system that has a constant marine diversity after an
initial sigmoidal growth explosion (May, 1973; Raup, 1976; 1976; Raup
and Stanley, 1978; and Sepkoski, 1976), and biases in the fossil record
(Sheehan, 1977) distort the diversity pattern observed. When these
biases are taken into account, the diversity resembles the steady state
system of a population near its carrying capacity in a logistic growth
equation (Mark and Flessa, l978; Cowen and Stockton, 1978; Marshall and
Hecht, l978).

Valentine, Foin, and Peart (1978) present the earth's biota as an
expanding biological system that has not yet reached its equilibrium
point. According to this model, the earth is still in the growth phase
of a pattern that has no specific end point and that probably does not
result in an equilibrium system. Preserved diversity is, in their
opinion, an accurate indicator of past absolute diversity.

Valentine, Foin, and Peart attempt to simulate species diversity
patterns with a logical model that works on the provincial and temporal
levels. This model uses only deterministic controls in its operation
and relies greatly on the actual Phanerozoic diversity data. Since
their model is totally deterministic, strict controls are incorporated
into the model that define the exact time of species bursts. These
controls build in the assumption that the time of origin for the
beginning of the "unprecedented rise of provinciality“ lay "near the
middle of the Cenozoic". The limits for the provinciality factor
"ranged within narrow limits before the Cenozoic" inevitably limiting
the calculated diversity for early periods. Their model does not take
into account Raup's (1976) analysis of the recorded diversity filtered

against the preserved rock volume for each geological period. They

7
also did not simulate the effect available shelf area would have on

the model.

CHAPTER III

DISCUSSION

Valentine, et a1. (1978) also depend on the tabulations of Bambach
(1977) for their diversity simulation. In his study of species packing
within a community, Bambach attempts to classify diversity patterns
through time on the basis of 386 fossil associations, derived from a
literature survey of fossil communities. Several factors exist that
might bias the data on community size in the literature.

One factor Bambach (1977) does not consider is sediment avail-
ability. Generally, Cenozoic faunas are collected from extensive unit
exposures and older faunas are collected from less extensive exposures.
As time passes, older rocks constitute less of the average volume and
area of exposed sedimentary rocks. This conclusion is supported by
sediment recyclying data presented by Garrels and MacKenzie (1971) and
Blatt and Jones (1975). The process of sediment cycling provides much
more time to erode older rocks, greatly reducing their volumes and
areas. Blatt and Jones (1975) present information on sediment exposures
from the Precambrian to the Cenozoic. Their data show that very little
(one percent) of the earth's land surface is sedimentary rock from the
Paleozoic and that about one third of the exposed earth's surface is
sedimentary rock from the Cenozoic. They conclude that older sedimentary
rocks are important sources for new sedimentary rocks. They suggest
that 80 percent of the grains in some new sediments are derived

8

9
from older sediments. The reduced volume and area, therefore, caused
by the recyclying make is harder to locate and document species rich-
ness patterns in older rocks, even at the community level.

Another factor that must be accounted for is the lithification of
a sediment. As sediments get older, the effects of lithification gen-
erally increase. Young (primarily Cenozoic) sediments are predominantly
unlithified and fossil extraction naturally produces greater species
richness. Pre-Cenozoic rocks, especially limestones, are more lith-
ified and fossil collection commonly produces only records of fossils
exposed on bedding planes.

Other aspects of diagenesis must be taken into account. Pre-
Cenozoic faunas have suffered most from these processes. Pre-Devonian
faunas, for example, have probably lost much of their species richness
because of dolomitization and solution replacement. Solution replace-
ment and dolomitization preferentially affect aragonitic skeletons
(Chave, 1964; Weyl, 1964) because of the high solubility and instability
of this mineral. Bambach considers differential aragonitic preservation
but does not agree that that it is important in potentially reducing
species richness. Murray (1964) and Blatt, Middleton, and Murray, (1972)
state that dolomitization does preserve original features but that it
would be unrealistic to expect that a rock subject to dolomitization
and solution replacement would emerge with an absolutely clear record
of original features. Aragonitic fossils are most common in high
diversity communities (Chave, 1964; Dodd and Schopf, 1972). If these
skeletons are destroyed by extensive dolomitization and solution
replacement, these high diversity communities would appear as low

diversity communities in the fossil record (Chave, 1964). Other

lO
diagenetic processes also affect preservation. Dissolution and cement-
ation erode away rock volume and destroy fossils and fossil fragments
leaving ghosts (Bathurst, 1964; 1971). Likewise, the porosity of a
sedimentary unit affects diagenesis. The more porous a unit is the
more severe the diagenetic effects. Shalier sediments have lower
porosity and generally show greater species richness through time with
much more preservation of aragonite. Dissolution, cementation, and
dolomitization are selective in their destruction. As a result, low
porosities in shales leave high diversity communities relatively free
of diagenetic effects and species richness intact. Aragonite is com-
monly preserved in shales as old as the Cretaceous. Bambach's data on
Pre-Cretaceous offshore communities show no significant temporal vari-
ation in species richness. Bambach does state that two Middle Cambrian
shales produced single fauna species richness typical of the Paleozoic
but assumes these are atypical examples of species packing.

A fourth factor that will affect the observed data is chronological
faunal differences. For example, during the Paleozoic, the shelf biota
contained many more bryozoans and crinoids than afterwards. Because
Paleozoic bryozoans are usually difficult to identify even to the genus
level without the use of thin section techniques, most community analysts
have lumped them into higher taxonomic levels (often no lower than
phylum). As a result, where ten species of brachiopods occur in a
community, researchers may report only "bryozoans" or a limited number
of bryozoan genera. Similarly, highly fragmentary organisms, such as
crinoids, are generally lumped into general categories. Unidentifiable
diagenetically produced molds, casts, and "ghosts" are generally not

tabulated in the reports of community diversity. Furthermore, it is

11
very difficult to equate the number of trace fossil form taxa with the
actual diversity of trace-producing organisms.

It is additionally possible that the data collected in the litera-
ture reflect inadequate geographic diversity variation. For example,
the observed diversity of Late Ordovician corals and bryozoans varies
significantly with geographic location (Anstey and Chase, 1974). If
geographic sampling is restricted, diversity patterns are biased. As
an illustration, in the Late Ordovician of the Cincinnati region, 220
species of bryozoans alone have been reported from the literature, but
Bambach's data indicate a median of only 19 species jg_tgtg_for lower
Paleozoic open marine communities. Also two low diversity Cincinnatian
communities described by Lorenz (1973) each contain 48 species. The
compilation of the Cincinnatian fauna provided by Dalvé (1948) indicates
much higher community species packing than that of Bambach's survey.

Finally, Bambach's number of fossil assemblages for each time
interval is quite small (only seven) and by chance alone could exhibit

the variation observed.

CHAPTER IV

MODEL OVERVIEW

This model simulates a spherical planet with rectangular continents
that have a probability of splitting randomly one time out of forty,
move apart in a random direction with a velocity of 10 to 60 kilometers
per million years (a realistic rate) with a speed dependent on the near-
est neighbor distance, and collide while conserving a rectangular shape
(for simplicity). The collided continents produce a single rectangular
continent with the same total area as the two original continents and
whose shape conserves that of its "parents". This continent is a
"sutured" mass whose marine biotic diversity depends upon its charac-
tistics alone rather than inheriting diversity from the parent continents.
In the real world, it would take time to create a new biota for the
"sutured" continent, which would be a blending of the two from the joined
continents. For simplicity, the model assumes this process is complete
in one iteration (one million years). Each continent has a marine shelf
area (taken from actual shelf width data) from 500 to 1900 kilometers
wide determined both randomly, to simulate topography of the continents,
and by the nearest neighbor distance, to simulate transgressions and
regressions related to variation in spreading rates.

The simulated globe has a climatic gradient divided into a number
of latitudinal zones of equal width. The number of such zones varies,

and depends upon the number of continents and degree of continental

12

l3
separation. Climatic zone limits, shorelines, and deep ocean basins
define provincial boundaries. Each province contains a variable number
of communities based upon spatial heterogeneity (simulated randomly),
and a number of species that depend on the number of communities, the
area of the province, and its location in the climatic gradient. The
global marine shelf diversity is the sum of the diversities of all
provinces for each iteration. A simple sediment survivorship model
is applied to both the number of communities and the number of species
so that an "actual" and a "preserved" record of global diversity can
be obtained. In summary, the overall model is based on 22 basic
assumptions (Table l). A flow chart and complete program listing are

provided in the Appendix.

14

Table l. A list of the basic assumptions used in the model.

#0)“)

CDNO‘U‘T

10.
ll.
12.
13.
14.

15.
16.
17.

18.
19.
20.
21.
22.

 

Constant sedimentary rates through time.
Constant exponential decrease in sediment survivorship.
Constant preservation at any time.

Linear acceleration/deceleration in rate of continental movement
from 10 to 60 kilometers per million years.

Inelastic collisions between continents.
Conservation of rectangular shape for the continents.
Total continental area remains constant through time.

The upper limit to the number of climate zones is 15. The lower
limit to the number of climate zones is 3.

The continents fragment, move apart, and recombine if they
collide.

The continents split either parallel or perpendicular to latitude.
The continents after splitting move away from each other at 180°.
Continents only split into two parts.

Continents split on the average of once in forty times.

The location of splitting is randomly determined within and among
continents.

Sea level is low when spreading rates are low.
Sea level is high when spreading rates are high.

Continental shelf width is constant during each iteration for any
given continent.

Continents can be totally submerged.

All continents move at the same rate each iteration.
Climatic gradients control species diversity.
Habitat area controls species diversity.

The biota instantaneously populate a province to its capacity.

 

CHAPTER V

STOCHASTIC VARIABLES

This simulation is based upon seven stochastic variables and seven
fundamental deterministic variables (Table 2). The random number gen-
erator used in the model calls a series of predetermined randomly
arranged numbers. Each call to this random number generator obtains
the same series of random numbers so that any run can be exactly repro-
duced. To change the temporal order of splitting, the random variable
ISPLIT is compared against a number from one to forty; forty different
unique runs can be generated by changing that number. Different runs
can also be generated by reordering the calls to the random variable
series.

The shoreline topography between two continents is not identical
in the real world and one continent's topography does not generally
affect the topography of another continent. Shoreline topographies of
the continents appear to vary randomly. Since shelf width around a
continent is partially an indicator of continental topography, this
variable is generated in part randomly, and in part by global sea level
(sea level is more important and thus weighted more heavily than topo-
graphy in this simulation).

Winder (1977) sumarizes recent splitting events. From his sum-
mary, splitting occurs independently of other variables. Since no

variable (other than time) seems to control splitting, it is adequately

15

16

Table 2. List of fundamental* deterministic and stochastic variables.

 

Deterministic Variables Stochastic Variables

 

Number of climate zones Time of splitting

Species packing within provinces Shoreline topography

Sediment Survivorship Selection of splitting continent
Rate of plate movement Direction of splitting

(global sea level)

Number of provinces Size of the split continent
Province boundaries Direction of plate movement
Continental shapes Community packing within provinces

 

*Some variables are omitted because of redundancy.

simulated by a stochastic model. Although not completely random in
actuality, choice of the specific continent that splits is randomly
simulated in this model for simplicity.

