Rank Statistics in Biological Evolution

We present a statistical analysis of biological evolution processes. Specifically, we study the stochastic replication-mutation-death model where the population of a species may grow or shrink by birth or death, respectively, and additionally, mutations lead to the creation of new species. We rank the various species by the chronological order by which they originate. The average population Nk of the k th species decays algebraically with rank, Nk ∼ M k, where M is the average total population. The characteristic exponent μ = (α − γ)/(α + β − γ) depends on α, β, and γ, the replication, mutation, and death rates. Furthermore, the average population Pk of all descendants of the k species has a universal algebraic behavior, Pk ∼ M k .