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arXiv · 1204.6023

Evolutionary Processes in Finite Populations

Dirk M. Lorenz·Jeong-Man Park·Michael W. Deem
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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.

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Dirk M. Lorenz, Jeong-Man Park, Michael W. Deem. 2013-01-25. Evolutionary Processes in Finite Populations. https://doi.org/10.1103/physreve.87.022704

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