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

Sona John; Johannes Müller

doi:10.1016/j.mbs.2023.109076

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

Math Biosci. 2023 Sep 15:365:109076. doi: 10.1016/j.mbs.2023.109076. Online ahead of print.

Authors

Sona John¹, Johannes Müller²

Affiliations

¹ School of Computation, Information and Technology, Department of Mathematics, Technical University of Munich, 85748 Garching, Germany; Comprehensive Pneumology Center (CPC)/Institute of Lung Health and Immunity (LHI), Helmholtz Center Munich, 81377 Munich, Germany.
² School of Computation, Information and Technology, Department of Mathematics, Technical University of Munich, 85748 Garching, Germany; Institute for Computational Biology, Helmholtz Center Munich, 85764 Neuherberg, Germany. Electronic address: johannes.mueller@mytum.de.

PMID: 37716407
DOI: 10.1016/j.mbs.2023.109076

Abstract

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.

Keywords: Age structure; Cooperation; Prisoner’s dilemma; Replicator equation.