From discrete to continuous evolution models: A unifying approach to drift-diffusion and replicator dynamics

Fabio A.C.C. Chalub and Max O. Souza

Theoretical Population Biology, 2009, vol. 76, issue 4, 268-277

Abstract: We study the large population limit of the Moran process, under the assumption of weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral evolution) or natural selection; for one precise scaling, both effects are present. For the scalings that take the genetic-drift into account, the continuous model is given by a singular diffusion equation, together with two conservation laws that are already present at the discrete level. For scalings that take into account only natural selection, we obtain a hyperbolic singular equation that embeds the Replicator Dynamics and satisfies only one conservation law. The derivation is made in two steps: a formal one, where the candidate limit model is obtained, and a rigorous one, where convergence of the probability density is proved. Additional results on the fixation probabilities are also presented.

Keywords: Moran process; Replicator dynamics; Kimura equation; Drift-diffusion equations (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:76:y:2009:i:4:p:268-277

DOI: 10.1016/j.tpb.2009.08.006

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