AMER. ZOOL.. 19:305-317 (1979).
Mechanisms of Fish Distribution in Heterothermal Environments
WILLIAM H. NEILL
Department of Wildlife and Fisheries Sciences, Texas A&M University,
College Station, Texas 77843
SYNOPSIS. While the fact of behavioral thermoregulation in fishes has been well
documented, mechanisms remain obscure. A successfully thermoregulating fish moves
through its habitat in such a way as to maximize time spent at temperatures favorable for
the joint conduct of its life processes. The dynamics of its distribution must be related
mechanistically to thermal structure of the habitat. Logic and research literature suggest
that appropriate distributional mechanisms fall into two classes, predictive and reactive.
Predictive thermoregulation comprises directed movements to a subset of habitat within
which the fish "expects," on the basis of individual or evolutionary experience, to find
acceptable temperatures. Reactive thermoregulation involves a sequence of undirected
movements that are biased by recent thermal experience so that net movement is towards
the thermal preferendum. Exploration of possible reactive mechanisms via computer
simulation indicates that successful thermoregulation could be accomplished by a fish that
tends to increase its rate of turning whenever recent experience implies worsening thermal
conditions.
INTRODUCTION
As a group, fishes have at their disposal
only one effective means of regulating
body temperature: behavioral regulation
of immediate environmental temperature.
This form of behavioral thermoregulation
necessarily involves locomotory movements. A successfully thermoregulating
fish moves through its habitat in such a way
as to maximize time spent at temperatures
This paper extends and details some ideas I originally presented in a Workshop on the Impact of
Thermal Power Plant Cooling Systems on Aquatic
Environments, convened 28 Sep.—2 Oct., 1975, at
Asilomar, CA, under auspices of the Electric Power
Research Institute. I thank C. C. Coutant and F. E. J.
Fry for their helpful comments on the text of that
presentation.
Subsequent modeling efforts and the resulting
present paper greatly benefitted from my discussions
with several persons, particularly L. J. Folse and J. D.
Bryan. Both the latter individuals and also M. K.
Hendricks critically reviewed the final draft of the
manuscript. I am grateful for their help.
This paper is Texas Agricultural Experiment Station Contribution No. TA14814. Page charges were
supported by N.S.F. Grant PCM-78-05691 to W. W.
Reynolds.
I thank W. W. Reynolds for inviting my participation in a forum suited to the content of this paper and
for his patience in awaiting the manuscript.
favorable for the joint conduct of its life
processes. In characteristically steep experimental gradients of temperature,
fishes tend to generate monomodal frequency distributions that are strongly
peaked; the temperature about which such
a distribution centers is called the preferred temperature, temperature preferendum, or selected temperature. The
'preferred temperature is a function of the
fish's state of temperature acclimation,
which represents physiological integration
of thermal experience over several preceding days or weeks. Typically, fish acclimated to relatively low temperatures prefer temperatures higher than acclimation
temperature while fish acclimated to relatively high temperatures prefer temperatures lower than acclimation temperature;
at some intermediate point, the preferred
and acclimation temperatures are the
same. Thus, the stage is set for a feedback
loop between the fish's behavior and its
physiology—the act of selecting a temperature different from the acclimation temperature necessarily involves exposure to
the new temperature, which changes acclimation state, which dictates a new preferred temperature, u.s.w., untilfinally,the
point is reached at which acclimation and
305
306
WILLIAM H. NEILL
preferred temperatures are identical. Fry
(1947) has aptly called this point the final
temperature preferendum.
In general, final temperature preferenda are species-specific and roughly
reflect zoogeographic distribution: thus,
salmonids have final preferenda below
20°C while more southerly distributed
fishes of the northern hemisphere, such as
centrarchids, have final preferenda between 25° and 32°C (see Coutant, 1977).
After species and state of temperature acclimation, season/photoperiod is perhaps
the major source of variation in fishes'
temperature preferences (Fry and Hochachka, 1970).
Temperature preferenda have now
been measured for many fishes, and the
effects of non-thermal factors on temperature preferenda are presently under intense investigation. But we still have no
clear notion of how fishes execute their
temperature preferences in simple laboratory gradients, much less in complex
heterothermal environments like areas
heated by thermal effluents from power
stations.
There would seem to exist the possibility
of two fundamentally different mechanisms of behavioral thermoregulation in
fishes. The critical distinction between the
two lies in whether or not the fish has and
can use predictive information about the
thermal structure of its environment. Requisite information may be obtained
through either the individual fish's own
experience or that of its ancestors; that is,
the information may be based in either
learning or instinct. We may call the effective use of such prior knowledge of environmental structure "predictive behavioral thermoregulation" and reserve
"reactive behavioral thermoregulation" for
the remaining class of thermoregulatory
mechanisms.
