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Behavioral Ecology Vol. 13 No. 2: 280-290
© 2002 International Society for Behavioral Ecology
Alternative forms of competition and predation dramatically affect habitat selection under foraging—predation-risk trade-offs
Department of Zoology, University of British Columbia, 6270 University Boulevard, Vancouver, BC V6T 1Z4, Canada
Address correspondence to T.C. Grand, 108 Roe Drive, Port Moody, BC V3H 3M8, Canada. E-mail: tgrand{at}sfu.ca .
Received 30 December 2000; revised 7 May 2001; accepted 31 May 2001.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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Habitat selection under foraging—predation-risk trade-offs has been a frequent topic of interest to theoretical behavioral and evolutionary ecologists. However, most habitat selection models assume that individuals compete exploitatively for resources and that predation is either density independent or diluted completely by competitor number, despite empirical evidence that other forms of competition and predation also occur in nature. I developed an individual-based model for studying the effects of alternative forms of competition and predation on the process of habitat selection under foraging—predation-risk trade-offs. To make the model more relevant to natural populations, I assumed that individuals vary continuously in traits related to competitive ability and vulnerability to predation and allowed resources and predators to be distributed across more than two habitats. The results of my investigation demonstrate that the predicted pattern of habitat selection can be affected dramatically by the form predation is assumed to take. When predation is density dependent or frequency dependent, individuals will tend to be distributed across habitats according to their absolute vulnerability to predation. In contrast, when predation is density dependent or vulnerability dependent, individuals will tend to segregate by competitive ability. Whether one assumes that individuals compete for resources via exploitation or interference also influences the predicted pattern of habitat selection. In general, interference competition results in a more even distribution of competitors across habitats.
Key words: competition, foraging, habitat selection, predation, predation risk, trade-offs.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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The process of habitat selection frequently requires individuals to choose among habitats that differ in growth potential and mortality risk due to predation. When the habitat that provides the highest rate of energetic gain is also the most dangerous, habitat selection will reflect a compromise between the conflicting demands of growth and survival (see Lima and Dill, 1990
, on the
ubiquity of this trade-off). In many cases, an individual's best resolution to
this conflict will be influenced by the presence of conspecifics, who may, for
example, reduce the growth potential in a habitat via competition for
resources (Abrahams and Dill,
1989; Grand and Dill,
1997). Habitat selection under foraging—predation-risk
trade-offs has been a frequent topic of investigation for behavioral and
evolutionary ecologists (for reviews, see
Brown, 1998;
Lima, 1998;
Lima and Dill, 1990). Much of
this work, however, is limited in its applicability to natural populations, as
only a single, common form of competition or predation is considered, and
individual variation in competitive ability and vulnerability to predation is
ignored.
Most theoretical studies of habitat selection under
foraging—predation-risk trade-offs assume that individuals compete
exploitatively (or "scramble";
Milinski and Parker, 1991) for
resources (Brown, 1998;
Grand and Dill, 1999;
Moody et al., 1996; but see
Hugie and Dill, 1994) and that
predation is either density independent
(Abrahams and Dill, 1989) or
diluted completely by competitor number
(Hugie and Dill, 1994;
Moody et al., 1996; but see
Grand and Dill, 1999, for a
treatment of variation in the strength of risk dilution). Empirical evidence,
however, suggests that other forms of competition and predation are more
common in nature (see Sutherland,
1996; Endler, 1991,
respectively, for reviews). For example, pairs of competitors might engage in
contest competition over individual prey items or defend territories against
all others (see Milinski and Parker,
1991). Predators might behave as optimal foragers
(Stephens and Krebs, 1986),
preferentially attacking common prey phenotypes or those whose morphology
renders them particularly vulnerable to capture. Furthermore, in contrast to
the continuous variation that is typically observed in traits related to
competitive ability and vulnerability to predation (e.g., body size;
Grand and Dill, 1997;
antipredator armor; Grand,
2000), most models of habitat selection under
foraging—predation-risk trade-offs assume that competitors are identical
(Moody et al., 1996) or belong
to one of two discrete classes of phenotypes
(Brown, 1998;
Grand and Dill, 1999).
