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Behavioral Ecology Vol. 13 No. 1: 94-100
© 2002 International Society for Behavioral Ecology
Asset protection in juvenile salmon: how adding biological realism changes a dynamic foraging model
Department of Zoology, University of British Columbia, Vancouver, Canada
Address correspondence to U. Reinhardt, who is now at the Department of Biology, Eastern Michigan University, 316 Mark Jefferson, Ypsilanti, MI 48197, USA. E-mail: ureinhardt{at}online.emich.edu .
Received 17 May 2000; revised 14 March 2001; accepted 24 March 2001.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHE MODELRESULTSDISCUSSIONREFERENCES |
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The "asset-protection principle" created by Clark is based on a dynamic programming model and states that individuals should (1) become more averse to predation risk as they accumulate fitness assets but (2) generally be more willing to accept predation risk later in the foraging season. To test whether these predictions hold under biologically meaningful foraging parameters, I constructed a dynamic model of the optimal trade-off between foraging and predator avoidance in juvenile salmon. The model incorporates temperature and body-size dependent bio-energetic constraints typical for juvenile fish, which grow by orders of magnitude over a season. In its simplest form using seasonally constant growth potential and a linear over-winter survival function, my results equal those of Clark's model. Adding a fitness function and environmental data from field studies accentuates the asset-protection effect and fundamentally changes the seasonal pattern of optimal effort. Simulation of typical poor feeding conditions in mid-summer yields the prediction of increased foraging in the spring in anticipation of worsening conditions. Increasing overall predation risk results in smaller fish at the end of the season with a trade-off between summer and winter survival. The model generates testable predictions for juvenile salmon and provides insights for other organisms (particularly poikilotherms) that are subject to size-dependent or seasonally changing foraging dynamics.
Key words: antipredator, behavior, dynamic programming, optimal foraging, physiological constraints, predation risk, salmonids, seasonal foraging.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTSDISCUSSIONREFERENCES |
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Mathematical models of optimal behavior often use arbitrary units of fitness and dynamics of fitness value accumulation. In that way, the models aim to be quite general and applicable to a variety of organisms and life history conditions. However before applying these general models to a specific organism and life history stage, one should determine how major limiting factors in the biology of the organism may change the predictions of the general model. Dynamic- or state-dependent programming is widely used to model optimal decisions as a forager moves through different states and time (Mangel and Clark, 1988
). The
dynamic programming model (DPM) by Clark
(1994; but see also
McNamara and Houston, 1986)
for example predicts that, if the fitness payoff at the end of a time period
of foraging increases linearly with accumulated assets (e.g., body size or fat
reserves), individuals with larger assets should be more averse to predation
risk than individuals with small assets. This effect, which Clark
(1994) named the
"asset-protection principle," arises because an individual with
greater assets gains less from a given absolute increase in assets relative to
what it would lose if caught by a predator. Here is an analogous numerical
example: if you have $100 on your account and you can gain from an investment
decision an additional $100 (outcome A) or lose all your money (outcome B),
your expected payoff is positive as long as the probability of A is greater
than 0.5; however if you have $200, a positive expected pay-off requires
p(A) =.67 or greater. The second prediction from the
general model is that, if time to accumulate assets is limited (e.g., one
foraging season) the optimal level of risk taking should increase over time
for any level of assets. This is because the multiplying effects of mortality
risk discount early-accumulated fitness gains over the remainder of the
season. Clark's (1994) model
is based on the assumption of asset-independent and temporally stable foraging
gains. Though realistic for some foragers (e.g., birds foraging through a
winter day; McNamara and Houston,
1986), the predictions may change fundamentally for other
organisms that are modeled over longer time periods or that undergo large
changes in body mass.
Here, I use the example of juvenile coho salmon (Oncorhynchus
kisutch) foraging through their first summer in streams as a specific
model to explore how an organism that requires particular assumptions about
the costs and benefits of foraging behaves in a dynamic modeling framework.
