Mixed strategies and natural selection in resource allocation

Irina Kareva; Faina Berezovkaya; Georgy Karev

doi:10.3934/mbe.2013.10.1561

Article Contents

2013, Volume 10, Issue 5&6: 1561-1586. Doi: 10.3934/mbe.2013.10.1561 open access

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Mixed strategies and natural selection in resource allocation

1.
School of Human Evolution and Social Change, Arizona State University, 900 S Cady Mall, Tempe, AZ, 85287
2.
Department of Mathematics, 2441 Sixth Street NW, Washington, DC, 20059
3.
National Institute for Biotechnology Information (NCBI), National Institutes of Health, 8600 Rockville Pike MSC 3830, Bethesda, MD 20894

Received: July 31, 2012

Revised: November 30, 2012

Published: July 2013

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Abstract

An appropriate choice of strategy for resource allocation may frequently determine whether a population will be able to survive under the conditions of severe resource limitations. Here we focus on two classes of strategies allocation of resources towards rapid proliferation, or towards slower proliferation but increased physiological and environmental maintenance. We propose a generalized framework, where individuals within a population can use either strategy in different proportion for utilization of a common dynamical resource in order to maximize their fitness. We use the model to address two major questions, namely, whether either strategy is more likely to be selected for as a result of natural selection, and, if one allows for the possibility of resource over-consumption, whether either strategy is preferable for avoiding population collapse due to resource exhaustion. Analytical and numerical results suggest that the ultimate choice of strategy is determined primarily by the initial distribution of individuals in the population, and that while investment in physiological and environmental maintenance is a preferable strategy in a homogeneous population, no generalized prediction can be made about heterogeneous populations.

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Mathematics Subject Classification: Primary: 37N25, 46N60; Secondary: 97M70.

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