HomeMy WebLinkAboutA Model for the Movement and Distribution of Fish in a Body of Water 1978ORNL/TM-6310
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A Model for the lViol!ement 2nd
Distribution of Fish in a
Body of W"ter
D.L.DeAngelis
ENI!IRON~iENTAL SCIENCES DIVISION
Publication No.1173
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Contract No.W-74DS-eng-26
A MODEL FOR THE MOVEMENT AND DISTRIBUTION
OF FISH IN A BODY OF WATER
O.L.DeAngelis
ENVIRONMENTAL SCIENCES DIVISION
Publication No.1173
DATE PUBLISHED -JUNE,197B
ORNL/TM-631O
OAK RIDGE NATIONAL LABORATORY
Oak Ridge.Tennessee 37830
operated by
UNION CARBIDE CORPORATION
for the
DEPARTMENT OF ENERGY
ACKNOWLEDGEMENTS
I wish to thank Dr.C. C.Coutant for his encouragement and help
in this work.I also thank Drs.J.S.Suffern and R.H.Gardner,who
have offered many useful criticisms.This work.was sponsored by the
Division of Biological and Environmental Research,U.S.Department of
Energy.under contract W-740S-eng-26 with Union Carbide Corporation.
iii
ABSTRACT
DEANGELIS.O.L.1978.A model for the movement and distribution
of fish in a body of water.ORNL/TM-6310.Oak Ridge
National Laboratory,Oak Ridge.Tennessee.78 pp.
A Monte Carlo mathematical model tracks the movement of fish in a
body of water (e.g.,a pond or reservoir)which is represented by a
two-dimensional grid.For the case of a long.narrow reservoir,depth
and length along the reservoir are the logical choices for coordinate
axes.In the model,it is assumed that the movement of fish is
influenced by gradients of temperature and dissolved oxygen.as well as
food availability and habitat preference.The fish takes one spatial
"step"at a time,the direction being randomly selected,but also
biased by the above factors.
In trial simulations,a large number of simulated fish were
allowed to distribute themselves in a hypothetical body of water.
Assuming only tamperature was influencing the movements cf the fish,
the resultant distributions are compared with experimental data on
temperature preferences.
v
TABLE OF CONTENTS
ACKNOWLEOGl'iNTS
ABSTRACT •••
LI ST OF TABLES
LIST OF FIGURES
GENERAl DESCRIPTION OF THE MODEL
MATHEMATICAl DESCRIPTION OF THE MODEL
COMPUTER PROGRAM • • • •
Part A.Input Cards .
Part 8.Output .
Part C.Computer program listing
TRIAl SIMULATIONS •••••••
Fish movements . .. . . .
Fish distribution patterns
S~1t'lARY • •
REFERENCES
APPENDIX •
vii
Page
iii
v
ix
xi
4
9
16
19
24
24
2B
2B
2B
37
43
45
Table
1
2
3
LI ST OF TABLES
The Program Variables .
Parameter Values Used in the Example shown in Figure 7
Changes in parameter values from Table 2 relevant to
the example shown in Fig.11 .
1x
Page
29
34
41
LIST OF FIGURES
Figure Page
1 A hypothetical reservoir.The vertical dimensioo 15
depth in meters (disproportionately scaled),and the
horizontal dimension 1s length along the reservoir in
kilometers,with the downstream dam at the left.
Isotherms in degrees Centrigrade (solid lines)and
dissolved oxygen isobars in parts per thousand (dotted
lines)are sketched In.The shaded region denotes high
food ava i lab i 1ity.A power p hnt is assumed loeated at
the upstream end of the reservoir.. . . . . . . . . . 5
2 The point (iii)in a grid of points,w'th the adjacent
points to which the fish can move in one step.. . . . 7
3 A grid of points representing a portion of the reservoir.
The shaded circles are water,while the open circles are
above the water surface.The shaded circles surrounded by
larger circles represent points along the preferred tempera-
ture isotherm.. • • • . • . . • • . . . . . . . . . . . • • 8
4 A plot of food availability to fish in a hypothetical
reservoir.The peaks and plateaus represent the regions
of high food availability.• • . . • • • . . . . . ...18
5 Input data for a sample trial simulation as it appe~rs on
the data cards . . . . . . . . . . . • ...20
6 Input data for a sample trial ~imulation as it is printed
out by the computer program ••. . . .••..•••.....25
7 Plot of simulated motions of two fish initially placed at
points A and 8.The assumed preferred temperature is
TEMP p =29.0°C and the force of temperature attraction,
PT'is 1.0 for case A and SO.O for case B . • • • • . .26
8 The distribution of 500 fish influenced only by temperature
in the reservoir after 200 steps.The assumed preferred
temperature is 29.0°C.Other parameters of the model are
given in Table 2 • . . • • . . . . ...• .27
xi
Figure Page
9 Histogram of percent distribution of fish in Fig.8
about the preferred temperature of 29.0°C .•.....•..38
10 Histogram of relative frequency of largemouth bass
in ambient water temperatures during daytime (from
Reynolds and Caster lin 1977)••••••....•..•39
11 The distribution of sao fish influenced by temperature.
dissolved oxygen.food availability and habitat
favorability in the reservoir after 200 steps.Parameter
values are givE!f'l in Table 3 ••....•...••40
xll
INTRODUCTION
The distribution of fish populations in bodies of water is
interesting to sportsmen,conmercial fishermen.and ecologists aliKe.
Several factors that may influence fish movements and spatial popula-
tion distribution have been proposed,including temperature,dissolved
oxygen in the water,pH values.the availability of food,the presence
of cover for protection from predators,and the occurrence of compe·
titors.These are not all independent.Dissolved oxygen is to some
extent related to water temperature,as is the availability of certain
types of prey.If the locomotor responses of fish to each of the
factors were known in detail,then one could feasibly predict the
average motions of a fish in a given body of water.The task of
identifying and quantifying all the influences on fish locomotor
behavior will not be easy,but significant progress has been made,
th~nks to ingenious laboratory experiments and telemetry methods useful
for the field.
As the factors involved in the spatial behavior of fish begin to
be understood,it can be applied to a host of practicll matters.For
example,one would like to know where in a body of water fish popula-
tioo densities will be highest at a given time of year.Also,htw will
the pop.dation distribution ~n space respond to sl(lll or rapid changes
in the conditioo of the water,either through natural processes such as
seasonal variations,or artificial changes such as those induced by
power plant operations?
Both basic research and practiFal applications in the area of fish
movements will rely on techniques of mathematical modeling.Models
incorporating specific hypotheses will form a framework far experi-
mental research,from which the data can be used to test the hypotheses.
When the fundamental parameters of the models have been quantified,the
model can be used predictively.This report describes a mathematical
model capable of being used in conujuncticn with laboratory experiments
and field studies,and later,for predictive purposes.
iPS·'
2
Much experimental research has gone into the study of the effects
of temperature on locomotor behavior in fishes.Temperature has been
called the most i~ortant influence on the behavior of many freshwater
fish (e.g.,Coutant 1975).It has long been noticed that fish move to
different areas of a body of water as water te~erature changes.For
exa~le,largemouth bass overwinter in deep water,~here the temperature
is warmest.Using underwater telemetry,Warden and Lorio (1973)found
that largemouth bass tend to move great distances to new home ranges in
spring and fall,when water temperature is changing most rapidly.In
winter.the population of largemouth bass congregate around the ttlermal
discharge!.of power plants (Gibbons,Hook and Forney 1972).In a Texas
cooling reservoir,it was noticed that largemouth bass sought out the
cooler shoreline zones in summer mornings when the remainder of the
reservoir had temperatures exceeding 37.8°C (Smith 1972).
Laboratory studies have been performed to refine the data on
temperature selection of several centrarchid species (Reynolds and
Casterlin 1976,Stuntz and Magnuson 1976).Researchers have also
sought to relate temperature preferenda with thermoregulation and tht!
optimization of physiological processes (e.g.,McCauley and Huggins
1976,Reynolds and Casterline 1976).Growth rates of largemouth bass
usually seem to be optimal near their temperature preferenda (Coutant
and Cox 1976),although this does not seem to be the case for bluegills
in thermal discharge areas during the sumner months (Kitchell et !!.
1974).81uegills were shown to actively avoid lethal temperatures
(Peterson and Schutsky 1976),and to vary their temperature preferenda
according to their daily rations (Stl6ltz and Magnuson 1976).
A question that has bearing on attempts to model fish movements is
what is the precise mechanism by which fish tend to center around their
preferred temperatures?Neill (1976)discusses different mechanisms in
detail and describes one·dimensional computer models based on some of
these mechanisms.Thermoregulatory movements can be broadly categorized
as predictive or reactive.In the former case,the fish is assumed to
have some knowledge,by prior experience or instinct,of the
3
temperature distribution in the body of water,and will use this
knowledge to move toward the desired temperature range.For example,
since lower water-strata are normally cooler than upper layers,the
fish should automatically move downwards when it feels too warm.
Reactive behavior presupposes no prior knowledge of the temperature
distribution,but only that the fish responds to different temperature
regimes by altering its locomotory behavior.Several models of reac·
tive movements have been developed.One type of model has been termed
orthokinetic by Fraenkel and Gunn (1961).According to this model,
fish slow their movements when in the preferred temperature range.
increasing their chances of staying there.Both Fraenkel and Gunn
(1961)and Neill (1976)have pointed out the inefficiency of this model
for producing aggregation about the preferred temperature.Fish whose
direction of motion was originally oriented away from the preferred
temperature would continue to move away from it.Neill was able to
obtain realistic aggregation only when his model specified a high
probability of changing directions when the fish was moving away from
the preferred temperature range.This form of behavior is called
klinokinesis.
Dissolved oxygen and pH in the water are important to the health
of the fish and,therefore,presumably influence its movements.While
fish have not been shown to exhibit dissolved oxygen and pH preferenda,
they might be expected to avoid unfavorable conditions.For example,
at 25°C the minimum oxygen requirement of small largemouth bass is
almost 0.92 ppm (Moss and Scott 1961);it would be advantageous for
such fish to preferentially move away from areas with dissolved oxygen
levels below this minimum.
The movement of fish in response to food availability and habitat
preference probably involve learning where favorable conditions exist
in a body of water.It is harder to develop models for response to
these factors than it is for motion in temperature gradients,since it
is difficult to know the extent of learning in the fish.
The model described in this report assumes that the fish acts as
if it can sense temperature gradient~and will move along a temperature
4
gradient 1n the direction of its oreferred temperature.We do not
specify whether the fish acts this way because it actually can perceive
temperature gradients or because its k.linokinl?tic activity increases as
it moves into less preferrable temperature ranges.On the scale length
we are dealing with (meters vertically and kilometers horizontally)~---.-._------------.-----_._---
the precise mechanisms of motion on the small scale may be unimportant.
We alsoassume·thati~fi;h~Tl-;;o~~-away from dissolved o~ygen
levels below that which is the minimum tolerable.and that they will
have a general tendency to move toward areas of greater available food
and more favorable habitat.These sevl!ral influences can either rein-
force each other or.to some extent.cancel each other under particular
circumstances.Aside from these basic assumptions.the model is very
general and can be parameterized to suit a variety of situations.
