The evolutionary game of interspecific mutualism in the multi-species model

Mutualistic interspecific interactions, including Müllerian mimicry and division of labor, are common in nature. In contrast to antagonistic interactions, where faster evolution is favored, mutualism can favor slower evolution under certain conditions. This is called the Red King effect. Since Bergstrom and Lachmann (2003) proposed the Red King effect, it has been investigated only in two-species models. However, biological examples suggest that mutualism can include three or more species. Here, I modeled the evolutionary dynamics of mutualism in communities where involving two or more species, and in which all species mutually interact. Regardless of the number of species in the community, it is possible to derive conditions for stable equilibria. Although nonlinear relationships exist between the evolutionary rates and the evolutionary fate of each species in the multi-species communities, the model suggests that it is possible to predict whether faster evolution is favored or disfavored for the relatively rapidly evolving species; however, it is difficult to predict the evolutionary fate of species that evolve relatively slowly because their evolutionary dynamics are affected by the evolutionary fate of species evolving rapidly.