The orientation of splitting zones appears to be random in nature
and is so simulated. As another simplification, the continents are
randomly split either parallel to or perpendicular to the equator (the
earth system has many directions of splitting). The new continents
then move apart in a straight line, and are not able to change their
direction of movement until either another splitting event occurs or
two continents collide. The direction is determined randomly so that
the direction of movement and the orientation of the split conserves
rectangular continents and allows a random orientation of splitting.
Location of splitting is a random event that determines the size of the
split fragments. The split fragments must be at least 20 percent of

the original area of the continent.

CHAPTER VI

MODEL SACRIFICES

According to Levins (1966), there are three types of information
loss in modeling complex systems. The first "sacrifice" is of gener-
ality to realism and precision. The second "sacrifice" is of realism
to generality and precision. The third "sacrifice" is of precision to
realism and generality. All three sacrifices have been made in this
simulation, which is a combination of recent models. It acts at the
macroevolutionary level. It does not try to explain evolutionary
mechanisms but assumes their operation. It attempts to assess the
interaction and the relative importance of some of the major postu-
lated controls on diversity variation through time.

The system as a whole is independent of the earth's physical
history but simulates many of the earth's actual boundary conditions as
closely as possible (as presently understood). A global system is set
up as a scale model of the earth. Rates of continental movement,
opportunity for splitting and continental and/or shelf area are estimated
from the real earth.

The system is made to be as general as possible. When mathematical
equations are used, they are generally simplified. The species area
equation, the community area equation, the movement rate change equation,
the survivorship equation, and the equations used to calculate the mar-

ginal province areas all assume simple general relationships. Square

17

18
continents with smooth margins are used to simplify calculations.
Their usage lowers the continental margin lengths making the system
less real. Also, when continents split, they only split into two
fragments with randomly fixed directions of movement. In the "real"
world, a continent does not necessarily split into only two continents
and can reverse its direction of movement.

Precision is usually lost to generality. In the climatic gradient,
province effect, area effect, and the climatic-continental interaction,
the system uses sound concepts but is not generally concerned with
their precise fit to the real earth system. For example, it is noted
that a climatic gradient exists from the poles to the equator but the
exact gradient that the earth has and the paleogradient the earth had
in the past is not used. A simplified mathematical relationship is

used instead.

CHAPTER VII

THE SIMULATION

At the beginning of the Phanerozoic, all the present continental
units were, according to some authors, bonded together into a single
supercontinent (Valentine, 1973; Winder, 1977). This simulation starts
out with that condition. One supercontinent (including shelf area)
that is about one third the surface area of the earth is created. This
continent is given an initial location (a theta and a phi coordinate)
on a sphere the present size of the earth; this location is determined
randomly. It is also randomly assigned a direction of potential move-
ment. The shelf width, randomly determined in part and also based on
global sea level, is a topographic variable that defines how much of
the continent is submerged at any given time. The range of the pos-
sible shelf widths varies from 0.08 to 0.30 radians. The upper limit
of the variance is dependent on the mean nearest neighbor distance
which also controls continental separation rate. The supercontinent
remains together until it is to split. For simplicity, the initial
supercontinent is square in shape.

The initial splitting of the large plate is a relatively slow
process. As the smaller plates move apart, the speed at which they
move can vary. Winder (1977) documents times when the spreading rates
increase or decrease as the plates separate. These changes in spreading

velocity seem to be related to the distance between continents. When

19

20
continents are clustered, spreading rates are low. As the continents
move apart, spreading rates increase. As Winder (1977) documents, the
present Atlantic's (a young and relatively small ocean) spreading rate
is slow in comparison to the Pacific's (an old and relatively large
ocean) spreading rate. For simplicity in this modeled simulation, the
plates (continents) move apart at a uniform global spreading rate.
That rate varies directly with the mean nearest neighbor distance of
all the continental plates. Therefore, at any given time, all the con-
tinents move with the same speed but the speed differs with each itera—
tion. When the nearest neighbor distance is at a minimum, the spreading
rate is one centimeter per year. When the nearest neighbor distance is

at a maximum, the global spreading rate is six centimeters per year.

VFACT = (AVE x 15.96) + O.84/6366.20 (l)

AVE is the mean nearest neighbor distance in radians and VFACT

is the spreading rate. The spreading rate generally increases or
decreases linearly in the simulation. Non-linear increases or decreases
in the spreading rate occur when continents split or collide changing
the mean nearest neighbor distance in a step function.

In the real earth system, plates seem to separate on the average
of once in forty to sixty million years (Winder, 1977). During each
one million year period (simulated by one iteration), the continents
have a finite chance of one out of forty of splitting or increasing in
number. This chance is controlled by a call to a random variable gen-
erator. 'If splitting does not occur, execution of the main program

continues. If splitting occurs, the program executes the SPLIT sub-

routine. The SPLIT subroutine randomly determines which continent

21
splits, in which direction it splits (north-south or east-west only,
for simplicity), and in what ratio the original continent splits into
two smaller ones. The total area of the two new continents is the
same as the total area of the old continent. Neither of the two new
continents contain less than twenty percent of the area of the old con-
tinent. Each new continent is rectangular in shape with its long edge
determined by the direction of the split.

When the continent, direction of split, and the areas have been
determined, the SPLIT subroutine calculates the centers of the new
continents, their theta and phi coordinates and lengths, the subse-
quent directions in which the continents move, and the width of the
continents' shelf areas. The direction in which the continents move
and their shelf area are determined randomly. The shelf area is also
controlled by the global sea level which is determined by the mean
nearest neighbor distance. After the number of provinces are deter-
mined on each continent, control returns to the main program.

During each iteration of the program, each continent moves a
uniform distance along its path. The continental movement is performed
in the MOCON subroutine. The amount of movement for all continents is
a constant vector sum during each iteration determined by the VELCITY
subroutine. The amount of movement ranges from 1 centimeter a year or
10 kilometers per iteration to 6 centimeters a year or 60 kilometers
an iteration. The magnitude of this movement is determined by the
mean distance between the continents. After each continent is moved
(assuming there is more than a single continent), each continent is
checked against the other continents to determine if during the next

movement any two continents met the criteria for a collision. If no

22
continents are to collide, control of the program returns from MOCON to
the main routine. If two continents are to collide, a subroutine that
sutures the two continents together is called. Two continents must be
within a certain distance to collide. This distance allows for a slight
overlap (-0.l7 radians or -10 degrees) to insure that a collision is a
"solid" collision instead of a grazing surface contact. This adjust-
ment tends to lower the number of collisions or postpone them in time.
This allows for more continents, thereby increasing the possibility for
extremes in the number of continents. This program treats a collision
as an inelastic, permanent, and irreversible event. The distances
between the continents are determined by using similar triangles and
trigonometric functions.

The COLLIDE subroutine which is only called by MOCON creates one
new continent from the two originals ones. This new continent has the
total land area of the two smaller continents. The continents are
sutured along one axis in either the theta or phi direction depending
upon the direction of impact. In the sutured direction, the length of
the new axis is the sum of the lengths of the axes from the two con-
tinents. The other axis is calculated from this information and the
area information. For simplicity, the new continent is a rectangle.
The remainder of the subroutine centers the new continent in the center
of the two collided masses, randomly sets a drift direction, randomly
defines the shelf area within the 0.08 to 0.30 radian limit (500 to
1900 kilometers, estimated from measuring actual global shelf widths),
and calculates the number of provinces present on the single continent
(the province calculation is performed for technical reasons only).

After all this is completed, the program returns to MOCON to finish

23
the checks for additional collisions and when it finishes the checks
returns to the main program.
After completing the MOCON subroutine, the number of climate zones
is calculated. The number of climate zone depends on the number of
continents and the mean nearest neighbor distance (Valentine, 1970; 1973)

which control the global circulation patterns.

NUM 1.2773 x AVE - 0.012773 (2)

IZONE (15 - (2 x (NC/2))) - NUM . (3)

IZONE is the integer truncated product, NC is the number of continents
and NUM is a numerical factor (between 1 and 4) used as a correction
for nearness. From this equation, the number of climate zones decrease
with increased number of continents and increased scattering (Valentine,
1970; 1973). The number of climatic zones on the sphere is not allowed
to fall below 3 (2 "polar" zones on either side of a "tropical" zone).
The climatic zone width is found by dividing PI by the number of zones.

All the climate zones have the same width.

ZOWID = PI/IZONE (4)

The climatic boundaries are calculated from this information.

In the CLIMATE subroutine, the top edge and the bottom edge of the
continents are reconstructed and compared against the climate zone
boundaries. This routine calculates the number of climatic zones that
cross each continent. From this information, it calculates the number

of provinces that are associated with each continent and the shelf area

24
of each province on each continent. The area calculation is of two
forms depending upon whether the province is on the side of the con-

tinent or at the top or bottom of the continent. For the sides,
AREA = ZOWID x C(L,10) (5)
For the top and bottom,

AREA = (C(LL,10) x (C(LL,5) - C(LL,10)) x 2)

+ (C(LL,10) x ZOWID)

ZOWID is the length of the climatic zone, C(LL,10) is the shelf width
of the continent, and C(LL,5) is one half of the theta length of the
continent.

The CLIMATE subroutine also calculates the value that is used in
the species per province calculation using the species area equation
from MacArthur (1965), Preston (1960), Simberloff (1974), and Sepkoski
(1976).

S=kAx (7)

S is the species per area, A is the area of the province, x is an
empirical constant (.263) taken from the literature (Sepkoski 1976;
MacArthur 1965; and Preston 1960), and kS is a constant that reflects
the pole to equator climatic gradient (Valentine 1968a; 1970b; 1972;
1973). In this model, k is small at the pole and approaches unity as
it goes to the equator. The minimum value k has is 0.125 when there is

a single continent and the maximum number of climate zones

25
(Valentine, 1973). The maximum value always occurs at the equatorial
or tropical climatic zone. The climatic gradient is mirrored above
and below the equator. Care has been given to the special case in
which a continent crosses a pole. If that occurs the number of pro-
vinces on that continent is reduced by two and the species and province
areas are also corrected.

The total global shelf area is also calculated in CLIMATE. The

total global shelf area is the sum of all the provincial areas.

NC

TAG = I TAC (8)
i=1

TAG is the global shelf area, TAC is the individual continental shelf
area which is the sum of the provincial areas, and NC is the number of
continents.

Upon return to the main program, the total number of provinces for

the globe is calculated by summing the number of provinces per continent.
NC

PROV = Z C(I,8) (9)
I=l

Ith continent and PROV is the

C(I,8) is the number of provinces on the
total global province number.

At this point, the number of communities per province is calcu-
lated. The number of communities per province depends on the spatial
heterogeneity of that province. Spatial heterogeneity in a marine
environment is in part a result of the rate of sedimentary influx and

movement and type of substrates which define that environment. Blatt,

Middleton, and Murray (1972) list a variety of sedimentary environments.

