Evolutionary games on the torus with weak selection

J. Theodore Cox and Rick Durrett

Stochastic Processes and their Applications, 2016, vol. 126, issue 8, 2388-2409

Abstract: We study evolutionary games on the torus with N points in dimensions d≥3. The matrices have the form Ḡ=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→∞ and w→0. If (i) w≫N−2/d then the limit is a PDE on Rd. 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 μ so that μ/w→∞ slowly enough then we arrive at Tarnita’s formula that describes how the equilibrium frequencies are shifted due to selection.

Keywords: Voter model; Voter model perturbation; PDE limit; Tarnita’s formula (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2016.02.004

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