The present model is offered not as a ~~~tion of the way fish
behave.but as a device bL'itlich-uarjetL.of .l!iP~the.!.ica!-_c!escriQ.t!~2.s
of''-oc-omotor behavior can be tested.A few examples are given to
i;lustrate the wa-Y-i~whic~h~-~odel is used.More thorough explora-
tion of the model will be undertaken later.in combination with field
studies.
GENERAL DESCRIPTION OF THE MODEL
The intent of this model is to predict the average spatial distri-
bution of a fish population in a closed body of water.To do this we
simulate the movements of individual fish,allowing a large number of
fish to start from random positions in the body of water,and to move
for a certain period of time.We assume that a small number of factors
influence the movements of the fish;temperature,dissolved oxygen.
food availability and habitat preference.
The rr.odel is designed to apply to a two-dimensional representation
of a hypothetical reservoir (Fig.1).The two dimensions are depth and
either length along the reservoir or width across a cross section.A
three-dimensional representation would be preferable,but would pose
J
5
Fig.1.A hypothetical reservoir.The vertical dimension is depth
in meters (disproportionately scaled),and the horizontal dimension is
length along the reservoir in kilometers,with the downstream dam at the
left.Isotherms in degrees Centrigrade (solid lines)and dissolved
oxygen isobars in parts per thousand (dotted lines)are sketched in.
The shaded region denotes high food availability.A power plant is
assumed located at the upstream end.of the reservoir.
-
6
problems both computationally and graphically.It is hoped that this
model will eventually be extended to three dimensions.but the present
two-dimensional model is useful.Note that the scaling 1n the vertical
(depth)dimension is greatly exaggerated relative to the horizontal
coordinate.Typical temperature and dissolved oxygen isoclines are
sketched in.and the area in which food availability is greatest
(usually the shallow water along shore lines)is shaded.We assume
that the position of those factors are stable over the time scale in
which a fish can move considerable distances.A typical fish will have
a preferred range of temperatures.will tend to avoid very low levels
of dissoh'ed oxygen,wi 11 be attracted by high food availability,and
will prefer ~~bitats that give it sufficient cover f~predators.On
this basis.~he avel"age distribution of a model fish population may be
reliably predicted.though ".he path of a given fish is unique.
For modeling purposes.it is necessary to represent the
two-dimensional space by a grid of points.Consider a fish located at
some point (i.J)in the grid points (Fig.2).The fish can move to one
of eight adjacent points (i+o,j+E),where 0 and E take on the values
-1,0 and +1 {but both cannot be 0 simultaneously}.It is assumed that
the following factors influence the next location of the fish:
1.The tendency of the fish to continue moving in the general
direction in which it is already moving.This can be termed
the "forward inertia"of motion.
2.The preferred temperature of the fish and the temperature at
the presen~location of the fish,(i,i),and the eig~t
surrounding points.
3.The location of food supplies and cover.
4.The boundary of the water body,which sets limits on the
motion of the fish.
These factors can be elucidated to some extent by examination of
Fig.3.Assume the fish is located at point (i,J)and has just moved
from the point (i,j-l).The black points in this figure are those in
the body of water while the white dots are above its surface.The
isotherm of the preferred temperature is represented by black dots
7
ORNL-DWG 77-2861
(i-l,j+1l•
(i -1,jl•
(i -1,j-ll•
(i,j+ll•
(i ,jl•
(i;j-ll•
(i+1,j +1)•
(i +1 J)•
(1+1,j-1l•
Fig.2.The point (i.j)in a grid of points,with the adjacent
points to which the fish can move in one step.
8
ORNL-OWG 78-1682
0 0 0 0 0 0 0 0 0 0
(i+,.j-'Hi.,.jHi+',j+t)
0 0 0 0 0 0 0 0 0
SURFACE_.
U,j-tl (i,j)(i,j +1)• •
•• •
l!>•••
(i-l,j+tl• • • •• •
@ • ••
•• • • • ••••
• • • • ••• • •
•• • • •••@ ••
••• ••••••
I
I'•••• ••• ••
•• •• • • ••••
Fig.3.A grid of points representing a portion of the reservoir.
The shaded circles are water.while th&open circles are above the water
surface.The shaded circles surrounded by larger circles represent
points along the preferred temperature isotherms.
9
surrounded by a circle.The most likely next "step"of the fish is to
the point (i.j+l),since this is in its direction of preferred tempera-
ture as well as its direction of inertia.The fish also has a high
probability of moving to point (i-l.j+l).Of course.the fish cannot
move to points (i>l,j-l),(i>l,j);or (i>l,j>l)because these lie above
the surface of the water.
It is conceptually and mathematically advantageous to discuss fish
movements in terms of the four factors listed above.but these factors
have not been quantified in detail (except for factor 4;the fish we
are dealing with cannot normally leave the wat~r).Data are available
on the response of some fish species to temperature and dissolved
oxygen variations,but other factors,such as food availability and
habitat preferences.complicate the situation in natural bodies of
water.making predictions based on mathematical models less reliable.
MATHEMATICAL DESCRIPTION OF THE MODEL
It is cO.lVenient to represent the probability of a fish moving one
step from a point (i.j)to another (k.m)in a two-dimensional grid as
an element of a transition matrix.po.k.Since the fish can movelJ.m
from one grid point only to an adjacent one in a single step.k and m
are constrained as follows:
I
I.j
I
k =>6 (6 =-1,0,>1)
m =j +C (c =-1.0,+1),
(la)
(1 b)
(see Fig.1).In all future discussion.k and m will be implicitly
subject to the limitations (la,lb).
The sum over all probabilities for direction of motion must equal
un ity:
..._.~~~~..Jo,
1+1
E
k=1-1
j+l
E
m=j-l
10
=1.0 (2 )
The model is event-oriented,where an event is a step in space.
This means that.given a fish initially at point (i,j),the next moment
of interest occurs only when the fish has moved to an adjacent grid
point.Therefore,the probability of the fish being in its same posi-
tion at the next locomotory event in the model is identically zero.or
=0.0.(3)
All of the transition elements together define a transition matrix.
f..Let !(l)be the probability vector for the position of the fish at
a given moment.The elements of !(l),which are Xij(I),represent
the probabilities of the fish being located at any given point (i,j).
The condition
...ri=-<lO
...
.rJ=_<XI (4)
must hold since the fish must be somf"oolhere in the water body.Then
m+l
f(2)=r
j=m-l
k+lr1=k-l
!(1l (5)
11
is the probability matrix for the position of the fish after its next
movement to a new grid point.
If the movement of the fish from one grid point to the next is
purely random (i.e.,"random walk"),then
Pij,km =1.0/8.0 =0.125 (6)
that is,there is an equal probability of 0.125 of the fish going to
any of the eight adjacent points.However,the motion of the fish is
biased by its forward inertia,temperature and dissolved oxygen
gradients,the location of food and favored habitat,and boundaries of
the body of water.
Consider first only the influence of forward inertia.It intro-
duces a directional bias on top of random motion.The transition
probability can be written
P ..k •(l.0 +l(k,m)}/(lJ.m
where (is the normalization factor,
(7)
r
and
i+1
(=~
k=1-1
j+l
m=I-1
P'..k ''J.m (8)
P'ij.ij :0:0.0 (9a)
Pij,km =1.0 +I(k,m)(m ~j.if k i).(9b)
Pij,km ={1.0 +l(k,m)+T(k,m)+OO(k,m)+F(k,m)+H(k,m»)/<(10)
Pij,km ={l.0 +l(k,m)+T(k,m)+DO(k,m)+F(k,m)+H(k,ml)B(k,m)/<,(12)
where ~is defined by Eq.(8)and now
(13)
(11 )
{l.0 +I(k,m)+T(k,m)+DO(k,m)+F(k,m)+H(k,m»)B(k,m),
The term Ifk..m)is a measure of the strength of forward inertia relative
to random effects in determining the next grid point in the fish's
course of movement.If I(k.m)«1.0,then the random effects dominate
the movement.On the other hand,if,say.I(i+l.j+l):»1.0 and
I(i+l.j+l}»I(k,m)for all seven other pertinent values of k and m.
then the fish is likely to move upward and to the right on its next
step.The magnitude of I(k,m)for particular values of k and m depends
on the past motion of thp.fish.For this reason,f.is not a Markov
process matrix.
In a similar manner,the effects of temperature and dissolved
oxygen can be incorporated into this mathematical scheme.If T(k,m),
OO(k ,m},Fek .m)and H(k ,m)represent the strengths with which temp(~ra
ture grad"ients.dissolved oxygen gradients and gradients in distribution
of food availability and habitat desirability.respectively.then one
can write
12
p'..k =1.0 +l(k,m)+T(k,m)+OO(k,m)+F(k,m)+H(k,m)lJ.m
where ~is defined by Eq.(8)and now
The effects of the boundary of the body of water on fish movement
is incorporated as follows.Define 8(k.m)as the boundary factor.and
now write Pij.km as
P'ij.km
I-,,
i
II
I
13
where
O.(k ,m)outside the body of water
(17)
(16)
(15a)
(15b)
=;'+6'
j=j'+('.
I(k.m)=Probability (6,<given 6',<'),
c =16-6'1 +1<-<'1·
B(k,m)(14)
where this probability is higher the more positive the correlation
between (o,e)and (6',(').In the model,a quantity,C.is defined,
where.
1.(k,m)in the body of water
Inertia of forward movement,I{k.m)
Assume the fish is at point (i.j)and its preceding location was
(i',j').where
and where 6'and c'have the same ranges of values as 6 and (;[see Eqs.
(1a,lb)).Then I(k,m),where k and m are given by Eqs.(la,lb),is a
conditional probability,
It is now appropriate to discuss the detailed formulations of
I(k,m),T(k,m),D)(k,m),F(k,m)and H(k,m).These are developed in as
simple and practical a manner as possible in the absence of definitive
field measurements.Subsequent studies may require alterations of
these formulations.
2)
)
14
The bars represent absolute values of the enclosed differences.The
quantity C can take on one of five different integer values,for each
of which I(k,m)is assigned a different value.e p as represented in
Eq.(l8),
e 1 (C •0)
e 2 (C =1)
[(k .m)=e 3 (C =2)(18)
e 4 (C =3)
e 5 (C =4),
where the constants e i are chosen so that e 1 >e Z >e 3 >e 4 >
eS 'The model fish is likely to continue in the same general direc-
tioo because I(k.m)is greatest when 6 '"6'and e:'"£'.