Juvenile salmon grow roughly by one order of magnitude in weight over a season
in a stream environment that undergoes seasonal changes in temperature and
food availability (Sandercock,
1991). Potential growth (if expressed as proportion of body mass)
in fish declines with increasing body size and increases with temperature in
this poikilotherm animal (Brett,
1979). Therefore, I incorporate bio-energetic growth parameters
and seasonal cycles of temperature and food availability typical of temperate
streams to examine whether asset protection is expected in salmon under those
constraints. Furthermore, I explore the effects of fitness functions derived
from field studies on the expected seasonal patterns of optimal foraging
effort under predation risk.
Dynamic modeling studies on specific organisms using field data on
survival, state-dependent reproductive value, and environmental conditions
have been done repeatedly (e.g., Clark and
Mangel, 2000). For example, DPM studies on food-caching and
singing in birds have incorporated metabolic variables in some detail (e.g.,
Brodin and Clark, 1997;
Hutchinson et al., 1993;
Lucas and Walter, 1991). The
situation for fish, however, is quite different from small birds because
foraging activity and growth potential of fish are more profoundly influenced
by temperature and their growth is indeterminate
(Brett and Groves, 1979).
Thus, small changes in body size and environmental temperature can have a
large effect on feeding metabolism and optimal foraging effort. A wealth of
available information on physiology and life history of juvenile and adult
salmonids make this family particularly well suited for modeling
state-dependent behavior under metabolic constraints.
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THE MODEL |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTSDISCUSSIONREFERENCES |
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Free-swimming coho salmon larvae (called fry) enter the stream from their gravel nests in early spring and forage throughout the summer on drifting invertebrates (Sandercock, 1991
). The model simulates in daily time steps the foraging
behavior of individual coho fry from the first spring in which juveniles start
to feed until the fall of the same year (180 days from early May to late
October). It is a dynamic programming model in which the model output, the
behavior that maximizes fitness at any time t, is derived by
back-calculating from a terminal reward function F(x, t)
that links fitness F to the value of a state variable x (see
Mangel and Clark, 1988). The
state variable in this case is body mass (modeled from 0.5 to 16 g in steps of
0.5 g) of the juvenile fish on any day during the summer. The maximum modeled
mass of 16 g is about twice that observed for wild juvenile coho salmon in the
fall (Sandercock, 1991), but
close to the maximum size a salmon can reach under ideal growth conditions at
intermediate (10°C) temperature (Cho,
1990). The proxy for fitness is the mass-dependent probability of
survival over the winter. Using this proxy is justified because winter
survival in juvenile salmonids is generally positively correlated with size
(Burrows, 1993;
Holtby and Hartman, 1982;
Quinn and Peterson, 1996).
Additionally, larger juvenile salmon in the fall also tend to be larger at the
time of migration to the ocean (Bohlin et
al., 1993) and therefore have a greater probability of survival to
adulthood (e.g., Bilton et al.,
1982). In the simulation, there is a choice of 0 to 100% foraging
effort in steps of 10% (with e0 and
emax denoting 0 and 100% foraging, respectively). The
effort steps vary in their profitability in terms of foraging gains,
g, and risk of predation, p, in a way that creates a
trade-off situation between growth and safety from predation. At
e0, growth is negative and p is zero (equivalent
to staying in a refuge and drawing on energy reserves for metabolic
maintenance); above zero effort, both g and p increase
linearly with e to gmax and
pmax at emax. The optimal behavior
e* at time t is the one that yields the maximum
expected fitness for a given body mass. It is derived by calculating for all
levels of e, growth, g(e), and survival
probability, 1 - p(e), and choosing the one that
maximizes F(x, t + 1) (formula 1)
 | (1) |
To achieve realistic foraging and growth parameters for juvenile salmonids,
I incorporated equations from a bio-energetic growth model for fish as a
sub-model in the DPM, with specific parameter values for coho salmon
(Hewett and Johnson, 1992).
