Evaluating the structure-coefficient theorem of evolutionary game theory

TL;DR

This paper develops a practical method to evaluate the structure-coefficient theorem in complex, heterogeneous populations, extending its applicability to asymmetric interactions and diverse evolutionary scenarios.

Contribution

It introduces a new approach for calculating structure coefficients in arbitrary population structures, accommodating asymmetric contests and various update mechanisms.

Findings

The method applies to a wide range of population structures.

Asymmetric interactions significantly influence evolutionary outcomes.

Results vary with social good types, spatial topology, and mutation rates.

Abstract

In order to accommodate the empirical fact that population structures are rarely simple, modern studies of evolutionary dynamics allow for complicated and highly-heterogeneous spatial structures. As a result, one of the most difficult obstacles lies in making analytical deductions, either qualitative or quantitative, about the long-term outcomes of evolution. The "structure-coefficient" theorem is a well-known approach to this problem for mutation-selection processes under weak selection, but a general method of evaluating the terms it comprises is lacking. Here, we provide such a method for populations of fixed (but arbitrary) size and structure, using easily interpretable demographic measures. This method encompasses a large family of evolutionary update mechanisms and extends the theorem to allow for asymmetric contests to provide a better understanding of the mutation-selection balance under more realistic circumstances. We apply the method to study social goods produced and distributed among individuals in spatially-heterogeneous populations, where asymmetric interactions emerge naturally and the outcome of selection varies dramatically depending on the nature of the social good, the spatial topology, and frequency with which mutations arise.