I developed a framework for studying the effects of alternative forms of
competition and predation on the process of habitat selection under
foraging—predation-risk trade-offs. As done for many other models of
this sort, I based this framework on Fretwell and Lucas's
(1970) theory of ideal free
distributions. To incorporate continuous variation in traits related to
competitive ability and vulnerability to predation, I used an individual-based
simulation approach. I considered two forms of competition, exploitative and
interference, and four forms of predation, density independent, density
dependent (i.e., risk is diluted by competitor number), vulnerability
dependent (more vulnerable phenotypes experience an increased risk of
predation), and frequency dependent (rare phenotypes experience a reduced risk
of predation). For simplicity, I focused primarily on an environment
containing two habitats. However, the framework allows for consideration of
multiple habitats and thus exploration of habitat selection patterns across
gradients of resource availability and predation risk (see
Shenbrot and Krasnov, 2000,
for further discussion of habitat selection across environmental
gradients).
I begin by describing the general pattern of habitat selection predicted under each of the eight competition-predation scenarios modeled, demonstrating that the assumed forms of competition and predation result in substantially different predicted patterns of habitat selection. I then consider the effects of the number of habitats available and the steepness of the resource and predation gradients on the predicted patterns of habitat selection. Where possible, I compare the predictions of this model to those of existing models, demonstrating the utility of using a single modeling framework to address the same question under different ecological scenarios.
The model
I modeled the distribution of a relatively large number of individuals
(i = 1 to NT, the total population size)
differing in traits related to competitive ability, ki
(i.e., their ability to compete for and acquire the resources required for
growth) and vulnerability to predation, vi (probability of
capture given attack). Individuals of high vulnerability are more likely to be
captured when attacked by a predator than are individuals of low
vulnerability. For simplicity, I assumed that ki and
vi are independent of habitat, competitor density (see
below), and one another and that both remain constant over an individual's
lifetime.
I considered an environment containing a number of habitats (j =
1, 2,...) differing in resource availability, Rj
(energy/time), and inherent riskiness
(Hugie and Dill, 1994),
Bj (probability of attack/time). Riskiness might be
expected to differ between habitats due to differences in predator abundance,
structural complexity, or the availability of refuge sites (see
Lima and Dill, 1990).
Throughout, I assumed that resources are continually renewing, and therefore
nondepleting, and that the rate of energy gain per unit of competitive ability
is inversely related to the sum of the competitive abilities in a habitat (see
below).
I used minimum and maximum values of Rj and Bj to create a gradient of resource availability and riskiness across habitats and assumed both gradients to be linear and inversely correlated. Thus, during habitat selection, individuals face a trade-off between energy intake (which increases reproductive output) and survival. For simplicity, I also assumed that Rj and Bj remain constant over time. Thus, I did not consider the dynamics of either the resources or the predator population. For a summary of all constants and variables used in the model, see Table 1.
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To compare the effects of different forms of competition and predation on
patterns of habitat selection, I used an individual-based simulation approach
(see Huston et al., 1988).
Each simulation begins by (1) specifying the form that competition and
predation will take (see below), (2) choosing minimum and maximum values of
resource availability and riskiness in the environment, (3) specifying the
population size and the number of habitats present, and (4) specifying the
minimum and maximum competitive abilities and vulnerabilities to predation
present in the population. Rj and Bj
are then calculated for all habitats (see above) and competitive abilities and
vulnerabilities are randomly assigned to all individuals (within the ranges
specified), resulting in a uniform distribution of the two continuous traits.
