The role of second-order punishers and non-participants in the evolution of altruism through punishment

Altruistic punishment has been hypothesized to be important in the evolution of human cooperative behaviour. Although theoretical models have sought to establish the plausibility of this hypothesis, the empirical validity and robustness of such models remains largely untested. Here, we replicate and extend a prominent deterministic model of the evolution of altruism through punishment by Fowler (Fowler 2005 Proc. Natl Acad. Sci. USA 102, 7047–7049. (doi:10.1073/pnas.0500938102)), exploring parameter sensitivity and varying key assumptions. We find that the evolution of cooperation depends critically on the possibility of voluntary non-participation as a strategy, allowing agents to survive while opting out of the public goods game altogether, as well as the presence of strong second-order punishment, where all first-order punishers are also second-order punishers. Although further modifications to the model allow cooperation to evolve with a low frequency of second-order punishers, the possibility of non-participation remains necessary for altruism to evolve. These results call into question the robustness and empirical validity of this model and stress the importance of exploring the key assumptions of theoretical models.