Journal
JOURNAL OF THEORETICAL BIOLOGY
Volume 258, Issue 4, Pages 614-622Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2009.02.010
Keywords
Evolutionary game theory; Finite populations; Stochastic effects
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Funding
- NIGMS NIH HHS [R01GM078986, R01 GM078986-03, R01 GM078986] Funding Source: Medline
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In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright-Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. our results allow a complete characterization of n x n games in the limit of weak selection. (c) 2009 Elsevier Ltd. All rights reserved.
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