26
There seems to be no apparent deterministic order to the location of
different bio-facies; therefore, these locations are considered to
occur randomly for this simulation. As a result, the number of com-
munities in a given province is controlled by a random variable and
the area in the province (Simberloff, 1974). The same equation used
to calculate the species area effect is used to calculate the number

of communities per province (Simberloff, 1974).
_ x
c - kCA (10)

The term kc is a random value representing heterogeneity that ranges
from 1.0 to 1.1. The communities per province are summed to give a
total number of communities for the globe.

The actual number of species per provinces depends on the number

of communities in the province and the province's geographical location.
= x
NS kC x kS A (11)

This actual number of species is summed to yield the total number of
species on the globe.

Sediment survivorship is applied to the total number of communities
and species (Raup 1970; 1976b; 1978). The sediment survivorship factor
used is a radioactive decay-type equation (one of several models accord-
ing to Lasker, 1978) from the present to 600 million years before the
present (Younker, 1976; Younker and Younker, 1977; Blatt and Jones,
1975). The sedimentary "half-life" is approximately 150 million years.
This value is well within sedimentary recycling limits (perhaps even a

little high) according to Younker and Younker (1977). The equation

27

that is used is:

-*'5°/t)" x 0.01 . (12)

Nt = (No x e
Nt is the decimal equivalent of the percent survival at time t, No is
0.16 (the population at time o), -A150 (a constant) is -4.62098120E-3,
and t is the present number of iterations. At time 1 looking from time
600, 6.25 percent of the sediment survives (a little high according to
Blatt and Jones, 1975). At time 600 (the present), 100 percent of the
sediment survives and is observable.

Species number change with and without sediment survivorship
analysis is calculated. This provides information on the variation in
standing diversity from time t1._1 to time ti'

Other variables that are determined include the mean shelf area
per province, the mean number of species per community, and the mean
preserved number of communities per province.

Correlation coefficients are calculated for 14 variables taken two
at a time (6 correlation coefficients are presented in Table 3). The
correlation coefficients test for a measure of linear association
between two variables. Product-moment correlation coefficients are
calculated in the COR subroutine (Sokal and Rohlf, 1969).

The VELCITY subroutine finds the nearest neighbor for each con-
tinent. This information is used to determine the mean nearest neighbor
distance. The mean distance is used to calculate the global spreading
velocity. It is also used to calculate the relative submergence of

the continents (VSHELF).

28

 

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29

VFACT (AVE x 15.9631667 + 9.840336833)/6366.197723 (1)

VSHELF 0.0702517933 x AVE + 0.000702517933 _ (13)

AVE is the mean nearest neighbor distance.

CHAPTER VIII

RESULTS

The fossil record shows a steady increase in the number or pre-
served species through time according to both Raup (1976) and
Valentine (1978). Both authors agree on this observation, but do not
concur in their explanations of what produces the observed pattern.
Valentine, et a1. (1978) feel that the observed information is real.
Raup concludes that the observed information is biased.

This simulation presents an attempt at combining both Raup's and
Valentine's ideas along with a consideration of Bambach's (1977) ideas
on species packing within a community, and Schopf's (1974) and Sepkoski
(l976) ideas on the species area relationship into a single working
system. The system contains many deterministic controls and a number
of stochastic variables (Table 2). Controls on the system were made as
'real' as possible while maintaining a reasonable degree of simplicity.

From the results of the correlation analysis (Table 3), several
variables emerge as important controls of speciation in this modeled
simulation. Since the number of provinces or shelf area was expected
to be the main controlling factor, it was surprising to find that the
most important control on global speciation was continental fragment-
ation. All the correlation coefficients are highly significant at the
0.01 level (Table 3). In Figure l, continent number (continental
fragmentation) is plotted against the actual species diversity. As

30

31

Figure 1. Plots of number of continents (heavy line) and actual
global species diversity (light line) in six randomly
varied simulations, numbered in the same order as in
Table 3.

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33
can be seen in the graphs (and from the correlation coefficients), when
continental fragmentation rises, species diversity increases and when
continental fragmentation declines, species diversity decreases. This
relationship appears to be very general.

As Valentine (1973) and Valentine, Foin, and Peart (1978) suggest,
province number also plays an important role (but less so than con-
tinental fragmentation) in the actual species diversification of the
global system. A highly significant correlation coefficient at the 0.01
level is obtained when province number and actual species diversity are
compared. The r-values for the 6 runs are, however, considerably lower
than the r-values for the continental fragmentation and global species
diversity comparison (Table 3). Figure 2 shows the province number
plotted with the actual species diversity. From the graphs, a general
trend of species diversity increase with province number increase is
apparent. However, this relationship is not as strong as is the con-
tinental fragmentation and species number relationship.

A third important variable in the simulation is global shelf area,
which produces result that corresponds to Schopf's (1974) and Sepkoski's
(l976) ideas. Global shelf area for the most part (except when ISPLIT
is equal to 15) is a highly significant factor at the 0.01 level when
compared with actual species diversity (Table 3). This implies that as
global shelf area increases, species diversity also increases (a rela-
tionship expected by the species area equation). This, however, is
not always true since area is not the only variable that influences
diversity (number of continents and their location in the climatic
gradient and the number of communities are also important species

control variables). Figure 3 shows the plots of global shelf area

34

Figure 2. Plots of number of provinces (heavy line) and actual
global species diversity (light line) in six randomly
varied simulations, numbered in the same order as in

Table 3.

 

  

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38
for various values of ISPLIT of global shelf area and actual species
diversity data.

The results of the correlation analysis show that the total number
of provinces is generally controlled by the number of continents
(Table 3). However, this is not always the case. At times, province
number is relatively low when the number of continents is relatively
high. This relationship can be explained by continental orientation
and size (Valentine, 1973). When many continents exist, climatic zone
width is relatively large and chances are good that a 'small' continent
(continental fragments are generally small when many continents exist)
would not be located in two or more 'large' climatic zones or that a
'small' continent could be totally submerged thus lowering the number
of provinces.- When the long axis of a continent is parallel to climatic
boundaries, the number of provinces is again lowered.

The number of provinces is negatively correlated with the number
of climatic zones. This negative correlation does not at first appear
correct (Valentine, 1973) but upon further consideration can be explained.
The strongest variable in the system is the number of continents.
According to Valentine (1973), the number and location of the continents
affect the number of climatic zones present on the globe. When con-
tinents are large and close together, the number of climate zones is
large because global circulation is restricted. When the continents
are smaller and separated, global circulation is good and the number of
climate zones is relatively small. As a result, as the number of con-
tinents increase (generally increasing the number of provinces), the
number of climatic zones decrease causing the negative correlation of

province number and climatic zone number.

39

The lowest level in the ecological hierarchy is the species net-
work. The actual global number of species is the total of all the
species in all the provinces at any specific time. This number also
reflects community structure. A preserved number of speCies can be
obtained by including sediment survivorship in the actual global species
calculation. This information is presented in Figure 4. The actual
species pattern varies greatly through time. The actual number of
species can reach its highest peak early in the program or near the
end of the program. After the peak is reached, the actual species
diversity can decrease, remain the same, or vary greatly to the end
of the program. The preserved species data show less pronounced
fluctuations that correspond in time with the actual species fluctu-
ations but not in magnitude. The preserved species diversity shows a
marked increase in fluctuation magnitude through a 600 million year
interval. The increase seen is a result of the sediment survivorship
factor. Because of the factor, as the time nears the present, the
magnitude of the fluctuations in the preserved record increases. (It
is curious to note that the preserved species pattern is always very
similar to the species diversity data seen in the real fossil record.)
The number of species in the preserved pattern is extremely low in the
beginning (at time 0) and reaches its peak near the present (at time
600). At time 600 (the present), the preserved record and the actual
record of species diversity correspond exactly. The preserved species
record near time 600, therefore, represents a closer picture of the
real world diversity data then in earlier times because less information
is lost to destructive forces (namely sediment survivorship). Different

computer runs (with different ISPLIT values) give slightly different

40

Figure 4. Plots of preserved (light line) and actual global
species diversity (heavy line) in six randomly varied
simulations, numbered in the same order as in Table 3.

41

 

 

 

 

 

 

 

    

   

 

 

 

 

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42
results because of the stochastic variables, but the overall patterns
are quite similar.

Bambach's (1977) work addressed the concept of species packing
within a community. To show species packing, in this model, the total
number of species is divided by the total number of communities at
time t. This produces the actual species packing information. This
actual species per community information is used to calculate the
preserved species packing information. Not surprisingly, it is similar
to the actual and the preserved global species diversity data (Figure 5).
Actual species packing is generally constant through time with major
fluctuations occurring relatively randomly. Preserved species packing
numbers increases constantly through time because of the sediment
survivorship factor. Also, the species per community information is
always highly correlated with both the actual and preserved species
diversity numbers (Table 3). The correlation analysis (Table 3)
reveals, however, that the number of species per community is not
always correlated with the number of provinces and the global shelf
area.

In a recent paper, Lasker (1978) presented different preserva-
tional models for sediments containing fossils. Lasker concluded that
variations in the actual fossil record can be dampened by including a
preservational model in the real data. The species and species packing
information calculated in this simulation support that conclusion.
Actual data fluctuates more than the preserved data. High early actual
diversity and diversity fluctuations appear extremely low when sediment

survivorship is taken into account.

43

Figure 5. Plots of preserved (heavy line) and actual number of
species per community (light line) in six randomly
varied simulations, numbered in the same order as
in Table 3.

44

                    

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>._23C:ou mum mm_ummm no xmmcaz c-~znzrou mud ww_uwmw no mumtnz
o o
0 o
L m
s #8
6 6
3 s
D a
fi 0 0
c o
- a... a...
. o
own on”
on an”
mR mRu
you.» DE
41 0T
0 CF OF
00 00
.mm .mm
o o
o n.
m 0
‘ ‘
2 2
0 O
o o
L m
.6 w
o o
o o
o. 0
a
o o
o. 111 I1. 11 I (1 .1 1 o.
wmu. 6606 66.6 6.66 6mwo . 66......0 66.. 66.6 66.6 6..6 66.6 66...0
>b~23ztcu mum wm_umam no mmmtnz >-23z::u «ma mw_uuaw mo «worn:

45

The average number of species per continent is plotted in Figure 6.
As can be seen in the graphs, actual species diversity per continent
varies only slightly through time. May (l974) predicts that this would
be the result if each continent has a limited number of Species it can
support. This value, according to May, could be almost constant through
time and might represent the finite limit to the number of ecological
niches on that continent. The actual number of species per continent
is slightly more complex then the average actual species per continent
value but this value provides a good first approximation of this capac-
ity on the continents.

The effects of random variation seem to influence the general
trends in the simulation results. The major result of the randomness
is to shift the fluctuations in the real patterns in time. These
temporal variations cause the differences in the absolute appearances
of the graphs. One of the major findings is that the actual diversity
reaches its peak much earlier than the preserved diversity. The actual
diversity seems to fluctuate randomly through time but the preserved
diversity (even mirroring these fluctuations) seems to steadily

increase.

