Rank Statistics in Biological Evolution
E. Ben-Naim and P.L. Krapivsky
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.
source,
ps,
pdf