  We study a general setting of neutral evolution in which the population is of
finite, constant size and can have spatial structure. Mutation leads to
different genetic types ("traits"), which can be discrete or continuous. Under
minimal assumptions, we show that the marginal trait distributions of the
evolutionary process, which specify the probability that any given individual
has a certain trait, all converge to the stationary distribution of the
mutation process. In particular, the stationary frequencies of traits in the
population are independent of its size, spatial structure, and evolutionary
update rule, and these frequencies can be calculated by evaluating a simple
stochastic process describing a population of size one (i.e. the mutation
process itself). We conclude by analyzing mixing times, which characterize
rates of convergence of the mutation process along the lineages, in terms of
demographic variables of the evolutionary process.
