Many species partial adaptive dynamics

A system of n asexual populations is considered in which both intra- and interspecific frequency-dependent matrix game conflicts with a lack of information are involved and the weak perturbation condition is satisfied (mutation is a very rare event and selection is quick). A new partial adaptive game dynamics is proposed that takes into account that the mutants interact not only with the residents but among themselves as well. It is also shown that if the Nash equilibrium (NE) is totally mixed and the interaction matrices are Replicator-Lyapunov stable (RL-stable), then the NE is an asymptotically stable point of these new dynamics.