Assortment and the evolution of cooperation in a Moran process with exponential fitness

JOURNAL OF THEORETICAL BIOLOGY

卷:409

Article

Cooney, Daniel¹  Allen, Benjamin^2,4  Veller, Carl^3,4 

[1] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA

[2] Emmanuel Coll, Dept Math, Boston, MA USA

[3] Harvard Univ, Dept Organism & Evolutionary Biol, Cambridge, MA 02138 USA

[4] Harvard Univ, Program Evolutionary Dynam, Cambridge, MA 02138 USA

关键词: Assortment;    Relatedness;    Cooperation;    Stochastic evolution;    Moran process;   

DOI  :  10.1016/j.jtbi.2016.08.026

来源: Elsevier

【 摘 要 】

We study the evolution of cooperation in a finite population interacting according to a simple model of like-with-like assortment. Evolution proceeds as a Moran process, and payoffs from the underlying cooperator-defector game are translated to positive fitnesses by an exponential transformation. These evolutionary dynamics can arise, for example, in a nest-structured population with rare migration. The use of the exponential transformation, rather than the usual linear one, is appropriate when interactions have multiplicative fitness effects, and allows for a tractable characterisation of the effect of assortment on the evolution of cooperation. We define two senses in which a greater degree of assortment can favour the evolution of cooperation, the first stronger than the second: (i) greater assortment increases, at all population states, the probability that the number of cooperators increases, relative to the probability that the number of defectors increases; and (ii) greater assortment increases the fixation probability of cooperation, relative to that of defection. We show that, by the stronger definition, greater assortment favours the evolution of cooperation for a subset of cooperative dilemmas: prisoners' dilemmas, snowdrift games, stag-hunt games, and some prisoners' delight games. For other cooperative dilemmas, greater assortment favours cooperation by the weak definition, but not by the strong definition. We also show that increasing assortment expands the set of games in which cooperation dominates the evolutionary dynamics. Our results hold for any strength of selection. (C) 2016 Elsevier Ltd. All rights reserved.

【 授权许可】

Free