The bio-energetic equations are based on a balanced energy budget approach
(Jobling, 1993) and calculate
basal metabolic rates, maximum potential daily rate of food consumption, and
growth after loss of energy as wastes. In fish those values are all strongly
dependent on the body weight of the animal and the ambient water temperature.
For example, the maximum growth rate of coho fry derived from the bioenergetic
sub-model is a decreasing power function of body weight and an increasing
function of temperature (Figure
1). The relationship between foraging effort and consumption of
food was modeled as a linear relationship between effort and consumption with
zero consumption at e0 and maximum potential daily consumption for
a given body weight and water temperature at emax. By
scaling maximum available food to an individual's body weight, I incorporated
an assumption that bigger fish can gather more food in absolute terms due to
their better swimming ability (Bams,
1967; Lister and Genoe,
1970) and the ability to swallow larger prey (e.g.,
Keeley and Grant, 1997).
Moreover, since maximum consumption is temperature-dependent, this method of
modeling food consumption simulates the fact that food availability for salmon
in streams generally is positively correlated with water temperature because
stream invertebrate life cycles are shorter when water temperatures are higher
(Horne and Goldman, 1994). In
some versions of the model, I modified this relationship between food
availability and temperature.
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The DPM calculates growth of the fish by subtracting from the consumed food
energy equivalent to waste losses and metabolic expenditure. The general form
of the growth equation is: growth = consumption—egestion—standard
dynamic action—excretion—(basal metabolism + activity metabolism).
Standard dynamic action is the metabolic cost of food processing and is set at
17% of the consumed minus egested energy
(Hewett and Johnson, 1992);
the detailed formulae for calculating temperature-dependent food consumption
and metabolism and the coho-specific parameter values are given by Hewett and
Johnson (1992). Activity costs
are accounted for by subtracting energy equivalent to the basal metabolic rate
at e0 and linearly increasing in cost to a maximum of
three times the basal metabolic rate at emax (based on
Brett and Groves, 1979: Table
2). If the energy expended in maintenance and activity surpasses the retained
energy from food intake, growth is negative. Energy equivalents of 4.18 kJ (1
kcal) per gram salmon body weight and 2.9 kJ (0.7 kcal) per gram of
invertebrate prey were chosen. I compared maximum growth of simulated fish
from my model to growth predictions by an empirically derived growth model for
hatchery salmonids (Cho, 1990)
to verify choice of realistic model parameters.
The simulated fish incurs a further cost of foraging activity in the form
of predation risk, p, which is zero at e0 and
increases linearly with e to reach pmax at
emax. The formula is:
 |
) for merganser ducks
preying on coho fry. Several values for pmax were explored
ranging from 1% to 2% daily mortality risk, based on survival estimates for
juvenile coho reported in the literature
(Sandercock, 1991).
To show the effect of the various input parameters on
e* of the simulated forager, I used two model outputs. The
first one was e* for various sizes over time, i.e., the
optimal behavioral choice by fish of different sizes (the natural weight range
shown in Sandercock, 1991),
determined by backward simulation. The second output was the seasonal
trajectory of e* and body weight of a fish starting at 1 g
in spring (from t30) through to tend,
i.e., a forward simulation using the optimal behavioral choices. The starting
weight of 1 g and the time step 30 were chosen because they represent the
smallest weight for which the model yielded realistic outputs and the time in
the foraging season (June) by which 1g has typically been attained
(Sandercock, 1991). In the
various simulations, I explored the effect of different terminal fitness
functions, levels of predation risk, seasonal temperature regimes, and
seasonal changes in stream productivity on the optimal foraging effort and
size at the end of the season.
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RESULTS |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTSDISCUSSIONREFERENCES |
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The effects of various fitness functions
I examined the effect of three different relationships between size at tend and over-winter survival probability on optimal foraging effort (Figure 2). The first was a linear relationship with a slope that made survival of the larger fish fall in-between the other two fitness functions that I derived from field studies on over-winter survival of coho fry (Holtby and Hartman, 1982
;
Quinn and Peterson, 1996).