Temperature term,T(k,m)
Assume the fish has a preferred temperature,TEMP p'The tempera-
ture at point (i,i)is defined as TEMP(i,i).Oefine the absolute
difference between the temperature at (i,j)and the optimal temperature
by dT(i,i)=ITEMP(i,i)-TEMPpl.Then,if (k,m)is a neighboring
point of (i.i).we define the temperature effect.T{k,m}.by
T(k,m)
={ST >0.0
0.0
(1g)
The quantita~ive value of the constant sr is assigned to reflect
strength of the effect of the temperature gradient on the fish.
mates of values might be obtained from experiments in which only
perature effects are present.
the
Esti-
tem-
15
Dissolved oxygen term,OO(k.m)
We have no information on the existence of a "preferred"00 level.
but there is evidence on minimum tolerable levels.Define by DISOX min
the minimum tolerable level and by OISOX(i.j)the dissolved oxygen at
point (i,j).Then if the fish is in a spatia~region in which the
dissolved oxygen is below the minimum tolerable limit,(i.e.,
DISOX(i.j)<.OISOX min ).then define the dissolved oxygen effect,
OO(k,m),by
OO(k,m)=
SOD >0.0 OISOX(k,m)>OISOX(i,j)
(20)
0.0 OISOX(k,m)<OISOX(i,j).
If the fish is in a region in which the amount of dissolved oxygen in
the water is above the m1n'mum tolerable limit.then DO(k.m)=0 for
all values of k and m.The constant Soo is a measure of the strength
of avoidance by fish of low dissolved oxygen levels.
Food availability terms.Fq(k,m)
Assume that there are q regicns in the body of water that are
attractive to fish because of high food availability.We assume that
the closest of these to the current position of the fish will exert
some attraction on the fish.Define by dF (i.j)the level of food,q
availability at point (i,j).Then if (k,m)is a point neighboring
(i.j).the force of attraction of the food is
=jSF,q >0.0
l 0.0
(21)
16
Habitat preference terms,H (k,m)
Assume that there are ~regions in the body of water that are
attractive to 'fish because of their favorability as habitat.We assume
that the closest of these to the current position of the fish will
exert some attraction on the fish.Define by dH,p(i,j)the level of
habitat favorability at point (i.j).Then if (k.m)is a point ne;gh~
boring (i,j).the force of attraction of habitat is
SH >0.0,p dH (k,m)<dH (i ,j).P ,p
0.0 dH p(k,m)>dH (i,j).,,p
COMPUTER PROGRAM
(22)
The computer program consists of a MAIN PROGRAM and three subrou-
tines,SUBROUTINE RANSET,FUNCTION URANO,SUBROUTINE PLOTT and
SUBROUTINE HIST.
The MAIN PROGRAM first reads in the input data.which is described
in Part A below,and then prints it Qut (see Part B.below).There are
two ways in which data on temperature and dissolved oxygen can be
entered;either by splcifying each grid point values.or by using
mathematical functions to express their spati 1 variation.As an
example of the latter.temperature might be given by the f"--;ction
TEMP 40000'/{10000 .•(i _B5.)2 •5.0(j -55.)2 1 ,(23)
which leads to the isotherms shown in Fig.1.Similar functions are
used for dissolved oxygen.Food distribution might be modeled by
functions of the form
=(24)
17
which are plotted in Fig.4.The peaks and plateaus in this figure
represent regions of high food availability.Similar functions are
used to describe habit::t preferences.
In the input data,the user specifies how many fish are released
at random locations in the body of water and how many spatial steps
they are allowed to take.The user also chooses whether or not the
paths of the fish are to be plotted.If they are not,only the final
positions of the fish will be shown by a dot.The user can also have
the computer print out the isotherms,if desired.
The program first randomly selects,using a pseudo-random number
generator,the position and direction of motion of the fish.There-
after.the movement of the fish from point to point on the grid is
determined by the pseudo-random number generator.in combination with
the transition probabilities.Pij.km'which are computed at each step.
Information on the paths and final positions of the fish is stored
for later printing.
The only purpose of SUBROUTINE RANSET and FUNCTION URANO is to
generate pseudo-random numbers on the interval (0,1).These subrou-
tines have been described elsewhere (HcGarth and Irving,1975)and so
will not be discussed here.The type of simulation that uses a pseudo-
random number generator is commonly referred to as a Monte Carlo simula-
tion.SUBROUTINE PLOTT handles the plotting of the outline of the body
of water,while SUBROUTINE HIST plots a histogram of the final tempera-
ture distribution of the fish.
The computer program is meant to be very general.If changes in
the program are necessary.however"the documentation of the program
below should be complete enough to enable the user to make these
changes.
The r~mainder of this section consists of a description of the
data input cards 'Part A).the printed output of the program (Part B).
and a listing o~the computer program (Part C).In the next section.
the use of the program is demonstrated by means of some trial simula-
tions.
I
18
~.."-0 so -0 ..LON~1 TUDt:.0
fig-4_~plot of food availa~ilitY to
reservoir-1he pea's and plat.
aus
represent
alla l1ab "ity.
90-0
fish ,n a hypotnetiCal
the regiOnS of high food
19
Part A.Input Cards
Figure 5 is a listing of the input cards relevant to an example
given in the next section.These input cards are described below:
Card A
Input parameters:NHOR.NVER.NREG
Fonnat:415
NHOR ::number of horizontal grid points
NVER ::number of vertical grid points
ilREG ::number of environmental regions (usually there will be only two;
(1)the body of water,and (2)the surrounding air and land
Card B
Input parameters:NREGP
Format:15
NREGP ::the number of points on the line to be drawn to define the
boundary of the body of water
Card Set C
Input parameters:(ARRAYX(I),l'l,NREGP)
Fonnat:7EI0.0
ARRAYX(I)::the horizontal coordinates of points on the line defining
the boundary of the body of water
Card Set 0
Input parameters:(ARRAYY(I),I=l,NREGP)
Fonnat:7EI0.0
ARRAYY(I}=the vertical coordinates of points on the line defining
the boundary of the body of water
Card Set E
Input paramete:-s:NVER cards containing the information IREG.
(IBEG(I),lENO(I),TYPE(I),1-I,IREG)
Format:12,ex,6(212,F5.1,IX)
I
.'
20
.. ..•"•2.D.•••01'.0 ,~.O 10.0 l~.O ~..,
)5."'1.11 ".0 10.0 ".0 'l.~n.",.....,..,..,,..'..0.'••••••'"'••••10.0 16.(1 n.1l ~o.o n.o 11.0 }•.o •n."",0 0.'••0"0 ...
•''''0 '.',..'O?...O)~S ,..06'0 ...,"'''1 •••~J"",..01_0 ...,"'Ill ...IHIl ,..tno •••,"",..."'lI ~..."'I'...,"'"..."122 ,..2)_,...,o HI;'"'I'll'•••n"'.',"'01 '.'OJH ,..~o,o ...,.....,...O}.·,..,~....,0101 ...!!n....",..•••,0102 ...01'~•••"'"•••,Ill1l1 '.'n',,..'Ull ...,"'01 '.."H'o.'.0.0 '.',0'''''.'"J'~•••"'0 ...,1)101 '.'Ill.,,..'J'O '.',"'01 ..."'"...nto •••,"'01 ...Il}.,,.......'.',"'01 '.'OUt 0.'U'G ...,"""...,,'u ,..50'0 ...,0102 ..."H'..."'0 ...•,"'D2 ...Il}"...•••0 ...•,"'02 ..."1",..·nll ...•,"'01 '.'01"'..•uo ...•,0101 ...0'"...foO·O ...•,"'D''.'OJ'",..nta '.'•,"'Ol '.'OHl ,..'""...•,"'01 ...IU'"•••~uo '.'•,1"'"'.'In_,,..17"...•,"'"''.'llJ'~'..•••0 '.'•,0'02 ...Illf'~.0 '""0 '.'0,OlU ...'llH ,..'1"·..•,0'12 ..•OJ'l ...11'\1 ...•,"'('1 1.~IlJ')•••""0 '.'•,I'.'n ...Il)l''.'"'"••••,.....,•••01"'.'"'0 ...0,0102 ...O)l6 '..'HO ·..•,Il •.".......0 ..."'0 ·..•,01nl '..OJ"'..u.,'.'•,..,,,,'"'"l'"o••..no ...•,"'01 ...IlJIl"...81'0 ...•,0""...II}"..."'0 ·..•,0'111 ...OH'...ano ...•,D.Il,...01'"..."'0 '.'•,",1)1 '.'Il,"'.,"I'"·..•,0'01 '.'"'0 ,'.'8100 ...•,"'01 ...018'...~na ...•,0'01 ...r1.''.'88tO ...•,0'01 ...n).,,.....0 ...•,0'01 ...nUl •••...0 ...•,~,n,...n18',..8 ••0 ...,0'02 ..."18'...noo •••,ftlO1 '.'0)8'...•..0 ·..,0'01 ...~,.,o •••,.0 ...,"101 ...r18'•••"00 ••••n,o,....
•o,.n ,.~
•nlOO ...
•ft ..O ...•0100 ...•,
19.0 ...,..'.',•••••,••'.'•0.00'O.~Ol 00.••••......•"'65 ,...'",•••".n.0.'•,".,
•.•
Fig.5,Input data for a sample trial simuhtion as it appears on
the data cards.
21
IREG number of different environmental types along ~given line of
grid points
IBEG(I)=the horizontal coordinate of the first grid pOlnt of a
particular environmental type along a 9iven horizontal line
tEND(I)The horizontal coordinate of ttY.:last grid point of a
particular environmental type along a given horizontal line
TYPE(I)=a numerical label attached to each environmental type to
distinguish if from others
Card F
Input parameters:ITEM.IDISOX
Format:215
JTHI 0 if spatial temperature data is given by an equation in the
pro:.ram
1 of spatial temperature data is read in point by point
IOISOX =0 if spatial dissolved oxygen is given by an equation in the
program
1 if spatial dissolved oxygen data is read in point by point
Card Set G (included only if ITEM =I)
Input parameters:(TEMPA(I.J).I=I,NHOR).J=I.NVER
Format:7EIO.0
TEMPA(I.J)=temperature at grid point (I.J)
Card Set H (included only if IDISOX =I)
Input parameters:(DISOX(I.J).I=I.NHOR).J·I.NVER
Format:7£10.0
DISOX(I.J)=dissolved ox,gen le,el at grid point (i,J)
Card I
Input parameters:TEMPRF,TEMFCR
Format:2EI0.0
TEMPFR ::preferred temperature of f"ish
TEMF~::force of attraction of preferred temperature of fish
22
Card J
Input parameters:OOXMIN,DOXFOR
Format:2EIO.O
DOXHIN =minimum tolerable dissolved oxygen level for fish
OOXFOR =attr~ctive force of higher dissolved oxygen levels on fish
Card K
Input parameter:NFOOD
Format:15
NFooD =nllmber of centers of high food avallability
Card L
Input parameter:FOAler
Format:ElO.O
FOAler =force of attraction of food availability on fish movements
Card Set M
Input parameters:
Format:5EIO.O
FONi.I'I(I)
FOALP{l)
FOBET(I)=
FO IQ(I)
FOJQ(I)
FONi.I'I(I),FDALP(I),FOBET(I),FOIQ(I),FOJQ(I)
parameters describing spatial distributions of
food about each of the centers of food
availability (see EQ.24 and Table I)
Card N
Input parameter:NHAB
Format:IS
NHAD ~umber of centers of high habitat favorability
Card 0
Input parameter:HBATCT
Format:EIO.O
HBATCT =force of attraction of habitat favorability on fish movements
Card Set P
Input parameters:
Format:5EIO.0
HBNIJoI(I)
HBALP(l)
HBBET(l)
HBIQ(l)
HBJQ(i)
23
HBNIJoI(I),HBALP(l),HBBET(I).HBIQ(I),HBJQ(I)
parameters describing the spatial distribution
of habitat favorability about the high habitat
favorability centers (analogous to Eq.(24);also
see Table 1 for definitions)
Card Set Q
Input parameters:RES(l),I=I,NREG
Format:7EIO.0
RES(I)=boundary crossing factors (causing fish to remain in the body
of water)
Card R
Input parameters:ERTIA(I),1=1,5
Format:5ElO.0
ERTIA(I)=Inertia of forward motion.e j (see Eq.18)
Card S
Input parameter:IX
Fonnat:15
IX =pseudo-random number generator initilization or "seed".It
must be an odd integer.A different value of IX should be used
each time the program is run .
