  We develop an iterative global solution scheme for the backward Kolmogorov
equation of the diffusion approximation of the Wright-Fisher model of
population genetics. That model describes the random genetic drift of several
alleles at the same locus in a population from a backward perspective. The key
of our scheme is to connect the solutions before and after the loss of an
allele. Whereas in an approach via stochastic processes or partial differential
equations, such a loss of an allele leads to a boundary singularity, from a
biological or geometric perspective, this is a natural process that can be
analyzed in detail. A clarification of the role of the boundary resolves
certain uniqueness issues and enlucidates the construction of hierarchical
solutions.

Analysis of PDEs