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The social brain hypothesis posits that species with larger brains tend to have greater social complexity. Various lines of empirical evidence have supported the social brain hypothesis, including evidence from the structure of social networks. Cooperation is a key component of group living, particularly among primates, and theoretical research has shown that particular structures of social networks foster cooperation more easily than others. Therefore, we hypothesized that species with a relatively large brain size tend to form social networks that better enable cooperation. In the present study, we combine data on brain size and social networks with theory on the evolution of cooperation on networks to test this hypothesis in non-human primates. We have found a positive effect of brain size on cooperation in social networks even after controlling for the effect of other structural properties of networks that are known to promote cooperation. 

Abstract Network structure is a mechanism for promoting cooperation in social dilemma games. In the present study, we explore graph surgery, i.e., to slightly perturb the given network, towards a network that better fosters cooperation. To this end, we develop a perturbation theory to assess the change in the propensity of cooperation when we add or remove a single edge to/from the given network. Our perturbation theory is for a previously proposed random-walk-based theory that provides the threshold benefit-to-cost ratio,$$(b/c)^*$$ ${(b/c)}^{\ast }$, which is the value of the benefit-to-cost ratio in the donation game above which the cooperator is more likely to fixate than in a control case, for any finite networks. We find that$$(b/c)^*$$ ${(b/c)}^{\ast }$decreases when we remove a single edge in a majority of cases and that our perturbation theory captures at a reasonable accuracy which edge removal makes$$(b/c)^*$$ ${(b/c)}^{\ast }$small to facilitate cooperation. In contrast,$$(b/c)^*$$ ${(b/c)}^{\ast }$tends to increase when we add an edge, and the perturbation theory is not good at predicting the edge addition that changes$$(b/c)^*$$ ${(b/c)}^{\ast }$by a large amount. Our perturbation theory significantly reduces the computational complexity for calculating the outcome of graph surgery.