Card T
Input parameters:NFISH,NSTEP
Format:215
NFISH =number of fish considered in the body of water
NSTEP =number of steps in space each fish is allowed to take
_.--_.~---
f 24
Card U
Input parameters:JPLOT,ISOTH
Format:2[5
IPlOT =-1 if the fish paths are to be plotted,0 otherwise
[SOTil :1 if the isotherms are to be plotted,0 otherwise
Card V
Input parameters:TEML,·TEMH.TEMINT
Format:3EI0.0
TEMl =-minimum isotherm to be plotted
TEHH =-maximum isotherm to be plotted
TEMINT :width of intervals between isotherms
Part B.Output
The printed output consists of two parts.First.the input data
is printed out (Fig.6).Second,a schemata of the body of water is
plotted.into which fish paths or spatial population distribution are
plotted (Figs.7 and B).The plotting is done using the DISSPLA
graphics package (Integrated Software Systems Corporation 1970)which
is available at many computer installations.Programming changes would
be necessary to adapt the program to other graphics packages.
Part C.Computer program details
The complete computer program listing is printed in the Appendix.
The comment cards interspersed through the program should enable the
user to unders tand its genera 1 des i g"",However I some add i tiona 1
comments may be useful.
1.The arrays are dimensioned to permit a maximum of 90x60 grid points
at present.This can be changed if desired.
2.A typical run dispersing 500 fish takes about 3 minutes of CPU time
in the IBM 360/91 computer.although this changes to some extent as
some of the model parameters are varied.The GO step uses less
than 230K of computer core.
I
!
I
f
0.00.0O.10
O.001
0.10
0.001
0.10
P.AlfDOII )1101181:1 IUTUTOR.II'•98165
FORCE or "frUeTlDI or GR!ATER fOOD UAIL'BILITf.pOATer.0.0
)l1OOO:E 0
T!rIPERATUR!IS DESCRIBED Sf A P1I,TlllIUTICAL 'UleTIC"
VALUES or PORIlAIlO JNER1U.EP1U •
POUMOA!lf CROSS]"G '..CTCFS.REStl)•
"UIIBER OF rISK Ilf BOD!or VATU.MFISH SAO
25
NHAB • 0
FOIlCE Of'ATTRACTION Or H"BITA'I PPEnU:If:ES.RBATeT •
fOlcr or ATTRACTIO'or KIGHER DIssoLUO (lUGE'LUtLS 0.0
DISSOLVEO OHeEll nOONTS DESCPIBED SY A P1ATUIlATIClL 'U)lCTlOJ
PIl~P!RRED TEIlPEILATORl.TEIlPR'•
IIDllen or unRoUE.TAL REctO'S,liRE:>•2
PISH !I0lllllMT rill A BODY cr IIATEP
rORCE or lTTRAeTlal or fREFUFfO TIrlPEP:lTORI.II:"rOIl •1.0000
!lfNI"O"ISCTHIIUI PLOTTED.TE"L'"'16.0000
DISTAIIC!IIlTV!!1 ISOTRlIUIS.TIRIHT '"'11.0000
""11"0"ISCTHFIIII PLO'!TU:.TEft./III.DOOO
11111111011 TOLERABLE DISSOLVED onGEIf LEVP.L.DOUX_•2.0000
NUften or HOBII0llTAL GRID POIlTS.IIHOI 90
HUflB!R or ¥!ITICU GRID POU1!,Iflil.60
1I0llBEIl OF STEPS EACH 'I~a IS ALLovID Tn TAKE.lfSTEPS 200
Fig.6.Input data for a sample trial simulation as it is printed
out by the computer program.
"."'
ORNl·DWG 78-2b43
fISH DISTRIBUTION
o
~
o
S
o
Ii!
o
$
:I:.....
t.J
00
il
o
lil
-------
A
-----.14°
zo'
,,'
_36°
_];10
~
o
2 --------"'---
10'0,.,
o6~• , •i ,ii,,•
20'0 30'0 40'0 SO'O 60'0 70'0 80'0 90'0 100'0
LENGTH
Fig.7.Plot of simulated motions of two fish initially placed at points A and B.The assumed
preferred temperature ;s TEMP p =29.0°C and the force of temperature attraction.PT'is 1.0 for case
A and 50.0 for case B.
'I.-...--
r -\1
r ------ -- -- -----,
ORNL-DWG 78-2Mb
fISH DISTRIBUTION
N
~
r--j ,I ,
60·0 10-0 80'0 90'0 100-0
J6'
iO'O",.,
n'
20'0
.·;:t • .:·":.":'f~··..
"\:)~..:':.:~;....'..'
.....,.:....:,.:......:.:..
.....:....•...;~,.:/..:,......::~";~:-;;_:"':-;...
.'.";",
,,'
10'0
16'--
~
~
0
lil
0
51
0
0
~
:l:....
ll.
W
"'0
51
0
~
0
~
0
'"0'0 50'0
LENGTH
Fig.8.The distribution of 500 fish influenced only by temperature in the reservoir after
200 steps.The assumed preferred temperature is 29.0 0 C.Other parameters of the model are given
in Table 2.
28
Table 1 is a compilation of the principal FORTRAN variables in the
computer program.The equivalent mathematical symbols.of any.and
definitions are given as well.
TRIAl SlfoULATlONS
The fundamental question that must be asked of this model is how
accurately it can simulate the movements of individual fish and the
spatial distribution patterns of populations of fish.There is not
enough data on either of these phenom(~a in natural environments to
allow parameters for a model to be thoroughly tested.However,
laboratory experiments provide some data on fish distributions in
environments in which only thermal effects are important.We shall
focus on the thermal influences on the 'i~h in our model and only
briefly note how the other factors influence fish distributions in
space.
Fish Movements
Consider the reservoir pictured in Fig.7.with only t~
temperature gradient assumed to have an effect on the fish.The
temperature isoclines are given by Eq.(23)and the remaining para-
meters of the model are given in Table 2.A simulated fish is placed
in the reservoir at the position A;it moves.with a fair amount of
meandering.toward the preferred temperature.TEMP p =29.0°C.The
amount of meandering can be decreased by increasing the force of the
temperature gradient on the fish movement;that is.by increasing
PT'When PT is increased from PT =1.0 to PT =SO .•and a fish
is released at point 8.it moves more directly toward the preferred
temperature.
Fish Distribution Patterns
Allow SOO fish to be releasL~at randomly selected initial
positions in the body of water.and to move in response to temperature
gradients only.After 200 steps.they have all had a chance to respond
Table I.Principal rogram variables
Fortran Dimension Mathematical
variable (if array)symbol Definition
"""
ARA'(50)Storage array for horizontal coordinates of
isotherm c~rves for later plo:ting
ARAY (50)Storage array for vertical coordinates of
isotherm curves for later plotting
ARRA'fX (50)Storage array for horizontal coordinates of
outline of body of water
ARRA'f'f (50)Storage array for vertical coordinates of
outline of body of water
D Random number chosen from uniform distribution
on the interval (0,1)
DOIFF Difference between the dissolved oxygen level N
at the current position of the fish and its ~
minimum tolerable dissolved oxygen leyel
DDIFFA Difference between dissolyed oxygen level of
any of the next eight possible positions of
the fish and its minimum tolerable dissolved
oxygen 1eve 1
DDR (l,l)I(k.m)Measure of the strength of the inertia of
forward moyement of the fish
DIA (l,l)DQ{k,ml Attraction of point (k.m)on fish because of
the difference In the dissolYed oxygen leyel
from that of the current location of the fish
DISOX nOD}DISOX(k,m)Storage array for dissolved oxygen Il:els
along some given horizontal line,k
00'OISOX(i,j)leyel of dissolyed osygen at the current
position of the fish
t --,
Table I.(continued)
Fortran Oimens ion Mathematical
variable (if array)symbol Definition
name
OOXFOR '00 Attractive force of higher dissolved oKygen
level on fis~movements
OOXMIN OISOX min Minimum tolerable dissolved oxygen level
for fi sh
ERTlA (5)';Strength of forward inertia of fish
FOAlP (20)'"Parameter describing the spatial distribution
of food about each of the centers of food
availability (see EC!.24)
FOAlel SF ,'I Force of attraction of food availability on
fish movemen ts
FOSEl (20)'"Parameter describing the spatial distribution
of food about each of the centers of food w
availability (see Eq.24)0
FDIQ ('0)'"Parameter (horizontal coordinate)describing
the spatial dhtribution of food about tdCh
of the centers of food availability (see [q.24)
'OJO (20)J"Same as above definition (vertical coordinate)
FOHUM '2O)'0 Parameter describing the spatial distribution
of favorable habitat about each of the centers
of food availability (see ['I.24)
FOR (3,3)FQ(k,m)Attraction of point (k,m)on fish because of the
difference in food availability from the current
location (I,j)
'000 Measure of the amount of food available to the
fish at Its currenl location
FOOOA Measure of the amount of food available to fish
in its possible next location
,
r ,
•
Table 1.(contln~~d)
Fortr.n Din;ens ion Ma theD'.a tical
v.rlable (If array)symbol Definition..""
GRID 190.501 Array that stores lnfomatlon QI'l the tiP!of
region each grid point h In.as well as 'I ts
temperature and dissolved oxy~en level
HAS Measure of the ravorabllity of habitat at the
current location of the fish
HA8A Measure of the favorabl1lty of habitat at the
possible next location of the (Ish
HA8AlP ('0)'H,Parameter describing the spatial distribution
of favorable habitat about each of the centers
of favorable habitat (In equation analogous
to EQ.24)
HBATCT 5H,q Force of attraction of habit (aYOr/lbillty on
flsh movements w-HBBET ('O)BH,Q Parameters describing the spathl distribution
of f ....or.ble habitat about each of the centers
of favorable habitat (In equation analogous
to [q.24)
HBIQ 1'0)I Center of a region of favorable habitatH"(horizontal coordinate)
H8JQ 1'01 JH,q Center of a region of favorable habitat
(vertical coordinate)
HBNUM ('0)HO Parameters describing the spatial distribution
of favorable habitat about each of the centers
of favorable habitat (in equation analogous to
[q.24)
IOISOX Logical variable specifying whether dissolved
oxygen levels are described by a mathe~tical
function (IOISOX.O)or point by point
(IOISOX·1)
'=='="=:;=::::::'!;:>...--....-------~-----~_====""'=""'.",;,.._.....iiiii..
