Evolution of contribution timing in public goods games.

Life-history strategies are a crucial aspect of life, which are complicated in group-living species, where pay-offs additionally depend on others' behaviours. Previous theoretical models of public goods games have generally focused on the amounts individuals contribute to the public good. Yet a much less-studied strategic aspect of public goods games, the timing of contributions, can also have dramatic consequences for individual and collective performance. Here, we develop two stage game theoretical models to explore how the timing of contributions evolves. In the first stage, individuals contribute to a threshold public good based on a performance schedule. The second stage begins once the threshold is met, and the individuals then compete as a function of their performance. We show how contributing rapidly is not necessarily optimal, because delayers can act as 'cheats,' avoiding contributing while reaping the benefits of the public good. However, delaying too long can put the delayers at a disadvantage as they may be ill-equipped to compete. These effects lead to bistability in a single group, and spatial diversity among multiple interacting groups.