Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models

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• 作者：Joe Yuichiro Wakano ; Laurent Lehmann
• 关键词：Fixation probability ; Stationary average frequency ; Canonical diffusion ; Adaptive dynamics ; Population genetics
• 刊名：Journal of Theoretical Biology
• 出版年：2012
• 出版时间：7 October, 2012
• 年：2012
• 卷：310
• 期：Complete
• 页码：206-215
• 全文大小：476 K

文摘

The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.