Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Spatial population dynamics in a producer-scrounger model

Pages: 1591 - 1607, Volume 20, Issue 6, August 2015      doi:10.3934/dcdsb.2015.20.1591

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Chris Cosner - Department of Mathematics, University of Miami, Coral Gables, FL 33146, United States (email)
Andrew L. Nevai - Department of Mathematics, University of Central Florida, Orlando, FL 32816, United States (email)

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.

Keywords:  Producer-scrounger, scramble kleptoparasitism, spatial ecology, population dynamics, reaction-diffusion.
Mathematics Subject Classification:  Primary: 92D25, 92D40; Secondary: 35K57.

Received: November 2013;      Revised: January 2014;      Available Online: June 2015.