The limits of weak selection and large population size in evolutionary game theory

Sample, Christine; Allen, Benjamin

doi:10.1007/s00285-017-1119-4

Cited by 27 publications

(40 citation statements)

References 47 publications

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“…This is in particular the case for the probability of identity by descent of two individuals in different demes, Q out : if we first take the small mutation limit, lim µ →0 Q out = 0, while if we first take the large population limit, lim N →∞ Q out = 1 (see Appendix C.2 for details). This remark complements findings by Sample & Allen (2017), who highlighted the quantitative differences between different orders of weak selection and large population limits.…”

Section: Discussionsupporting

confidence: 87%

Imperfect strategy transmission can reverse the role of population viscosity on the evolution of altruism

Débarre

2019

Preprint

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Population viscosity, i.e., low emigration out of the natal deme, leads to high withindeme relatedness, which is beneficial to the evolution of altruistic behavior when social interactions take place among deme-mates. However, a detrimental side-effect of low emigration is the increase in competition among related individuals. The evolution of altruism depends on the balance between these opposite effects. This balance is already known to be affected by details of the life cycle; we show here that it further depends on the fidelity of strategy transmission from parents to their offspring. We consider different life cycles and identify thresholds of parent-offspring strategy transmission inaccuracy, above which higher emigration can increase the frequency of altruists maintained in the population. Predictions were first obtained analytically assuming weak selection and equal deme sizes, then confirmed with stochastic simulations relaxing these assumptions. Contrary to what happens with perfect strategy transmission from parent to offspring, our results show that higher emigration can be favorable to the evolution of altruism.

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Section: Discussionsupporting

confidence: 87%

Imperfect strategy transmission can reverse the role of population viscosity on the evolution of altruism

Débarre

2019

Preprint

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“…The integrals that give these probabilities, see (6), are difficult to evaluate in general, but they do allow us to compute the ranking order when c is small or c is large. The dichotomy between small c and large c is similar to that of wN and N w limits introduced by Jeoeng et al [5] and recently studied by Sample and Allen [8]. In the first case one lets the strength of selection w → 0 the number of individuals N → ∞.…”

Section: Introductionsupporting

confidence: 53%

Extrapolating Weak Selection in Evolutionary Games

Wang

Durrett²

2018

Preprint

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This work is inspired by a 2013 paper from Arne Traulsen's lab at the Max Plank Institute for Evolutionary Biology [10]. They studied the small mutation limit of evolutionary games. It has been shown that for 2×2 games the ranking of the strategies does not change as strength of selection is increased [11]. The point of the 2013 paper is that when there are three or more strategies the ordering can change as selection is increased. Wu et al [10] did numerical computations for fixed N . Here, we will instead let the strength of selection β = c/N and let N → ∞ to obtain formulas for the invadability probabilities φ ij that determine the rankings. These formulas, which are integrals on [0, 1], are intractable calculus problems but can be easily evaluated numerically. Here, we concentrate on simple formulas for the ranking order when c is small or c is large.

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“…All of our analytical results involve the limit of either weak selection or certain edge weights going to zero. Some of our results combine these limits, meaning that they apply only in rather extreme scenarios, and the results may depend on the limit ordering [58].…”

Section: Limitationsmentioning

confidence: 84%

Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs

et al. 2020

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The spatial structure of an evolving population affects which mutations become fixed. Some structures amplify selection, increasing the likelihood that beneficial mutations become fixed while deleterious mutations do not. Other structures suppress selection, reducing the effect of fitness differences and increasing the role of random chance. This phenomenon can be modeled by representing spatial structure as a graph, with individuals occupying vertices. Births and deaths occur stochastically, according to a specified update rule. We study death-Birth updating: An individual is chosen to die and then its neighbors compete to reproduce into the vacant spot. Previous numerical experiments suggested that amplifiers of selection for this process are either rare or nonexistent. We introduce a perturbative method for this problem for weak selection regime, meaning that mutations have small fitness effects. We show that fixation probability under weak selection can be calculated in terms of the coalescence times of random 1 arXiv:1906.01036v1 [q-bio.PE] 3 Jun 2019 walks. This result leads naturally to a new definition of effective population size. Using this and other methods, we uncover the first known examples of transient amplifiers of selection (graphs that amplify selection for a particular range of fitness values) for the death-Birth process. We also exhibit new families of "reducers of fixation", which decrease the fixation probability of all mutations, whether beneficial or deleterious.

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The limits of weak selection and large population size in evolutionary game theory

Cited by 27 publications

References 47 publications

Imperfect strategy transmission can reverse the role of population viscosity on the evolution of altruism

Imperfect strategy transmission can reverse the role of population viscosity on the evolution of altruism

Extrapolating Weak Selection in Evolutionary Games

Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs

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