  A population genetics model based on a multitype branching process, or
equivalently a Galton-Watson branching process for multiple alleles, is pre-
sented. The diffusion limit forward Kolmogorov equation is derived for the case
of neutral mutations. The asymptotic stationary solution is obtained and has
the property that the extant population partitions into subpopulations whose
relative sizes are determined by mutation rates. An approximate time-dependent
solution is obtained in the limit of low mutation rates. This solution has the
property that the system undergoes a rapid transition from a drift-dominated
phase to a mutation-dominated phase in which the distribution collapses onto
the asymptotic stationary distribution. The changeover point of the transition
is determined by the per-generation growth factor and mutation rate. The
approximate solution is confirmed using numerical simulations.
