A comparison of foraging strategies in a patchy environment 1 Research supported in part by the National Science Foundation via grant DMS 96-25741. 1 (original) (raw)

A comparison of foraging strategies in a patchy environment

Mathematical Biosciences, 1999

In this paper we compare foraging strategies that might be used by predators seeking prey in a patchy environment. The strategies dier in the extent to which predators aggregate in response to prey density. The approach to the comparison is suggested by the idea of evolutionarily stable strategies. A strategy is said to be evolutionarily stable if it cannot be invaded by another strategy. Thus we examine scenarios where a small number of individuals using one strategy are introduced into a situation where a large number of individuals using the other strategy are already present. However, our foraging models do not explicitly incorporate predator population dynamics, so we use net energy uptake as a surrogate for reproductive ®tness. In cases where all of the patches visited by predators sustain prey populations, we ®nd that for any pair of strategies one of them will have a higher net energy uptake than the other whether it is the resident or the introduced strain. However, which one is higher will typically depend on the total predator population, which is determined by the resident strain. If the predators leave prey densities high, the more aggregative strain will have the advantage. If the predators reduce prey densities to low levels the less aggregative strain will have the advantage. In cases where one strain of predators aggregates in response to prey density and the other does not, then there might be patches which do not contain prey but do contain (nonaggregating) predators. In those cases, there is the possibility that whichever strategy is used by the introduced strain will yield a higher energy uptake than that used by the resident strain. This suggests that if some patches are empty of prey then aggregative . 0025-5564/99/$ ± see front matter Ó 1999 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 5 -5 5 6 4 ( 9 9 ) 0 0 0 2 7 -9

A functional response model of a predator population foraging in a patchy habitat

Journal of Animal Ecology, 2006

Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of prey is developed. 3. The model includes the density and the spatial distribution of the prey population, the aggregative response of the predators and their mutual interference. 4. The model provides explicit solutions to a number of scenarios that can be independently combined: the prey has an even, random or clumped distribution, and the predators show a convex, sigmoid, linear or no aggregative response. 5. The model is parameterized with data from an acarine predator-prey system consisting of Phytoseiulus persimis and Tetranychus urticae inhabiting greenhouse cucumbers. 6. The model fits empirical data quite well and much better than if prey and predators were assumed to be evenly distributed among patches, or if the predators were distributed independently of the prey. 7. The analyses show that if the predators do not show an aggregative response it will always be an advantage to the prey to adopt a patchy distribution. On the other hand, if the predators are capable of responding to the distribution of prey, then it will be an advantage to the prey to be evenly distributed when its density is low and switch to a more patchy distribution when its density increases. The effect of mutual interference is negligible unless predator density is very high. 8. The model shows that prey patchiness and predator aggregation in combination can change the functional response at the population level from type II to type III, indicating that these factors may contribute to stabilization of predator-prey dynamics.

Optimal foraging and predator–prey dynamics III

Theoretical Population Biology, 2003

In the previous two articles ( Theor. Popul. Biol. 49 (1996) 265-290; 55 (1999) 111-126), the population dynamics resulting from a two-prey-one-predator system with adaptive predators was studied. In these articles, predators followed the predictions of optimal foraging theory. Analysis of that system was hindered by the incorporation of the logistic description of prey growth. In particular, because prey self-regulation dependence is a strong stabilizing mechanism, the effects of optimal foraging could not be easily separated from the effects of bottom-up control of prey growth on species coexistence. In this article, we analyze two models. The first model assumes the exponential growth of both prey types while the second model assumes the exponential growth of the preferred prey type and the logistic growth of the alternative prey type. This permits the effect of adaptive foraging on two-preypredator food webs to be addressed. We show that optimal foraging reduces apparent competition between the two prey types, promotes species coexistence, and leads to multiple attractors. r

Optimal Foraging and Predator�Prey Dynamics, II

Theoretical Population Biology, 1999

In this paper we consider one-predator two-prey population dynamics described by a control system. We study and compare conditions for permanence of the system for three types of predator feeding behaviors: (i) specialized feeding on the more profitable prey type, (ii) generalized feeding on both prey types, and (iii) optimal foraging behavior. We show that the region of parameter space leading to permanence for optimal foraging behavior is smaller than that for specialized behavior, but larger than that for generalized behavior. This suggests that optimal foraging behavior of predators may promote coexistence in predator prey systems. We also study the effects of the above three feeding behaviors on apparent competition between the two prey types. ] 1999 Academic Press

Optimal Foraging and Predator�Prey Dynamics

Theor Pop Biol, 1996

Continuous cycling of grouped vs. solitary strategy frequencies in a predator-prey model

2004

We present a model of predator and prey grouping strategies using game theory. As predators respond strategically to prey behavior and vice versa, the model is based on a co-evolution approach. Focusing on the ''many eyes-many mouths'' trade-off, this model considers the benefits and costs of being in a group for hunting predators and foraging prey: predators in a group have more hunting success than solitary predators but they have to share the prey captured; prey in a group face a lower risk of predation but greater competition for resources than lone prey. The analysis of the model shows that the intersections of four curves define distinct areas in the parameter space, corresponding to different strategies used by predators and prey at equilibrium. The model predictions are in accordance with empirical evidence that an open habitat encourages group living, and that low risks of predation favor lone prey. Under some conditions, continuous cycling of the relative frequencies of the different strategies may occur. In this situation, the proportions of grouped vs. solitary predators and prey oscillate over time. r