Individuals are randomly assigned to a habitat and fitness of all individuals
in their chosen habitat calculated (see details below). The fitness of each
individual in all other habitats is then determined in turn (i.e., assuming
all other individuals remain in their original habitat), and the individual
that can increase its fitness most by switching habitats is moved to the
habitat where its fitness is greatest. The simulation continues to move
individuals between habitats according to the above rule until no individual
can increase its fitness further. By definition, the resultant distribution is
the equilibrium distribution of individuals across habitats. This distribution
is always stable to small, local perturbations.
Individuals compete for resources via (1) exploitative or (2) interference competition and are subject to predation which is (1) density independent, (2) density dependent, (3) vulnerability dependent (more vulnerable phenotypes experience an increased probability of capture), or (4) frequency dependent (rare phenotypes experience a reduced probability of capture).
Expected fitness, wij, of the ith individual
in the jth habitat is the product of expected energy intake,
eij, and expected survival, sij, in
that habitat divided by the energetic cost of producing a single offspring,
. For simplicity, I assume that all energy acquired is available to be
translated directly into offspring (see also
Grand and Dill, 1999), that
there is no upper limit to the number of offspring that an individual can
produce, and that is identical for all individuals in all habitats.
Thus,
 | (1) |
Under exploitative competition, individuals do not interact directly with
one another while acquiring resources, but scramble for as large a share as
possible (see Grant, 1993;
Milinski and Parker, 1991).
Consequently, all resources are used and divided among all individuals within
the habitat according to their relative competitive ability (see
Parker and Sutherland, 1986;
Sutherland and Parker, 1985).
Thus,
 | (2) |
kij is the sum of
competitive abilities of all individuals in the jth habitat.
In contrast, under interference competition, direct interactions between
individuals during resource acquisition are common
(Sutherland, 1996). In this
case,
 | (3) |
).
An individual's probability of survival in habitat j depends on
both its probability of being attacked by a predator in that habitat,
pijatt, and its probability of being captured
given an attack, vi. Thus,
 | (4) |
When prey forage solitarily or predators are capable of capturing entire
foraging groups in a single attack, an individual's probability of being
attacked may be density independent, and
 | (5) |
) or confuse (Milinski and
Heller, 1978) them, or because, after the first predatory attack,
all surviving members escape, an individual's risk of being attacked will be
density dependent:
 | (6) |
) of
predation risk is complete. Note that Equation 6 assumes that predators are
equally likely to attack individuals in large and small groups (see
Turner and Pitcher, 1986, for
discussion of relationship between group size and predator attack rate).
In some cases, an individual's relative vulnerability may influence its
probability of attack such that individuals whose morphology renders them
particularly vulnerable are preferentially attacked (i.e., if predators are
optimal foragers; Stephens and Krebs,
1986). Such vulnerability-dependent predation might be expected to
occur if attacking less vulnerable prey imposes significant costs on the
predator (e.g., damage caused by antipredator morphology such as spines or
chemical repellents). When predation is vulnerability-dependent,
 | (7) |
vij), the lower its probability of being attacked
by the predator.
