The effect of fecundity derivatives on the condition of evolutionary branching in spatial models

JOURNAL OF THEORETICAL BIOLOGY

卷:416

Article

Parvinen, Kalle^1,2  Ohtsuki, Hisashi³  Wakano, Joe Yuichiro^4,5 

[1] Univ Turku, Dept Math & Stat, FI-20014 Turku, Finland

[2] Int Inst Appl Syst Anal, Evolut & Ecol Program, A-2361 Laxenburg, Austria

[3] SOKENDAI Grad Univ Adv Studies, Sch Adv Sci, Dept Evolut Studies Eiosystems, Kanagawa 2400193, Japan

[4] Meiji Univ, Sch Interdisciplinary Math Sci, Tokyo 1648525, Japan

[5] Meiji Inst Adv Study Math Sci, Tokyo 1648525, Japan

关键词: Adaptive dynamics;    Cooperation;    Evolutionary branching;    Natural selection;   

DOI  :  10.1016/j.jtbi.2016.12.019

来源: Elsevier

【 摘 要 】

By investigating metapopulation fitness, we present analytical expressions for the selection gradient and conditions for convergence stability and evolutionary stability in Wright's island model in terms of fecundity function. Coefficients of each derivative of fecundity function appearing in these conditions have fixed signs. This illustrates which kind of interaction promotes or inhibits evolutionary branching in spatial models. We observe that Taylor's cancellation result holds for any fecundity function: Not only singular strategies but also their convergence stability is identical to that in the corresponding well-mixed model. We show that evolutionary branching never occurs when the dispersal rate is close to zero. Furthermore, for a wide class of fecundity functions (including those determined by any pairwise game), evolutionary branching is impossible for any dispersal rate if branching does not occur in the corresponding well-mixed model. Spatial structure thus often inhibits evolutionary branching, although we can construct a fecundity function for which evolutionary branching only occurs for intermediate dispersal rates.

【 授权许可】

Free