On the instability of evolutionary stable strategies in small populations

Fogel, Gary B.; Andrews, Peter C.; Fogel, David B.

doi:10.1016/s0304-3800(98)00068-4

Cited by 64 publications

(44 citation statements)

References 19 publications

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“…Evolutionary game dynamics in finite populations has also been studied in a frequency dependent Wright Fisher process (Imhof and Nowak, 2006). For further models of finite population game dynamics, see (Riley, 1979;Schaffer, 1988;Fogel et al, 1998;Ficci and Pollack, 2000;Schreiber, 2001). …”

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confidence: 99%

Pairwise comparison and selection temperature in evolutionary game dynamics

Traulsen

Pacheco

Nowak

2007

Journal of Theoretical Biology

330

304

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Recently, the frequency dependent Moran process has been introduced in order to describe evolutionary game dynamics in finite populations. Here, an alternative to this process is investigated that is based on pairwise comparison between two individuals. We follow a long tradition in the physics community and introduce a temperature (of selection) to account for stochastic effects. We calculate the fixation probabilities and fixation times for any symmetric 2 × 2 game, for any intensity of selection and any initial number of mutants. The temperature can be used to gauge continuously from neutral drift to the extreme selection intensity known as imitation dynamics. For some payoff matrices the distribution of fixation times can become so broad that the average value is no longer very meaningful.

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confidence: 99%

Pairwise comparison and selection temperature in evolutionary game dynamics

Traulsen

Pacheco

Nowak

2007

Journal of Theoretical Biology

330

304

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“…This may be why the hooknose-jack 316 game yields a balanced polymorphism similar to those examined in other systems such as 317 scale-eating cichlid fish (Hori 1993 PThe previous findings seem to suggest that sneakers and hooknoses coexist stably are 323 relatively stable even in a very small populations (Gross 1984(Gross , 1985(Gross , 1991(Gross , 1996. However, the 324 traditional ESS analysis assumes an infinite population size and the evolutionary outcomes of a 325 finite population size are often unstable, and/or different from the ESS equilibrium, or both 326 (Riley 1979;Fogel et al 1998;Taylor et al 2004). In the orangutan mating system, large 327 population sizes tend to increase the proportion of subordinate mating strategies (Tainaka et al 328 2007).…”

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confidence: 76%

Breeding games and dimorphism in male salmon

Tanaka¹,

Hayashi²,

Miller³

et al. 2009

Animal Behaviour

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“…Evolutionary game theory has also been extended to finite populations, based upon the original Moran process Moran (1962) where different concepts are needed to deal with the stochastics effects which are not present in infinite populations, and where the single most important concept is that of the fixation probability of a rare mutant (equivalent to a small fraction of mutants within an infinite population, whose establishment within a population is either certain or impossible), important examples include Fogel et al (1998); Nowak et al (2004); Taylor et al (2004); Traulsen et al (2005);. Within this general theory, there have also been developments based upon multiplayer games, and these are well-reviewed in Gokhale and Traulsen (2014).…”

Section: Discussionmentioning

confidence: 99%

Nonlinear and Multiplayer Evolutionary Games

Broom

Rychtář

2016

Advances in Dynamic and Evolutionary Games

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract Classical evolutionary game theory has typically considered populations within which randomly selected pairs of individuals play games against each other, and the resulting payoff functions are linear. These simple functions have led to a number of pleasing results for the dynamic theory, the static theory of evolutionarily stable strategies, and the relationship between them. We discuss such games, together with a basic introduction to evolutionary game theory, in Section 1. Realistic populations, however, will generally not have these nice properties, and the payoffs will be nonlinear. In Section 2 we discuss various ways in which nonlinearity can appear in evolutionary games, including pairwise games with strategy-dependent interaction rates, and playing the field games, where payoffs depend upon the entire population composition, and not on individual games. In Section 3 we consider multiplayer games, where payoffs are the result of interactions between groups of size greater than two, which again leads to nonlinearity, and a breakdown of some of the classical results of Section 1. Finally in Section 4 we summarise and discuss the previous sections. Permanent repository link

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On the instability of evolutionary stable strategies in small populations

Cited by 64 publications

References 19 publications

Pairwise comparison and selection temperature in evolutionary game dynamics

Pairwise comparison and selection temperature in evolutionary game dynamics

Breeding games and dimorphism in male salmon

Nonlinear and Multiplayer Evolutionary Games

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