The recently introduced two-parameter infinitely-many neutral alleles model extends the celebrated one-parameter version, related to Kingmans 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.

Species dynamics in the two-parameter Poisson-Dirichlet diffusion model

RUGGIERO, MATTEO
2014-01-01

Abstract

The recently introduced two-parameter infinitely-many neutral alleles model extends the celebrated one-parameter version, related to Kingmans 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.
2014
51
1
174
190
http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.jap/1395771422&page=record#info
alpha diversity; infinite-alleles model; infinite dimensional diffusion; mutation rate; Poisson-Dirichlet distribution; weak convergence
Matteo Ruggiero
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/132941
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