Modeling density dependence in heterogeneous landscapes: dispersal as a case study

J Theor Biol. 2010 Jul 21;265(2):160-6. doi: 10.1016/j.jtbi.2010.03.032. Epub 2010 Mar 24.

Abstract

Population models often pose density-dependent rates as relations between current population size on a habitat patch, n, and some threshold size defined by limiting resources, r. In fourteen recent modeling studies incorporating density-dependent dispersal, formulations of the density-dependent rate (or probability) fall into two distinct groups, expressing the rate as a function of n-r or n/r. These two depictions of the same process differ fundamentally: they can cause strikingly different dynamics in otherwise identical systems and they have different scaling properties in heterogeneous landscapes. Here I consider the implications of the two formulations under two broad ecological scenarios: scramble competition for an equally divided resource (e.g. food) and contest competition for an unequally divided resource (e.g. nest sites). In both cases, simple arguments show that the n/r form is preferable when density dependence is driven by individual access to resources. Other circumstances may require different formulations, but modelers must ensure that these have appropriate scaling and non-equilibrium behavior.

MeSH terms

  • Humans
  • Models, Biological*
  • Population Density*
  • Population Dynamics