Alternatively, if prey detection relies on the formation of a search image
(e.g., Endler, 1988) or the
skills required to capture prey of different phenotype interfere with one
another (e.g., cruising vs. ambush predation; see also
Endler, 1991), predators might
be expected to preferentially attack common phenotypes. Under
frequency-dependent predation (or "apostatic selection"; see
Endler, 1991):
 | (8) |
i is a coefficient that scales the reduction in
attack probability of the ith individual. i
depends on the discrimination abilities of the predator and the number of
other individuals who are perceived by the predator as being of similar
vulnerability. Individuals are grouped into bins, with individuals of similar
vulnerability. Each bin represents an equal proportion of the complete range
of vulnerability values in the population. When predator discriminations
abilities are good, many bins exist. When predator discrimination abilities
are poor, only a few bins exist. Bins are ranked according to frequency; the
bin with the highest frequency of individuals receives a rank of 1. Thus,
 | (9) |
i is the rank of the bin in which individual
i has been grouped. When discrimination abilities are poor (i.e., the
predator sees only one category of prey), all individuals are perceived as
being equally vulnerable to predation and i = 1 for
i = 1 to NT. When predator discrimination
abilities are good (i.e., the predator sees 10 categories of prey),
individuals of the most common phenotype will not experience any reduction in
attack probability (i.e., i = 1), while individuals
of the least common phenotype will have their probability of attack reduced,
in this example, by 90% (i.e., i = 0.1). Below, I describe the general patterns of habitat selection predicted by the model under the eight competition—predation scenarios outlined above. Although the model has been formulated to allow for multiple habitats, for clarity of presentation, I focus primarily on the results for a two-habitat environment (but see Figure 4). Unless otherwise noted, general patterns of habitat selection in multihabitat environments do not differ qualitatively from the simple results presented (see "Habitat Number"). I then explore the effects of steepness of the resource and predation gradients on the predicted patterns of habitat selection.
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I conducted sensitivity analyses on each of the model's parameters by
systematically varying the value of one parameter while holding all others
constant. As suggested by Gladstein et al.
(1991) and Houston et al.
(1992) (for dynamic
programming models, specifically, but also simulation models in general), I
report the range of values over which qualitatively similar results were
obtained (see Table 1).
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RESULTS |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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General patterns
Exploitative competition
When individuals compete exploitatively for resources and predation is independent of the density of competitors in a habitat, individuals tend to segregate across habitats according to their relative vulnerability to predation (Figure 1a). Individuals whose morphology renders them least susceptible to capture given an attack occupy the more productive but riskier habitat. This is because the increased risk of predation associated with that habitat is offset by increased growth for them, but not for their more vulnerable conspecifics. Such segregation by vulnerability is a common prediction of habitat selection models that consider both competition and predation, although here the pattern is generated by absolute differences in vulnerability (which are independent of habitat), rather than differences in the ratio of vulnerabilities across habitats (Grand and Dill, 1999
) or interphenotypic trade-offs between competitive ability
and vulnerability to predation (Brown,
1998). As in Grand and Dill
(1999), the predicted pattern
of habitat selection is independent of competitive ability (but see
"Predation Gradient" below).
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In contrast, when predation is density dependent (i.e., predation is
completely diluted by competitor number), the pattern of habitat selection is
independent of relative vulnerability to predation. Instead, individuals tend
to be distributed according to competitive ability
(Figure 1b). However, rather
than being strictly segregated across habitats, as in the case of
density-independent predation described above, some phenotypes are predicted
to use a mix of habitats. Individuals of the highest competitive ability are
found only in the risky, more productive habitat (i.e., they behave
selectively; Rosenzweig,
1981), whereas individuals of lower competitive ability are found
in both risky and safe habitats (i.e., they behave opportunistically;
Rosenzweig, 1981).
Density-dependent predation also tends to result in a slight increase in the
number of individuals using the risky habitat (see
Table 2). These results are
similar to that predicted by the model of Grand and Dill
(1999), who found that the
tendency of competitors to aggregate in the risky, more productive habitat
depended on the strength of risk dilution (among other things).
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When an individual's probability of attack depends not on its absolute vulnerability to predation (as above), but on its vulnerability relative to that of all other individuals in the habitat, individuals tend to be distributed according to competitive ability (Figure 1c). As in the case of density-dependent predation, vulnerability-dependent predation results in the best competitors using only the risky, most productive habitats, while all other phenotypes are found in both risky and safe habitats. The competitive ability of the poorest competitors using the selective strategy, however, is slightly higher than that predicted by the density-dependent scenario, although densities in the risky habitat are similar under the two scenarios (see Table 2).
