Avoidance behavior in intraguild predation communities: A cross-diffusion model

Daniel Ryan; Robert Stephen Cantrell

doi:10.3934/dcds.2015.35.1641

Article Contents

2015, Volume 35, Issue 4: 1641-1663. Doi: 10.3934/dcds.2015.35.1641

This issue Previous Article Spreading speeds and traveling waves of nonlocal monostable equations in time and space periodic habitats Next Article On principal spectrum points/principal eigenvalues of nonlocal dispersal operators and applications

Avoidance behavior in intraguild predation communities: A cross-diffusion model

Daniel Ryan^1, and
Robert Stephen Cantrell^2,

1.
National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville, TN 37996
2.
Department of Mathematics, University of Miami, Coral Gables, FL 33146

Received: July 2013

Revised: August 2014

Published: May 2017

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Abstract

A cross-diffusion model of an intraguild predation community in a two-dimensional bounded domain where the intraguild prey employs a fitness based avoidance strategy is examined. The avoidance strategy employed is to increase motility in response to negative local fitness. Global existence of trajectories and the existence of a compact global attractor is proved. It is shown that if the intraguild prey has positive fitness at any point in the habitat when trying to invade, then it will be uniformly persistent in the system if its avoidance tendency is sufficiently strong. This type of movement strategy can lead to coexistence states where the intraguild prey is marginalized to areas with low resource productivity while the intraguild predator maintains high densities in regions with abundant resources, a pattern observed in many real world intraguild predation systems. Additionally, the effects of fitness based avoidance on eigenvalues in more general systems are discussed.

Keywords:

Mathematics Subject Classification: 35K59, 35B40, 92D40.

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