Spatial population dynamics in a producer-scrounger model

Chris  Cosner; Andrew L.  Nevai

doi:10.3934/dcdsb.2015.20.1591

Article Contents

2015, Volume 20, Issue 6: 1591-1607. Doi: 10.3934/dcdsb.2015.20.1591

This issue Previous Article Extinction in discrete, competitive, multi-species patch models Next Article Partial differential equations with Robin boundary condition in online social networks

Spatial population dynamics in a producer-scrounger model

Chris Cosner^1, and
Andrew L. Nevai^2,

1.
Department of Mathematics, University of Miami, Coral Gables, FL 33146
2.
Department of Mathematics, University of Central Florida, Orlando, FL 32816

Received: October 31, 2013

Revised: December 31, 2013

Published: July 2015

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Abstract

The spatial population dynamics of an ecological system involving producers and scroungers is studied using a reaction-diffusion model. The two populations move randomly and increase logistically, with birth rates determined by the amount of resource acquired. Producers can obtain the resource directly from the environment, but must surrender a proportion of their discoveries to nearby scroungers through a process known as scramble kleptoparasitism. The proportion of resources stolen by a scrounger from nearby producers decreases as the local scrounger density increases. Parameter combinations which allow producers and scroungers to persist either alone or together are distinguished from those in which they cannot. Producer persistence depends in general on the distribution of resources and producer movement, whereas scrounger persistence depends on its ability to invade when producers are at steady-state. It is found that (i) both species can persist when the habitat has high productivity, (ii) neither species can persist when the habitat has low productivity, and (iii) slower dispersal of both the producer and scrounger is favored when the habitat has intermediate productivity.

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Mathematics Subject Classification: Primary: 92D25, 92D40; Secondary: 35K57.

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