Species dynamics in the two-parameter poisson-dirichlet diffusion model

• Autores: Matteo Ruggiero
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 51, Nº. 1, 2014, págs. 174-190
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • The recently introduced two-parameter infinitely-many-neutral-alleles model extends the celebrated one-parameter version (which is related to Kingman's distribution) to diffusive two-parameter Poisson-Dirichlet frequencies. In this paper 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 frequency dynamics are driven by state-dependent rather than constant quantities