Evolutionary game dynamics in phenotype space

TL;DR

This paper introduces phenotype space as a new framework for evolutionary game dynamics, analyzing how behavioral strategies evolve based on phenotypic distance and providing conditions favoring cooperation.

Contribution

It develops an analytic approach combining coalescence theory with evolutionary game dynamics in phenotype space, including conditions for cooperation evolution.

Findings

Derived a precise cooperation condition in one-dimensional phenotype space

Established a fundamental evolutionary game condition in phenotype space

Explored higher-dimensional phenotype spaces

Abstract

Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of space to evolutionary game dynamics: phenotype space. The population is well-mixed in the sense that everyone is equally likely to interact with everyone else, but the behavioral strategies depend on distance in phenotype space. Individuals might behave differently towards those who look similar or dissimilar. Individuals mutate to nearby phenotypes. We study the `phenotypic space walk' of populations. We present analytic calculations that bring together ideas from coalescence theory and evolutionary game dynamics. As a particular example, we investigate the evolution of cooperation in phenotype space. We obtain a precise condition for natural selection to favor cooperators over defectors: for a one-dimensional phenotype space and large population size the critical benefit-to-cost ratio is given by b/c=1+2/sqrt{3}. We derive the fundamental condition for any evolutionary game and explore higher dimensional phenotype spaces.