  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.
