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Calculating Evolutionary Dynamics in Structured Populations
, 2009
"... Evolution is shaping the world around us. At the core of every evolutionary process is a population of reproducing individuals. The outcome of an evolutionary process depends on population structure. Here we provide a general formula for calculating evolutionary dynamics in a wide class of structure ..."
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Cited by 27 (3 self)
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Evolution is shaping the world around us. At the core of every evolutionary process is a population of reproducing individuals. The outcome of an evolutionary process depends on population structure. Here we provide a general formula for calculating evolutionary dynamics in a wide class of structured populations. This class includes the recently introduced ‘‘games in phenotype space’ ’ and ‘‘evolutionary set theory.’ ’ There can be local interactions for determining the relative fitness of individuals, but we require global updating, which means all individuals compete uniformly for reproduction. We study the competition of two strategies in the context of an evolutionary game and determine which strategy is favored in the limit of weak selection. We derive an intuitive formula for the structure coefficient, s, and provide a method for efficient numerical calculation.
Mutation–selection equilibrium in games with multiple strategies.
 J. Theor. Biol.
, 2009
"... a b s t r a c t We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an n Â n payoff matrix. Players can use mixed strategies, which are given by the vector ..."
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a b s t r a c t We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an n Â n payoff matrix. Players can use mixed strategies, which are given by the vector ðp 1 ; . . . ; p n Þ. Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S n . We study evolutionary dynamics in a wellmixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutationselection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the HawkDove game. We prove general statements about the relationship between games with pure and with mixed strategies.
Evolutionary dynamics in finite populations can explain the full range of . . .
 JOURNAL OF THEORETICAL BIOLOGY
, 2012
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Article Dynamic Properties of Evolutionary Multiplayer Games in Finite Populations
, 2013
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"... en niv rou ual m de on titi a rsp has en y ar s t rev 1. INT An evo uals, reprod arise if emerge compe tant m evoluti polyme langua the se approa within nonlin behavi Evo ematic evoluti standin evoluti tion of mathem ues of n the ndent n the types en as scape encylation ver it to the Smith onary o ..."
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en niv rou ual m de on titi a rsp has en y ar s t rev 1. INT An evo uals, reprod arise if emerge compe tant m evoluti polyme langua the se approa within nonlin behavi Evo ematic evoluti standin evoluti tion of mathem ues of n the ndent n the types en as scape encylation ver it to the Smith onary ol for Price come every mund comay & host– ay & ak & May 2000), the competition between phages for bacterial cells (Turner & Chao 1999), the evolution of metabolic pathways (Pfeiffer et al. 2001) and the evolution of human language (Nowak et al. 2002). Electronic supplementary material is available at
Contents lists available at SciVerse ScienceDirect Journal of Theoretical Biology
"... journal homepage: www.elsevier.com/locate/yjtbi Multiplayer games on the cycle ..."
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journal homepage: www.elsevier.com/locate/yjtbi Multiplayer games on the cycle
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"... Finite population size Stochastic process Hawk–Dove game for ion use to u y i siz ans ect calculate the average abundance of every mixed strategy in the stationary distribution of the mutation–selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selec ..."
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Finite population size Stochastic process Hawk–Dove game for ion use to u y i siz ans ect calculate the average abundance of every mixed strategy in the stationary distribution of the mutation–selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The study o, 1973; bull, 1