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March 2014 Species dynamics in the two-parameter Poisson-Dirichlet diffusion model
Matteo Ruggiero
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J. Appl. Probab. 51(1): 174-190 (March 2014). DOI: 10.1239/jap/1395771422

Abstract

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.

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Matteo Ruggiero. "Species dynamics in the two-parameter Poisson-Dirichlet diffusion model." J. Appl. Probab. 51 (1) 174 - 190, March 2014. https://doi.org/10.1239/jap/1395771422

Information

Published: March 2014
First available in Project Euclid: 25 March 2014

zbMATH: 1291.60162
MathSciNet: MR3189450
Digital Object Identifier: 10.1239/jap/1395771422

Subjects:
Primary: 60J60
Secondary: 60G57, 92D25

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 1 • March 2014
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