46

Figure 6. Mean number of species per continent in six randomly
varied simulations, numbered in the same order as in
Table 3.

1.60

-20

l

0.00

040

47

 

 

 

NUMBER OF SPECIES PER CONTINENT

cp.00

l.00

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0.00 l

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NUMBER 0: SPfCIES PER CONTINENT

c0.00

I-BO
60

£20

A

0.40

A

NUMBER OF SPECIES PER CUNYINENY

 

 

 

 

 

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N0.0F ITERRTIONS N0.0F ITERRTIONS
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0.0F ITERRTXONS N0.0F ITERGTIONS

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00.00 100.00 200.00 350.00 “0.00 000.00 000.00 290.00 00.00 100.00 :0o.0o 320.00 000.00 000.00 500.00
No.0? ITERRTIONS N0.0F ITERRTIONS

MBER 0F SPECIES PER CONTINENT

00

 

 

 

 

9.00
8

CHAPTER IX

CONCLUSIONS

(l) In the majority of runs, the number of species varies through

time, but does not consistently increase or decrease. In four out of
six runs, there is a marked positive increase. In one run there is

an early period of increase followed by a sharp decrease near the end
of the time period. In one run there is continuous oscillation around
a mean value. Based on the correlation analysis, the dominant control
(within the context of the overall model) is the variation in the

number of continents. The number of continents also controls the global
number of biotic provinces and the total global shelf area. The effects
of continental fragmentation and reassembly override the effects of

global climatic variation and change in global sea level.

(2) Global biotic equilibrium cannot be achieved within the assumptions
of the model because of the dominant effect of the variation in the
number of continents. As long as the number of continents is allowed

to vary the number of species will vary. In some runs, diversity
oscillation is achieved that resembles equilibrium, but is only in

fact a pseudoequilibrium caused by a stochastically induced stability

in the number of continents. However, the number of species per con-
tinent area remains nearly constant through time in all the runs, and

perturbations cause only temporary disequilibrium, following which

48

49

biotic equilibrium is restored in all cases. Therefore, this model
supports the concept of dynamic biotic equilibrium at the continental
level, suggesting that each continental shelf region holds a finite
number of ecological niches that remain nearly stable after the con-
tinental saturation level has been reached. The global system, in
contrast, is characterized by continuous increases and decreases in
total diversity. Variation in the continental system resembles a

K-strategy, whereas, global variations resemble an r-strategy.

(3) A model of sediment survivorship based upon differential preserv-
ation through time produces two effects on the preserved record of
biosphere diversity. Firstly, all runs exhibit an apparent increase
in global diversity in the preserved record, whether such increases
are present in the real record or not. Secondly, actual variations in
the diversity are not preserved in the older parts of each simulated
fossil record, but diversity fluctuations are more faithfully mirrored
in the younger portions of each record. The effects of differential
preservation, therefore, produce a record that appears to reflect
nearly constant diversity through time if preserved diversity were
normalized by rock volume. If this model is correct, then large
diversity variations in the older part of the fossil record may not

have been preserved.

(4) Although the actual number of species per community in this

simulation does not consistently increase or decrease through time, it
does appear to be a predictor of actual and preserved species diversities.
This supports the concept that the number of species per community

reflects the global species diversity and that this species packing

50
information can be used in constructing past diversity patterns. Even
though the actual number of species per community displays no set
pattern, the preserved number of species per community always increases.
This increasing pattern is an artifact of preservational biases resulting
from sediment survivorship factors. These factors (as well as diagenesis,
lithification, and dolomitization) act to reduce observed diversity, thus
lowering the early species packing index. These factors produce a pattern
in the preserved number of species per community that is not an accurate

reflection of the real pattern of the number of species per community.

APPENDIX

 

C START >
I

 

I

INITIALIZE VARIABLES:]

 

 

                

 

 

APPENDIX

 

 

 

 

 

 

 

 

 

T.
‘RANF(D) -— <~ — 6---]
yes SUBROUTINE SPLIT T g
SPLIT A CONTINENT j i
(no ( i
SUBROUTINE MOCON f A
CALL VELCITY(ANGLE) -~».6+——————J ;
MOVE EACH CONTINENT '
1-_.D_._..n
V
’ SHOULD es I SUBROUTINE COLLIOE )
CONTINENTS y COLLIDE THO CONTINENTS I
’ A:>——- CALL CLIMATE ;
K\ COLLIDE? -__L -V ..
‘ I
no '
‘ CALCULATE CLIMATE ZONES""‘ “TWW” '
SUBROUTINE CLIMATE
, CALCULATES AREA, SPECIES ANO , \\
i NUMBER OF CLIMATES ON EACH .1 _.
: CONTINENT AND THE NUMBER OF ‘”‘9"’\\EONEf/’
% PROVINCES ON EACH CONTINENT. \ /
CALCULATE NUMBER OF COMMUNITIEs, ETC. Tyes
.- .6. -A ., __ V

END

 

 

 

 

 

 

 

T- ""7

i PLOTs INFORMATION

I SUBROUTINE COR

_\ g CALCULATE CORRELATION
'.M<E.I COEFFICIENTS.

[— , ,, _, _ . (“J

HHH‘OGVOUTOUBJH

f-JHO II II II II II II II II II

II N "00000000

N

DODCCOOOCOO

H II N H N

uuwwwwwwmww
HOQCOVOLDbNT'JH

32:0
33:0
34:0
35:0
36:0
37=c
38=C
39:0
40:0
41:0
42:0
43:0
44:
45=
46:
47=
48=
49:
50:0

PRO
NC 13 T
C(Nvl)
C(N92)
C(N04)
C(NPS)
C(Nrb)
C(Nr7)
C(N’B)
C(Nr9)
C(N710
ANG RE
V1 IS
V2 IS
V3 IS
V4 IS
V5 IS

VA6 IS
TO STO
R STOR
BS IS
DSS IS
AVE IS
ZUUID
NC IS
ZONE 3
IZONE
KOUNT!
SAREA
NOFZ I
SAP IS
CAREA
VSHELF
SHELF
CU
+(1
+6)
DI
+)9
DI
SETTIN

52

GRAM DIVER(INPUT=64POUTPUT=64TTAPE1=64)

HE NUMBER OF CONTINENTS PRESENT IN THE SYSTEM.
IS THE THETA COORDINATE OF CONTINENT N.

IS THE PHI COORDINATE OF CONTINENT N.

IS THE VELOCITY OF N IN THE PHI DIRECTION.

IS 1/2 THE UIDTH OF N.

IS 1/2 THE LENGTH OF N.

IS A FLAG VARAIBLE.

STORES THE NUMBER OF PROVINCES IN N.

STORES THE NUMBER OF CLIMATES EFFECTING N.

) STORES THE SHELF UIDTH OF N.

PRESENTS A RANDOM ANGLE 0F MOVEMENT OF N.

THE NUMBER OF ITERATIONS: A REAL VALUE.

THE PRESERVED GLOBAL SPECIES DIVERSITY.

THE NUMBER OF CONTINENTSP A REAL VALUE.

THE PRESERVED GLOBAL NUMBER OF COMMUNITIES.
THE PRESERVED NUMBER OF COMMUNITIES PER PROVINCE.
IS THE ACTUAL NUMBER OF SPECIES PER COMMUNITY.
THE TOTAL GLOBAL SHELF AREA.

TNE MEAN AREA PER PROVINCE.

‘ THE REAL NUMBER OF CLIMATE ZONES.

THE GLOBAL NUMBER OF PROVINCES.

THE VELOCITY FACTOR.

ACTUAL GLOGAL SPECIES DIVERSITY.

THE ACTUAL GLOBAL NUMBER OF COMMUNITIES.

‘ THE PRESERVED NUMBER OF SPECIES PER COMMUNITY.

ALSO USED IN A DIFFERENT VERSION OF THE PROGRAM
RE THE AVERAGE NUMBER OF SPECIES PER CONTINENT.
ES THE CORRELATION COEFFICIENTS.
THE CHANGE IN SPECIES.
THE PRESERVED CHANGE IN NUMBER OF SPECIES.
THE VALUE OF THE MEAN NEAREST NEIGHBUR DISTANCE.
IS THE WIDTH OF THE CLIMATE ZONES.
THE INTEGER NUMBER OF CONTINENTS.
TORES THE LIMITS FOR EACH CLIMATE ZONE.
IS THE INTEGER NUMBER OF CLIMATE ZONES.
N7 NN ARE COUNTER VARIABLES.
IS THE SPECIES AREA PER PROVINCE (ACTUAL).
S THE ACTUAL NUMBER OF CLIMATES THAT CROSS ONE CONTINENT.
A AREA PER PROVINCE PARAMETER.
IS THE COMMUNITIES PER EACH AREA.
IS USED TO DETERMINE THE LIMITS FOR CONTINENTAL
UIDTH.
MMON ZOUID9C(16012)yNCvaAVEyNNvZONE<40)vIZONEvROUNlrFXvFYPSAREA
6770)vNUFZ(16)vSAP(1672)vCAREA<16940)yVFACTvNITrVSHELFrTAGPCPC(1
rRANDY<16)rSCON(16)
MENSION VS(602)0VA7(602)0V6(602)0V7(602)!V8(602)9V9(602)9VA1(602
VA2(602)9DS(602)0R(150)9VA5(602)0VA6(602)yDSS(602)
MENSION IBUF<257)9V1(602)0V2(602)7V3(602)0V4(602)
G THE INITIAL VALUES FOR THE VARIABLES.

51:
52:
53:
54a
55:
50:
57:

58=4

53

NC=1

IG=1

C(197)=0.

AVE: 0 01

IZONE=15

TOPI=6.28318

PRINT 4

FORMAT<¥ ENTER VALUE OF ISPLIT FOR SPLITTING. --*)

59=C THIS READS THE VALUE FOR THE ISPLIT CHECK.

60=
61=7
62:
63:9
64=
65=
66=
67=
68=
69:
70=
71=
72=
73=
74=
75=
76=
77:
78:
79=
80=
81:101

READ 79NUMBER

FORMAT(I2)

URITE(109)NUMBER

FORMAT(* BIZX = SPLITTING NUMBER.X)
KOUNT=0

NIT=0

PROV=0.

D1=2.*TUPI

C(105)=SORT(D1)/3.

C(106)=C(1!5)

C(191)=(RANF(D)*TUPI)
C(192)=(RANF(D)*TOPI/2.)
ANG=(RANF(D)¥TOPI)
C(193)=COS(ANG)XTOPI*1.E-3
C(174)=SIN(ANG)¥TOPIXI.E*3
C(I,8)=28.

C(199)=15.
VSHELF=<RANF(D)¥3.13159+.01)*.07025179333+.00070251/933
VFACT=((RANF(D)*15.953167*3.14159+.01)+9.84033683)/6366.2
RANDY ( NC)=RANF(II)+.08
C(NC’10)=RANDY(NC)*VSHELF
ISPLIT=(RANF(D)X40.)

