Darwinian evolution and a predator-prey ecology

Bulletin of Mathematical BiologyPublished 1 August 1975

Peter M. Allen

DOI10.1007/bf02459521

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Citations42

SJR quartileQ1

SJR score0.70

SNIP0.98

TL;DR

A model is developed for the biological evolution of a predator-prey ecology using a Volterra-Lotka ecology as an example and it is shown that as a result of random mutations the ecosystem drifts irreversibly through this space.

Abstract

In order to represent the biological evolution of a predator-prey ecology it is necessary to add to the equations of population dynamics terms corresponding to spontaneous mutation. Using a Volterra-Lotka ecology as an example, a model is developed for this. It is based on the assumption of two levels of description; a local one containing mutation probabilities, and the other the macroscopic average equations for the whole system. Diffusion processes link the two. The "evolutionary state" of a species is interpreted as an average effectiveness in terms of a genetic parameter space and it is shown that as a result of random mutations the ecosystem drifts irreversibly through this space. © 1975 Society for Mathematical Biology.

Keywords

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