Evolution dynamics in terraced NK landscapes

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