82=C THIS IS THE MAIN LOOP OF THE PROGRAM.

83:
84:
as:
as:

IF(ISPLIT .Eu.NUMBER) CALL SPLIT
CALL MOCON

TS=O 0

TC=0 0

87=C DETERMINING CLIMATE GRADIENTS AND ZONE UIDTHS.

88:
89:
90=
91=
92:
93:
94=
95=
96=
97:8

NUM=1.2773*AVE-.012773
IZONE=(15-(2X(NC/2)))-NUM
IF(IZONE.EO.1)IZONE=3
IF(IZONE.E0.0)IZONE=3
IF(IZONE.EG.*1)IZONE=3
IF(IZONE.EO.-2)IZONE=3
ZO=IZONE

ZOUID=TOPI/2./ZO
ZONE(1)=TOPI/2.-ZOUID
FORMAT(* *F12.S)

98=C SETTING THE CLIMATE ZONES BOUNDARIES.

99=
100=

DO 60 R=QIIZONE
RA=K-1

54

101=6O ZONE(K)=ZONE(KA)*ZOUID

102= CALL CLIMATE

103=C CALCULATING THE TOTAL NUMBER OF PROVINCES.

104= DO 61 K=19NC

105=61 PROV=PROV+C(K98)

106=C CALCULATING THE GLOBAL NUMBER OF COMMUNITIES AND
107=C THE GLOBAL NUMBER OF SPECIES.

108=3 DO 111 KK=17NC

109= CPC(KK)=0.

110= SCON(KK)=0.

111= NT=C(KK98)

112= DO 1111 KM=1rKT

113= D2=RANF(D)*.1+1

114= IF(KM.EO.1.0R.KM.EO.KT)GO TO 112
115= CAREA(KK9KM)=(SAP(KK91)#*.263)¥U2
116= GO TO 113

117=112 CAREA(KKyKM)=(SAP(KK72)**.263)*D2
118=113 CPC(KK)=CPC(KK)+CAREA(KK7KM)
119= SPCPP=SAREA(KK9KM)*D2

120= SCON(KK)=SCON(KK)+SPCPP

121=1111 CONTINUE

122= TC=TC+CPC(KK)

123= TS=TS+SCON(KK)

124=111 CONTINUE

125=5 FORMAT(¥ IZONE= *ISX NIT= #15)
126= NPROV=PROV

127= NIT=NIT+1

128=C STORAGE OF THE VARIOUS VARIABLES FOR FUTURE
129=C REFERENCE IN THE PLOTTING PROGRAM AND THE CORRELATION
130=C COEFFICIENT SUBROUTINE.

131= V1(NIT)=NIT

132= TT=-4.620981203E-3*V1(NIT)
133= TUM1=.01/(.16*EXP(TT))
134= V2(NIT)=(TSXTUM1)

135= V3(NIT)=NC

136= V4(NIT)=(TC*TUM1)

137= V5(NIT)=(TC*TUM1/PROV)
138= V6(NIT)=(TS/TC)

139= VA7(NIT)=((TS/TC)¥TUM1)
140= V7(NIT)=ALOG(TAG)

141= V8(NIT)=(TAG/PROV)

142= V9(NIT)=ZO

143= VA1(NIT)=PROV

144= VA2<NIT)=VFACT

145= VA6(NIT)=(TS)

146= VA5(NIT)=(TC)

147= IF(NIT.EO.1)GO TO 82
148= NHI=NIT~1

149= TSl=TS¥TUM1

150= DSS<NIT>=TS-(VA6(NHI))

55

151= DS(NIT)=TSI-V2(NHI)
152= GO TO 83

153=82 DS(NIT)=0.0

154= DSS(NIT)=0.0

155=83 CONTINUE

156=C OUTPUTTING OF SOME INFORMATION.

157= 1 WRITE (1778) NITvNCyNPROVvTCvTSvVFACT

158=78 FORMAT(¥ NIT= *vI4o* NC= *vIJv* NRROU= *vIévX TC= ¥9F10.5v* TS= *9
159= +2F10.5)

160= GO TO 3

161=C RESETTING VARIABLES T0 0.0.

162= 3 PROV=0.

163= NRROV=0

164= KOUNT=0

165=C CHECK TO SEE IF PROGRAM SHOULD STOP.
166= IF(NIT.EO.600) GO TO 2000

167= GO TO 101

168=2000 CONTINUE

169= GO TO 303

170=C THE RLOTTER ROUTINE. THE SECTION OF CODE HAS THE
171=C ABILITY TO PLOT ALL THE VARIABLES ON A LARGE PLOT.

172= X=0.0

173= Y=1.0

174= CALL PLOTS(IBUF!25770)

17S= CALL FACTOR(.8)

176= CALL PLIMIT<60)

177= CALL PL0T(0.590.59-3)

178=C THIS SECTION PLOTS ALL THE AXES.

179= CALL SCALE(V5910.0960091)

180= CALL AXIS(O.090.0930HNO OF COMMUNITIES FER PROVINCE930910.y9O.v
181= + V5(601)9V5(602))

182= CALL SYMBOL(X7Y!.14923v9oov-1)

183= CALL PLOT(.570.09-3)

184= CALL SCALE(V6910.0760091)

185= CALL AXIS(O.070.0919HSPECIES/COMMUNITIES!19910.0790.9V6(601)9
1863 + V6(602))

187= CALL SYMBOL<X9Y9.14!24!90.1-1)

188= CALL PLOT(.5!0.0v-3)

189= CALL SCALE(VA7910.0160091)

190= CALL AXIS(0.090.0937HSPECIES/COMMUNITIES UITH SURVIVORSHIP!
191= + 37910.v90.9VA7(601)!VA7(602))

192= CALL SYMBOL(X9Y!.14713v90o1-1)

193= CALL PLOT(.570.Ov-3)

194= CALL SCALE(V7910.0960091)

195= CALL AXIS(O.0!0.0717HGLOBAL SHELF AREA917910.0r90.9V7(601)9V7(602)
196= +)

197= CALL SYMBOL(X7Y!.14!9!90.r-1)

198= CALL PLOT(.590.01-3)

199= CALL SCALE(V8710.0960071)

200= CALL AXIS(0.070.0919HSHELF AREA/PROVINCE,19y10.0990.vV8(601)9

.3.
J

'l.‘ f-J [a] fi- lt f- f‘ I
O‘OQNOLfib

IT IT II TI H II II

F.) I-J '0 k3 To F.) M f

56

+V8(602))

CALL SYMBOL(XOYO.1495990ov-1)

CALL PLOT(.5!0.07‘3)

CALL SCALE(VA2110.0v600v1)

CALL AXIS(0.90.75HVFACT95'10.990.7VA2(601)9VA2(602))

CALL SYMBOL(X!YI.1477990.v-1)

CALL PLOT(.590.07~3)

CALL SCALE(V9710.0!60091)

CALL AXIS(0.090.0919HNO OF CLIMATE ZONESrl9vIO.O!90.9V9(601)9
+V9(602))

CALL SYMBOL(X!Y!.14!21!90.9-1)

CALL PLOT(.590o0i-3)

CALL SCALE(V3910.0!600!1)

CALL AXIS<0.090.0!16HNO OF CONTINENTSvIéle.990.9V3(601)9V3(602))
CALL SYMBOL‘XIY901493I9Oor-1)

CALL PLOT(.590.0!-3)

CALL SCALE(VA1910.0!600I1)

CALL AXIS(0.070.0715HNO OF PROVINCE8915v10.079O.9VA1(601)7VA1(602)
+)

CALL SYMBOL(X9Y!.14I4990.v-1)

CALL PLOT(.590.0v-3)

CALL SCALE(V4710.0160091)

CALL AXIS(0.090.0717HNO OF COMMUNITIES!17710.990.9V4(601)9V4(602))
CALL SYMBOL(X!Y!.1471990.v-1)

CALL PLOT(.590.09-3)

CALL SCALE<DSv10.v600v1)

CALL AXIS(0.0!0.0!17HCHANGE IN SPECIES!17710.0I90.vDS(601)9DS(602)
+)

CALL SYMBOL<X1Y9.1498790.9-1)

CALL RLOT(.590.0!“3)

CALL SCALE<DSSI10.760091)

CALL AXIS(0.090.734HCHANGE IN SPECIES U/O SURVIVORSHIP934!

+ 10.990.vDSS(601)vDSS(602))

CALL SYMBOL(X9Y!.14910790.9‘1)

CALL PLOT(.5!0.01*3)

CALL SCALE<VA6710¢960071)

CALL AXIS(0.090.0924HACTUAL NUMBER OF SPECIE81249

+ 10.990.7VA6(601)7VA6(602))

CALL SYMBOL(X7Y9.14!11990.9-1)

CALL PLOT(.5!0.0v-3)

CALL SCALE(VA571O.960091)

CALL AXIS(0.090.0128HCOMMUNITIES U/O SURVIVORSHIP728910.7

+ 90.!VA5(601)1VA5(602))

CALL SYMBOL(XIY!.14!15990.9‘1)

CALL PLOT(.5!0.09‘3)

CALL SCALE(V1710.0760071)

CALL SCALE(V2!10.07600!1)

CALL AXIS(O.090.0716HNO.OF ITERATIUNS!“16910.90.0vV1(601)rV1(602))
CALL AXIS(0.070.0713HNO OF SPECIES!13!10.'90.!V3(601)1V2(602))
CALL PLOT(0.070.013)

57

251=C THIS SECTION PLOTS THE ACTUAL DATA POINTS.

