Fixation of strategies for an evolutionary game in finite populations

Details Fixation of strategies for an evolutionary game in finite populations Fixation of strategies for an evolutionary game in finite populations

2005-09-08

arxiv.org/abs/q-bio/0509008v1

Bulletin of Mathematical Biology 68, 1923 (2006)

Biology

Quantitative Biology

Populations and Evolution

22 pages, 2 eps figures

Scientific paper

10.1007/s11538-006-9061-4

A stochastic evolutionary dynamics of two strategies given by 2 x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with arbitrary hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.

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