Evolutionary games on the torus with weak selection

J. Theodore Cox, Rick Durrett

Research output: Contribution to journalArticle

4 Scopus citations

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) WªN−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.

Original languageEnglish (US)
Pages (from-to)2388-2409
Number of pages22
JournalStochastic Processes and their Applications
Volume126
Issue number8
DOIs
StatePublished - Dec 7 2015

Keywords

  • PDE limit
  • Tarnita's formula
  • Voter model
  • Voter model perturbation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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