252= CALL LINE(V19V2v6009190v0)
253= CALL LINE(V19V3!600717193)
254: CALL LINE(V17VA6!600r1v1911)
255: CALL LINE(V17D3816009171v10)
256= CALL LINE(V19VA5!6009191115)
257= CALL LINE(V17V4!600717191)
258= CALL LINE(V19VA1!600719194)
25?: CALL LINE(V19V596007191923)
260= CALL LINE(V17V676009191724)
261: CALL LINE(V19VA796009171913)
26L= CALL LINE(V1yV77600!191v9)
263= CALL LINE(V1!V876007191r5)
264= CALL LINE(V17VA29600I17197)
265: CALL LINE(V19V97600)1!1921)
266= CALL LINE(V17DS¢600719178)
267= CALL PLOT<207107999)

268:303 CONTINUE

269=C THIS SECTION CALCULATES THE CORRELATION COEFFICIENTS.
270= CALL COR(V29V3!IGIR)

271= CALL COR(V2!V49IG!R)

272= CALL COR(V29V51IGIR)

273= CALL COR(V27V69IG!R)

274= CALL COR(V27V7!IG¢R)

275: CALL COR(V29V891G9R)

276= CALL COR(V27V9!IGvR)

277= CALL COR(V27VA19IG:R)

278= CALL COR (V29VA2vIGrR)

279= CALL COR<V27DSrIGrR)

280= CALL COR(V21VA59IGrR)

281= CALL COR(V29VA69IGvR)

282= CALL COR(V2!VA79169R)

283= CALL COR(V39V4IIGvR)

284: CALL COR(V37VSIIGvR)

285= CALL COR(V3:V69IG!R)

286= CALL COR(V37V7vIGvR)

287= CALL COR(V3IV89IG!R)

288= CALL COR<U3IV9!IGVR)

289= CALL CORTV3IVAIvIGvR)

290= CALL COR(V3!VA29IG!R)

291= CALL COR(V3!DS!IG!R)

292= CALL COR(V37VA57IG!R)

293= CALL COR(V31VAévIGvR)

294: CALL COR(V39VA7IIG:R)

29S= CALL COR(V49VSrIGvR)

296= CALL COR(V4yVévIGvR)

297= CALL COR(V47V77IG!R)

298: CALL COR(V49VSvIGiR)

299: CALL COR(V49V99IG!R)

300= CALL COR(V47VA19IG!R)

301:
302:
303:
304:
305:
306=
307:
308:
309:
310:
311:
312:
313=
314:
315:
316=
317:
318=
319=
320:
321:
322:
323:
324:
325:
326:
327:
328:
329:
330:
331:
332:
333:
334:
335:
336:
337:
338:
339:
340:
341:
342:
343=
344:
345:
346:
347:
348=
349:
350:

CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL

COR(V49VA2IIGvR)
COR(V47USIIGIR)
COR(V49VASvIGvR)
COR(V49VAvaGvR)
COR(V49VA77IGIR)
COR<V5varIGvR)
COR(VSIU7IIGIR)
COR(V59V89IO!R)
COR(V5!V99IG!R)
COR(V59VA19IG?R)
COR(V57VA2!IG?R)
COR(V5!DS!IG!R)
COR(V59VA57IG!R)
COR(V57VAérIGvR)
COR(V57VA7vIGvR)
COR(V69V7QIGIR)
COR(V69V89I69R)
COR(V6!V9IIG!R)
COR(V69VA1!IG!R)
COR(V67VA2!IG!R)
COR(V69DSvIGvR)
COR(V67VA5!IG!R)
COR<V67VA6VIGIR)
COR(V69VA7yIGvR)
COR(U77UBIIGIR)
COR(V77V9!IG!R)
COR(V79VA1IIG!R)
COR(V79VA2910!R)
COR(U77DSIIGIR)
COR(V7!VASvIGvR)
COR(V7IVAévIG!R)
COR(V77VA7!IG!R)
COR(V87V9IIGIR)
COR(V89VA1!IGVR)
COR(V8!VA21IGvR)
COR(V8!DS!IG!R)
COR(V8!VASIIGIR)
COR(V87VA69IGQR)
COR(V8!VA79IG!R)
COR(V99VA11IG!R)
COR(V99VA29IGIR)
CUR(V9IDSIIGIR)
COR(V97VA59IG!R)
COR(V97VA69IGIR)
COR(V99VA7IIG!R)
COR(VA17VA27167R)
COR(VA19DS!IGIR)
COR(VA19VASIIGvR)
COR(VA19VAéyIGvR)
COR(VA1!VA7!IGIR)

58

59

351= CALL COR(VA21DS!IGvR)

352= CALL COR(VA2:VA5IIG:R)

353= CALL COR(VA2!VAvaGvR)

354= CALL COR(VA2vVA7vIGvR)

355= CALL COR(DSvVA5»IGrR)

356= CALL COR(DS!VAérIGvR)

357= CALL COR(DSrVA7vIGvR)

358= CALL COR(VA51VA69IGvR)

359= CALL COR(VA59VA7vIGrR)

360= CALL COR(VA6!VA7vIGvR)

361= IG=IG~1

362= DO 59 NH=1vIG

363=C PRINTS OUT THE CORRELATION COEFFICIENTS.
364= IF(NIT.GT.400) URITE (1953) NH9R(NH)

365=43 FORMAT<¥ NH=¥vIQIX R= *9F10.5)
366=S9 CONTINUE

367= END

368=C

369= SUBROUTINE MOCON

370= COMMON ZONID9C(16112)vNCvN;AVEvNNrZONE(40)vIZONEvKOUNTyFXvFYySAREA
371= +(16970)9NOFZ(16)rSAP(1692)ICAREA(16940)vVFACTyNITyVSHELFpTAGvCRC(1
372= +6)9RANDY(16)ISCON(16)

373=C MOCON IS THE SUBROUTINE THAT WILL MOVE THE CUNTINENTS
374=C AROUND THE GLOBE.
375=C THIS LOOP MOVES THE CONTINENTS.

376= DO 1 I=19NC

377= IF(NC.NE.1)CALL VELCITY

378= IF(NC.EO.1)GO TO 101

379= IF(RANDY(I).EO.-1.0)GO TO 101

380= C(1910)=RANDY(I)#VSHELF

381=101 CONTINUE

382= CK=ABS(C(193)*VFACT)

383= IF(CK.GT.C(I!1).AND.C(I93).LT.0.)GO TO 16

384= C(I:1)=C(I91)+C(173)*VFACT

385=1S CT=ABS(C(I74)XVFACT)

386= IF(CT.GT.C(I72).AND.C(Iv4).LT.O.) GO TO 17

387= C(1’2)=C(192)+C(Iv4)*VFACT

388=14 CONTINUE

389=C CHECKS FOR SPECIAL CONDITIONS.

390= IF(C(192).LT.0..OR.C(I)2).GT.3.14159)C(1'4)=-C(Iv4)
391= IF(C(I!1).GT.6.28318)C(I!1)=AMOD(C(Iyl)v6.28318)
392= IF(C(192).GT.3.14159)C(I92)=3.14159-(C(1'2)-3.14159)
393: IF(C(Irl).LT.0.)C(Iyl)=6.28318+C(Irl3

394= IF(C(Iv2).LT.0.)C(I12)=-C(I122

395: GO TO 1

396:16 C(Ir1)=-(CK-C(Ivl))

J97= GO TO 15

398=17 C(Iv2)=-(CT-C(192))

399= GO TO 14

400:1 CONTINUE

60

401=33 IF(NC.EO.1)GO TO 18

402: KOUNT=0

403=C RECONSTRUCTION AND POSITIONING OF THE CONTINENTS.
404= N1=NC-1

405= DO 7 M1=11N1

406= N=M1

407= N2=N+1

408= DO 7 M2=N29NC

409= NN=M2

410= IF(C(NN77).NE.0.) GO TO 7

411= IF(ABS(C(N!1)-C(NN91)).GT.3.14159)GO TO 2
412= C01=C(N91)

413= CO2=C(NN:1)

414= GO TO 3

415=2 C01=AMOD(C(Nv1)+3.1415976.28318)

416= COZ=AMOD(C(NN91)+3.14159v6.28318)

417=3 IF(ABS(C(Ny2)-C(NN,2)).GT.3.14159) GO TO 4
418= C03=C(N92)

419= CO4=C(NN92)

420= GO TO 5

421=4 CO4=3.14159-((C(NNv2)+1.S70795)-3.14159)
422= C03=3.14159-((C(Nv2)+1.57079S)-3.14159)
423=5 21=ABS(C(N94)-C(NN94))XVFACT

424= ZB=ABS(C(N93)-C(NN93))XVFACT

425=C DETERMINATION OF THE DISTANCES BETUEEN EACH PLATE.
426=C CHECKS TO DETERMINE IF ANY CONTINENTS COLLIDE.

427:
428=
429:
430:
431:
432:
433:
434:
435:
436=
437:
438:
439:
440:
441:

442:70

443:
444:

445=71

446=

447=78

448:
449:7
450:

451:18

“ .-
.42—

453:

DETX=ABS(COI-COZ)

DETY=ABS(C03—CO4)

TANDY=DETY/DETX

ANGE=ATAN(TANDY)

T=”7 o

IF(SIN(ANGB).LT.ABS(10**T))GO TO 71
IF(COS(ANGZ).LT.ABS(10**T))GO TO 70
HYP=DETY/SIN(ANGQ)
HYP1=C(N75)/COS(ANGZ)
HYP2=C(NN95)/COS(ANGZ)
FLAG=HYP*(HYP1+HYP2)
FX=FLAG¥COS(ANG2)

FY=FLAGXSIN(ANG2)
IF(FX.LT.“.17453.AND.FY.LT.’.17453)CALL COLLIDE
GO TO 78

FY=DETY-(C(N!6)+C(NN!6))
IF(FY.LT.-.17453)CALL COLLIDE

GO TO 78 ‘
FX=DETX-(C(N95)+C(NN95))
IF(FX.LT.-.17453)CALL COLLIDE
CONTINUE

IF(KOUNT.EO.-1)GO TO 33

CONTINUE
IF(C(NN97).NE.0.)C(NN77)=C(NN97)-1.
CONTINUE

RETURN

END

61

454:0

455: SUBROUTINE COLLIDE

456=C THIS SUBPROGRAM IS CALL ON TO COLLIDE Two CONTINENTS.
457=c THIS SUBPROGRAM CALCULATES THE NEH VALUES FOR THE
458=C CONTINENTS THAT COLLIDE.

459= COMMON ZOWIDTC(16912)TNCTNTAVETNNTZONE(4O)pIZONErKOUNTvFXoFYrSAREA
460= +(16970)9NOFZ(16)vSAP<1692)TCAREA(16940)vVFACTyNITyVSHELFrTAGvCPC<1
461= +6)9RANDY(16)TSCON(16)

462= KOUNT=NC+1

463=C CALCULATION OF THE AREAS OF THE TWO CONTINENTS.

4643 A1=‘.*C(Nv5)*2.XC(Nv6)

465= A2=2.¥C(NN95)*2.¥C(NNT6)

466= AREA=A1+A2

467=C RESTRAINS TO LIMIT THE SIZE OF CONTINENTS TO LESS
468=C 5 RADIANS IN ONE DIRECTION.

469: IF(C(N96).GT.2.5.OR.C(NN96).GT.2.5) GO TO 20
470= IF(C(N95).GT.2.5.OR.C(NN95).GT.2.5)GO TO 22
471= IF(FX.LE.FY)GO TO 22

472= GO TO 20

473=C CONSTRUCTS A SHORT CONTINENT IN THE PHI DIRECTION.
474=20 C(KOUNTTS)=C(N95)+C(NN95)

4753 C(KOUNT96)=AREA/(C(KOUNT95)¥4.)

476= ‘ GO TO 28

477=C CONSTRUCTS A LONG CONTINENT IN THE PHI DIRECTION.

478=22 C(KOUNTvé)=C(N96)+C(NN96)

479= C(KOUNTTS)=AREA/(C(KOUNT96)#4.)

480=°8 CONTINUE

481=C CENTERS THE CONTINENT IN THE MIDDLE OF THE TUO OLD ONES.
482=24 D2=C(NN91)

483= D1=C(N71)

4843 Y=AMIN1(D19D2)

485= Z=AMAX1(D1ID2)

486= IF(Z-Y.GT.3.1)Y=Y+6.28318
487= P=(Y+Z)/2.