PREDICTIVE BEHAVIORAL THERMOREGULATION
Undoubtedly, predictive behavioral
thermoregulation plays a large role in the
distribution of fishes relative to temperature, but it seems not to have received
much serious attention.
To be sure of the concept, let us first
consider an extreme and highly improbable case of predictive behavioral thermoregulation. Suppose a fish lives in an
environment characterized by thermal
structure that is temporally and spatially
variable—but completely predictable.
Then all the fish needs to behaviorally
thermoregulate with the maximum precision possible are the neural equivalents of
a clock, a navigational system, a threedimensional map, and a schedule giving
the future thermal regime of the system.
Note that this fish has no need of any ability to directly sense environmental temperature. If temperature varies in space
but not in time, the fish can dispense with
the clock as well. (If temperature varies
through time but not in space independent
of time, no behavioral thermoregulation is
possible). Of course, this case is farfetched. No fish has a completely adequate
set of tools for predictive behavioral thermoregulation, and no environment is entirely predictable. However, the environment need not be 100% predictable, nor
the tools perfect, for the fish to use this
scheme; the population must only be
sufficiently prolific to make up for losses
due to thermoregulatory mistakes and accidents.
To illustrate this last point, I will set aside
for the moment the problem of thermoregulation and consider an analogous
problem, the ocean-phase of the homing
migration in Pacific salmon {Oncorhynchus
spp.). Suppose a Pacific salmon from the
Columbia River system is feeding 2200 km
to the west in the North Pacific when approaching maturity causes the physiological command, "seek home," to be registered. Saila and Shappy (1963) have used a
simulation model to demonstrate that such
a fish need have only a modest bias in favor
of swimming eastward (southward, for a
fish having reached the coastline north of
home) in order to return with probability
0.22 to within 75 km of the home-river's
mouth. A 20% rate of homing success is
probably adequate to ensure stock perpetuation in the Pacific salmons; Hartt
(1960) reported an average recovery rate of
only 10% for mature salmons tagged on the
high seas.
The key element of this migration
307
MECHANISMS OF FISH DISTRIBUTION
scheme is that the homing salmon's goal
bears a spatially predictable relation to the
fish's starting and intermediate positions;
the goal, on the average, lies to the east. The
implicit assumption of the model is that the
fish has and can use predictive information
about the compass bearing of the goal.
Perhaps the circumstances of high-seas,
pelagic fishes relative to thermoregulation
are not too different. Their thermal environment is predictable in the sense that
temperature tends to decrease as latitude
and depth increase. Thus, a crude measure
of behavioral thermoregulation could be
achieved quite simply, as indicated by the
scheme shown in Figure 1. Circumstantial
evidence is beginning to point to predictive
behavioral thermoregulation by depth in
tunas (NeWletaL, 1976; Barkley^«/., 1978).
An obvious shortcoming of predictive
thermoregulation is that it may become
suddenly and drastically maladaptive when
the environmental system changes. An
example may be inferred from observations by Gallaway and Strawn (1974) on
Gulf menhaden (Brevoortia patronus) living
in the discharge area of a power station at
Galveston Bay, Texas. Under normal conditions these fish fared well in the discharge
area. They concentrated in the plume and
fed on entrained detrital foodstuffs whenever effluent temperatures were below
30°C, and moved away at higher temperatures. But a menhaden "kill" occurred
when an inversion of the vertical temperature structure caused lethally warm waters
to underlie somewhat cooler surface waters. One can speculate that the kill ensued
when a normally effective thermoregulatory response failed under abnormal circumstances.
The predictive thermoregulatory responses so far suggested are ones that
might have their origins in the cumulative
experience of species. Fishes, through individual experience, may develop individual
patterns of behavior that also accomplish
predictive thermoregulation. Predictive
thermoregulation based on learned environmental relations must logically be
more likely in fishes that make repeated
visits to various parts of their habitat than in
widely-ranging pelagic fishes that may
never visit the same spot twice.
That some fishes can and do learn the
spatial relations of their habitat can scarcely
be doubted. Probably the most astounding
example of such landmark learning in
fishes is that described by Aronson (1951)
for the frillfin goby, Bathygobhis soporator.
During high tide, these fish learn the arrangement of tide pools in their home area;
then, during low tide, they are able to jump
unerringly from one pool to another.
Again, the key element is predictability:
The spatial relations of rocky tide pools
change very little through the life span of a
goby.
Within the home range of most fishes,
predictability of temperature-space (aside
from depth) relations is probably of such
low order as to preclude predictive thermoregulation. But power-station-outfall
areas are an exception; they are predictably
the warmest places in the habitat. Analogously, springs provide fishes relatively cool
and warm refugia in summer and winter,
respectively. I suggest that some fishes inhabiting waters with such thermal
anomalies learn their spatial locations, to
which they are then able to swim directly
from any position in the habitat.
