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Asymptotic analysis of first passage processes : with applications to animal movement

University of British Columbia

Understanding the dependence of animal behaviour on resource distribution is a central problem in mathematical ecology. In a habitat, the distribution of food resources and their accessibility from an animal's location together with the search time involved in foraging, all govern the survival of a species. In this work, we investigate various scenarios that affect foraging habits of animals in a landscape. The work, unlike previous studies, analyzes the first passage quantities on complex prey-predator distributions in a given domain in order to derive simple analytical problems that can readily be solved numerically. We use standard stochastic models such as the Kolmogorov equations of first passage times and splitting probability, to model both the foraging time of a predator and the chances of survival of prey on a landscape with prey and predator patches. We obtain an asymptotic solution to these Kolmogorov equations using a hybrid asymptotic-numerical singular perturbation technique that utilizes the fact that the ratio of the size of prey patches is small in comparison to the overall landscape. Results from this hybrid approach are then verified by undertaking full numerical simulations of the governing partial differential equations of the first passage processes. By using this hybrid formulation we identify the underlying parameters that affect the search time of a predator and splitting probability of prey, which are otherwise difficult to ascertain using only numerical tools. This analytical understanding of how parameters influence the first passage processes is a key step in quantifying foraging behavior in model ecological systems.

Text

2011-08-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/36961

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/