Evolutionary dynamics on any population structure

TL;DR

This paper derives a universal formula for weak selection in evolutionary dynamics on any population structure, enabling analysis of diverse networks and their influence on cooperation.

Contribution

It introduces a general weak selection formula applicable to any graph or social network, using coalescent theory and meeting times of random walks.

Findings

Cooperation is most favored in societies with strong pairwise ties.

The method allows evaluation of how structural changes affect evolution.

The formula applies to arbitrary population structures and selection intensities.

Abstract

Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been absent for a long time, but have recently emerged for special structures where all individuals have the same number of neighbors. But the problem of determining which trait is favored by selection in the natural case where the number of neighbors can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class which suggests there is no efficient algorithm. Whether there exists a simple solution for weak selection was unanswered. Here we provide, surprisingly, a general formula for weak selection that applies to any graph or social network. Our method uses coalescent theory and relies on calculating the meeting times of random walks. We can now evaluate large numbers of diverse and heterogeneous population structures for their propensity to favor cooperation. We can also study how small changes in population structure---graph surgery---affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.