Predictive thermoregulation may partly
account for the distributional responses of
TP
TA
JL
{
TOO C O O L ' TCO WARM'
(Tp>T A )
(T P <T A )
SWIM TOWARD
EQUATOR
OR
UPWARD
SWIM
POLEWARD
OR
DOWNWARD
FIG. 1. A hypothetical scheme for predictive behavioral
thermoregulation in fishes. T P and T A refer to preferred
and ambient temperatures, respectively.
308
WILLIAM H. NEILL
fishes in experimental temperature gradients. Ordinarily, a particular distribution
of temperature is maintained for a period
of time probably sufficient to allow some
learning of the temperature gradient's directionality. (That relation need not be
learned in a vertical temperature gradient;
as suggested above, fishes may already possess the information, temperature *
depth" 1 , prior to any experience in the experimental system.) Once the spatial distribution of temperature is learned, the rest
is easy:
Too hot (TA > T,>)? Swim toward the
cooler part of the tank.
Just right (TA = T,.)? Stay put.
Too cold (TA < T].)? Swim toward the
warmer part of the tank.
(TA and T(. refer to ambient and preferred
temperatures, respectively.)
A dramatic example of fishes' ability to
exercise learned control over their thermal
environment has been provided by Rozin
and Mayer (1961). These researchers were
able to train goldfish (Carassius auratus) to
limit the upper temperature of their tank
by an arbitrary response, lever-pushing.
REACTIVE BEHAVIORAL THERMOREGULATION
Many thermoregulatory problems confronting fishes are not subject to efficient
solution by predictive means. This is because a large part of environmental-temperature structure is either inherently unpredictable, or is virtually unpredictable
given the individual fish's limited store of
information. In the absence of predictive
information about thermal "lay of the
land," fishes still can achieve control of environmental temperature through links
between swimming behavior and recent
thermal experience. Such links form the
crux of reactive behavioral thermoregulation.
Recall that thermoregulation in fishes
depends on locomotory movements. These
movements may be considered a series of
discrete steps, each completely described by
its duration, length, and direction (Sullivan,
1954). Clearly, behavioral thermoregulation can occur only if a) the potentially
available environment is spatially hetero-
thermal, b) the fish is not completely inactive, and c) at least one of the components
of movement is non-randomly associated
with the distribution of environmental
temperature. Even if these three requirements are all met, reactive thermoregulation in fishes must still be tricky business,
as we shall see.
The search jor mechanisms and models
Research relevant to the problem of
reactive thermoregulatory mechanisms has
a long history. The monographic work of
Fraenkel and Gunn (1961; original edition,
1940) appraised much of the early literature on animals' orientative responses and
offered an insightful classification of those
responses. Patlak (1953a,b) contributed
a rigorous mathematical approach to the
design and analysis of experiments on animals' orientative mechanisms. In the second paper, Patlak used his "random"-walk
equations (derived, ultimately, from the
Fokker-Planck equation) to re-evaluate
several published experiments on orientation of terrestrial invertebrates in heterogeneous environments. Unfortunately,
Patlak's works are difficult going for all but
the most mathematically inclined students
of animal orientation; and, as yet, there appears to have been no application of his
methods to the problem offish distribution
relative to environmental temperature.
Among efforts devoted specifically to unravelling the mechanism of temperature
selection in fishes, those of Sullivan (1954)
and Ivlev (1960) are most prominent. Sullivan (1954) drew attention to the difference
between the activity-temperature relations
of fishes at thermal equilibrium and those
of fishes under conditions of changing
temperature. She noted that thermally
equilibrated fishes move most frequently at
the preferred temperature, whereas fishes
subjected to changing temperature have
their minimum frequency of spontaneous
movements at the preferred temperature.