Table I.(continued)
",
Fortran
variaDle
""""
IPlOT
IPRES
ISOTH
ISTRT
ITEM
IX
JPRES
JSTRT
HOiST
NFISH
IlFOOO
NHAB
HHOR
NREG
NSY
Dimension
(if array)
Ha thema t i ell 1
symbol oef;01 tion
Logical variable specifying whether or not fish
paths are to be plotted
Current position of the fish (horizontal
coordinate)
logical variable specifying whether or not the
isotherms are to be plotted
Horizontal coordinate of the starting position
of 11 given fish
Logical variable specifying whether temperature
is described by a mathematical function (ITEHmO)
or by point-by-point data (ITEM-l)
Pseudo-random number generator initiator
Current position of the fish {vertical coordinate)
Starting position of tne flSh (vertical coordinat~)
Integer variable that increases by 1 for each
step a particular fish takes.When NDIST=NSTEPS.
no further steps are taken
liumber of fish simulated in the body of water
Number of centers of food availability
Number of centers of high habitat favorability
lIumber of horizontal grid lines
NUr:lber of env i ronmen ta 1 reg ions [u sua 11y there
will be only two;(1)the body of water,and
(2)the surrounding air and land]
Integer variable that increases by 1 for each
fish that is "inserted"into the body of water.
When NSV ~NFISH,no further fish are inserted.
W
N
Table 1.(continued)
Fortran
varlable
"..
IlSTEPS
NVER
RES
SAYl
SAVJ
TDIFF
TDIFFA
TOR
TEMIl
TEHINT
TEHl
TEMFOR
TEMP
TEMPA
T£HPRF
V
Dimension
(if array)
(SOl
(SOOI
(SOO)
13.31
(l00)
{3.31
Ma~hematical
symbol
B(k,m)
dT(i ,J 1
dT(k,m)
Tq(k,m)
ST
TEMP(i ,j)
TEMP P
Pij,km
Definition
Number of steps in space that each fish Is
allowed to take
Number of vertical grid lines
Boundary crossing factors (causing fish to
remain In the body of water)
Array that stores horizontal coordinates of
fish movement for later plotting
Array that stores vertical coordinates of
fish movement for later plotting
Difference between temperature of current
position of fish and its preferred temperature
Difference between temperature of possible
next position of the fish and its preferred
temperature
Attraction of point (k,m)on the fish because
of the difference on tenlperature from it~
current position
Temperature or maxilll:l::l isotherm to be plotted
Width of intervals between Isotherms
Temperature of minimum isotherm to be plotted
Force of attraction of preferred temperature
of fish
Temperature at current location of fish
Storage array for temperature data along a
given horizontal line,t
Preferred temperature of the fish
Transition probability from grid point (i,Jj
to grid point (k,m)
ww
34
Table 2.Parameter values for the example in Fig.5
NHOR '"90 MYER '"60 NREG a 2
NREGP '"17
ARRAY'(I)(1'1,17)•2.0.5.0,10.0,15.0,20.0.25.0.30.0,35.0,'3.0,55.0,
10.0.77.0.82.0. 88.0.2.0.2.0
ARRAVY(I)(l s 1.17)=3.0.3.0.4.0.5.0.6.0.7.0.9.0.10.0.16.0.22.0,30.0.
36.0.38.0.39.0,55.0.55.0.3.0
IREG l'E~(l)!Er1O(l)TYPE (1)l'EG(2)IENO(2)TYPE(2)l'EG(3)IENO(3)TYPE(3)
1 01 90 1.0
1 01 90 1.0
3 01 02 1.0 03 05 3.0 06 90 1.0
3 01 02 1.0 03 07 3.0 08 90 1.0
3 01 02 1.0 03 12 3.0 13 90 1.0
3 01 02 1.0 03 1.3.0 15 90 1.0
3 01 02 1.0 03 "3.0 23 90 1.0
3 01 02 1.0 03 26 3.0 27 90 1.0
3 01 02 1.0 03 29 3.0 30 90 1.0
3 01 02 1.0 03 31 3.0 32 90 1.0
3 01 02 1.0 03 3.3.0 35 90 1.0
3 01 02 1.0 03 36 3.0 37 90 1.0
3 01 02 1.0 03 38 3.0 39 90 1.0
3 01 02 1.0 03 39 3.0 .0 90 1.0
3 01 02 1.0 03 40 3.0 .1 90 1.0
3 01 02 1.0 03 42 3.0 43 90 1.0
3 01 02 1.0 03 44 3.0 45 90 1.0
3 01 02 1.0 03 45 3.0 46 90 1.0
3 01 02 1.0 03 47 3.0 48 90 1.0
3 01 02 1.0 03 49 3.0 50 90 1.0
3 01 02 1.0 03 51 3.0 52 90 1.0
3 01 02 1.0 03 53 3.0 54 90 1.0
3 01 02 1.0 03 55 3.0 56 90 1.0
3 01 02 1.0 03 57 3.0 58 90 1.0
'I
35 .\
!
Table 2.(continued)
IREG I8£G(1)IEIlO(I)TYPE{I)IBEG{Z)IENO(Z)TYPE(Z)IBEG(3)l(fm{3)TYPE(3)
3 01 OZ 1.0 03 59 3.0 60 90 1.0
3 01 OZ 1.0 03 61 3.0 6Z 90 1.0
3 01 OZ 1.0 03 03 3.0 6'90 1.0
3 01 OZ 1.0 03 65 3.0 66 90 1.0
'3 01 OZ 1.0 03 66 3.0 67 90 1.0
3 01 OZ 1.0 03 68 3.0 69 90 1.0
3 01 OZ 1.0 03 69 3.0 70 90 1.0
3 01 OZ 1.0 03 71 3.0 72 90 1.0
3 01 OZ 1.0 03 72 3.0 73 90 1.0
3 01 OZ 1.0 03 73 3.0 74 90 1.0
3 01 OZ 1.0 03 74 3.0 75 90 1.0
3 01 OZ 1.0 03 75 3.0 76 90 1.0
;1
I
3 01 OZ 1.0 03 76 3.0 77 90 1.0
3 01 OZ 1.0 03 80 3.0 81 90 1.0 (II
3 01 OZ 1.0 03 87 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0 ,
I
3 01 OZ 1.0 03 87 3.0 88 90 1.0 II
3 01 OZ 1.0 03 87 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0 II,
3 01 OZ 1.0 OZ 87 3.0 88 90 1.0 'I301OZ1.0 03 87 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0 I
3 01 OZ 1.0 03 81 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0
3 01 OZ 1.0 03 87 3.0 88 90 1.0
I 01 90 1.0
I 01 90 1.0
I 01 90 1.0
I 01 '0 1.0
I 01 90 1.0 "
HHINT '"4.0
NST[P "200
ISOTH "1
TEHH "44.0
36
Table Z.(continued)
ITEM"0 J~ISOX ~0
T£HPA(I,J)not entered
DISOX(I.J)not entered
T£HPRF =29.0 TEHFOR ..1.0
OOXHIH =2.0 OOXFOR ..0.0
HrQOD ..0 FOATer "0.0
FOHUH(I).FOAlP(I).FOSH(I),FOIQ(I).FOJQ(I)
NHAB " 0 HBATCT ::-0.0
HBNUM(!).HBAlP(I),HSBH(I),HBIQ(!).HBJIHI)
RES(!)(1'1,3)-0.001,0.001.10.0
ERTlA(I)(1-1.5)•0.1, 0.1,0.1.0.0.0.0
IX =9876'5
NFJSH " 2
IPlOT " 1
TEMl "16.0
not entered
not entered
37
to the preferred temperature.The distribution of fish after 200 steps
is stoW"in Fig.8,for parameter values given in Table 2.except that
now NFISH =500 and IPlOT =O.It is interesting to look at the histo·
gram describing the percent distribution of fish about the preferred
temperature of 29.0OC ~Fig.9).since this can be compared with
laboratory data.such as that shown in Fig.10 for largemouth bass
{Reynolds and Casterlin 1975}.The agreement is not bad (although the
model results are more peaked and lack.the skewing seen in the
experiment),which is some indication that we have chosen a reasonable
set of parameters for our model;however,other choices of parameter
va hies may give better results.
Next we add in the effects of dissolved oxygen (Fig.I),food
availability (Fig.4),and habitat preferendJ,with the appropriate
changes in parameter values frem Table 2 shown in Table 3.The ulti-
mate average distribution of fish is nCM greatly altered (Fig.11).
DISCUSSION AND SUMMARY
The model described in this report is designed to simulate the
movements of individual fish in a body of water and to predict the
spatial patterns of a population of fish under the influence of
temperature,dissolved oxygen levels,fl'lOd availability and habitat
preferences.The body of water is represented by a two-dimensional
grid of points,with water depth and longitudinal axis being the
coordinates.The simulated fish t3kes one spatial step at a time,the
direction of travel being chosen by·a pseudo-random number generator,
but biased by the initial direction of motion of the fish,as well as
its response to temperature gradients and the other factors mentioned
above.Model output is plotted in graphs.
This mOOel is designed for use in planning and evaluating the
results of experimental laboratory and field studies of fish movement
~nd spatial distribution.The application of the model to experimental
data is sti 11 in a prel iminary stage,and the development of the model
into an effective predictive tool will take continued work.The model
I
I
38
ORNL-OWG 78-427715,--,--,--,--,--,__,--,.-_,--,_,--_.,
;e
~
>-u 10z
UJ
:::>
0
UJa:
"-
UJ>5I-
<[
...J
UJa:
0
24 25 26 27 28 29 30.31 32 33 34 35
TEMPERATURE (Oe)
Fig.9.Histogram of percent distribution of fish in Fig.8 aboutthepreferredtemperatureof29.0°C.
·--&...0
39
ORNl-OWC 78-3270
TEMPERATURE SELECTION
0
:l ~~
0x
0..~
""0u.z'"~ow.oo-...
0 I-w·>"~-..
0;0
...J';w-oo
0
Co ~
0..I-
0•I-
0 ~f--;,
11-
.
0 h n,;
.0 .po ~O ~o 4 0 00/'0 .po
~
TEMPERATURE
I ..
Fig.10.Histogram of relative frequency of largemouth bass in
ambient water temperatures during daytime (from Reynolds and Casterlin
1977)•
r
,
ORNL-OWG 78-2647
o
~
FISH DISTRIBUTION
o
S
Ao
.'.
JO'
'.'.
..);)/~~./:.;~
lI'
:.~.:::'::'~'~'~?;/~:(::.
!l..'".~~.~;;:-"••..;:~.~"•...:::.~
2J'
ZJ"
o
R
o
:il
o
iI
;';
~
Co
~
10-
6~I _____
0"10'0 20·.",..to·Q 50·.
LENGTH
....70'0 ",..",..100'0
Fig.11.The distribution of 500 fish influenced by temperature,dissolved oxygen.food
availability and habitat favorability in the res~rvoir after 200 steps.Parameter values aregiveninTable3.
