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Quantitative Biology > Populations and Evolution

Title:Rank Statistics in Biological Evolution

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^{mu} k^{-mu}, where M is the average total population. The characteristic exponent mu=(alpha-gamma)/(alpha+beta-gamma)$ depends on alpha, beta, and gamma, the replication, mutation, and death rates. Furthermore, the average population P_k of all descendants of the kth species has a universal algebraic behavior, P_k ~ M/k.
Comments: 4 pages, 3 figures
Subjects: Populations and Evolution (q-bio.PE); Statistical Mechanics (cond-mat.stat-mech); Probability (math.PR); Genomics (q-bio.GN)
Journal reference: J. Stat. Mech. L10002 (2005)
DOI: 10.1088/1742-5468/2005/10/L10002
Cite as: arXiv:q-bio/0508023 [q-bio.PE]
  (or arXiv:q-bio/0508023v1 [q-bio.PE] for this version)

Submission history

From: Eli Ben-Naim [view email]
[v1] Thu, 18 Aug 2005 04:52:50 UTC (12 KB)