When rare phenotypes experience a reduced risk of predation, segregation by vulnerability to predation once again occurs (Figure 1d). However, unlike the single segregation boundary which characterized the density-independent scenario (Figure 1a), multiple segregation boundaries are predicted. That is, although groups of similarly vulnerable individuals will tend to occur in the same habitat, the risky and safe habitats will not be populated by the least and most vulnerable individuals, respectively. Typically, individuals of the most rare phenotype will experience a sufficient reduction in attack probability as to make the risky, more productive habitat profitable. When this occurs, groups of individuals with similarly high vulnerability will join their less vulnerable counterparts in the high-risk—high-growth habitat. Unlike the three previous forms of predation, under frequency-dependent predation, the predicted pattern of habitat selection is highly dependent on starting conditions (for alternative outcomes, see Figure 2), in particular, the distribution of vulnerability phenotypes in the population and the habitat to which they were initially (and randomly) assigned. At least for the parameter values illustrated in Figures 1 and 2, frequency-dependent predation tends to result in a substantial increase in the number of individuals using the risky, more productive habitat (see Table 2), although the outcome appears to be more variable than those for the other predation scenarios considered (compare SEs in Table 2). For an ecologist collecting data on associations between habitat and phenotype, it may appear that individuals of different vulnerability are distributed randomly across habitats, when, in fact, according to the predictions of this model, frequency-dependent predation is structuring the spatial distribution of the population.
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Interference competition
In general, the patterns of habitat selection predicted by the model under
interference competition do not differ substantially from those predicted when
competition is exploitative (Figure
3). In all cases, the principal effect of interference competition
is to reduce the number of individuals using the risky, more productive
habitat (Table 2), making the
distribution of individuals across habitats more even. A similar effect has
been reported by Hugie and Dill
(1994) for predators in a
tri-trophic habitat selection game. The effect of interference competition is
most pronounced when individuals are distributed across habitats according to
competitive ability (e.g., under density- and vulnerability-dependent
predation; Figure 3b,c), and it
results in an increase in the competitive ability of the poorest competitors
using only the risky habitat. This is because the effects of interference
competition vary with competitive ability (i.e., poor competitors suffer a
proportionally greater reduction in energy acquisition) and only for the best
competitors is the substantial predation risk associated with that habitat
offset by high rates of energy gain.
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When individuals are distributed across habitats according to vulnerability to predation (e.g., under density-independent and frequency-dependent predation; Figures 3a,d), interference competition results in a reduction in the vulnerability of the least vulnerable individuals using the risky, more productive habitat. Again, this occurs because reduced growth in the risky habitat no longer balances the risk of predation experienced there by the individuals most susceptible to predation. Once again, specifics of the pattern of habitat selection expected under frequency-dependent predation depend on the distribution of phenotypes within the population and the habitat to which those individuals were assigned at the start of the simulation (see Figure 2).
Habitat number
The general patterns of habitat selection described above remain
qualitatively similar (within the range of parameter values described in
Table 1) for environments
characterized by three, four, or five habitats. That is, individuals remain
distributed according to vulnerability to predation under density-independent
and frequency-dependent predation (Figure
4a,c,d) and according to competitive ability under
density-(Figure 4b) and
vulnerability-dependent predation. When the number of habitats exceeds five,
however, patterns become less clear, in particular, for scenarios in which
habitat selection is characterized by segregation by competitive ability. Only
by increasing population size significantly (more than 1000 individuals) and
essentially removing the variation in competitive ability and vulnerability to
predation do patterns once again emerge. These results suggest that in order
for patterns like those described above to be evident along the environmental
gradients typical of many natural environments, population sizes will need to
be relatively large.
