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Evolution of prosocial behaviours in multilayer populations


Human societies include diverse social relationships. Friends, family, business colleagues and online contacts can all contribute to one’s social life. Individuals may behave differently in different domains, but success in one domain may engender success in another. Here, we study this problem using multilayer networks to model multiple domains of social interactions, in which individuals experience different environments and may express different behaviours. We provide a mathematical analysis and find that coupling between layers tends to promote prosocial behaviour. Even if prosociality is disfavoured in each layer alone, multilayer coupling can promote its proliferation in all layers simultaneously. We apply this analysis to six real-world multilayer networks, ranging from the socio-emotional and professional relationships in a Zambian community, to the online and offline relationships within an academic university. We discuss the implications of our results, which suggest that small modifications to interactions in one domain may catalyse prosociality in a different domain.

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Fig. 1: Evolutionary games in multilayer populations.
Fig. 2: General rule for the evolution of cooperation in multilayer populations.
Fig. 3: Multilayer games can promote cooperation.
Fig. 4: When coupling promotes cooperation.
Fig. 5: Multilayer coupling can promote cooperation even when cooperation is disfavoured in individual layers.
Fig. 6: Proportion of small networks that permit the evolution of cooperation.
Fig. 7: Multilayer coupling can catalyse the evolution of cooperation in random networks.
Fig. 8: Evolution of cooperation in six real-world two-layer networks.

Data availability

All the network datasets used in this paper are freely and publicly available at

Code availability

All code has been deposited into the publicly available GitHub repository at


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We thank E. Akçay for helpful comments. This work is supported by the Simons Foundation (Math+X Grant to the University of Pennsylvania), the National Science Foundation (grants DMS-1907583, 2042144) and The David & Lucile Packard Foundation (J.B.P.), and the John Templeton Foundation (J.B.P.).

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Authors and Affiliations



Q.S. and A.M. conceived the project and derived analytical results. Q.S. performed numerical calculations. Q.S., A.M., Y.M. and J.B.P. analysed the data. Q.S., A.M. and J.B.P. wrote the main text. Q.S. and A.M. wrote the supplementary information.

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Correspondence to Qi Su or Alex McAvoy.

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Peer review information Nature Human Behaviour thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

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Supplementary Methods, Results, Discussion, Tables 1 and 2, and Figs. 1–17.

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Su, Q., McAvoy, A., Mori, Y. et al. Evolution of prosocial behaviours in multilayer populations. Nat Hum Behav 6, 338–348 (2022).

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