Age structure, replicator equation, and the prisoner's dilemma

TL;DR

This paper explores how age structure influences evolutionary dynamics and cooperation in populations, revealing a universal time scale structure that simplifies complex models to a modified replicator equation, with implications for understanding cooperation.

Contribution

It introduces a reduced one-dimensional replicator equation capturing age-structured dynamics under weak selection, linking life-history traits to cooperation outcomes.

Findings

Age structure can promote cooperation under certain conditions.

Universal time scales emerge in weak selection and life-history interactions.

Reduced model effectively predicts evolutionary outcomes in age-structured populations.

Abstract

We investigate the evolutionary dynamics of an age-structured population under weak frequency-dependent selection. It turns out that the weak selection is affected in a non-trivial way by the life-history trait. We can disentangle the dynamics, based on the appearance of different time scales. These time scales, which seem to form a universal structure in the interplay of weak selection and life-history traits, allow us to reduce the infinite dimensional model to a one-dimensional modified replicator equation. The modified replicator equation is then used to investigate cooperation (the prisoner's dilemma) by means of adaptive dynamics. We identify conditions under which age structure is able to promote cooperation. At the end we discuss the relevance of our findings.