Cumulant Dynamics in a Finite Population: Linkage Equilibrium Theory

Magnus Rattray and Jonathan L. Shapiro

Working Papers from Santa Fe Institute

Abstract: The evolution of a finite population at linkage equilibrium is described in terms of the dynamics of phenotype distribution cumulants. This provides a powerful method for describing evolutionary transients and we elucidate the relationship between the cumulant dynamics and the diffusion approximation. A separation of time-scales between the first and higher cumulants for low mutation rates is demonstrated in the diffusion limit and provides a significant simplification of the dynamical system. However, the diffusion limit may not be appropriate for strong selection as the standard Fisher-Wright model of genetic drift can break down in this case. Two novel examples of this effect are considered: we show that the dynamics may depend on the number of loci under strong directional selection and that environmental variance results in a reduced effective population size. We also consider a simple model of a changing environment which cannot be described by a diffusion equation and we derive the optimal mutation rate for this case.

Keywords: Evolutionary dynamics; mutation-selection dynamics; theoretical population biology; diffusion approximation (search for similar items in EconPapers)
Date: 1999-07
New Economics Papers: this item is included in nep-evo
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Persistent link: https://EconPapers.repec.org/RePEc:wop:safiwp:99-07-055

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