Quinn and Peterson's (1996)
data represent one season of assessing size-related winter survival of
individually marked fish in Big Beef Creek, Washington, USA, whereas Holtby
and Hartman's (1982) data
represent mean survival of a multiple coho cohorts in Carnation Creek, British
Columbia, Canada, in relation to mean body size of the cohort in the fall.
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With the linear fitness function, e* of smaller
individuals is greater than that of larger individuals
(Figure 3a, left panel). Over
the season, e* increases for all sizes, so that it
converges over time to emax. This result is very similar
to that of Clark (1994), and
shows that the prediction of asset protection made by Clark's
(1994) model holds for coho
salmon when bio-energetic constraints on feeding and growth are incorporated
into a DPM. In the forward simulation, as the animal grows, it becomes
progressively more risk averse which cancels out the seasonal increase in risk
taking so that the realized foraging effort of the growing animal is roughly
constant over time (Figure 3a,
right panel).
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When using the fitness functions derived from field data (Carnation Creek), the foragers face a diminishing increase in fitness at each percentage weight increment. The result is that the difference in e* between body weight classes becomes more pronounced over time (Figure 3b, left panel). Optimal effort also increases over the season, but compared to the linear fitness function, the increase is small in larger fish. Early in the season, the asset-protection effect is weaker, which can lead to e* of larger individuals being greater than that of small fish (Figure 3b, left) because larger animals pay relatively lower metabolic costs for active foraging. Because of the decelerating relationship between fitness and size, e* is lower than in the model with the linear fitness function, so that the fish are much smaller at the end of the season, but have suffered lower summer mortality (Figure 3b, right). Simulations using the second fitness function derived from field data (Big Beef Creek) showed qualitatively very similar patterns of optimal behavior and are therefore not shown in a graph. However, since the Big Beef Creek fitness function (BBCF) increases less steeply with size than does the Carnation Creek fitness (CCF) function (see Figure 2), the optimal level of effort is somewhat lower when the BBCF is used. The consequence is that at tend forward simulated fish under BBCF have lower body weight (4.9 g versus 6.1 g under CCF), but a greater whole-summer survival probability (0.4 versus 0.36 under CCF).
The effect of a seasonal temperature regime
I simulated different temperature regimes because water temperature
strongly impacts on metabolic costs and growth potential of fish and because
varying the temperature parameter of the model is a means of simulating
seasonal variation in stream productivity. I used stream temperature records
from Carnation Creek (Brown and McMahon,
1987) from May to October, the time during which juvenile coho
salmon typically forage. The temperatures, transformed into 1°C steps for
the model, increased from 9°C in May to 14°C in August and then
dropped to 8°C by the end of October
(Figure 4).
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When seasonal changes in temperature are combined with a fitness curve derived from field data (CCF) the optimal effort increases strongly with increasing productivity early in the season and then, toward the end of the season, decreases for all but the smallest body weights (Figure 3c, left). In the forward iteration (Figure 3c, right), we observe a rapid increase of e* as temperature increases, and fast growth in the first half of the season, then a rapid decline of e* as decreasing growth potential (due to seasonally dropping temperatures) and the asset-protection effect combine to make foraging progressively less profitable. This results in growth slowing to a halt late in the season.
The effect of predation risk
To explore the impact of different levels of predation risk, I changed
pmax, the parameter that determines the mortality risk at
maximum foraging effort. Doubling the maximum predation risk from 1 to 2% per
day (other parameters as in the previous section), leads to generally lower
e* and maximum foraging being concentrated around the
times of highest growth potential in the summer. Because the simulated animal
can avoid predation mortality only at the cost of reduced growth, increasing
risk leads to a trade off-between summer survival and size in the fall. At
pmax = 1% per day, fish end the season at 7 g with a
summer survival probability of 0.5, yielding a total survival probability to
the next spring of 0.44. At pmax = 2% per day, fish weigh
4.8 g in the fall with a summer survival probability of 0.32, and a total
survival probability of 0.23. In that way, summer predation risk indirectly
influences the winter survival of the animal.
