EVOLUTION ON A SMOOTH LANDSCAPE

We study in detail a recently proposed simple discrete model for evolu tion on smooth landscapes. An asymptotic solution of this model for lo ng times is constructed. We find that the dynamics of the population i s governed by correlation functions that although being formally down by powers of N (the population size), nonetheless control the evolutio n process after a very short transient. The long-time behavior can be found analytically since only one of these higher order correlators (t he two-paint function) is relevant. We compare and contrast the exact findings derived herein with a previously proposed phenomenological tr eatment employing mean-field theory supplemented with a cutoff at smal l population density. Finally, we relate our results to the recently s tudied case of mutation on a totally flat landscape.