Extrapolating weak selection in evolutionary games.

Published

Journal Article

This work is inspired by a 2013 paper from Arne Traulsen's lab at the Max Plank Institute for Evolutionary Biology (Wu et al. in PLoS Comput Biol 9:e1003381, 2013). They studied evolutionary games when the mutation rate is so small that each mutation goes to fixation before the next one occurs. It has been shown that for [Formula: see text] games the ranking of the strategies does not change as strength of selection is increased (Wu et al. in Phys Rev 82:046106, 2010). The point of the 2013 paper is that when there are three or more strategies the ordering can change as selection is increased. Wu et al. (2013) did numerical computations for a fixed population size N. Here, we will instead let the strength of selection [Formula: see text] where c is fixed and let [Formula: see text] to obtain formulas for the invadability probabilities [Formula: see text] that determine the rankings. These formulas, which are integrals on [0, 1], are intractable calculus problems, but can be easily evaluated numerically. Here, we use them to derive simple formulas for the ranking order when c is small or c is large.

Full Text

Duke Authors

Cited Authors

  • Wang, Z; Durrett, R

Published Date

  • January 2019

Published In

Volume / Issue

  • 78 / 1-2

Start / End Page

  • 135 - 154

PubMed ID

  • 30056505

Pubmed Central ID

  • 30056505

Electronic International Standard Serial Number (EISSN)

  • 1432-1416

International Standard Serial Number (ISSN)

  • 0303-6812

Digital Object Identifier (DOI)

  • 10.1007/s00285-018-1270-6

Language

  • eng