Parvinen Kalle, Ohtsuki Hisashi, Wakano Joe Yuichiro
Department of Mathematics and Statistics, University of Turku, FI-20014, Finland; Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), A-2361 Laxenburg, Austria.
Department of Evolutionary Studies of Biosystems, School of Advanced Sciences, SOKENDAI (The Graduate University for Advanced Studies), Shonan Village, Hayama, Kanagawa 240-0193, Japan.
J Theor Biol. 2017 Mar 7;416:129-143. doi: 10.1016/j.jtbi.2016.12.019. Epub 2016 Dec 28.
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.
通过研究集合种群适应性，我们根据繁殖力函数给出了赖特岛模型中选择梯度、收敛稳定性和进化稳定性条件的解析表达式。这些条件中出现的繁殖力函数各阶导数的系数具有固定符号。这说明了哪种相互作用促进或抑制了空间模型中的进化分支。我们观察到泰勒消去结果对任何繁殖力函数都成立：不仅奇异策略，而且它们的收敛稳定性与相应的完全混合模型中的相同。我们表明，当扩散率接近零时，进化分支从不发生。此外，对于一大类繁殖力函数（包括由任何成对博弈确定的函数），如果在相应的完全混合模型中不发生分支，那么对于任何扩散率，进化分支都是不可能的。因此，空间结构常常抑制进化分支，尽管我们可以构建一个繁殖力函数，对于该函数，进化分支仅在中等扩散率时发生。
