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

• Published in: Mathematical biosciences Vol. 365; p. 109076
• Main Authors: John, Sona, Müller, Johannes
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.11.2023
• Subjects: Age structure; Biological Evolution; Cooperation; Game Theory; Humans; Models, Biological; Population Dynamics - statistics & numerical data; Prisoner Dilemma; Prisoner’s dilemma; Replicator equation; Prisoner’s dilemma; Age structure; Replicator equation; Cooperation
• ISSN: 0025-5564; 1879-3134; 1879-3134
• DOI: 10.1016/j.mbs.2023.109076

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. •We develop a generalized replicator equation for age structure and weak selection.•Generally, we find 3 time scales that seem to be universal.•We show by adaptive dynamics that age structure can promote cooperative traits.