Correlated pay-offs are key to cooperation.

The general belief that cooperation and altruism in social groups result primarily from kin selection has recently been challenged, not least because results from cooperatively breeding insects and vertebrates have shown that groups may be composed mainly of non-relatives. This allows testing predictions of reciprocity theory without the confounding effect of relatedness. Here, we review complementary and alternative evolutionary mechanisms to kin selection theory and provide empirical examples of cooperative behaviour among unrelated individuals in a wide range of taxa. In particular, we focus on the different forms of reciprocity and on their underlying decision rules, asking about evolutionary stability, the conditions selecting for reciprocity and the factors constraining reciprocal cooperation. We find that neither the cognitive requirements of reciprocal cooperation nor the often sequential nature of interactions are insuperable stumbling blocks for the evolution of reciprocity. We argue that simple decision rules such as 'help anyone if helped by someone' should get more attention in future research, because empirical studies show that animals apply such rules, and theoretical models find that they can create stable levels of cooperation under a wide range of conditions. Owing to its simplicity, behaviour based on such a heuristic may in fact be ubiquitous. Finally, we argue that the evolution of exchange and trading of service and commodities among social partners needs greater scientific focus.