Sullivan felt that the temperature effect on
frequency of movements was too small to
account, by itself, for aggregation at the
preferred temperature; however, she
found no e\idence of directed movements
MECHANISMS OF FISH DISTRIBUTION
309
in thermoregulating fish. Ivlev (1960) ob- from one to the other half of a partitioned
tained results analogous to those reported aquarium. Experiments with fish accliby Sullivan (1954) for conditions of chang- mated and tested at 14, 22, and 29°C
ing temperature. He observed that young yielded rate-constants in the ratio 1 : 1 . 1 :
Atlantic salmon (Salmo salar) and carp (Cyp- 23.1. Thus, the bluegill's dispersive activity
rinus carpio) in water being warmed or would seem to be much greater near its
cooled at about 0.1 °C min"1 tended to swim final preferred temperature —30-32°C,
at speeds proportional to the absolute dif- according to the compilation by Coutant
ference between preferred and experi- (1977)—than at lower temperatures. But
mental temperatures (Fig. 2). Moreover, the design of the experiment was such that
Ivlev used his results to generate a simple interactions among fish may have greatly
model of fish distribution in temperature influenced the outcome: 40 5-cm-long fish
gradients: Density of fish at a particular were first restricted to one-half the 37.8temperature is inversely proportional to liter aquarium, then given access to the
swimming speed at that temperature. Good other half. One might suppose that aggresagreement between fish distributions pre- sion in the bluegill reaches maximal intendicted and observed in experimental tem- sity near the final temperature preferenperature gradients (Fig. 3) convinced Ivlev dum; if so, aggressive behavior may have
that his model adequately accounted for the facilitated dispersal in the 29°C experiment
mechanism of temperature preference in to a greater extent than in the 14 and 22°C
fishes.
experiments. In any case, the absence of
Ellgaard^a/. (1975) established temper- substantial temperature-change within exature-dependence for the rate at which periments suggests that the bluegill bebluegill (Lepomis macrochirus) dispersed haved in accordance with Sullivan's (1954)
0.05'
10
20
30
O
10
TEMPERATURE (°C)
FIG. 2. Speculative relations between swimming
speed and temperature for young Atlantic salmon and
carp. Swimming speed is treated as a function of both
body temperature and |T X |, the absolute difference
between ambient and body temperatures (see text).
Circles indicate values observed by Ivlev (I960).
310
WILLIAM H. NEILL
o10
AMBIENT
20
30
TE" B ER£TJRE ,""C)
FIG. 3. Fish-temperature distributions observed (0)
by Ivlev and predicted (X) under his orthokinetic
model. (Data from Ivlev, 1960)
observations on thermally equilibrated fish
and not, therefore, in the manner of thermoregulating fish.
At this point, then, we are where Ivlev
(1960) left us—with the notion that fishes
orient randomly in temperature gradients
but tend to aggregate at the preferred temperature, perhaps because that is where
speed or frequency of spontaneous movements is minimum. This sort of aggregating
mechanism is an orthokinesis in the sense of
Fraenkel and Gunn (1961). But, as Fraenkel and Gunn have pointed out, orthokineses are inefficient in producing
aggregation. Even if speed is very much
reduced at the preferred temperature
(unless it is zero), all fish in an unbounded
temperature gradient ultimately die from
exposure to lethal temperatures.
To gain insight into the minimal requirements for an effective mechanism of
the reactive type, I have built some computer simulation models of fish distribution
in unbounded, one-dimensional temperature gradients. Hypothetical fish endowed
only with orthokinetic responses like those
observed by Sullivan (1954) and Ivlev
(1960) were, indeed, unsuccessful thermoregulators; even when swimming speed at
the preferred temperature was only l/60th
that at the lethal limits, fish were rapidly lost
from the system owing to lethaltemperature mortality. The same late ulti-
mately (but, in some cases, more slowly)
befell randomly orienting fish that turned
at rates variously dependent only on the
absolute difference between ambient and
preferred temperatures (pure klinokineses, in the sense of Fraenkel and Gunn,
1961). Only when klinokinetic-avoidance
behavior was invoked did there emerge a
plausible model, reasonably consistent
with logic and with actual behavior of
real fishes in gradients of temperature.
Figure 4 summarizes the essential components of this speculative model. The model's main argument is as follows: In order
for fishes to accomplish efficient reactive
thermoregulation, it is sufficient that their
rate of turning vary stochastically as a function of the interaction between two input
variables, 1) kind and degree of current
temperature stress and 2) recent experience with the rate of environmental temperature change. Under conditions of only
slight thermal stress or small rates of temperature change, the fish orient randomly,
the probability of a turn being set to a constant, BASE. But turning becomes biased as
thermal stress or the rate of temperature
change increase to the extent that their
combination exceeds a threshold level (indicated by the inner set of curved lines in
the large box, Fig. 4). The bias is directed
only in that worsening temperature conditions (TOO WARM, WARMING; TOO
COOL, COOLING) lead to increased
probabilities of turning whereas improving
temperature conditions (TOO WARM,
COOLING; TOO COOL, WARMING) result in turning probabilities less than or
equal to BASE. This kind of hypothesis
seems logically consistent with such observations as that of Fisher and Scott (1942),
who noted that electrically stimulated trout
made longer darts in experimental temperature gradients when moving toward than
when moving away from the preferred
temperature. As Fisher and Scott remarked, "If now the direction in which any
given dart commences is determined by
chance, it follows that the result of a series
of darts will be a net movement towards the
[preferred temperature] . . ."
