Abstract. 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 N_k of the kth species decays algebraically with rank, N_k ~ M^μk^−μ, 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 P_k of all descendants of the kth species has a universal algebraic behaviour, P_k ~ M k⁻¹.

Key words: models for evolution (theory)

E-print number: q-bio.PE/0508023
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Refers: to

Received 18 August 2005, accepted for publication 4 October 2005
Published 18 October 2005