In environments with few habitats, however, the trait values of boundary phenotypes (e.g., the vulnerability value which separates risky and safe habitat occupants in Figure 1a) and the strategy (i.e., opportunistic or selective) of a particular phenotype may vary with habitat number. This occurs primarily as a consequence of changes in the densities of individuals in the riskiest and safest habitats with the addition of habitats of intermediate riskiness (cf. Tables 2 and 3). For example, when competition is exploitative and predation is density independent, the vulnerability of the least vulnerable individuals using the safest habitat increases with habitat number (cf. Figures 1a and 4a). When competition is exploitative and predation is density dependent, the best competitors switch from using only the riskier of two habitats (Figure 1b) to the two riskiest of three habitats (Figure 4b). Poorer competitors continue to be opportunistic, using all habitats, regardless of habitat number. When predation is frequency dependent, the most vulnerable members of the population tend to avoid the riskiest habitat (see Figure 4c, d), although which of the safer habitats is chosen depends once again on initial conditions (see above). As for the two-habitat scenario (Figures 1d and 2), the least vulnerable individuals are always found in the riskiest habitat.
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Steepness of environmental gradients
The general patterns of habitat selection outlined above are independent of
the steepness of both resource availability and predation risk gradients (or,
in the two-habitat case, the absolute difference in resource availability and
predation risk between them). Environmental gradients do, however, tend to
influence the trait values of boundary phenotypes.
Resource gradient
When predation risk is density independent, the principle effect of
increasing the steepness of the resource gradient is an increase in the
maximum vulnerability of individuals using the risky, more productive habitat
(Figure 5a-c). This is because,
as the steepness of the resource gradient increases, there is relatively more
food available in the risky habitat; food which now offsets the risk of
predation experienced by individuals of higher vulnerability. Similarly, when
predation risk is density dependent, increasing the availability of resources
in the riskier habitat results in a decrease in the mean competitive ability
of individuals there (Figure
5d-f). Increasing the steepness of the resource gradient simply
increases the carrying capacity of the riskier habitat (and less risky
habitats, in multiple-habitat environments). In both cases, increasing the
steepness of the resource gradient results in an increase in the density of
competitors using the risky, more productive habitat.
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Predation gradient
When competition is exploitative and predation is density independent,
increasing the predation gradient primarily results in a decrease in the mean
vulnerability of individuals using the risky, more productive habitat
(Figure 6a-c). This is because,
as predation risk increases in the riskier habitat, only individuals of
relatively low vulnerability can continue to accept this risk. When the
predation gradient is extremely shallow (i.e., habitat differences in
riskiness are only slight), both vulnerability and competitive ability
interact to produce the pattern of habitat selection
(Figure 6a). Highly vulnerable
individuals are predicted to occur in the risky habitat if they also possess
traits rendering them highly competitive. In contrast, when predation is
density dependent, increasing the predation gradient has no apparent effect on
the predicted pattern of habitat selection.
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min = 0.25, |
DISCUSSION |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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In generating a framework for studying habitat selection under foraging—predation-risk trade-offs by individuals differing in traits related to competitive ability and vulnerability to predation, I have demonstrated that the predicted pattern of habitat selection can be affected dramatically by the form that predation is assumed to take. When predation is density independent (as is frequently assumed) or frequency dependent, individuals will tend to segregate across habitats according to vulnerability to predation. In contrast, when predation is density dependent or vulnerability dependent, segregation by competitive ability will tend to occur. Thus, when competitive ability and vulnerability to predation are determined by different traits, the trait that appears to structure the spatial distribution of a population will depend on the form that predation takes. Whether one assumes that individuals compete for resources via exploitation or interference also influences the predicted pattern of habitat selection, albeit less dramatically than does the form of predation. In general, interference competition results in a more even distribution of competitors across habitats and a simple dampening of the patterns predicted under exploitative competition.
