Carrying Capacity of a Population Diffusing in a Heterogeneous Environment

D.L. DeAngelis, Bo Zhang, Wei-Ming Ni and Yuanshi Wang
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D.L. DeAngelis: U.S. Geological Survey, Wetland and Aquatic Research Center, Gainesville, Florida, FL 32653, USA
Bo Zhang: Department of Environmental Science and Policy, University of California at Davis, Davis, CA 95616, USA
Wei-Ming Ni: School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
Yuanshi Wang: School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Mathematics, 2020, vol. 8, issue 1, 1-12

Abstract: The carrying capacity of the environment for a population is one of the key concepts in ecology and it is incorporated in the growth term of reaction-diffusion equations describing populations in space. Analysis of reaction-diffusion models of populations in heterogeneous space have shown that, when the maximum growth rate and carrying capacity in a logistic growth function vary in space, conditions exist for which the total population size at equilibrium (i) exceeds the total population that which would occur in the absence of diffusion and (ii) exceeds that which would occur if the system were homogeneous and the total carrying capacity, computed as the integral over the local carrying capacities, was the same in the heterogeneous and homogeneous cases. We review here work over the past few years that has explained these apparently counter-intuitive results in terms of the way input of energy or another limiting resource (e.g., a nutrient) varies across the system. We report on both mathematical analysis and laboratory experiments confirming that total population size in a heterogeneous system with diffusion can exceed that in the system without diffusion. We further report, however, that when the resource of the population in question is explicitly modeled as a coupled variable, as in a reaction-diffusion chemostat model rather than a model with logistic growth, the total population in the heterogeneous system with diffusion cannot exceed the total population size in the corresponding homogeneous system in which the total carrying capacities are the same.

Keywords: carrying capacity; spatial heterogeneity; Pearl-Verhulst logistic model; reaction-diffusion model; energy constraints; total realized asymptotic population abundance; chemostat model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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