Alpha-diversity processes and normalized inverse-Gaussian diffusions

The infinitely-many-neutral-alleles model has recently been extended

of two-parameter Poisson-Dirichlet type. This paper introduces

different subclass of Gibbs partitions, induced by normalized inverse-

evolution of the frequencies of infinitely-many types together with

an alpha-diversity diffusion. Constructed as a dynamic version, relative

the latter is explicitly derived from an underlying population model

of a critical Galton-Watson branching process. The class of

generator on an appropriate domain, and shown to be the limit

types. Moreover, a discrete representation is provided by means

the particles are samples from a normalized inverse-Gaussian random

the two-parameter model is also discussed.