  We consider an infinitely-many neutral allelic model of population genetics
where all alleles are divided into a finite number of classes, and each class
is characterized by its own mutation rate. For this model the allelic
composition of a sample taken from a very large population of genes is
characterized by a random matrix, and the problem is to describe the joint
distribution of the matrix entries. The answer is given by a new generalization
of the classical Ewens sampling formula called the refined Ewens sampling
formula in the present paper. We discuss a Poisson approximation for the
refined Ewens sampling formula, and present its derivation by several methods.
As an application we obtain limit theorems for the numbers of alleles in
different asymptotic regimes.
