How small are small mutation rates?

Wu, Bin; Gokhale, Chaitanya S.; Wang, Long; Traulsen, Arne

doi:10.1007/s00285-011-0430-8

Cited by 100 publications

(106 citation statements)

References 41 publications

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“…In this example, the approximation by π seems to be fairly accurate for ≤ 10 −4 . A theoretical investigation of the quality of this type of approximation in a related model has recently been carried out by Wu et al (2011).…”

Section: Numerical Examplesmentioning

confidence: 99%

Phenotype Switching and Mutations in Random Environments

Fudenberg

Imhof

2011

Bull Math Biol

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Cell populations can benefit from changing phenotype when the environment changes. One mechanism for generating these changes is stochastic phenotype switching, whereby cells switch stochastically from one phenotype to another according to genetically determined rates, irrespective of the current environment, with the matching of phenotype to environment then determined by selective pressure. This mechanism has been observed in numerous contexts, but identifying the precise connection between switching rates and environmental changes remains an open problem. Here, we introduce a simple model to study the evolution of phenotype switching in a finite population subject to random environmental shocks. We compare the successes of competing genotypes with different switching rates, and analyze how the optimal switching rates depend on the frequency of environmental changes. If environmental changes are as rare as mutations, then the optimal switching rates mimic the rates of environmental changes. If the environment changes more frequently, then the optimal genotype either maximally favors fitness in the more common environment or has the maximal switching rate to each phenotype. Our results also explain why the optimum is relatively insensitive to fitness in each environment.

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Section: Numerical Examplesmentioning

confidence: 99%

Phenotype Switching and Mutations in Random Environments

Fudenberg

Imhof

2011

Bull Math Biol

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“…The quantities π x are payoff functions [26]. In contrast to the fitness functions f x employed in the other updating rules considered here, these payoff functions may take negative values.…”

Section: Link Dynamicsmentioning

confidence: 99%

“…The error induced by that assumption has been previously studied by Wu et al [26]. Their study employs the Fermi process as updating rule on a well-mixed model of population size N. Of particular interest is their result for coexistence games, in which the best reply to every strategy is a different strategy.…”

Section: Introductionmentioning

confidence: 99%

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Nonequivalence of updating rules in evolutionary games under high mutation rates

et al. 2014

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Moran processes are often used to model selection in evolutionary simulations. The updating rule in Moran processes is a birth-death process, i. e., selection according to fitness of an individual to give birth, followed by the death of a random individual. For well-mixed populations with only two strategies this updating rule is known to be equivalent to selecting unfit individuals for death and then selecting randomly for procreation (biased death-birth process). It is, however, known that this equivalence does not hold when considering structured populations. Here we study whether changing the updating rule can also have an effect in well-mixed populations in the presence of more than two strategies and high mutation rates. We find, using three models from different areas of evolutionary simulation, that the choice of updating rule can change model results. We show, e. g., that going from the birth-death process to the death-birth process can change a public goods game with punishment from containing mostly defectors to having a majority of cooperative strategies. From the examples given we derive guidelines indicating when the choice of the updating rule can be expected to have an impact on the results of the model.

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“…Yet, experimental studies have revealed that many natural systems exhibit frequency-dependent selection [4][5][6], which means that an individual's fitness not only depends on its genotype, but also on its interactions with other individuals and hence on the frequency of the different genotypes in the population. Although such frequency-dependent selection had already been studied early by Crow & Kimura [3], only recently has it received more attention [7][8][9][10][11][12][13][14]. In these theoretical and computational studies, individuals' interactions are represented by interaction matrices from game theory.…”

Section: Introductionmentioning

confidence: 99%

Frequency-dependent fitness induces multistability in coevolutionary dynamics

Arnoldt

Timme

Großkinsky

2012

J. R. Soc. Interface.

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Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a fundamental aim of theoretical research. Recent works quantitatively studied coevolutionary dynamics of competing species with a focus on linearly frequency-dependent interactions, derived from a gametheoretic viewpoint. However, several aspects of evolutionary dynamics, e.g. limited resources, may induce effectively nonlinear frequency dependencies. Here we study the impact of nonlinear frequency dependence on evolutionary dynamics in a model class that covers linear frequency dependence as a special case. We focus on the simplest non-trivial setting of two genotypes and analyse the co-action of nonlinear frequency dependence with asymmetric mutation rates. We find that their co-action may induce novel metastable states as well as stochastic switching dynamics between them. Our results reveal how the different mechanisms of mutation, selection and genetic drift contribute to the dynamics and the emergence of metastable states, suggesting that multistability is a generic feature in systems with frequency-dependent fitness.

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How small are small mutation rates?

Cited by 100 publications

References 41 publications

Phenotype Switching and Mutations in Random Environments

Phenotype Switching and Mutations in Random Environments

Nonequivalence of updating rules in evolutionary games under high mutation rates

Frequency-dependent fitness induces multistability in coevolutionary dynamics

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