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

Sona John, Johannes Müller

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number109076
JournalMathematical Biosciences
StatePublished - Nov 2023


  • Age structure
  • Cooperation
  • Prisoner's dilemma
  • Replicator equation


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