Pattern Formation and the Spatial Scale of Interaction between Predators and Their Prey

Theoretical Population Biology, 1998

We study interactions of predators and prey that are characterized by a scale difference in their use of space. Prey are assumed to occupy patches, forming a metapopulation with low migration among patches. Predators are homogeneously distributed over these patches, due to broad-scale foraging behavior or long-range juvenile dispersal. The predator population thus exerts a globally uniform predation pressure on the prey subpopulations. Under these conditions a nonlinear predator functional response depending on local prey density leads to multiple equilibria that can occur for the same parameter values. These equilibria differ in the fraction of prey patches that are (nearly) empty. Equilibria with a larger fraction of empty prey patches are more stable. The system tends to approach equilibria with a sufficiently high number of empty prey patches, so that local and global population dynamics are stable. If unstable dynamics are observed at all, the fluctuations in local prey density exhibit predictable characteristics. Our main conclusion is that a nonlinear functional response of the predator to local prey density can induce the formation of static patterns in prey density and, hence, lead to stable local and global dynamics. It is shown that these results are sufficiently general to carry over to situations in which prey migration between patches does occur or the spatial domain occupied by the prey population is continuous instead of subdivided into patches.

The advantage of alternative tactics of prey and predators depends on the spatial pattern of prey and social interactions among predators

Population Ecology, 2012

Individual variation in behavioral strategies is ubiquitous in nature. Yet, explaining how this variation is being maintained remains a challenging task. We use a spatially-explicit individual-based simulation model to evaluate the extent to which the efficiency of an alternative spacing tactic of prey and an alternative search tactic of predators are influenced by the spatial pattern of prey, social interactions among predators (i.e., interference and information sharing) and predator density. In response to predation risk, prey individuals can either spread out or aggregate. We demonstrate that if prey is extremely clumped, spreading out may help when predators share information regarding prey locations and when predators shift to area-restricted search following an encounter with prey. However, dispersion is counter-selected when predators interact by interference, especially under high predator density. When predators search for more randomly distributed prey, interference and information sharing similarly affect the relative advantage of spreading out. Under a clumped prey spatial pattern, predators benefit from shifting their search tactic to an area-restricted search following an encounter with prey. This advantage is moderated as predator density increases and when predators interact either by interference or information sharing. Under a more random prey pattern, information sharing may deteriorate the inferior search tactic even more, compared to interference or no interaction among predators. Our simulation clarifies how interactions among searching predators may affect aggregation behavior of prey, the relative success of alternative search tactics and their potential to invade established populations using some other search or spacing tactics.

A predator equalizes rate of capture of a schooling prey in a patchy environment

Behavioural Processes, 2017

Prey individuals are often distributed heterogeneously in the environment, and their abundances and relative availabilities vary among patches. A foraging predator should maximize energetic gains by selectively choosing patches with higher prey density. However, catching behaviorally responsive and group-forming prey in patchy environments can be a challenge for predators. First, they have to identify the profitable patches, and second, they must manage the prey's sophisticated anti-predator behavior. Thus, the forager and its prey have to continuously adjust their behavior to that of their opponent. Given these conditions, the foraging predator's behavior should be dynamic with time in terms of foraging effort and prey capture rates across different patches. Theoretically, the allocation of its time among patches of behaviorally responsive prey should be such that it equalizes its prey capture rates across patches through time. We tested this prediction in a model system containing a predator (little egret) and group-forming prey (common gold fish) in two sets of experiments in which (1) patches (pools) contained equal numbers of prey, or in which (2) patches contained unequal densities of prey. The egret equalized the prey capture rate through time in both equal and different density experiments.

Patch Choice under Predation Hazard

Theoretical Population Biology, 2000

In this paper we study optimal animal movement in heterogeneous environments consisting of several food patches in which animals trade-off energy gain versus predation risk. We derive a myopic optimization rule describing optimal animal movements by fitness maximization assuming an animal state is described by a single quantity (such as weight, size, or energy reserves). This rule predicts a critical state at which an animal should switch from a more dangerous and more profitable patch to a less dangerous and less profitable patch. Qualitatively, there are two types of behavior: either the animal switches from one patch to another and stays in the new patch for some time before it switches again, or the animal switches between two patches instantaneously. The former case happens if animal state growth is positive in all patches, while the latter case happens if animal state growth is negative in one patch. In particular, this happens if one patch is a refuge. We consider in detail two special cases. The first one assumes a linear animal state growth while the second assumes a saturating animal state growth described by the von Bertalanffy curve. For the first model the proportion of time spent in the more profitable and more risky patch increases with profitability of this patch when state growth is positive in both patches. On contrary, if state growth is negative in the less profitable and safer patch, animals spend proportionally less time in the more profitable and more risky patch as its profitability increases. As a function of the predation risk in the more profitable patch the time spent there proportionally decreases. When animal state growth is described by the saturating curve, time spent in the more risky patch is a hump-shaped curve if state growth is positive in both patches. Our results extend the +Â f rule, which predicts that animals should behave in such a way as to minimize mortality risk to resource intake ratio. ]

A comparison of foraging strategies in a patchy environment 1 Research supported in part by the National Science Foundation via grant DMS 96-25741. 1 (original) (raw)

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