  A number of discrete time, finite population size models in genetics
describing the dynamics of allele frequencies are known to converge (subject to
suitable scaling) to a diffusion process in the infinite population limit,
termed the Wright-Fisher diffusion. In this article we show that the diffusion
is ergodic uniformly in the selection and mutation parameters, and that the
measures induced by the solution to the stochastic differential equation are
uniformly locally asymptotically normal. Subsequently these two results are
used to analyse the statistical properties of the Maximum Likelihood and
Bayesian estimators for the selection parameter, when both selection and
mutation are acting on the population. In particular, it is shown that these
estimators are uniformly over compact sets consistent, display uniform in the
selection parameter asymptotic normality and convergence of moments over
compact sets, and are asymptotically efficient for a suitable class of loss
functions.
