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ESS modelling of diploid populations I: anatomy of one-locus allelic frequency simplices

Published online by Cambridge University Press:  01 July 2016

W. G. S. Hines
W. G. S. Hines*
Affiliation:
University of Guelph
*
* Postal address: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada, N1G 2W1.
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Abstract

In order to determine the robustness of the mean-covariance approach to exploring behavioural models of sexual diploid biological populations which are based on the evolutionarily stable strategy (ESS) concept, relevant features of the probability simplex of allelic frequencies for a population with genetic variability at a single locus are explored. Singularities and related properties of mappings from the space of allele frequencies to the space of strategy frequencies are examined, and related to a certain covariance measure of variability present in the population.

A companion paper builds on this characterization to establish that previous claims of stability in fact hold under slightly weaker conditions than initially indicated. The pair of papers also determines conditions under which unstable equilibria can occur, and establishes that these conditions are exceptional in practice.

Keywords

ANIMAL CONFLICT MODELSCOMPLEX POPULATIONSESS THEORYMEAN-COVARIANCE SUMMARIESSEXUAL POPULATIONSSIMPLEX ANATOMYSINGULAR SURFACES
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 341 - 360
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research supported by NSERC Operating Grant A6187.

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