~\=.::...============-------~=--.-'1
IY
41
Table 3.Changes in paremeter values from Table 2.relevant to the case
shown in Fig_11
NFOOO •1
FONUM(l)•10.0 FOALP(l)•0.02 FOBET(l)•0.2
FOIQ(l)•60.0 FOJQ(l)•45.0
FONUM(2)•10.0 FOALP(2)•0.10 FOBET(2)•0.20
FOIQ(2)•70.0 FOJQ(2)•50.0
NHAB • 1
HBNUM(l)•10.0 HBALP(l)•0.05 HBET(l)•0.20
HBIQ(l)•45.0 HBJQ(l)•53.0
HBNUM(7)•10.0 HBALP(2)•0.05 HBBET(2)•0.2
HBIQ(2)•45.0 HBJQ(2)•53.0
NfISH ..500
!PLOT •0
42
is flexible enough to take into I1ccount most of the important factors
influencing fish movement,but considerable effort needs to be expended
in quantifying these factors.
I
i
43
REFERENCES
Coutant.C. C.1975.Responses of bass to natural and artificitll
temperature regimes.pp.272-285.IN:Stroud.R.H.t and H.
Clepper (eds.).Black Bass Biology and Managem~t.Sports Fishing
Institute.Washington,DC.534 pp.
Coutant.C.C.,and D.K.Cox.1976.Growth rates of subadult large-
mouth bass at 24 to 35.5 C.pp.188-120.IN:Esch,G.W.,and
R.W.McFarlane (eds.).Thermal Ecology II.ERDA Symposium Series
CONF-750425.National Technical Information System.Springfield,
VA.
Fraenkel.G.S.,and D.L.Gunn.1961.The Orientation of Animals
(revised edition).Dover P.lb.,Inc.,Ne.r.r York.376 pp.
Gibbons.J.W.,J.T.Hook,and D.l.Forney.1972.Winter responses
of largemouth bass to heated effluent from a nuclear reactor.
Prog.Fish Cult.34(2):88-90.
Kitchell.J.F.,J.F.Koonce.R.V.O'Neill,H. H.Shugart.Jr.,
J. J.Magnuson,and R.S.Booth.1974.Model of fish biomass
energetics.Trans.Am.Fish.Soc.103(4):786-798.
McCauley.R.,and N.Huggins.1976.Behavioral thermoregulation by
rainbOl'i trout in a temperature gradient.pp.171-175.IN:[sch,
G.W.,and R.W.McFarlane (eds.),Thermal Ecology II.ERDA
Sympo3ium Series CONF-750425.National Technical Information
System,Springfield,VA.
McGarth,E.J .•and D.C.Irving.1975.Techniques for efficient Monte
Carlo simulation.Vol.II.Random number generation for selected
probability distributions.ORNL/RSIC-38 (Vol.2).Oak Ridge
National laboratory,Oak Ridge.TN.
Moss,D.D.,and D.C.Scott.1961.Dissolved oxygen requirements of
three species of fish.Trans.Am.Fish.Soc.90(4):377-393.
Neill,W.H.1976.Mechanisms of behavioral the"ll1oregulation in
Fishes.pp.156-169.IN:Sigma Research Inc.(ed),Report of a
Workshcp on the Impact of Thermal Power Plant Cool ing Systems on
Aquatic Environments.Electric Power Research Institute,Palo
Alto,CA.
44
Peterson,S.E.,and R.M.Schutsky.1976.Some relationships of upper
thermal tolerances to preference and avoidance responses of the
bluegill.pp.148-153.IN:Esch,G.W.,and R.W.McFarlane
(eds.),Thermal Ecology II.ERDA Symposium Series CONF-750425.
National Technical Information System.Springfie1d.VA.
Reynolds,W.W.,and M.E.Caster lin.1976.Thermal preferenda and
behavioral thermoregulation in three centrarchid fishes.IN:
Esch,G.W.,and R.W.McFarlane (eds.),Thermal Ecology II.ERDA
Symposium Series CONF-750425.National Technical Information
Syst(~ml Springfield,VA.
Smith,S.F.1972.Effects of a thermal effluent on aquatic life in an
East Tennessee reservoir.Prot.25th Annu.Conf.S.E.Game and
Fish Coon.,374-384.
StlJ'ltz.W.Eo,and J.J.Magnuson.1976.Daily ration,temperature
selection.and activity of bluegi 11.pp.180-184.IN:Esch.
G.W.,and R.W.McFarlane (eds.),Thermal Ecology II.ERDA
SympJsium Series CONF-750425.National Technical Information
System,Springfield,VA.
Warden.R.L.•Jr .•and W.J.Lorio.1975.Movements of largemouth
bass (Micropterus salmoides)in ifT1)ounded waters as determined by
underwater telemetry.Trans.Am._Fish.Soc.104(4):696-702.
1
45
APPENDIX:THE COMPUTER PROGRAM
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C •••••IlUD til TilE Iltlllllllll AIIO lUlIllUII ISOTlfUltS to It PLOTTED.kS IIELL AS
C Tilt !t!lPtlATtlU lITtIllYlLS IS"U!I TUIL,
01!l2
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0151
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01'i9
01"0
OH 1
011,,2
016)ou.
0165
0166
016"1
0161
l'(ISOU .to.01 GO TO 59
Pl!lO (5,100',TlIlL,TI!"'K,r I!!I tiT
WIlITI!16,20191 1!:IlL.TI!IIK.TtllllT
2019 FOIlIlY 111 ,51,'1I1111IlUIl IS0TIltill PLOTTtO,TilL"',"'0.'dl,61,
1 '111.11111111 IS0TIltllll PLOTTtO,TISIlIL "'',"0,'dl,61,
2 'OlStA'CI!ISI!TlIl!rI lSOt"l!llIlS.tr.llll1 •',"0 ••,1'1'1
59 COITIIO!,,,
ClLL PLOTT,,
c .•.••CROOSt ...1I1U1L 1'051':"1011 liD SUSt 0'OIIECno.0'Til!'ISH IlUOO!lLf,
60 CO'TUar:
ISY •1
10151 • 0
5101 •IIKOIl
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65 COIl1'III1£o _0'.1'0 (001111
Oil •SIO'-O
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DY •SYtll-O
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r,
'I
0169
0170
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0172
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on"
0175
0116
0171
0178
0179
o ,itO
0181
0192
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01811
0185
011'16
0181
01118
0189
0190
0191
0192
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019'
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0196
0191
01'18
0199
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0201
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0205.,.,
0201
0208
0209
0210
0211
0212
0213
02111
0215
0216
1 :1
52
.IS,""..OY
tPAST ..ISTII,.
JPAST ...15111
SUI un,..1S'f1lT
SA ".I 1t:!:Y)..J!TIlT
o ..O'''I)IDU~'f)
rtlAC ...125
DO 80 t-'.]no 80J_1.J
Ull .ro....UG.J .:0:0.2)GO TO 80
I'(0 .U.""CI GO TO liS
ruc ..rllAc ...125
80 CClnUOE
85 COIIT1I01:
1011 ..I
.1011 ..J
tPIES ..ISTIT - 1 ..tD~
JPIlES ..JSTllT - 2 •,lOll
IrIClIItUS"l'ItT.JSTIlTl .U.1.0)GO TO 65
c
c
c •..••8'0IlllIlG or TIll!IT£llA'!'IOI
C
100 COITUDt
e
C•••••D!TtIIlltl'COIIREIT 1!::'!!'tU'!'llH ...0 OISSOLf!O Ducr.
e
1PIGnO(TPIlE~.JPRr:S1 .CT.).01 GO TO 105
Tltll'..IGIIIDI1l'PES.JPIlESI -2.0)·1('00.
LYEll ..TEll'
STtll ..LTEIl
DOl ..IT!'IIP-ST!I'l1 -100.
GO TO 107
105 CDnlJlI::'
nil'..(GIl1D IIPlUS.JPIlP:SI -J.OI-'OOO.
LTP:II -TP:II'
ST!II -LTP:Il
COl -ueIlP-SUIII-'OO.
107 COlfTIIIO!
Ttllp -O.'-'!tllp
TOIFP -AIlS(TrIIl'-TFJlP!l'1
oon,-001 -0011ln
!oJl'l ST JPl SI
SIPlST IPlST
5151'111'151'11
SJSTIT "STU
SII'RtS Il'Rt!
SJPRtS JI'RU
c
C•••••DtTl'IlIllt CURPP:1lT POClD UlYUBYL.ITT
e
IP(IIPOCO .eo.01 CO Tn '1'
POOO -0.0
00"0 I-',.Pooo
OISTI -18S(SIPfltS-POIOIII1
OISTJ -AIlS(SJl'US -POlO (11)•
llPlRG _UP I-POlLP(I)-OISTI -ponT III -OISTJI
pooo -roOD _'011011(1)-UPl.C
I
I
I_____l
0211
0218
0219
0220
0111
02'1
022l
02211
0225
0226
0227
53
110 CO.TIIO!
11\CO'TlInc
C •••••0!ttllllIlt COIl.!'T HUllnT P.,O.UILIT!
C
IP'I"'U .tg.01 :>0 TO 116
NUl •0.0
DO 115 ]*'.'"AI
olSTI •US ISIP.!S -!!III a II II
D]ST..I •US(S..I'US -ll&..Jall))
n'AIIG •tlP(-NULP(l1 aOISTI IIll1ltT(Tl a tlur..l1
IIAI·IIAI •IlfIlJIl(I)-!IP".G
115 CO.!Utl!
116 CCIT!Jot
c
C
C •.•••CALCOUTIO.OP Tilt tPPP:TS OP IU:lITU OP POUA,t 1I0TIO••TM!EPP!CT:;
C OP T!IlftllATtlllf AllD DISSJUto o,tGtII ",lOItITS.AID Til!I,'LOEK!OP
C SPlTUL POOl'OISTPHlll'ilOI "'0 IUlnl!,IlEPUUcts
C
0228
0229ono
0211
0212
02JJ
DO 200 ]·'.l
00 200 J*1.l
1'1 •IPIl!S I
..IPI •..IfIlES J
S]PI •1'1
S..I'I *..1'1c
C •••••rl!IlTIII EPfECTS
C
,,
02H
0215
0216
0237
0218
0239
02110
02111
02112
021l
0204
02115
02116
02111"..02119
0250
""0252
""02~1
0255
0 .....6
0257
025.",.
51 • 1
SJ •J
51011 •101
SJOII •JOt
C·Ul5CSI-SII:Il)•USISJ·~..ID"I
tr (C .GT.0.0):>0 TO 12lnn• ,
GO TO 129
123 lP'IC .GT.1.0):>0 TO 12'
1111'• 2
GO TO 129
1211 rr IC •lOT.2.0)GO TO 125
IEIIT •1
GO TO 129
125 IPCC .Gt.l.OI :>0 ",12'
lIlT.II
GO TO 129
126 lP'(C .Gt.11.01 .0 TO 127
IEin'• 5
GO TO 129
121 un •5
129 COIlTUOE
0111l.JI •EIITtIl(Iflltl
c
C •••••ilOOIUn UPIC1'5
C
lP'II'].ca••11011 .01 •..IPI".Gt.nt',GO TO 60
IF lIP!.Lt.0 .or •..IPI •Lt.0)GO TO 60
IGIl1DP'•GIlID 11't •..I'!)
0260
"0 ,
02b2
02f,3
02611
"'"0266
0267
""""0270
0271
0272
0273
02711
0275
0276
0277
0278
0279
0280
""0282
"03
02ell
""0286
""02fl8
':.2fl9
0290
""0292".,
02911
0~5
0296
""0298
0299.".
