Emergence of a complex and stable network in a model ecosystem with extinction and mutation.

We propose a minimal model of the dynamics of diversity-replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the conventional replicator equation and the generalized Lotka-Volterra equation. We reach several significant conclusions as follows: (1) a complex ecosystem can emerge when mutants with respect to species-specific interaction are introduced; (2) such an ecosystem possesses strong resistance to invasion; (3) a typical fixation process of mutants is realized through the rapid growth of a group of mutualistic mutants with higher fitness than majority species; (4) a hierarchical taxonomic structure (like family-genus-species) emerges; and (5) the relative abundance of species exhibits a typical pattern widely observed in nature. Several implications of these results are discussed in connection with the relationship of the present model to the generalized Lotka-Volterra equation.