Asymptotic behaviour of an infinitely-many-alleles diffusion with symmetric overdominance

Youzhou Zhou

doi:10.1016/j.spa.2014.03.011

Asymptotic behaviour of an infinitely-many-alleles diffusion with symmetric overdominance

Youzhou Zhou^*

^*Corresponding author for this work

McMaster University

Research output: Contribution to journal › Article › peer-review

Abstract

This paper considers the limiting distribution of πλ, _θ, the stationary distribution of the infinitely-many-alleles diffusion with symmetric overdominance (Ethier and Kurtz, 1998). In Feng (2009) the large deviation principle for πλ,_θ indicates that there are countably many phase transitions for the limiting distribution of πλ,_θ, and the critical points are λ=k(k+1),k≤1. The asymptotic behaviours at those critical points, however, are unclear. This article provides a definite description of the critical cases.

Original language	English
Pages (from-to)	2771-2798
Number of pages	28
Journal	Stochastic Processes and their Applications
Volume	124
Issue number	8
DOIs	https://doi.org/10.1016/j.spa.2014.03.011
Publication status	Published - Aug 2014
Externally published	Yes

Keywords

Homozygosity
Overdominant selection
Phase transition

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abstract = "This paper considers the limiting distribution of πλ, θ, the stationary distribution of the infinitely-many-alleles diffusion with symmetric overdominance (Ethier and Kurtz, 1998). In Feng (2009) the large deviation principle for πλ,θ indicates that there are countably many phase transitions for the limiting distribution of πλ,θ, and the critical points are λ=k(k+1),k≤1. The asymptotic behaviours at those critical points, however, are unclear. This article provides a definite description of the critical cases.",

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AB - This paper considers the limiting distribution of πλ, θ, the stationary distribution of the infinitely-many-alleles diffusion with symmetric overdominance (Ethier and Kurtz, 1998). In Feng (2009) the large deviation principle for πλ,θ indicates that there are countably many phase transitions for the limiting distribution of πλ,θ, and the critical points are λ=k(k+1),k≤1. The asymptotic behaviours at those critical points, however, are unclear. This article provides a definite description of the critical cases.

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KW - Overdominant selection

KW - Phase transition

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Asymptotic behaviour of an infinitely-many-alleles diffusion with symmetric overdominance

Abstract

Keywords

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