Resource allocation in tragedy of the commons game in plants for belowground competition

The tragedy of the commons (TOC) has been well known since it was proposed and has been widely applied not only to human society but also to many taxa. An increasing number of studies have focused on TOC in belowground competition in plants. In the presence of neighbors, plants overproduce roots to acquire more nutrients than their competitors, resulting in a reduction in reproductive yield. Game-theoretic studies on TOC in plants usually consider the amount of root biomass as a strategy and do not consider the growth of plants. However, root volume is considered an outcome of the decision-making of plants on whether they allocate more resources to the root. In this study, we incorporated resource allocation and growth dynamics into the TOC game in plants and explored the evolutionarily stable resource allocation strategy in the presence of neighbors. We demonstrated that TOC generally occurs when fitness per individual is always reduced because of the competitive response. However, the overproliferation of roots, which is emphasized as an indicator of TOC, did not necessarily occur, or was sometimes difficult to detect when fitness is largely or completely determined by root biomass. This result suggests the importance of careful observation for examining whether plant species engage in a TOC game.