ArticleJournal of mathematical biology2017
The limits of weak selection and large population size in evolutionary game theory.
Article in Journal of mathematical biology, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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9 citing papers in PubMed.
- The rules of multiplayer cooperation in networks of communities.PLoS computational biology · 2024Article
- Competition for resources can reshape the evolutionary properties of spatial structure.bioRxiv : the preprint server for biology · 2024Article
- Fixation probabilities in evolutionary dynamics under weak selection.Journal of mathematical biology · 2021Article
- Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs.PLoS computational biology · 2020Article
- A mathematical formalism for natural selection with arbitrary spatial and genetic structure.Journal of mathematical biology · 2019Article
- Fixation probabilities for the Moran process in evolutionary games with two strategies: graph shapes and large population asymptotics.Journal of mathematical biology · 2019Article
- Extrapolating weak selection in evolutionary games.Journal of mathematical biology · 2019Article
- Invasion and effective size of graph-structured populations.PLoS computational biology · 2018Article
- Fixation probabilities in populations under demographic fluctuations.Journal of mathematical biology · 2018Article
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2 authors.
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Abstract
Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two limits are both mathematically convenient and biologically relevant: weak selection and large population size. These limits can be combined in different ways, leading to potentially different results. We consider two orderings: the [Formula: see text] limit, in which weak selection is applied before the large population limit, and the [Formula: see text] limit, in which the order is reversed. Formal mathematical definitions of the [Formula: see text] and [Formula: see text] limits are provided. Applying these definitions to the Moran process of evolutionary game theory, we obtain asymptotic expressions for fixation probability and conditions for success in these limits. We find that the asymptotic expressions for fixation probability, and the conditions for a strategy to be favored over a neutral mutation, are different in the [Formula: see text] and [Formula: see text] limits. However, the ordering of limits does not affect the conditions for one strategy to be favored over another.
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