Maximization principles for frequency-dependent selection I: the one-locus two-allele case

Theoretical Population Biology
Kristan A Schneider

Abstract

In this article we study the one-locus two-allele version of the pairwise-interaction model of frequency-dependent selection in discrete and continuous time. Our main aim is to provide necessary and sufficient conditions for the validity of maximization principles. We provide a systematic approach that covers all possible facets of the dynamical behavior of the model, and we illustrate our results by concrete examples. We show that the mean fitness of the population is nondecreasing if the interaction coefficients are symmetric and positive. Moreover, monotonic convergence to the set of equilibria always occurs, which is not true if we also consider negative interaction coefficients. For asymmetric interaction, we provide necessary conditions when the mean fitness is nondecreasing and sufficient conditions when it is not. Furthermore, in discrete time, we show that limit cycles cannot occur, unless some interaction coefficients are negative.

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Citations

Dec 15, 2010·Proceedings. Biological Sciences·Erol Akçay, Joan Roughgarden
Aug 27, 2009·Journal of Mathematical Biology·Kristan Alexander Schneider
Jun 16, 2012·Theoretical Population Biology·Tadeas Priklopil
Oct 13, 2009·Theoretical Population Biology·Meredith V Trotter, Hamish G Spencer
Mar 17, 2009·Theoretical Population Biology·Carlo Matessi, Kristan A Schneider
Jan 18, 2014·Evolution; International Journal of Organic Evolution·Michael Doebeli, Iaroslav Ispolatov
Nov 23, 2017·Scientific Reports·Sylvain MoulheratJean Clobert
Sep 23, 2016·G3 : Genes - Genomes - Genetics·Hamish G Spencer, Cuilodair Mitchell

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