Evolution dynamics in terraced NK landscapes

We consider populations of agents evolving in the fitness landscape of an extended NK model with a tunable amount of neutrality. We study the statistics of the jumps in mean population fitness which occur in the "punctuated equilibrium" regime and show that, for a wide range of landscapes parameters, the number of events in time t is Poisson distributed, with the time parameter replaced by the logarithm of time. This simple log-Poisson statistics likewise describes the number of records in any sequence of t independently generated random numbers. The implications of such behavior for evolution dynamics are discussed.