Evolutionary games on the torus with weak selection


Journal Article

© 2016 Elsevier B.V. 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.

Full Text

Duke Authors

Cited Authors

  • Cox, JT; Durrett, R

Published Date

  • December 7, 2015

Published In

Volume / Issue

  • 126 / 8

Start / End Page

  • 2388 - 2409

International Standard Serial Number (ISSN)

  • 0304-4149

Digital Object Identifier (DOI)

  • 10.1016/j.spa.2016.02.004

Citation Source

  • Scopus