Hypothetical fishes that behaved according to the a\oidance model thermo-
MECHANISMS OF FISH DISTRIBUTION
regulated successfully even when swimming speed was held constant. Addition of
an appropriate orthokinetic component improved the precision of thermoregulation.
In what way do the two environmental
inputs invoked by the avoidance model present themselves to fishes? Kind and degree
of temperature stress (or thermal quality of
the immediate environment) are logically
some function of the difference between
ambient and preferred temperatures
(TA—TP). Rate of temperature change is no
doubt a more complex issue, for fishes
thermoregulate perfectly well in gradients
that are too gentle to yield a perceptible
temperature difference between two points
on the surface of the individual's body. An
effective solution to the problem of gradual
temperature change would seem to be some
memory device that stores information on
recent thermal history so that the fish can
311
compare present and past values of environmental temperature. Fraenkel and
Gunn (1961) carefully explained that such a
memory device need not involve the central
nervous system and, in fact, might consist of
nothing more than sensory adaptation in
the receptor system itself. The plausibility
of an adequate thermal memory in fishes
deriving from sensory adaptation cannot be
fairly judged at present, because the thermoreceptor systems of fishes are still very
poorly understood (Murray, 1971).
The model shown in Figure 4 invokes an
alternative memory scheme proposed and
discussed by Neill et al. (1976). This scheme
depends on the fact that fishes' core temperatures lag changes in environmental
temperature. For a fish swimming up a
temperature gradient, actual core temperature is lower than simultaneous equilibrium core temperature (TB < T E ); for
movements down the gradient, the reverse
is true—actual core temperature exceeds
equilibrium core temperature (TB > TE).
Thus, sign of the difference, TB—TE, signals directionality of the gradient relative to
swimming direction. Magnitude of TB—TE
is proportional to steepness of the gradient,
TP
the fish's body size and swimming speed,
and the persistence of swimming direction.
Together, sign and magnitude of T B - T E
comprise a summary of the fish's recent
thermal history—a summary low in physiological cost, relevant in its time constant,
and perhaps adequate as an informational
•^-COOLING
WARMING - •
base for control of thermoregulatory turn(TE < T B )
(T E > T B
ing behavior.
We need not be concerned here with
identifying the anatomical site(s) at which
fishes "measure" core temperature. Neill et
al. (1976) implicitly assumed that in skipjack tuna (Katsuwoniis pelamis) the site is
within the trunk musculature, where thermal inertia is maximum. Experiments by L.
I. Crawshaw and his associates (Crawshaw
and Hammel, 1971, 1974; Crawshaw,
1977; Crawshaw, this volume) strongly sugRANDOM
gest involvement of the anterior brainstem.
ELEMENT
DIRECT.
Several testable predictions follow from
properties of the avoidance model deFIG. 4. A hypothetical scheme for reactive behavioral scribed above and in Figure 4, under the
thermoregulation in fishes. TV is preferred temperature;
TA is ambient temperature; TK is equilibrium body assumption of model validity: 1) In a given
heterothermal environment, small fish will
temperature; TB is actual body temperature.
312
WILLIAM H. NEILL
tured the model to mimic the conditions of
Ivlev's (1960) experiments with Atlantic
salmon and carp. Simulated 4-cm-long
salmon and 1.5-cm-long carp were required to perform in linear temperature
gradients of 0.17°C cm"1 and 0.16°C cm"1,
respectively. The range of available temperatures was in each case 0-40°C, giving a "tank" length of about 235 cm for
salmon and 250 cm for carp. Simulation
began with the tank uniformly at the fish's
acclimation temperature—17.0°C for salmon and 20.4°C for carp—and with 100
salmon or carp evenly distributed along the
length of the tank. Each point in the tank
approached its final temperature linearly
over the first 10 min of the simulated experiment, which lasted 50 min.
Each fish made up to 3000 1-sec "steps"; a
step was the time-interval between successive opportunities for a change in swimming direction. A fish's walk ended prematurely if its upper lethal temperature
limits were exceeded. Salmon "died" instantly whenever core temperature, T B
(computed as the exponentially filtered
series of ambient temperature experience,
with the rate coefficient k=2°C min"'°C~';
see Neill et ai, 1976), exceeded 28°C or
water temperature exceeded 32°C. Similarly, upper instantaneously-lethal core
(k=5°C min~|0C~') and skin temperatures
of carp were set at 36°C and 40°C, respectively. For both species, the only penalty for
venturing into very cold water was a drastic
reduction in swimming speed (Fig. 2; also,
see below).
