Evolutionary processes in finite populations.

We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov-Moran process. We show that to O(1/N), the time-averaged fitness is lower for the finite population than it is for the infinite population. We also show that fluctuations in the number of individuals for a given genotype can be proportional to a power of the inverse of the mutation rate. Finally, we show that the probability for the system to take a given path through the fitness landscape can be nonmonotonic in system size.