ArticleJournal of mathematical biology2020
Fixation probabilities for the Moran process with three or more strategies: general and coupling results.
Article in Journal of mathematical biology, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Martingales and the fixation time of evolutionary graphs with arbitrary dimensionality.Royal Society open science · 2022Article
- Martingales and the characteristic functions of absorption time on bipartite graphs.Royal Society open science · 2021Article
- Are Adaptive Chemotherapy Schedules Robust? A Three-Strategy Stochastic Evolutionary Game Theory Model.Cancers · 2021Article
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2 authors.
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Abstract
We study fixation probabilities for the Moran stochastic process for the evolution of a population with three or more types of individuals and frequency-dependent fitnesses. Contrary to the case of populations with two types of individuals, in which fixation probabilities may be calculated by an exact formula, here we must solve a large system of linear equations. We first show that this system always has a unique solution. Other results are upper and lower bounds for the fixation probabilities obtained by coupling the Moran process with three strategies with birth-death processes with only two strategies. We also apply our bounds to the problem of evolution of cooperation in a population with three types of individuals already studied in a deterministic setting by Núñez Rodríguez and Neves (J Math Biol 73:1665-1690, 2016). We argue that cooperators will be fixated in the population with probability arbitrarily close to 1 for a large region of initial conditions and large enough population sizes.
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