Energetic constraints and the paradox of a diffusing population in a heterogeneous environment

Theoretical Population Biology
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Abstract

Previous mathematical analyses have shown that, for certain parameter ranges, a population, described by logistic equations on a set of connected patches, and diffusing among them, can reach a higher equilibrium total population when the local carrying capacities are heterogeneously distributed across patches, than when carrying capacities having the same total sum are homogeneously distributed across the patches. It is shown here that this apparently paradoxical result is explained when the resultant differences in energy inputs to the whole multi-patch system are taken into account. We examine both Pearl–Verhulst and Original Verhulst logistic models and show that, when total input of energy or limiting resource, is constrained to be the same in the homogeneous and heterogeneous cases, the total population in the heterogeneous patches can never reach an asymptotic equilibrium that is greater than the sum of the carrying capacities over the homogeneous patches. We further show that, when the dynamics of the limiting resources are explicitly modeled, as in a chemostat model, the paradoxical result of the logistic models does not occur. These results have implications concerning the use of some ubiquitous equations of population ecology in modeling populations in space.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Energetic constraints and the paradox of a diffusing population in a heterogeneous environment
Series title Theoretical Population Biology
DOI 10.1016/j.tpb.2018.11.003
Volume 125
Year Published 2019
Language English
Publisher Elsevier
Contributing office(s) Wetland and Aquatic Research Center
Description 8 p.
First page 30
Last page 37