  The recently introduced two-parameter Poisson-Dirichlet diffusion extends the
infinitely-many-neutral-alleles model, related to Kingman's distribution and to
Fleming-Viot processes. The role of the additional parameter has been shown to
regulate the clustering structure of the population, but is yet to be fully
understood in the way it governs the reproductive process. Here we shed some
light on these dynamics by providing a finite-population construction, with
finitely-many species, of the two-parameter infinite-dimensional diffusion. The
costruction is obtained in terms of Wright-Fisher chains that feature a
classical symmetric mutation mechanism and a frequency-dependent immigration,
whose inhomogeneity is investigated in detail. The local immigration dynamics
are built upon an underlying array of Bernoulli trials and can be described by
means of a dartboard experiment and a rank-dependent type distribution. These
involve a delicate balance between reinforcement and redistributive effects,
among the current species abundances, for the convergence to hold.
