Evolutionary Processes in Finite Populations

TL;DR

This paper analyzes how finite population size affects evolutionary dynamics on arbitrary fitness landscapes, revealing differences from infinite populations in average fitness, fluctuations, and path probabilities.

Contribution

It introduces a Markov Moran process framework to quantify finite population effects, including lower average fitness and non-monotonic path probabilities.

Findings

Finite populations have lower time-averaged fitness than infinite populations.

Fluctuations in genotype counts can scale with the inverse mutation rate.

Path probabilities can vary non-monotonically with system size.

Abstract

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 $\mathcal O(1/N)$, 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 non-monotonic in system size.