Jun 2, 2020

Fixation probabilities for the Moran process with three or more strategies: general and coupling results

Journal of Mathematical Biology
Eliza M Ferreira, Armando G M Neves

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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Mentioned in this Paper

Fixation - Action
Study
Upper Jaw Region
Cessation of Life
Biological Evolution
Problem
Population Group
G-Protein-Coupled Receptors
Cooper

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