In accordance with Ivlev's (1960) observations on swimming speed, an orthokinetic component of motion was included in
the model; the relations used are shown in
Simulation of Ivlev's temperature-preference
Figure 2. Experiments by Peterson and
experiments: Shaping a model to fit
Anderson (1969) suggested to me that
The klinokinetic-avoidance model seems swimming speed of Atlantic salmon, under
to work, at least in a general way; i.e., under conditions of changing temperature, is eleconditions of a suitable temperature gra- vated above the steady-state value by an
dient; hypothetical fish obeying its rules amount proportional to the absolute differspend most of their time near the preferred ence between equilibrium and actual core
temperature and avoid exposure to lethal temperatures, |T X |=|T E —T B | (which for
temperatures. But can the model be spe- small fishes is essentially |TA — TB|, because
cifically formulated to generate facsimiles T E — TA). Ivlev's activity experiments inand cooling rates of about
of fish distributions actually observed in volved warming
1
gradient experiments? To find out, I struc- 0.1°C min" , implying that the values of T x |
thermoregulate less precisely than will
larger conspecifics; in particular, the thermal limits of distribution will be more extreme for the smaller fish. 2) Steep linear
gradients of temperature will produce
strongly peaked monomodal distributions
of fishes centered about the preferred temperature; moderate linear gradients will
produce more flattened monomodal distributions; and, gentle linear gradients may
produce bimodal fish distributions, one
mode near each lethal limit (thermal endeffect). In even gentler gradients, fishes will
be unable to thermoregulate successfully
and will be killed by exposure to temperatures beyond the lethal limits (if such temperatures are available). 3) In environments characterized by large expanses of
isothermal or nearly isothermal water separated by relatively narrow thermal discontinuities {e.g., oceanic frontal systems),
fishes will be relatively concentrated near
the discontinuities, regardless of temperature. However, unless the preferred temperature lies within a given discontinuity,
greatest fish concentrations may be expected in low-gradient waters on the upgradient side of relatively cold discontinuities and on the down-gradient side of
relatively warm discontinuities. 4) Temporal changes in the spatial distribution of
temperature can have dramatic and sometimes incongruous effects on the distribution of thermoregulating fishes, especially
in thermally complex environments like
power-station cooling areas. In particular,
fish may be thermally trapped in a "pocket"
of cool (warm) water when mean temperature of the system increases (decreases).
(
313
MECHANISMS OF FISH PISTRIBUTION
for his salmon and carp were about 0.05°C
and 0.02°C, respectively. Therefore, the
lines that I fitted to his data are labeled
accordingly in Figure 2. To arrive at estimates of his fishes' swimming speeds under
conditions of thermal steady-state (|TX| =
0.0), I assumed that basal speed in each
species is exponentially related to bodycore temperature, with a Q,o of 2.6 for salmon (based on Peterson and Anderson,
1969) and a Q10 of 2.0 for carp (based on
Schmeing-Engberding, 1953; and Meuwis
and Heuts, 1957); further, I assumed on
the basis of Peterson and Anderson's (1969)
work that the speed-minima observed by
I vlev, at 19°C for salmon and 29°C for carp,
are on the species' respective basal speedtemperature lines. More arbitrarily, I decided to let a |Tx|s:0.2oC result in maximal speed at any T B , that speed not to exceed 6 body-lengths sec"'. Finally, continuous relations among speed, TB, and T x (Fig.
2) were implemented with the following
FORTRAN statements:
TXFACT=ABS(TA-TB)
IF(TXFACT.GT.0.2)TXFACT=0.2
IF(BLNBLS.GT.LNBLS)BLNBLS=
LNBLS
If(salmon)MULT=1.2
lf(carp)MULT=2.0
ELNBLS=BLNBLS + (MULT*
(l.-EXP(-35.*TXFACT))
*(LNBLS-BLNBLS))
BLS = EXP(ELNBLS)
1F(BLS.GT.6.)BLS=6.
SPEED=FL*BLS
where
TXFACT is the TX-effect on speed;
BLNBLS is ln(basal speed in lengths
sec"1);
LNBLS is ln(speed in lengths sec"1
shown by the heavy lines in Fig. 2);
MULT is a scaling constant;
ELNBLS is ln(resultant speed in
lengths sec"1);
BLS is resultant speed in lengths sec"1;
SPEED is resultant speed in cm sec"';
and
FL is fish length in cm.
The speed sub-model suggests that very
small values of |TX| are sufficient to markedly affect swimming speed. Ifso, thiseffect
could account for the "plateaus" regularly
reported (see Fry, 1971) in relations between the logarithm of fishes' routine
metabolic rates and temperature. Even if
environmental temperature is carefully
controlled, there may still exist sufficient
TA-variation (in time or space) to produce
values of |TX| on the order of 0.005- 0.01°C,
which result under the model in a region of
near-independence between spontaneous
activity and temperature (Fig. 2).
