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

Mutualistic interspecific interactions, including Mullerian 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 some conditions. This is called the Red King effect. After Bergstrom and Lachmann (2003) proposed Red King effect, it has been investigated in two species models. However, biological examples suggest that the mutualisms can include three or more species. Here, I modeled the evolutionary dynamics of mutualism in communities where there exist two or more species, and all species mutually interact with one another. Regardless of the number of species in the community, it is possible to derive conditions for the stable equilibria. Although there exist nonlinear relationship 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 the faster evolution is favored or disfavored for the relatively fast species; on the other hand, it is difficult to predict the evolutionary fate of relatively slow species because the evolutionary dynamics of the slow species is affected by the evolutionary fate of the fast species.