Impact of seasonal changes in stream productivity
Studies on the seasonal production of invertebrates in streams suggest that
food availability to juvenile salmonids does not perfectly follow stream
temperature regimes. Food availability is probably greatest in early summer
(May/June), low in mid-summer when temperatures are highest, and shows a small
peak in early fall (September/October)
(Allan, 1987;
Bachman, 1984;
O'Hop and Wallace, 1983). To
explore the effects of those seasonal trends in food availability on optimal
foraging behavior, I modified the relationship between temperature and maximum
food consumption by reducing maximum temperature-dependent consumption in
mid-summer and fall as shown in Figure
4. This way, the available food in spring was the same as in the
preceding simulations that included a seasonal temperature pattern, but with a
reduction in mid-summer (to 60% of gmax) and fall.
Figure 3d shows the results of a simulation with the Carnation Creek fitness function, seasonal changes in temperature, and seasonal trends in food availability. The lower food availability at the time of greatest metabolic and activity costs in mid-summer produces a decline of e* during that time. After the summer low in food availability, there is another smaller peak in e*, after which e* declines with temperature for all but the smallest sizes (Figure 3d, left). In the forward simulation (Figure 3d, right panel), the decline in effort in the summer is quite pronounced with the parameter values chosen, so that metabolic costs outweigh foraging gains and the animal loses weight for some time. Notable in this simulation is that, compared with the situation without seasonal adjustment of food availability there is a markedly higher e* early in the season (compare early e* in Figure 3c,d) despite identical parameter values for spring in the two simulations. While the biological interpretation of this result is that animals forage in anticipation of worsening conditions, the mathematical explanation lies in the fact that the DPM proceeds backward in time so that the size-fitness relationship (the basis for calculating e*) in the spring has been influenced by prior optimal choices in the summer period.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTSDISCUSSIONREFERENCES |
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The optimal foraging behavior calculated by a DPM represents a long-term average that provides the individual with the maximum fitness in a predictable environment. My model shows how the incorporation of biological information for a specific organism can profoundly influence the predictions of a dynamic programming model of behavior. When temperature- and size-dependent foraging constraints typical for juvenile salmon are added, the optimal effort changes from the gradual seasonal increase in the simpler models (Clark, 1994
, and
Figure 3a in this study). A
spring and fall peak in foraging effort
(Figure 3d) emerge when
accounting for predictable seasonal trends in growth potential of the
organism.
The use of parameters estimated from data on salmon, however, does not
change a core prediction from other models
(Clark, 1994;
Grand, 1999): animals with
greater fitness assets should take fewer risks when foraging than animals with
small asset values. It is instructive to examine what causes the
asset-protection effect in the various models. In Clark's
(1994) original model,
foraging gains were fixed in absolute terms, so that the ratio of reward to
assets declined with size, leading to diminishing rewards with size even at a
linear fitness function. In a model tailored to juvenile salmon by Grand
(1999), rewards per unit
predation exposure were added relative to body weight (i.e., a fixed percent
increase). Therefore an asymptotic shape of the fitness function similar to
the one used in this study was necessary to cause an asset-protection effect.
Finally in my model, size-dependent constraints on growth rate cause the
rewards per predation exposure to decrease with body size. This by itself
causes asset-protection behavior, which is enhanced by an asymptotic fitness
function. Thus when considering whether asset-protection behavior can be
expected for a target organism, one should consider which dynamics of foraging
rewards and terminal fitness capture the biology of the organism in the most
realistic way. My study shows that the finer details of food acquisition and
resulting growth can matter considerably in a dynamic foraging model.