According to the predictions of the model, segregation by vulnerability to
predation can take two forms. When predation is density independent, each
habitat will house a single group of similarly vulnerable individuals, with
the most vulnerable individuals occurring in the safest habitat and the least
vulnerable individuals occurring in the riskiest habitat. Thus, the phenotypic
gradient will mirror the environmental gradient (see Figures
1a and
4a). In contrast, when
predation is frequency dependent, each habitat may house multiple groups of
individuals who differ in their vulnerability to predation, such that the
riskiest habitat may contain individuals of both low and high vulnerability
(see Figures 1d,
2, and
4d). This is because some
highly vulnerable phenotypes, by virtue of their rarity, will experience a
reduced probability of capture by the predator, making the riskier, more
productive habitat the habitat in which fitness is maximized. Thus, under
frequency-dependent predation, the phenotypic gradient will no longer mirror
the environmental gradient. Consequently, depending on the scale at which data
are collected and analyzed, an ecologist studying associations between habitat
and morphology in a population subject to frequency-dependent predation might
conclude that individuals are distributed randomly with respect to phenotype
and that the population's spatial distribution is independent of predation
risk. I know of no other habitat selection models that incorporate such
frequency-dependent predation, despite its presumed importance in the
maintenance of variation in natural populations (see
Endler, 1991). Regardless of
which of the above two forms the pattern of segregation takes, individuals of
similar phenotype will tend to be strict habitat selectors
(Rosenzweig, 1981). That is,
they will all occur in the same habitat type.
In contrast to the effects of frequency-dependent predation, when predation
depends on the density of individuals in a habitat or their relative
vulnerability to predation, individuals will be distributed according to
competitive ability, with only the best competitors occurring in a single
habitat (the riskiest, most productive habitat; see Figures
1b,c and
3b,c). Poorer competitors will
occur in multiple habitats, using an opportunistic strategy
(Rosenzweig, 1981). Taken
together, these results suggest that simply determining whether
phenotype—habitat associations are based on resource acquisition or
antipredator traits and whether phenotypes in a particular population behave
as habitat selectors or habitat opportunists may provide insight into the form
of predation involved in habitat-related foraging—predation-risk
trade-offs.
Empirical studies of habitat selection under foraging—predation-risk
trade-offs often report correlations between phenotype and habitat use.
Frequently, the phenotypic trait of interest is body size. For example,
Sillett and Foster (2000)
observed that small juvenile stickleback (Gasterosteus aculeatus)
tend to spend more time in vegetated habitats than their larger counterparts.
These authors (and authors of similar studies) argue that such data support
the hypothesis that individual differences in antipredator morphology lead to
differences in habitat use, and hence, that individuals are segregated across
habitats according to vulnerability to predation. However, because body size
is sometimes positively correlated with competitive ability (see
Grand, 1997), size-related
habitat selection could also be interpreted as evidence for segregation by
competitive ability. Ideally, researchers interested in determining the form
that competition and predation might take in a particular system would be wise
to choose traits whose ecological function is clear. The three-spined
sticklebacks studied by Sillett and Foster
(2000) would seem to be an
appropriate species in which to test the ideas introduced here. In addition to
differing in body size, individuals also differ in the length of their dorsal
spines and in the number of lateral plates and pelvic girdle components they
possess (Grand, 2000), traits
known to influence susceptibility to vertebrate predators
(Hoogland et al., 1957;
Reimchen, 1994). Simply
quantifying the relationship between antipredator armor and habitat choice
would provide information about whether predation was likely to be density
dependent, density independent, vulnerability dependent, or frequency
dependent.
As is true of most models, my model makes a number of assumptions that may
have influenced the predicted patterns of habitat selection. For example, in
an effort to limit the complexity of the model, I assumed that predation risk
was spatially fixed and that neither the predator populations nor the
population of resources consumed by competitors varied in size over time.
