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From Individual Movement Rules to Population Level Patterns: The Case of Central-Place Foragers

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Dispersal, Individual Movement and Spatial Ecology

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2071))

Abstract

We consider a model for the dynamics of a consumer-resource population where the foraging behavior of the central-place forager is explicitly modeled as a random walk. The model consists of a discrete map between generations and a partial differential equation within a season. We determine analytically the conditions under which the consumer can stay in the system. We then explore numerically how different assumptions on the foraging strategy affect the stability of the coexistence equilibrium. We find a number of ways in which foraging behavior destabilizes the coexistence equilibrium and leads to population cycles. We also find an instability resembling a flip bifurcation even though the model has compensatory dynamics. This modeling framework can serve in the future to explore the evolution of foraging strategies, thereby complementing previous ecological theory of central-place foraging.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave., Ottawa, ON, Canada, K1N6N5

    Hsin-Hua Wei & Frithjof Lutscher

Authors
  1. Hsin-Hua Wei
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  2. Frithjof Lutscher
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Correspondence to Frithjof Lutscher .

Editor information

Editors and Affiliations

  1. Mathematical & Statistical Sciences, University of Alberta, Central Academic Building 632, Edmonton, T6G 2G1, Alberta, Canada

    Mark A. Lewis

  2. Mathematical Institute, Centre for Mathematical Biology, University of Oxford, St. Giles Street 24-29, Oxford, OX1 3LB, United Kingdom

    Philip K. Maini

  3. Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

    Sergei V. Petrovskii

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Wei, HH., Lutscher, F. (2013). From Individual Movement Rules to Population Level Patterns: The Case of Central-Place Foragers. In: Lewis, M., Maini, P., Petrovskii, S. (eds) Dispersal, Individual Movement and Spatial Ecology. Lecture Notes in Mathematics(), vol 2071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35497-7_6

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