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

We investigate the evolutionary dynamics of an age-structured population subject to weak frequency-dependent selection. It turns out that the weak selection is affected in a non-trivial way by the life-history trait. We 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.

Automated summary

In this study, we investigate the evolutionary dynamics of an age-structured population under weak frequency-dependent selection and find that the weak selection is non-trivially affected by the life-history trait. By analyzing different time scales, which seem to have a universal structure in the interplay between weak selection and life-history traits, we simplify the infinite dimensional model to a one-dimensional modified replicator equation. Using this equation, we explore cooperation in the prisoner's dilemma through adaptive dynamics and identify conditions under which age structure can promote cooperation.