Allowing predators to redistribute themselves according to the distribution of
their prey (i.e., making the model a game between predators and prey; see
Hugie and Dill, 1994;
Sih 1998, for a discussion of
such habitat selection games) might be expected to reduce the tendency of
competitors to aggregate in the risky, more productive habitat when predation
is density dependent (see Hugie and Dill,
1994), although it is unclear how the relationship between
phenotype and habitat choice might change. For simplicity, I also assumed that
neither predators nor competitors satiate and, thus, that the general patterns
of habitat selection predicted by the model are independent of population
size. In reality, there is an upper limit to the rate at which most animals
can process resources, presumably resulting in proportionally greater use of
the risky, more productive habitat when population size is small (see
Brown, 1998; Morris,
1988,
1992). However, changes in
population size will also affect the predation risk experienced by
individuals, in particular, when predation is density, vulnerability, or
frequency dependent, making it difficult to predict how population size might
influence the association between phenotype and habitat. I have also assumed
that the fitness value of energy remains constant over time and is the same
for all competitors, regardless of phenotype. As demonstrated by McNamara and
Houston (1990) and Moody et
al. (1996), however,
relaxation of these assumptions can lead to competitor distributions that
reflect neither the distributions of resources nor the distribution of
predation risk. Finally, I have assumed that individuals have perfect
information about the distributions of resources, competitors, and predators
and that movement between habitats incurs no cost (see
Fretwell and Lucas, 1970).
Incorporating less than perfect information and time or energy costs of
habitat selection would presumably result in a more even distribution of
individuals across habitats (see Abrahams,
1986; Brown,
1998).
To allow for multiple habitats and continuous variation in traits related
to competitive ability and vulnerability to predation, I used an
individual-based simulation approach. Individual-based models (IBMs) are being
used more frequently in ecological studies, in particular for studying the
outcomes of complex, spatially explicit interactions between individuals that
differ phenotypically from one another
(Grimm, 1999;
Huston et al., 1988). Although
IBMs are relatively straightforward to program, they are often more difficult
to interpret than their analytic counterparts, in part because they tend to
have more parameters (which may interact with one another in complex ways),
but also because their predictions are often sensitive to initial conditions
and stochastic events. Typically, one must conduct many experiments, in which
parameter values are changed one at a time, to ensure an understanding of the
results produced (Grimm,
1999). Although I investigated a relatively large range of values
for most parameters (see Table
1), I did not exhaustively investigate the entire parameter space
of the model (with its 10 parameters). Thus, it is possible that beyond the
range of values investigated, other patterns of habitat selection may
emerge.
Unlike previous models of habitat selection under
foraging—predation-risk trade-offs, which typically consider only a
single form of competition (exploitative; but see
Hugie and Dill, 1994;
Sih, 1998) and one or two
forms of predation (density independent and density dependent;
Brown, 1998;
Grand and Dill, 1999;
Hugie and Dill, 1994;
Moody et al., 1996), the model
described here allows for simultaneous consideration of two forms of
competition and four forms of predation, resulting in eight ecological
scenarios available for study. In addition to allowing for the consideration
of ecological interactions not previously studied in this context (e.g.,
vulnerability- or frequency-dependent predation), the common framework
generated makes it relatively easy to compare the patterns of habitat
selection predicted under the various competition-predation scenarios. Using
this framework, it would be relatively straightforward to explore additional
forms of predation (e.g., cannibalism) and competition (e.g.,
kleptoparasitism; see Parker and
Sutherland, 1986) and even other types of ecological interactions
(e.g., intraguild predation; see Holt and
Polis, 1997). Such a framework should be particularly useful for
guiding empirical studies of habitat selection under
foraging—predation-risk trade-offs, as it provides not just a single
hypothesis for testing, but multiple, alternative hypotheses to which data can
be compared.
|
ACKNOWLEDGEMENTS |
|---|
I thank Jenny Boughman for stimulating discussions during the development of the model and Peter Wright for writing a readable introductory guide to programming in Visual Basic 5.0. Mark Abrahams, Jenny Boughman, Bernie Crespi, David Westneat, and an anonymous reviewer provided comments that helped to improve the manuscript. My research was funded by a Natural Sciences and Engineering Research Council (NSERC) Canada Post-Doctoral Fellowship and an NSERC operating grant to D. Schluter.
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REFERENCES |
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