Quasi-Species in High Dimensional Spaces

We show that, under certain assumptions, the fitness of almost all quasi-species becomes independent of mutational probabilities and the initial frequency distributions of the sequences in high dimensional sequence spaces. This result is the consequence of the concentration of measure on a high dimensional hypersphere and its extension to Lipschitz functions knows as the Levy's Lemma. Therefore, evolutionary dynamics almost always yields the same value for fitness of the quasi-species, independe...