Evolutionary games on the torus with weak selection

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Cox, J. Theodore¹  Durrett, Rick² 

[1] Syracuse Univ, Dept Math, 215 Carnegie Bldg, Syracuse, NY 13244 USA

[2] Duke Univ, Dept Math, POB 90320, Durham, NC 27708 USA

关键词: Voter model;    Voter model perturbation;    PDE limit;    Tarnita's formula;   

DOI  :  10.1016/j.spa.2016.02.004

来源: Elsevier

【 摘 要 】

We study evolutionary games on the torus with N points in dimensions d >= 3. The matrices have the form (G) over bar =1+wG, where 1 is a matrix that consists of all 1's, and w is small. As in Cox Durrett and Perkins (2011) we rescale time and space and take a limit as N ->infinity and w -> 0 . If (i) w >> N-2/d then the limit is a PDE on R-d. If (ii) N-2/d >> w >> N-1, then the limit is an ODE. If (iii) w << N-1 then the effect of selection vanishes in the limit. In regime (ii) if we introduce mutations at rate mu, so that mu/w -> infinity slowly enough then we arrive at Tarnita's formula that describes how the equilibrium frequencies are shifted due to selection. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free