  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.