That asset-protection may be more than a theoretical construct with
intuitive appeal is shown by several experimental studies on juvenile salmon
in which a negative correlation between body size and risk taking was apparent
(Grand and Dill, 1997;
Grant and Noakes, 1987;
Mikheev et al., 1994;
Reinhardt and Healey, 1997,
1999; but see
Johnsson, 1993). Similar
size-dependent risk taking patterns have also been reported for stream
invertebrates (Culp and Scrimgeour,
1993). Dynamic optimization may help to explain these observations
of size-dependent foraging behavior under predation.
In addition to the prediction of lower risk taking in bigger fish, the model makes a series of testable predictions regarding salmon foraging behavior under predation risk in relation to body size and season:
- Increasing predation risk should result in lower individual growth rates.
In field and laboratory experiments
(Reinhardt and Healey, 1997,
Reinhardt et al., 2001), the
mean growth rate of groups of salmon fry was reduced in the presence of a
predation threat. Werner and Anholt
(1996) observed a similar
effect of predation risk on growth in frog larvae. A theoretical exploration
of how predation risk may influence growth of prey and population-level
predation rate in behaviorally flexible animals is given by Abrams and Matsuda
(1993) and Clark
(1994).
- In the fall, large juvenile salmon should cease foraging earlier than small
fish. Coho salmon fry are believed to stop foraging completely in the fall in
October—November (Sandercock,
1991) at about the time predicted by my model when seasonal
temperatures are considered. However, in line with the model predictions, some
field observations suggest that under favorable conditions smaller fry
continue foraging in the winter (Bratty,
1999). Alternative timing of the future out-migration to the ocean
(discussed in more detail below) can also influence the intensity of salmon
fry foraging in the fall (e.g., Thorpe et
al., 1992). Therefore, a diagnostic test of Prediction 2 has to
involve fish that are followed through to assure only individuals migrating at
the same age are considered together.
- Foraging activity should anticipate seasonal trends in growth conditions
(see also Clark, 1994). It is
well established that salmonids follow seasonal trends in food availability,
for example by stopping foraging activity or becoming nocturnal when growth
potential is low (Metcalfe et al.,
1999; Sandercock,
1991). However, my model also predicts changes in foraging in
anticipation of changes in growth conditions. For salmon, the prediction from
my model is that individuals adapted to a predictably changing stream should
show different seasonal changes in behavior than individuals from an
unchanging stream. Salmon adapted to predictably changing streams should be
more willing to accept predation risk before the change under otherwise equal
conditions (temperature, body size, food reward offered). Bull et al.
(1996) developed a dynamic
optimal foraging model for Atlantic salmon fry in the winter and showed
experimentally that motivation to feed depended on the period in the winter
when the experiment was carried out. As predicted by their model, the animals'
feeding motivation was matched to anticipated energy requirements in the
spring. Swift (1955) showed a
period of lower feeding motivation in sub-adult brown trout in May/June,
independent of temperature. Simpson et al.
(1996) observed a decline in
feeding motivation in juvenile Atlantic salmon in June/July under a constant
feeding regime and argued that this pattern represented an adaptation to
seasonal cycles in food production in the wild.
Some limitations of my model need to be considered. First, the model does
not account for possible competitive interactions among juveniles or
density-dependent survival rates in juvenile salmonids
(Elliott, 1990;
Sandercock, 1991). Designing a
game-dynamic DPM that simulates territorial conflict was beyond the scope of
this study. However, I suspect that simulating direct competitive interactions
among salmon in my model would have increased optimal foraging effort early in
the spring. This is because territorial dominance appears to be decided early
in the spring (Elliott, 1990)
with territory holders enjoying a subsequent growth advantage over nonholders,
which will result in out-migration and high mortality of the latter
(Elliott, 1990;
Sandercock, 1991). The outcome
of territorial conflicts in juvenile salmon is partly determined by body size
(Abbott et al., 1985;
Cutts et al., 1999) so that
salmon fry should show increased foraging effort early in the season to obtain
a competitive size.