Runs of the model at this stage (orthokinesis only) yielded the expected result: At the end of simulation, 36% of the
carp and 70% of the salmon were outside
the temperature-zones they occupied in
Ivlev's experiments.
I next incorporated the klinokineticavoidance scheme described above. Many
formulations were tried; a few gave reasonable fits to the data. Here I will describe only
the simplest model that seemed reasonably
adequate.
The effect of thermal stress was defined as
T
A-T,.
STRESS =
0.
if T A <
T,.|. or
TA>
TL,.,
otherwise
where
is ambient
ambient temperature;
temperature
TI AA is
T P is the appropriate avoidance threshold
(or, boundary of the preferred zone of
temperature): TLP if TA < TM., TLT if
nrA ^>T,
T
•
T
and
is the appropriate value of TA at
which |STRESS| = 1: T LCRIT if TA <
T|,i>, TUCRIT if T A >
T L |..
The temperature-change signal was represented as
TXINFO =
(M1N (
TX > 0
(MAX (TX/2.,-l.)) :! if
TX < 0
That is, the information-content of T x was
assumed to range from - 1 to 1 as T x
314
WILLIAM H. NEILL
ranged from - 2 (or less) to +2 (or more).
The full-response value was set at 2°C in
view of the fact that fishes consistently give
unconditioned responses to temperature
changes of this magnitude but not to lesser
changes (Neill and Magnuson, 1974).
The probability of a turn at the end of
any step was modeled as
PRTURN = BASE + GAIN*TXINFO*
STRESS
IF(PRTURN.LT.PMIN)PRTURN =
PMIN
IF(PRTURN.GT.0.95)PRTURN = 0.95
where
BASE is the probability of turning in the
absence of thermal information or
stress;
GAIN is an amplifying parameter;
and
PMIN is the minimum probability of a
turn.
Note that maximum PRTURN was set
(arbitrarily) at 0.95.
How well the shaped and fitted model
reproduced Ivlev's fish distributions may be
judged from the middle panels of Figure 5.
A better fit to the salmon data scarcely could
be expected. The fit to the carp distribution
is decidedly poorer, with both tails underrepresented and the dip at 22.5°C (perhaps
anomalous?) not there at all. Still, for
neither species could the simulated distribution at the end of the final step
(3,000th) be statistically distinguished at P
= 0.2 from that reported by Ivlev (Kolmogorov-Smirnov one-sample test—see Siegel, 1956).
CARP
SALMON
1.0
05
or
Q.
\
1
1
1
1
1
1
H
1
1
1
1
1
1
u
o
or
W
<J
o
h
i
1
1
1
1
1
1
1
h
O
UJ
or 10
10
20
30
40 O
10
20
30
40
AMBIENT TEMPERATURE (°C)
temperature distributions simulated (broken line)
FIG. 5. TOP PANELS: Turning probability as a
under the klinokinesis-with-adaptatwn model and obfunction of ambient temperature and T x (difference
between ambient and body temperatures) under the
served (circles) by Ivlev (1960). Each of the simulated
klinokinetic-avoidance model. MIDDLE PANELS: Fish- distributions is an average of those on the wholetemperature distributions simulated (broken line)
minute over the last 10 min of a simulated 50-min
under the khnnhinetic-aioidance model and observed experiment.
(circles) by Ivlev (1960). BOTTOM PANELS: Fish-
MECHANISMS OF FISH DISTRIBUTION
Requisite relations among PRTURN, T A ,
and T x are represented graphically in the
upper part of Figure 5. The same
avoidance model was used for both species;
only the parameter values differed:
TUCRIT
TUP
TLP
Salmon
28.0°C
19.1°C
18.9°C
0.0°C
0.25
Carp
36.0°C
28.5°C
18.0°C
16.0°C
315
formulated as a function of only the magnitudes (and not the signs) of TX INFO and
STRESS:
PRTURN = BASE+GAIN*ABS
(TXINFO*STRESS).
In essence, this change converted the klinokinetic-avoidance model into what Fraenkel
and Gunn (1961) would have termed a
model of khnokinesis with adaptation.
Under this model, the probability of a
change in swimming direction increases
0.0
whenever thermal stress is combined with
3.0
1.0
increasing |T |, whether T x is positive or
0.25( = BASE) 0.0 (=BASE) negative. A Xseries of closely
sequenced
turns leads to reduction of |T X | (i.e., '"adapSeveral features of these parameter sets de- tation"), resulting then in decreased probaserve comment. For each species, TUCFUT bility of a subsequent turn.
