Calculating evolutionary dynamics in structured populations.

Charles G Nathanson,Corina E Tarnita,Martin A Nowak

doi:10.1371/journal.pcbi.1000615

Charles G Nathanson, Corina E Tarnita + Show 1 more

Open Access

https://doi.org/10.1371/journal.pcbi.1000615

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Abstract

Evolution is shaping the world around us. At the core of every evolutionary process is a population of reproducing individuals. The outcome of an evolutionary process depends on population structure. Here we provide a general formula for calculating evolutionary dynamics in a wide class of structured populations. This class includes the recently introduced “games in phenotype space” and “evolutionary set theory.” There can be local interactions for determining the relative fitness of individuals, but we require global updating, which means all individuals compete uniformly for reproduction. We study the competition of two strategies in the context of an evolutionary game and determine which strategy is favored in the limit of weak selection. We derive an intuitive formula for the structure coefficient, σ, and provide a method for efficient numerical calculation.

Highlights

Constant selection implies that the fitness of individuals does not depend on the composition of the population
In evolutionary set theory individuals interact with others who are in the same set and two individuals interact as many times as they have sets in common; in games in phenotype space, individuals interact with others who share the same phenotype
It has been shown that evolutionary dynamics in a structured population can be described by a single parameter, s, if we are merely interested in the question, which of the two competing strategies, A or B, is more abundant in the limit of weak selection [41]

Summary

Introduction

Constant selection implies that the fitness of individuals does not depend on the composition of the population. The success of individuals is affected by what others are doing. We are in the realm of game theory [1,2,3] or evolutionary game theory [4,5,6,7,8] The latter is the study of frequency dependent selection; the fitness of individuals is typically assumed to be a linear function of the frequencies of strategies (or phenotypes) in the population. There is a close relationship between evolutionary game theory and ecology [10]: the success of a species in an ecosystem depends on its own abundance and the abundance of other species

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