  The recently introduced two-parameter infinitely-many neutral alleles model
extends the celebrated one-parameter version, related to Kingman's
distribution, to diffusive two-parameter Poisson-Dirichlet frequencies. Here we
investigate the dynamics driving the species heterogeneity underlying the
two-parameter model. First we show that a suitable normalization of the number
of species is driven by a critical continuous-state branching process with
immigration. Secondly, we provide a finite-dimensional construction of the
two-parameter model, obtained by means of a sequence of Feller diffusions of
Wright-Fisher flavor which feature finitely-many types and inhomogeneous
mutation rates. Both results provide insight into the mathematical properties
and biological interpretation of the two-parameter model, showing that it is
structurally different from the one-parameter case in that the frequencies
dynamics are driven by state-dependent rather than constant quantities.