488= C(KOUNTyl)=AMOD(PT6.28318)
489= D3=C(N92)

490= D4=C(NN72)

491= Y=AMIN1<D37D4)

492= Z=AMAX1(D39D4)

493= IF(Z‘Y.GT.2.1)Y=Y+3.14159

494= P=(Y+Z)/2.

495= C(KOUNTv2)=3.14159+(P-3.14159)
496= CL1=C(N99)

497= CL2=C(NN99)

498= X=AMIN1<CL19CL2)

499= C(KOUNT98)=(C(Ny8)+C(NN98))-(X*2.-2.)
500=C SETS NEU DRIFT DIRECTION.

501= ANG=(RANF(D)*6.28318)

502= C(KOUNTr3)=COS(ANG)

503= C(KOUNT94)=SIN(ANG)

62

504=C NOT GREATER THAN THE CONTINENTS WIDTH OR LENGTH.

505= RANDY(KOUNT)=RANF(D)+.08

506= C(KOUNTy10)=RANDY(KOUNT)#VSHELF

507= IF(C(KOUNT910).GE.C(KOUNT76).OR.C(KOUNT910).GE.C(KOUNTT5))GO TO 10
508= +2

509= GO TO 104

510=C CORRECTION FOR TO BIG A SHELF WIDTH IN THE PHI DIRECTION.
511=102 Cl=C(KOUNT15)

512= C2=C(KOUNT96)
513= CC=(AMIN1(C19C2))
514= C(KOUNT910)=CC
515= RANDY(KOUNT)=-1.0

516=C AT THIS POINT NC IS ONE MORE THAN THE NUMBER

517=C OF CONTINENTS. THE NEH CONTINENT SHOULD BE ADDED AT NC.
518=C THIS SECTION DELETES THE TWO OLD CONTINENTS IN STORAGE
519=C AND STORES THE NEW CONTINENT AT NC.

520=104 DO 8 L=NN9NC
521= NO=L+1

522= RANDY(L)=RANDY(NO)
523= DO 8 LL=1912

524= L8=L+1

525=8 C(LrLL)=C(L8vLL)
526= NC=NC-1

527= DO 9 L=N9NC

528= NO=L+1

529= RANDY(L)=RANDY(NO)
530: DO 9 LL=1!12

531= L1=L+1

532:9 C(L’LL)=C(L19LL)
533= KOUNT=-1

534= NOT=NC+1

535= DO 15 IJ=19NOT
536:15 C(IJ'7)=00

537= CALL CLIMATE

538= RETURN

539= END

541:
542:0
543:0
544:0
545:
546=
547:
548=
549=
550:
551=c

552=

553=
554=C
555=
556=
557=
558=
559=
560=
561=
562=
563=C
564=C
565=
566=
567=
568=
569=C
570=40
571=
572=
573=
574=
S75=
576=
577=
578=
579=
580=
581=
582=
583=
584=C
585:45
586=
587=
588=
589=
590=

63

SUBROUTINE SPLIT
THIS SUBPROGRAM IS DESIGNED TO SPLIT A RANDOM CONTINENT
IN TO TUO COMPONENTS AND THEN SEND THEM ON THEIR
SEPARATE HAYS.

COMMON ZOUID9C(16912)vNCvaAVEvNNrZONE<40)’llONETKOUNTTFXIFYTSAREA
+(16970)7NOFZ(16)vSAP(1692)vCAREA(16y40)rVFACTyNITrVSHELFTTAGvCPC(1
+6)'RANDY(16)78CON(16)

CON=NC

NSC=(RANF(D)XCON)+1.

SC=NSC

DETERMINATION OF PERCENTAGE OF CONTINENT TO SPLIT FROM PARENT.
PAREA=(RANF(D)¥13.+4.)15.
AREA=(C(NSC95)X2.)*(C(NSC96)*2.)*(PAREA/100.)

DETERNIMATION OF SPLITTING DIRECTION.

IDIRC=<RANF(D)*2.)

A=(C(NSC75)#2.)¥(C(NSCT6)*2.)-AREA

NC=NC+1

C(NC97)=S.

RANDY(NC)=RANF(D)+.08

C(NCv10)=RANDY(NC)¥VSHELF

RANDY(NSC)=RANF(D)+.08

C(NSCv10)=RANDY(NSC)*VSHELF

CONTROL TO MAKE SURE THE CONTINENTS STAY NITHIN

A CERTAIN RANGE OF LENGHTS AND UIDTHS.

IF(C(NSCT5).GT.2.0)IDIRC=1

IF(C(NSC96).GT.2.0)IDIRC=0

IF(IDIRC.EO.1) GO TO 40

GO TO 45

THE SPLIT IN THE THETA DIRECTION.

C(NC76)=C(NSC96)

C(NC95)=(AREA/C(NCT6))/4.

C(NSC95)=(A/C(NSC96))I4.

C(NCTI)=AMOD(C(NSC91)+C(NC15)'6.28318)

C(NC92)=C(NSCv2)

C(NSCyl)=C(NSC71)*C(NSC95)

IF(C(NSC91).LT.O.)C(NSC!1)=6.28318+C(NSC91)

ANG=((RANF(D)#3.14159))+(3.14159*.5)

C(NSC73)=COS(ANG)

C(NSC94)=SIN(ANG)

ANG=AMOD<ANG+3.1415996.28318)

C(NC93)=COS(ANG) ‘

C(NCT4)=SIN(ANG)

GO TO 50

THE SPLIT IN THE PHI DIRECTION.

C(NC95)=C(NSC95)

C(NC96)=(AREA/C(NC75))/4.

C(NSCv6)=(A/C(NSCyS))/4.

C(NC72)=3.14159-((C(NSC72)+C(NCT6))-3.14159)

C(NCv1)=C(NSC71)

C(NSC92)=C(NSC92)-C(NSC96)

S91=
592:46
593=47
594=
595=
596=
597=
598=
599=50

64

IF(C(NSCT2).LT.O.)C(NSC72)=3.14159+C(NSC:2)
C(NC98)=1.

ANG=(RANF(D)*3.14159)

C(NC13)=COS(ANG)

C(NC94)=SIN(ANG)

ANG=ANG+3.14159

C(NSC!3)=COS(ANG)

C(NSC94)=SIN(ANG)

CONTINUE

600=C THIS TAKES CARE OF FACT THAT SHELF COULD BE GREATER
601=C THAN THE LENGTH OR UIDTH OF THE CONTINENT.

602=
603=8
604=
605=10
606=
607=
608=
609=
610=
611=11
612=
613=
614=
615=
616=12
617=
618=
619=C

IF(C(NSC910).GT.C(NSCT5).OR.C(NSC910).GT.C(NSC!6))GO TO 10
IF(C(NC910).GT.C(NC95).OR.C(NC910).GT.C(NC16))GO TO 11

GO TO 12

C1=C(NSC:5)

C2=C(NSC96)

CC=AMIN1<CITC2)

C(NSCv10)=CC

RANDY<NSC)=-1.0

GO TO 8

C1=C(NCv5)

C2=C(NC96)

CC=AMIN1(C19C2)

C(NC910)=CC

RANDY(NC)=-1.0

CONTINUE

RETURN

END

620=
621=C
622=C
623=
624=
62S=
626=
627=
628=C
629=C
630=
631=
632=
633=
634=
635=
636=
637=8
638=C
639=C
640=C
641=C
642=
643=
644=71
645=C
646=C
647=C
648=C
649=
650=
651=C
652=C
653=C
654=70
655=
656=
657=
658=
~659=
660=
661=
662=C
663:17
664=
665:
666=
667=
668=
669=

65

SUBROUTINE CLIMATE
THIS SUBPROGRAM IS DESIGNED TO CALCULATE THE NUMBER OF
CLIMATE ZONES THAT CROSS EACH CONTINENT.

COMMON zouID7C(16’12),NC'N'AvEINNiZONE(40),IZUNE’KOUNTVFX!FYISAREA
+(16970)9NOFZ(16)vSAP(16!2)rCAREA<16740)'VFACTINITTVSHELFOTAG!CRC(1
+6)9RANDY(16)!SCON
+(16)

DIMENSION TAC(16)

TOP REPRESENTS THE TOP EDGE OF THE CONTINENT.
BOTTOM IS THE LOWER EDGE OF THE CONTINENT.

PI=3.14159

FH=00

DO 91 LL=19NC

ICZ=1

ICZI=ICZ

TOP=C(LL92)+C(LL!6)

BOTTOM=C(LL!2)—C(LL!6)

CONTINUE
THIS IS A CHECK TO DETERMINE IF THE TOP OF THE
CONTINENT IS GREATER THAN PI.
IF TOF’ IS LARGER THAN F'Ir A SPECIAL SET OF CALCULATIONS
MUST BE PERFORMED TO CALCULATE THE NUMBER OF CLIMATE ZONES
ON THAT CONTINENT.

IF(TOP.GT.3.14159)GO TO 70

CONTINUE
THIS IS A CHECK TO DETERMINE IF THE LOWER EDGE OF THE CONTINENT
IS SMALLER THAN 0.0 IF SO! A SPECIAL SET OF
CALCULATIONS MUST BE PERFORMED TO CALCULATE THE NUMBER
OF CLIMATE ZONES ON THAT CONTINENT.

IF(DOTTOM.LT.0.)GO TO 72

GO TO 75
IF THE TOP OF THE CONTINENT IS GREATER THAN PI
THAN THIS LOOP IS PERFORMED TO CALCULATE THE NUMBER OF
CLIMATE ZONES THAT HANG OVER THE TOP(FOLE).

T=TOF-3.I4159

TOF2=3.14159-T

TOF=3.14159

ICZI=0

DO 73 IK=19IZONE

IF(ZONE(IK).GT.TOR2)GO TO 173

IF(ICZIoNE.ICZ)GO TO 174

GO TO 73

THIS ADDS TUO MORE PROVINCES TO THE RECORD FOR THAT CONTINENT.
3 ICZI=ICZ

ICZ=ICZ+1

J=IZONE-IK+1

JO=IZONE/2+1

O1=JQ

T=J

66

670= 0:01/7

671= NI=ICZ$2-1

672= NJ=NI-1

673= SAREA<LLvNI)=C(LL910)XZONID**.263*G
674: SAREA<LL.NJ>=C(LL,10)xzow1uxx.263xu
e75: IF(IK.EG.1)GO TO 176

676= GO TO 73

677=C THIS ADDS THE TERMINAL PROVINCE TO THE CONTINENT.
678=174 J=IZONE-IK+1

679= IF(IK.GT.J)J=IK

680a JG=IZONE/2+1

681= GI=JO

682= T=J

683= D=QI/T

684= IF(IK.EO.1)GO TO 175

68S= ICZI=ICZ

686= SAREA(LL91)=((C(LLv10)*2.¥(C(LL95)-C(LL910)))+(2.*C(LL910)XZOUID/2
687= +0 ))**o263*0

688= GO TO 73

689=C THIS IS THE SPECIAL CASES WHERE THE TERMINAL PROVINCE IS
690=C IN THE POLAR CLIMATE ZONE.