Simulation using the klinokinesis-withwas the upper-lethal body temperature.
adaptation model, fitted with the same valTI.CRIT for salmon was 0.0°C; but, T|jCRIT for
carp was 16.0°C, only 4.4°C below the ac- ues of the parameters as before, produced
climation temperature. The avoidance distributions similar to those generated
thresholds (Tu>, TLT) for salmon converged under the klinokinetic-avoidance model —
on Ivlev's estimate of the preferred tem- except that after 3,000 sec one of 100 carp
perature, 19.0°C. In contrast, a reasonable was "trapped" at 0°C and one of 100 salmon
fit for carp required a 10.5 — °C separation was "dead" at 30°C (Fig. 5, lower panels).
of the avoidance thresholds; the upper limit Moreover, goodness-of-fit was statistically
corresponds closely with Ivlev's estimate of poorer; simulated distributions after the
the preferred temperature, 29.0°C. The last step could be declared different from
probability BASE for salmon was 0.25, im- the observed distributions, at P — 0.02 for
plying an average time between turns of 2.4 salmon and at P — 0.07 for carp (Kolmosec (= ln(0.5)/ln(0.75)) in the absence of gorov-Smirnov one-sample test).
thermal stress and/or information. I could
Perhaps, the klinokinesis-with-adaptanot fit Ivlev's distribution for carp without tion model could be improved by new sets
setting BASE to 0.0. (Even BASE= 0.01 of parameters. (This I did not attempt.)
gave distributions that were too leptokurtic That it performed as well as it did can be
at 28-30°C). Whatever the real carp did, the explained in the following way: Simulated
simulated carp swam between 18 and fish at any particular extreme temperature
28.5°C without turns. Finally, for each (|STRESS|>0) lended to arrive there from
species, the best value for PMIN turned out less extreme temperatures, owing to the
to be BASE. This was automatic for carp, orthokinetic effect on distribution. Thus,
given that optimum BASE was 0.0 (for the fish's T x , if large in magnitude, tended
PRTURN could not be negative). But for to have the proper polarity (positive if TA >
salmon, this result is more intriguing—it TLT, negative if TA < Tu>); extracting the
means that the model could be shaped to absolute value of T x , then, generally had
yield Ivlev's distribution without assuming little effect on the magnitude of PRTURN.
salmon swim with greater persistence of di- But exceptions to these tendencies, inrection (PRTURN < BASE) under improv- frequent though they may have been, were
ing thermal conditions (too cool, warming; sufficient to cause an occasional fish to stray
too warm, cooling).
to or beyond the critical temperature limits.
Realization that the model could be fitted
Further scrutiny of the klinokinesiswith PMIN=BASE encouraged me to try a with-adaptation model will be required to
further simplification. PRTURN was re- decide if it might be logically sufficient after
TLCRIT
BASE
GAIN
PMIN
316
WILLIAM H. NEILL
all. In any event, the biological evidence at
hand would suggest that fishes are as likely
to sense T x as |TX |, for at least some can be
trained to discriminate between warming
and cooling (Dijkgraaf, 1940; also see Murray, 1971).
Are we then to accept the klinokineticavoidance model as an accurate representation of the distributional mechanisms
operating in Ivlev's (1960) fishes? Certainly
not. If his salmon and carp behaved according to the model's specifications, then
their distributions in his temperaturegradient tank are reasonably explained.
But the extent to which biological reality is
reflected in this or any other model of reactive thermoregulation can only be judged
from research yet to be performed.
CONCLUSION
DeAngelis (1978) has developed a model
for simulating the movements of fishes in
two-dimensional space relative to the distribution of multiple environmental variables, including temperature. Like the
reactive models I described in the preceding section, this model is a digital-computer
program that specifies rules by which individual fish swim a stochastic sequence of
steps (spatial rather than temporal, in this
case) biased by the distribution of environment; the output is a simulated fish distribution that can be compared with spatially corresponding distributions of environmental factors.
I regard DeAngelis' model as bold and
commendable. It not only operates in twodimensional space, but also it recognizes
that real fishes inhabit multivariate environments. Most importantly, DeAngelis'
model underscores the practical importance (and reflects a growing hope) of ultimately coming to quantitative grips with the
problem of predicting fish distribution in
nature.
On the issue of mechanisms, however,
DeAngelis' and my philosophies diverge.
With regard to temperature, for example,
DeAngelis' model requires only that simulated fish move probabilistically along a
temperature gradient in the direction of
the preferred temperature (as long as con-
flicting stimuli are not encountered); how
fish are able to do this is not specified.
DeAngelis justifies his strategy with the argument that "on the [largej scale . . . the
precise mechanisms of motion on the small
scale may be unimportant." I tentatively
agree, if the mechanisms involved are in the
class I have labeled predictive. But, in the
case of reactive enviroregulation, I believe
that it is precisely the mechanisms of motion on the small scale that primarily determine fish distribution on the large scale.
The task now is to refine our understanding of the mechanisms.
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