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

JOURNAL OF THEORETICAL BIOLOGY

卷:310

Article

Wakano, Joe Yuichiro^1,2  Lehmann, Laurent³ 

[1] Meiji Univ, Meiji Inst Adv Study Math Sci, Tokyo 101, Japan

[2] Japan Sci & Technol Agcy, PRESTO, Tokyo, Japan

[3] Univ Lausanne, Dept Ecol & Evolut, CH-1015 Lausanne, Switzerland

关键词: Fixation probability;    Stationary average frequency;    Canonical diffusion;    Adaptive dynamics;    Population genetics;   

DOI  :  10.1016/j.jtbi.2012.06.036

来源: Elsevier

【 摘 要 】

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. (c) 2012 Elsevier Ltd. All rights reserved.

【 授权许可】

Free