Second, I assumed that susceptibility to predation was independent of body
size of the fish. Size-dependent predation risk in DPMs is discussed for
example by Clark (1994) and
Grand (1999). Increasing
probability of capture by a predator with size of the prey (positive size
dependence) leads to a stronger asset-protection effect. Conversely, if
capture risk decreases with body size, foragers gain an extra advantage of
growing, which should lead to a diminished effect of asset protection. Both,
positive and negative size-dependence of susceptibility of fish to capture by
natural predators have been reported in the literature (for juvenile coho
e.g., Healey and Reinhardt,
1995; Wood and Hand,
1985). The sign of size-dependence apparently depends on the type
of predator (Sogard, 1997).
Juvenile coho salmon are hunted by a wide variety of bird and fish predators
(Sandercock, 1991) and, as
they outgrow the prey size range of one predator, probably become available to
a different one. This makes it difficult to generate a prediction of a
relationship between size and susceptibility to predation over the whole
season and range of juvenile salmon body sizes. However, because predation
risk scales with foraging time in my model, I can estimate by how much
predation risk would have to decrease for a larger fish to make up for its
lower growth potential. For example, at 14°C a salmon of 0.5 g would take
about 12 days of unrestricted feeding to double its weight whereas a 5 g
salmon would need 24 days. Therefore, making a 5 g salmon half as susceptible
to predation as a 0.5 g salmon in my model would approximately neutralize its
metabolic disadvantage. However given the asymptotic shape of the fitness
function, asset-protection behavior would still be predicted.
Third, I did not incorporate into my model the effect of alternative future
life history trajectories. Coho salmon are known to forage in their natal
streams for two seasons before migrating to sea if growth conditions are poor
(Holtby and Hartman, 1982;
Randall et al., 1987). In
Atlantic salmon, which show the same pattern, small individuals that delay the
ocean migration will stop foraging in the fall of their first year, whereas
fish that grow above a certain size threshold in their first summer continue
to feed through the winter to migrate out in their second spring. Detailed
observations of this kind are lacking for coho salmon, but Grand
(1999) developed a DPM of
juvenile coho foraging that showed likely behavioral effects of different
options regarding the age at migration. Her model suggests that, as the
feeding season progresses, it becomes more advantageous for small fish to
reduce foraging effort and delay smolting for a year than to continue to
increase foraging under risk. In line with her prediction, experimental
studies on juvenile salmon (Reinhardt and
Healey, 1999; Thorpe et al.,
1992) showed a drop in risk taking of small (1-2 g) salmon fry
between summer and fall.
Although my model is tailored to reflect juvenile salmon foraging, my
findings should apply to other organisms, especially those that (1) undergo
profound changes in body size over the modeled time frame, (2) are
poikilotherms, and (3) encounter pronounced seasonal patterns in feeding
opportunities. The first point arises because animals changing in size or
shape are likely to change in growth physiology or foraging mode so that the
energy gain per unit foraging time changes. Second, foraging by other
poikilotherms should be treated with models that account for
temperature-induced changes in growth physiology. Finally, as previously
pointed out by Clark (1994),
the prediction of anticipatory foraging should hold for any organism adapted
to environments with pronounced, yet predictable, fluctuations in growth
conditions. The asset-protection principle and the "anticipatory
foraging effect" are intuitive and sometimes readily visible (e.g., in
food storing animals); I think they merit wider attention in foraging theory
and experimentation.
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ACKNOWLEDGEMENTS |
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This study profited from help by Colin Clark and Ron Ydenberg, who taught me dynamic computer modeling, Robin Liley, Tony Pitcher, Larry Dill, Lee Gass, and particularly Mike Healey gave valuable input at the program development and manuscript stage. Peter Bednekoff's comments improved the final manuscript. Financial support was provided by the Canada Department of Foreign Affairs and International Trade, Canada Award Program.
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