Data from: The evolution of generalized reciprocity on social interaction networks

Generalized reciprocity (“help anyone, if helped by someone”) is a minimal strategy capable of supporting cooperation between unrelated individuals. Its simplicity makes it an attractive model to explain the evolution of reciprocal altruism in animals that lack the information or cognitive skills needed for other types of reciprocity. Yet, generalized reciprocity is anonymous and thus defenseless against exploitation by defectors. Recognizing that animals hardly ever interact randomly, we investigate whether social network structure can mitigate this vulnerability. Our results show that heterogeneous interaction patterns strongly support the evolution of generalized reciprocity. The future probability of being rewarded for an altruistic act is inversely proportional to the average connectivity of the social network when cooperators are rare. Accordingly, sparse networks are conducive to the invasion of reciprocal altruism. Moreover, the evolutionary stability of cooperation is enhanced by a modular network structure. Communities of reciprocal altruists are protected against exploitation, because modularity increases the mean access time, i.e., the average number of steps that it takes for a random walk on the network to reach a defector. Sparseness and community structure are characteristic properties of vertebrate social interaction patterns, as illustrated by network data from natural populations ranging from fish to primates.

广义互惠（Generalized reciprocity，即"受助于人则助人于任何人"）是一种可维系无亲缘关系个体间合作的极简策略。其简洁性使其成为解释缺乏其他互惠类型所需信息与认知技能的动物的互惠利他主义（reciprocal altruism）演化过程的极具吸引力的模型。然而，广义互惠具有匿名性，因此无法抵御背叛者的剥削。鉴于动物的互动几乎并非随机发生，我们探究社交网络（social network）结构能否缓解这一脆弱性。我们的研究结果表明，异质性互动模式可显著促进广义互惠的演化。当合作者稀缺时，利他行为获得回报的未来概率与社交网络的平均连接度呈反比关系。据此，稀疏网络有利于互惠利他主义的侵入与扩散。此外，模块化网络结构（modular network structure）可提升合作的演化稳定性。互惠利他者构成的社群可免受剥削，因为模块化提升了平均访问时长——即网络上随机游走（random walk）抵达背叛者所需的平均步数。稀疏性与社群结构是脊椎动物社交互动模式的典型特征，这一点可通过从鱼类到灵长类的各类自然种群的网络数据得到佐证。