0301
"'"0303
03011
0305
0306
0307
54
BOTlI,JI ·IlUIIGIlIOrl,,
C•••••urECTs OP POOO ATnACTtOI,
tr(~rOOo .EO.01 GO TO n1
fOOD"-0.0
00 1110 1Ii"',IIPooo
01STI •"8SISIl'l -POI011li1)
01STJ -US ISJPJ -raJOI iii))
npoIoRG _EIPI-PULPllt,-OISTI P'J8tTlllil"aISrJI
rOOD""rooo"-rOlltllllltl·EKPUG
1'0 CO.TUDE
Iflrooo".LT.rOOOI GO"'O Ul
fDlllI,JI "PCATeT
GO TO 1112
1'1 COIITIIIDE
rtlll(I.J)·0.0
1112 CONTIMO!,
C•••••EPrECTs or '!AlIT"T PPEFUEICE,
tr IIlHA!•EO.01 GO T'"151
H"8"-0.0
DO 150 1t·1,llHAB
DIST!"185(SIPl -HilI 0(11:1 )
01STJ "USISJPl -KIIJOIIl'II
np"RG "EIP I-HflALPIItI ·OlS1'1 -KBBET(KI "DIST"I
flAB""H"U_HBIIDII(It,·EXPUG
150 COlITllIOr
trlK"U .LT.HAB)GO TO 151
KDllll,JI "HUTeT
GO TO 152
151 CONtIllat
KDR(!,J)·0.0
152 COllTlllOl,
C •••••TEIIPEJlATDRt uo 01SSCLf!0 OnGE.E"ECTS
c
TORlI,oJl •0.0
JrIGRIOllPl,JPl).GT.3.01 GO TO 180
TElll'-IGRtOjlPl.JPII -2.01·'000.
LTEft •'nllP
STEil"LTEII
001 "ITEIlP-STEIlI -100.
GO TO 185
180 COlITtlO!
TEIlP -(GRlOIIPl."PII -L01-1000.
LTEII "TElIl'
STEil"LT!1l
001 _l'IEIlP-S'tEIl)-100 •
185 COll1'lIlU!
TEIlP -O.l-TEIlP
TOl""_"8S ITlKP-TEIlPRrl
DIllr'A "DOt -OOIIlU
IrITOIr"".G1.TOIFrl GO TO 190·
TOR(I,oJ)"TtllPOR
GO TO 191
•
'.
0308"0'OJ10
0)11
0312
0313
03111
0315
OJ16
OJ17
0318
0319
0320
0321
OJ12
0323
OJJ'
0)25
0326
0327
032 8
0329
0])0
OJll
0331
0333
OlH
O]~5
OJ]6
OlJ1
OlJ8
OB9
03110
0311 1
01112
0313
OJU
03\15
OJII6
031i'7
0.1118
03119
0350
0351
0352
0353
OlS.
0355
55
190 CO'TIIlDI:
TDllfI,JI •0.0
191 cOlITuor
UIGOIr,.CT.0.01 GO TO 199
001(1,.11 •0.0
IF(DOnn .LT.0.0)r.0 TO 195
00111 •.11 •0011"01I
GO TO 199
195 CGllTlIlOr
DDR (I.J)O.C
199 COIlTIIIut
200 co,Tun
c
c
C •••••USIIIG TilE "eot'!CUCllLATlnllS TO 08TAlII THE PROBlBtLITII!S ,op TN!
c OIRZctIOII 0'Till!:'[IT STEP If UCII or TN!IIGKT POSSIBLE DureTI0.S.
c
'SOil.0.0
DO 210 t-',3
00 210 Jat,3
'f1I.JI -C1.0 •10D II •.I1 •OIP.(I.JI •oOIlU,l1 •'01111,.11
1 •IIDR 11.,))'80f(I,JI
Irlt .EO.2 •.1010.J .10.21 co TO 210
'SOil''5011 •'(I,oll
210 COIlTUOE
T •ORUO(DUIl'f)
PEl'0.0
DO 250 t.'.]
DO 250 .1_1,3
I?II .t\1.2 .UO.J .to.21 GO TO 2115
PtR -C'II.J)""SUftl •p",
Irt'.GT.nl)GO TO 2 ..5
GO TO 251
2..5 COIlTIIlO!
250 COIITIIlDI:
251 COIlTIIlOt:
IP _IPRtS
JP •JSlltS
IPIlt:S IPlIlS 2.
JPRtS JPRI:S 2.
IPlST IP
JPAST JP
lOR I
JOR -Jc
c
c .••..COftPDTIIlG Tftl:DlSTPlBunOIl or FHA
c
1I0IST •110151'• 1
lr(IfDI5T .GT.N5TEPSI G:)TO 280
I?(lPRt5 .LI:.0 .OR.JPRtS .LI!.01 GO '1"0 280
I?IIPRt5 .GT.1Ill0R .011.JPR!S .GT.II1'UI GO TO 280
IS'_IS'• 1
SAtICIH)IPIIlS
SUJ IIs'l -JU!S
GO TO 100
280 CONTIIlO!
F1 -DUIIDCODIIJ)
I..
I,;
Ii<'.0356
O~7
O]S,
.'.,015'
0360.",".,
OJ63
OJ"
0365.,,'0367
'''80369
0310
0]7 1
0372
0373
O)H
037S
0316
0317
0378
037'
03110
OJ'"0382
Ola]
OJU...,
0386
03111
0388
0389.m
03".m
0393
0394
03'5
0396
0397
0398
OJ"o~oo
0'0'
O~O2
Oll03
0110.
0"105
01106
01101
01108
0"0'
0"0
56
,.2 ...OU.1I0(DOll11
SIr.1'111:5
SJP a J.IlZS
5PII1:51 (11 SIP -0.5 •"
SPUS,J 11)S.:I.-0.5 •,.2
CALL IIlIltUlll
CALL SCtrIC(.1251
CALL COIU:eSPIZSt.5PI!SJ.1,-1)
1S1'~,• 1
Ttll 0.0
DO 285 1··',80
T!Il,1.O ...TZII •O.S
IF(T!II ••LT.nil .OR.nllP .CT.T""PLOI co TO 2"
TEllS ...(I)...TlftS."In •1.0
2811 COIITIIUIi
TE"...'tEll •0.5
285 conlin
Ir(IPl01 .zo.01 GO '!'O 290
CALL CURfZ(SUl,SUJ.ISf,O,
290 connot
l'IIIS'.zg_,,;OISHI GO '!'O JOO
GO TO 60
300 (01111101,
c •.•..PlOTTIIlG 0'I~OTHEILIIS,
TEll ...1EIIL
II[(TEIlII -TVllllT'"mT
18 t
00.00 K-',lIl
SJ •0.0
JlA • 0
DO 350 J·1."U
5,)•,)
ltGT •1'00000.-16 -(SJ-SS.I --2-10000.I -:rt:t),ItEn -0.81
lrlUGT •U.0.01 co TO )20
s:r •85.-SOlTe lIlCTI
Ir(SI .LT.1.0.011.SI .:;T.'0.01 GO T0)20
I •51
1r(GIlID(I.J).LT.2.01 ~o TO 320
"A •II:A • 1
AIUI (ICAI •51
UA!(II:AI •SJ
GO TO 1'5
120 CO'TIIDr
Ir fICA •EO.01 00 TO litO
CALL ceRn:IAUI•.IdI"f.';A.OI
u.-0
ICI -Itt •
1"0 COITIIIIE
1.5 COIITII10!
SJ-SJ.1.0
150 CO IlTI Ie E
TEll.1EII •"IEIIII1T
1100 COIITIIOI
'01 connol
CALL UDPL(11
C"LL DCUPL
I
•
0.11
0.12
011130."
0.1~
O.Hi
57
c
C •••••PLOTTIIl.or T!IlPUATUP!HISTOCPAII
C
DO SOO 1-1.80
SOO CO.TIlIOI
CUL KIST (TIIISA'1
CALL OOUPL
"or".
0001
58
rOIlCTIC.OlluqrIlAIj,,
C •••••t.J.ItCGAlITK lID D.C.IPnIG.197':>.TtClilIQOtS rOil trnCIE.T "ont CULO
C SIIIOUTIOll.YOL.2.RAMOO~IOlIlItR GelERATIO.rOR Sr:ltCTEo PIIOBUILITT
C OISTIIIIIOTIO.5.ORlL-IlSIC-l8,,
0002
OOOl
00011
""0006
0001
0008
0009
0010
001'
0012
0013
00111
0015
OOU,
0011
0018
00'9
0020
0021
0022
0023
002/1
0025
0026
0021
0028
0029
OOJO
0031
0032
30
2D
1D
CO""OI/"I RIIG/RA.(10)•G!II (101 •'IIRo.IlA St,"00,Pill St.rllOO
DIll tiS 1011 50"(10)
III TIGtR IlA.,Gt ••III S1'..C AR III ,SO II.PROO,liP 1100
0030 15-'.111110
5011(151_0.
001 IG-l.lIlflit
'2-'.10-IG+l
DO 1 11_1,'2
IS-U+IG-l
PIIOO _u.(Iftl +Gt.(IGI
KPROD-FROD/BAS!
LPIlOD-PIlOD-II PROO+BlSt
SU"IISI-SU II (1 SI +:'PIIOD
IF (IS.LT ••IIPDI SOIl{JS.'I-SUII (15+1,+IIPIIOO
CO'Tun
.2-.1111[-1
DO S 1!-,••2
CA lin-SOl!(lSI/lIAS t
5011 {lSI-SOli (I 51-CAIlIIT-""st
SO 11115.1)-50"115+'l+cAP:n
COllTtlOt
5011 ('11101 -SOIlI'IIIlDl-"OO·(S 0"In 1I01/"ODI
DO 20 IS-1.,II,D
IlAIlIISI-SOIl1l51
PIlA._50"111
DO 10 15-2.1111'0
PIl ..-PI1II/P8l St.SO"(1 51
PR AII-P RAN/PIIO[
OIlA.O-fIlA.
AtTUIl.n,
000'
59
SOBllOOTUE 1l""SET llUIDlT.llstllTIc
C
c •••••!.J.IlClOU'nl ..,D O.C.ll1n'G.'97">.TECUIQOtS 1'01 ErFIeI"T 1I0.T£CAILO
C SIIIUUTIO••'OL.2.11"'0011 .UftIEIl CtlllltATIOIL 1'0'SELECTEO PROB"81L1~T
C OISTUlIllTIO.5.OllfL-RSIC-38
C
C
«
0002
000'
000'
000'
000.
0007
0008
000.
0010
0011
0012
DOll
oon
001 S
0016
0017
0018
00'.
0(120
OC:t 1
0022
0023
00"
0025
0026
Don
0028
0029
00)0
DOH
DOll
0033
OOJfI
00)5
DOl'oon
00)8
OOH
..
100
'01
'"'00
)00
COllIlOIl/IIIRIGI ""1'0I,c;r:I(101.'''IIO,IIo\5£.1I00,'1I15£,'"00
I1Ttc;l:l Ill ••G1I,lllSI:.ClIllT ,II!!.
1I1U-Ill1IIT/fI
18-0
lolS!-'
II'(!lA!!.G1.III,UI GO "n 100
I.St-llSt-.
