E Ben-Naim and P L Krapivsky J. Stat. Mech. (2005) L10002 doi:10.1088/1742-5468/2005/10/L10002
E Ben-Naim1 and P L Krapivsky2
Show affiliationsWe 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 kth species decays algebraically with rank, Nk ~ Mμk−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 Pk of all descendants of the kth species has a universal algebraic behaviour, Pk ~ M k−1.
E-print Number: q-bio.PE/0508023
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87.23.Kg Dynamics of evolution
87.23.Cc Population dynamics and ecological pattern formation
60B15 Probability measures on groups, Fourier transforms, factorization
92D10 Genetics (For genetic algebras, see 17D92)
Issue 10 (October 2005)
Received 18 August 2005, accepted for publication 4 October 2005
Published 18 October 2005
E Ben-Naim and P L Krapivsky J. Stat. Mech. (2005) L10002
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