Neutral aggregation in finite-length genotype space

The advent of modern genome sequencing techniques allows for a more stringent test of the neutrality hypothesis of Darwinian evolution, where all individuals have the same fitness. Using the individual-based model of Wright and Fisher, we compute the amplitude of neutral aggregation in the genome space, i.e., the probability of finding two individuals at genetic (Hamming) distance k as a function of the genome size L, population size N, and mutation probability per base ν. In well-mixed populations, we show that for Nν<1/L, neutral aggregation is the dominant force and most individuals are found at short genetic distances from each other. For Nν>1, on the contrary, individuals are randomly dispersed in genome space. The results are extended to a geographically dispersed population, where the controlling parameter is shown to be a combination of mutation and migration probability. The theory we develop can be used to test the neutrality hypothesis in various ecological and evolutionary systems.