The ease with which neutral fixation probabilities can be derived is
deceptive. The Wright-Fisher model does not yield any other exact results
(other than the actual eigenvalues of the transition matrix). In
particular, we cannot derive expressions for the frequency spectrum of
even the two-allele case, nor can we determine, for example, the expected
time until fixation for an allele. Fisher and Wright used approximate
methods to analyze these aspects of the model, and Kimura[8] was
able to derive a more general solution. The essential strategy is to
approximate the given discrete process by a continous process, using a
little diffusion theory borrowed from physics (specifically, the
Kolmogorov forward or Fokker-Planck equation)
. The general diffusion solution
yields, among other thing, expressions for fixation probabilities for
alleles under some type of selection, and we now briefly discuss selection
models.