 Maximization principles for frequency-dependent selection I: the one-locus two-allele caseKristan A. Schneider Theoretical Population Biology, 2008, vol. 74, issue 3, 251-262 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. Keywords: Frequency-dependent selection; Pairwise interaction; Mean fitness; Limit cycles (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:74:y:2008:i:3:p:251-262 DOI: 10.1016/j.tpb.2008.07.006 Access Statistics for this article Theoretical Population Biology is currently edited by Jeremy Van Cleve More articles in Theoretical Population Biology from Elsevier |
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