18-18"
GO TO "
elst-2"11
rUSE-eASI:
nlItO·"/II"
1!1I_'7_1'+('''"0_1)
1100-2--IIEII
FIlOo-IICD
DO 101 '-',10
IIUIIl)-O
lOt.(').0
GUp,-s
DO 200.*'."
CAUTaO
DO 190 '-','11110
GEIlI')-CtM (')-s.c lllIT
CAIl.T·O
IF (GU(Il).LT.lIl51:'roo n '90
CAIlIlY"Gt_IIlI/BlSt
G!II (II)"Grllllli -!AS !-CA II liT
COIT1IlO!
COIlTIIlOr
IST.UT"'STIIT
11"(IIS'l'A".L!.O)IlSTAI'T-200'
IlSrARr-2-(IISUIIT/21-'
DO )00 ,"'.....,D
IIT!IIP-IISTART/US!
RAlllll).IlSTlJt't-JT!IIrIU S!
IISTAIlT""!""
PtTORI
no
•
0001
000'
000)
000'
000'
000'
0007
000'
000'
0010
DOl'
0012
001]
00111
001S
0016
0017
0018
00"
0020
0021
0022
60
SO IIOOTUI PLeTT
C0880,/'1.8L.,.,I ••••'G'
eOllllo./oIlU/A nn I (50.50)•.lIl1l AT'(50,501
COIl80./1111."/IA.18.I'1T'
OIIIUSIO.II 15001 •YT (500)
cau cucar
CALL lea'L (-11
CALL ,&Gll'•••l1.1
CALL tItLE I''1511 DISTill lOTIO'",100.'1.1.Gll1'.6.'tlIPTII'.~.10 ••6.,
caLL CU'(O.,'SC&1.1!'.l00 ••0.,'SClLE',65.1
UU 100.
UIl 0.0
!Illlt •60.
Till'•0.0
I • 1
DO 50 ,J_l ••IIr.GP
IX (JI •UUTI (t.ol)
ncol)•URlTl(t.Jl
SO COIlTUOI
r.ALL COIl'!{II.1'f.lln:;p.OI
UtO u
,"0
I,
\
J
•
•
000'
000'
0003
000'
000'
0006
000'
0008
0009
0010
0011
0011
(01)
00"
00lS
0016
0011
0018
0019
0020
0021
00;2
002l
002'
002S
0026
61
501111001111:IlI!TITlIlSlY}
OIlU:IIS1CII TEIlSUltOOI
DIIlEISIO.CLA!SI10D).r1lEQ11001
COIlIlOII/IIPIlLOK/llrISIl
SIIPISH •"PISII
IICLASS •"0
lIolT • 1
PIlOR!•1."
tStEP •2.(l
DO '01-','0
51 • I
CUSSlJl •20 ••0.S-51
,nOlI)•TEIISUll a llOI/s,rlSll
10 COnIllll!
CALL llGI'L(-11
CALL 'ACEClI ••l'.1
call TI'll.E('TEIlPEIlATUI!E SEU:CTI0IlS'.100.
"TEIlPEJATUllES'.lQO,'llllll11EI'or PUMS',100.7.,'.)
CALL U:UllC(1I5.)
CALL G 1'1.1,1'(20 ••1ST!P ,II 0 ••0 •••seA u:I •rllOIlI)
CALL tIlTIlOIIlOlT.9.50,Q.61
BIIlOTH •7./I"CLASS-ll
CALL 811518110'111'
call COIlY!(CLISS,PIlI:O,IlCLlSS.Ol
CALL UOPL 101
Ii.ETun
no
l
•
ORNL/TM-6310
INTERNAL OISTRIBUTION
•1.
2-11.
12.
13.
14.
15.
16.
17-26.
27.
2B-3B.
39.
40.
41.
42.
43.
44.
45.
46.
47.
S.M.Ada ..
S.I.Auerbach
l.W.Barnthouse
R.W.Brocksen
R.l.Burgess
O.S.Carro 11
S.W.Christensen
C. C.Coutant
D.K.Cox
O.L.DeAngelis
J.W.n""od
W.R.Emanuel
R.H.Gardner
W.F.Harris
K.D.Kum!r'
J.B.Mankin
J.S.Matt ice
R.B.McLean
R.V.O'Neill
4B.
49.
SO.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62-63.
64-65.
66.
67.
6B.
H.Postma
O.E.Reichle
C.R.Richmond
B.Schaich
H. H.Shugart
R.H.Strand
E.G.Struxness
J.S.Suffern
R.I.Van Hook,Jr.
W.Van Winkle.Jr.
O.S.Vaughan
H.Waddle
J.A.Watts
Biology library
Central Research library
laboratory Records Dept.
laboratory Records.ORNl-RC
ORNl Y-12 Technical libr"ary
ORNl Patent Offi ce
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EXTERNAL DISTRIBUTION
69.Richard O.Anderson,Cooper~tive Fishery Research Unit,
University of Missouri,Columbia,MO 65201
70.C.A.Barans.South Carolina Marine Resources Research Insti-
tute.P.O.Box 12559,Charleston.SC 29412
71.Roger A.Barnhart,Cooperative Fishery Research Unit.Humboldt
State University,Arcata,CA 95521
72.T.L.Beitinger,Dept.of Fisheries and Wildlife.Texas A &M
University.College Station,TX 77840
73.O.H.Bennett,Virginia Polytechnic Institute and State Univer-
sity,Blacksburg,VA 24060
74.Theodore C.Bjornn,Cooperative Fishery Research Unit.
University of Idaho,Moscow.10 B3B43
75.Charles F.Bryan,Cooperat~e Fishery Research Unit.Louisiana
State University,Baton Rouge.LA 70B03
76.Robert l.Butler,Cooperative Fishery Research Unit,
Pennsylvania State University.University Park.PA 16B02
77.O.S.Cherry,Center for Environmental Studies.Virginia Poly-
technic Institute and State University,Blacksburg,VA 24060
7B.J.P.Clugston,Southeast Reservoir Investigations.Clemson
University,Clemson.SC 29631
79.Daniel W.Coble,Cooperative Fishery Research Unit,University
of Wisconsin.Stevens Point,WI 54481
BO.A.E.Dizon.National Marine Fisheries Service,Honolulu,HI
96Boo
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81.l.Farges.IAEA,Karnter Ring 11.P.O.Box 590 A-lOll.Vienna,
Austria
82.R.Don Estes,Cooperative Fishery Research Unit.Tennessee
Technological University.Cookeville,TN 38501
83.F.E.J.Fry,University of Toronto.Toronto,Ontario,Canada
84.J.R.GafTlllon.Biology Department,DePauw University,
Greencastle,IN 46135
85.J.W.Gibbons.Savannah River Ecological laboratory,Aiken,SC
29801
86.J.Gift.Ichthyological Associates,Inc.,New Jersey Marine
Ecological Study,3201 Bayshore Ave.,Brigantine,NJ 08203
87.C.P.Goodyear,Power Plant Te~m.U.S.Department of the
Interior.Ann Arbor,HI 48105
88.Richard W.Gregory,Cooperative Fishery Research Unit,Montana
State University,Bozeman,HT 59715
89.Bernard l.Griswold,Cooperative Fishery Research Unit.Ohio
State University,Columbus,OH 43210
90.Donald C.Hales,Cooperative Fishery Research Unit,South
Dakota State University,Brookings.SO 57006
91.Richard W.Hatch,Cooperative Fishery Research Unit.University
of Maine at Orono,Orono.ME 04473
92.Melvin T.Huish,Cooperative Fishery Research Unit.North
Carolina State University,Raleigh.NC 27606
93.P.R.Kamath,Bhabha Atomic Research Center.Trombay,
Bombay.India
94.J.R.M.Kelso,Canada Centre for Inland Waters,Burlington.
Ontario,l7R 4A6,Canada
95.W.C.leggett,Biology Department.McGill University,Montreal.
Canada
96.John A.Maciolek,Cooperative Fishery Research Unit.
University of Hawaii.Honolulu,HI 96822
97.J.J.Magnuson,laboratory of limnology,Univ.of Wisconsin,
Madison,WI 53703
98.O.Eugene Maughan,Cooperative Fishery Research U~it.
Oklahoma State University.Stillwater.OK 74074
99.James A.McCann,Chief,Division of Fishery Research.U.S.
Department of the Interior.Fish and Wildlife Service,
Washington.DC 20240
100.R.W.McCauley.Biology Oepartme'ht.Wi lfred laurier
University.Waterloo.Ontario.N2l 3C5.Canada
101.William J.McConnell.Cooperative Fishery Research Unit,
Colorado State University,Fort Collins.CO 80521
102.J.H.McCormick,USEPA.Environmental Research laboratory.
Duluth,MN 55800
103.J.McMaho.Atomic Energy of Canada.ltd.,Chalk River,Canada
104.J.W.Meldrin,Ichthyological Associates.100 S.Cass St .•
Middletown,DE 19709
105.D.Miller.USEPA.Environmental Research laboratory.
Narragansett.RI 02882
106.Robert J.Muncy.Cooperative Fishery Research Unit,I('·.i
State University.Ames.IA 50010
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W.Neil 1.Dept.of Fisheries and Wildlife,Texas A &M
University,College Station.TX 77840
John G.Nickum.Cooperative Fishery Research Unit,Cornell
University,Ithaca,NY 14850
Garland 8.Pardue,Cooperative Fishery Research Unit,
Virginia Polytechnic Institute and State University,
Slacksbur9,VA 24061
John S.Ramsey,Cooperative Fishery Research Unit,Auburn
University,Auburn,Al 36830
Roger J.Reed.Cooperative Fishery Research Unit.University
of Massachusetts,Amherst.MA Olooe
Robert E.Reinert.Cooperative Fishery Research Unit,
University of Georgia,Athens,GA 30601
J.M.Reutter,F.T.Stone Laboratory,Put-In-Bay,OH 43456
W.Reynolds,Biology Dept .•Pennsylvania State University,
Wilkesbarre,PA 1870e
F.P.Richards,Ecological Analysts,Melville,NY 11746
W.Schikarski,Nuclear Research Center,Karlsruhe,Federal
Republic of Gennany
M.Schneider,Ecosystems Dept.,Battelle Northwest,Richland,
WA 99352
Carl B.Schreck,Cooperative Fishery Research Unit,Oregon
State University,Corvallis,OR 97331
S.A.Spigarelli,Argonne National Laboratory,Argonne,IL
60439
J.R.Stauffer,Gunter Hall,Frostbury State College,
Frostbur9,HD 21532
Jerry C.Tash,Cooperative Fishery Research Unit,University
of Arizona,Tucson,AZ 85721
M.Van deu Avyle,Cooperative Fisheries Unit,Tennessee Tech.
University,Cookville,TN 38501
t.Wilson,Dept.of Forestry,Wildlife,and Fisheries,
University of Tennessee,Knoxville,TN 37916
Richard R.Whitney,Cooperative Fishery Research Unit,
University of Washington,Seattle,WA sa105
Richard S.Wydoski,Cooperative Fishery Research Unit,Utah
State University,Logan,UT 84321
Research and Technical Support Division,DOE-ORO.
Technical Infonnation Center,Oak Ridge,TN 37830