691=175 SAREA<LL’17=LO*C(LL'10)*ZO“ID**0263*Q+((C(LL,10)*20*(C(LL'S)-C(
692= +LL910)))+(2.*C(LL910)¥ZOUID/2o))**o263#0

693= ICZI=ICZ

694= ICZI=ICZI-1

695= GO TO 73

696=176 CONTINUE .
697=C THIS DELETES 2 PROUINCES AND MAKES THE POLAR TWICE
698=C THE NORMAL SIZE OF THE PROVINCES ON THAT CONTINENT.

699= IF(ZONE(1).LToBOTTOM)GO TO 73
700= SAREA(LL9NI)=2.*SAREA(LL9NI)
701= SAREA(LL7NJ)=2.*SAREA(LL9NJ)
702= GO TO 73

703=73 CONTINUE

704= IF(ICZ.EO.ICZI)ICZ=ICZ+1

705= GO TO 71

706:72 HOTTOM2=Oo-BOTTOM

707= BOTTOM=Oo

708: FB=-1.

709=75 CONTINUE

710=C THIS LOOP CALCULATES THE NUMBER OF CLIMATE ZONES

711=C THAT CUT ACROSS EACH CONTINENT FROM THE TOP TO THE BOTTOM.
712= DO 88 I=19IZONE

713= IF(ZONE(I).LT.TOP.AND.ZONE(I).GT.BOTTOM)GO TO 198
714= IF(ICZI.NE.ICZ)GO TO 197

715= IF(I.EO.1)GO TO 188

716= V 60 TO 88

717=C THIS CALCULATES THE PROUINCES AND CLIMATE FACTOR.
718=198 ICZI=ICZ
719= ICZ=ICZ+1

67

720= J=IZONE-I+1

721= IF(I.GT.J)J=I

722= J0=IZONE/2+1

723= 01=J0

724= T=J

725= 8=QIIT

726= IF(IoEGol.AND.TOP.EG.3.14159)GO T0191
727= IF(ICZ.EG.2)GO T0 196

728= NI=ICZIX2~1 ‘

729= NJ=NI-1

730= SAREA(LL9NI)=C(LL910)*ZONID*#.263*0
731= SAREA(LL9NJ)=C(LL910)*ZUUID¥¥.263¥U
732= GO TO 88

733=C LAST CLIMATE ZONE CONTINENTS IS IN.
734=197 J=IZONE~I+1

735= IF(ICZI.EG.0.AND.TOP.EG.PI)GO T0 190
736= IF(I.GT.J)J=I

737= JQ=IZONE/2+1

738= GI=JG

739= T=J

740= 0:01/T

741= NJ=ICZI¥2

742= SAREA<LLrNJ)=((C(LLv10)*2.*(C(LL95)-C(LL910)))+2.¥(C(LL710)*ZOUIU/
743= +2.))**.263#G

744= ICZ=ICZI

745= GO TO 88

746=C SPECIAL CASE--FIRST PROVINCE.

747:196 SAREA(LL11)=((C(LL!10)*2o*(C(LL95)-C(LL910)))+(2.#C(LL110)¥ZOUIU/2
749= GO TO 88

750=C SPECIAL CASE‘-FIRST ZONE MAYBE NOT FIRST PROVINCE.

751=188 IF(TOP.NE.3.14159)GU T0 88

752= J=IZUNE-I+1

753= IF(I.GT.J)J=I

754= JG=IZONEI2+1

755= 01=JO

756= T=J

7S7= G=O1/T

758= NJ=ICZI*2-1

759= SAREA(LLINJ)=2.XSAREA(LLvNJ)+((C(LLy10)*2.#(C(LL95)-C(LL910)))+
760= + (2.!(C(LL910)*ZOUID/2o)))**.263*G
761= ICZ=ICZI

762= GO TO 88

763:189 ICZ=ICZ-l

764= ICZI=ICZI-1

765= IF(ICZI.EO.1)GO T0 187

766= NI=ICZI*2‘1

767= NJ=NI-1

768= SAREA<LL9NI)=SAREA(LLvNI)#2o

769= SAREA<LL9NJ)=SAREA(LLyNJ)*2.

68

770= GO TO 88

771=187 SAREA<LL91)=2o*SAREA(LLy1)
772= GO TO 88

773=190 C(LL91)=C(LL91)*2.
7743 GO TO 88

7753191 ICZ=ICZ-1

776= ICZI=ICZI-1

777= GO TO 88

778=88 CONTINUE

779= IF(FB.EG.-1.)GO T0 279
780= GO TO 280

781=C THIS LOOP IS PERFORMED IF THE BOTTOM OF THE CONTINENT
782=C IS LESS THAN 0.0.

783=279 DO 74 III=19IZONE

784= II=IZONE-III

785= IF(ZUNE(II).LT.BOTTON)GO T0 274
786= IF(ICZ.NE.ICZI)GO T0 275

787= ICZI=ICZ

788= GO TO 74

789=274 ICZI=ICZ

790= ICZ=ICZ¥1

791= JG=IZONE/2+1

792= 01=JQ

793= T=II

794= G=01/T

795= IF(III.EG.1)GO T0 276

7963 NI=ICZ*2-1

7978 NJ=NI~1

798= SAREA(LL7NI)=C(LL910)*ZOUID**.263#G
799= SAREA(LL!NJ)=C(LL910)¥ZONID*¥.263*0
800= GO TO 74

801=°76 ICZI=ICZI-1

802= ICZ=ICZ-1

803= NI=ICZ*2-1

804= NJ=NI-1

805= SAREA(LL7NI)=SAREA(LL:NI)X2.
806a SAREA(LL9NJ)=SAREA(LLvNJ)*2o
807= GO TO 74

808=275 JG=IZUNEI2+1

809= 01=JG

810= T=II

811= G=01/T

812= NI=ICZ¥2

813= IF(III.EG.1)GO T0 278

814= SAREA(LL9NI)=((C(LLv10)*2.X(C(LLvS)-C(LLv10)))+(2.*(C(LLv10)*ZOUID
815= +/2.)))¥*.263*O

816= ICZI=ICZ

817= GO TO 74

818=278 SAREA(LL9NI)=2.*SAREA(LL9NI)+((C(LLv10)*2¥(C(LLr5)-C(LL910)))+
819= + (2.¥(C(LL910)*ZOUID/2o)))**.263*Q

69

820= ICZI=ICZ

821= GO TO 74

822=74 CONTINUE

823=C THIS PART OF THE SUBPROGRAH STORES THE NUMBER OF CLIHATE
824=C PER CONTINENT IN THE PROPER UARIZBLE IN THE ARRAY.

825=280 C(LL99)=ICZ

826= NOFZ(LL)=ICZ

827= IF(C(LL99).EO.O.)GO TO 89
828= IF(C(LL99).EO.1.)GO TO 89
829= C(LL18)=2.*(C(LL99)-1.)
830= GO TO 90

831=89 C(LL98)=1.
832=90 CONTINUE
833=C STORAGE OF THE SHELF AREA PER PROVINCE.

834= SAP<LL91)=C(LL910)¥ZOUID

835= SAP(LL92)=C(LL910)*2.*(C(LL95)'C(LL910))
836=C CALCULATION OF THE SHELF AREA PER CONTINENT.
837= T1=SAP(LL!1)*(C(LLv9)-2.0)

838= IF(T1.LE.0.0)T1=0.0

839= T2=SAP(LL12)*2.

840= TAC(LL)=T1+T2

841= IF(C(LL78).EG.1)T2=SAP(LL!2)

842= TAG=0.0

843= FB=O.

844= IF(C(LL98).EQ.2.0)SAREA(LL92)=SAREA(LL91)
846= + ((C(LL!10)*2.X(C(LL15)*C(LL910)))+(2.*C(LL!10)*ZOUID/2.))*#.263XQ

847=91 CONTINUE
848=C CALCULATION OF THE TOTAL GLOBAL SHELF AREA.

849= DO 1 L=19NC
850=1 TAG=TAG+TAC(L)
851= RETURN

852= END

853=C

70

854= SUBROUTINE VELCITY

855= COMMON ZOUIDvC<16912)vNCvaAVErNNvZONE(40):IZONEvKOUNTvFXvFYvSAREA
856= + (16970)vNOFZ(16)rSAP(1692)vCAREA(1694O)yUFACTrNITvUSHELF!TAGrCPC(
857= + 16)7RANDY(16)98CON(16)

858: DIHENSION DNBOR(12)

859= PIE=3.14159

860=C FIND NEAREST NEIGHBOR

861= DO 1 L=19NC '

862= CLOSE=10.

8b3= DO 1 LL=1vNC

864: IF(L.EO.LL)GO TO 1

865= CALL ANGLE (C(L71)7C(LL71)909TH)
866= CALL ANGLE(C(L92)9C(LL92)ylvPH)

867= TH=TH~C(L95)-C(LL95)

868= PH=PH-C(L96)-C(LL76)

869= IF(TH.LE.0.0)TH=O.

S70= IF(PH.LE.0.)PH=O.

871= DIS=SGRT<TH**2.+PH**2.)

872= IF(DIS.GE.CLOSE) GO TO 1

873= CLOSE=DIS

874= DNBOR(L)=DIS

875=1 CONTINUE

876=C FIND HEAN DISTANCE.

877= SUH=O.

8782 D0 2 H=11NC

879= SUH=SUH+DNBOR(H)

880=2 CONTINUE

881= A=NC

882= AVE=SUH/A

883= IF(AUE.LT..01)AUE=.01

884= VFACT=<AUEX15.9631667+9.840336833)/6366.197723
885= VSHELF=.O702517933*AUE+.000702517933
886= RETURN

887= END

888=C

889= SUBROUTINE ANGLE(AvaIvE)

890=C E=THE DIFFERENCE BETWEEN A AND B
891=C I=0 FOR THETA, I=1 FOR PHI

e92: PI=3.141592654

893= C=AMAX1<AyB)

894: D=AHIN1(AyB)

89S= E=C-D

8962 IF(I.EG.O.AND.E.GT.PI) GO TO 1
897: GO TO 2

898=1 E=D + PI-C

899: IF(E.GT.PI)E=E - PI
9oo= IF(E.LT.O.)E=E + PI
901:2 CONTINUE

902: RETURN

905: END

904=C

71

905= SUBROUTINE COR(X9Y9IG!R)

906= DIMENSION R(150)9X(600)2Y(600)

907=C CALCULATION OF THE PEARSON MOMENT CORRELATION COEFFICIENT.
908= X1=0.0

909= X4=0.0

910= X5=00.0

911= X2=0.0

912= X3=0.0

913= DO 1 I=19600

914= X1=X1+X(I)¥Y(I)

915= X2=X(I)+X2

916= X3=Y(I)+X3

917= X4=(X(I)¥¥2.)+X4

918= X5=(Y(I)#¥2.)+X5

919=1 CONTINUE

920= SX1=ABS(X4-(X2**2./600.))
921= SX2=ABS<X5-(X3XX2./600.0))
Y22= SP=X1-((X2*X3)/600.)

923= R(IG)=SP/(SORT(SX1¥SX2))
924= IG=IG+1

925= RETURN

926= END

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72

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