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arXiv · 2606.03071

Evolution of cooperation in spatially structured group-selection models of the continuous Prisoner's Dilemma

Yaroslav Ispolatov·Burton Simon·Michael Doebeli
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Abstract

We consider continuous Prisoner's Dilemma games played in a spatial setting by group-structured populations. The evolutionary dynamics is driven by within-group individual-level birth and death events, and by group-level fission and extinction events. Within groups, individuals play well-mixed games, while groups play games on a 1-dimensional spatial grid against their nearest neighbours. Payoffs from individual-level games affect birth rates of individuals, and payoffs from group-level games affect group extinction and fission probabilities. It is well known that the within-group evolution by itself always results in a complete loss of cooperation, and that in the group-level games, defection is also favoured if these games are played in well-mixed populations of groups. Here we show that despite this double disadvantage, cooperation can be maintained due to spatially structured group-level dynamics. Mirroring results from one-level selection models, the spatial nature of games between groups and the resulting fissioning and extinction events is essential for the evolution of cooperation in these models, but needs to manifest itself in specific ways in order to be effective: we find that higher levels of cooperation evolve when the selection generated by games between groups acts locally rather than globally.

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Yaroslav Ispolatov, Burton Simon, Michael Doebeli. 2026-06-02. Evolution of cooperation in spatially structured group-selection models of the continuous Prisoner's Dilemma. https://arxiv.org/abs/2606.03071

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