Journal
PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES
Volume 273, Issue 1598, Pages 2249-2256Publisher
ROYAL SOC
DOI: 10.1098/rspb.2006.3576
Keywords
evolutionary dynamics; frequency-dependent selection; fixation probability; spatial games; evolutionary graph theory; Prisoner's Dilemma
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Funding
- NIGMS NIH HHS [R01 GM078986, R01 GM078986-01] Funding Source: Medline
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Traditional evolutionary game theory explores frequency-dependent selection in well-mixed populations without spatial or stochastic effects. But recently there has been much interest in studying the evolutionary game dynamics in spatial settings, on lattices and other graphs. Here, we present an analytic approach for the stochastic evolutionary game dynamics on the simplest possible graph, the cycle. For three different update rules, called 'birth-death' (BD), 'death-birth' (DB) and 'imitation' (IM), we derive exact conditions for natural selection to favour one strategy over another. As specific examples, we consider a coordination game and Prisoner's Dilemma. In the latter case, selection can favour cooperators over defectors for DB and IM. updating. We also study the case where the replacement graph of evolutionary updating remains a cycle, but the interaction graph for playing the game is a complete graph. In this setting, all three update rules lead to identical conditions in the limit of weak selection, where we find the '1/3-law' of well-mixed populations.
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