Department of Biology, University of Pennsylvania, Philadelphia, PA, USA.
Proc Biol Sci. 2020 May 27;287(1927):20200735. doi: 10.1098/rspb.2020.0735.
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.
生活史策略是生命的一个重要方面，在群体生活的物种中更为复杂，因为收益还取决于他人的行为。先前关于公共物品博弈的理论模型通常侧重于个体对公共物品的贡献数量。然而，公共物品博弈中一个研究得较少的策略方面是贡献的时间，这也会对个体和集体的表现产生巨大影响。在这里，我们开发了两个两阶段博弈理论模型来探索贡献的时间如何演变。在第一阶段，个体根据表现计划为阈值公共物品做出贡献。一旦达到阈值，第二阶段就开始，然后个体根据表现进行竞争。我们展示了快速贡献并不一定是最优的，因为延迟者可以充当“骗子”，避免贡献而享受公共物品的好处。然而，延迟太久会使延迟者处于劣势，因为他们可能没有能力进行竞争。这些影响导致了单个群体中的双稳态和多个相互作用群体之间的空间多样性。
