Abstract
We study a general predator—prey system in a spatially heterogeneous environment. The predation process, which occurs on a behavioural time-scale, is much faster than the other processes (reproduction, natural mortality and migrations) occurring on the population dynamics time-scale. We show that, taking account of this difference in time-scales, and assuming that the prey have a refuge, the dynamics of the system on a slow time-scale become donor-controlled. Even though predators may control the prey density locally and on a behavioural fast time-scale, nevertheless, both globally and on a slow time-scale, the prey dynamics are independent of predator density: the presence of predators generates a constant prey mortality. In other words, in heterogeneous environments, the prey population dynamics depend in a switch-like manner on the presence or absence of predators, not on their actual density.
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Poggiale, J.C., Michalski, J. & Arditi, R. Emergence of donor control in patchy predator—prey systems. Bull. Math. Biol. 60, 1149–1166 (1998). https://doi.org/10.1006/S0092-8240(98)90006-4
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DOI: https://doi.org/10.1006/S0092-8240(98)90006-4