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Individual Decisions and the Distribution of Predators in a Patchy Environment

Carlos Bernstein, Alejandro Kacelnik and John R. Krebs
Journal of Animal Ecology
Vol. 57, No. 3 (Oct., 1988), pp. 1007-1026
DOI: 10.2307/5108
Stable URL: http://www.jstor.org/stable/5108
Page Count: 20
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Individual Decisions and the Distribution of Predators in a Patchy Environment
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Abstract

(1) The theoretical distribution of non-omniscient predators in a heterogeneous multi-patch environment is studied by numerical simulation. Although various relative densities are explored, we mostly attend to environments where prey density is approximately one order of magnitude higher than predator density. (2) Predators are assumed to follow the rule of abandoning their current patch when local capture rate is lower than estimated capture rate in the environment as a whole. This rule was chosen because it is known to maximize long-term capture rate in many foraging situations. For convenience, we assume that after abandoning a patch, predators arrive at random at any patch in the environment. (3) Predators detect precisely the capture rate in their current patch but `learn' about the environmental average. Learning is simulated using a linear operator model which estimates global capture rate as a weighted average of past and current experienced capture rate. Following a common approach is psychological models of simple learning, the relative weight of past and present capture rate is controlled by a parameter denominated the `memory factor'. (4) In the absence of depletion, the predators distribute themselves close to the predictions of the Ideal Free Distribution model. This result indicates that the IFD prediction is not dependent on assuming omniscient predation, but instead can be jointly derived from reasonable assumptions about learning and optimal foraging at individual level. (5) When the environment depletes as a consequence of predation, cumulative prey mortality can be positively or negatively density-dependent, depending on the interaction between predator efficiency and the velocity of the learning process as determined by the memory factor. (6) The learning model converges towards the IFD faster than `omniscient' variants in which the predators, instead of using a learned estimate and migrating `blindly' to any patch, use the true environmental average for the migration decision and migrate only to patches with capture rate higher than their current capture rate. (7) Both spatial and temporal between-patch variance in prey density affect the behaviour of our model.

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