Modeling Neutral Evolution Using an Infinite-Allele Markov Branching Process | Zendy

Xiaowei Wu | Zendy; Marek Kimmel | Zendy

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Modeling Neutral Evolution Using an Infinite-Allele Markov Branching Process

Author(s) -

Xiaowei Wu,

Marek Kimmel

Publication year - 2013

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.19

H-Index - 28

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2013/963831

Subject(s) - mathematics , branching process , birth–death process , point process , hypergeometric function , markov chain , markov process , limit (mathematics) , spectrum (functional analysis) , statistics , mathematical analysis , population , physics , demography , quantum mechanics , sociology

We consider an infinite-allele Markov branching process (IAMBP). Our main focus is the frequency spectrum of this process, that is, the proportion of alleles having a given number of copies at a specified time point. We derive the variance of the frequency spectrum, which is useful for interval estimation and hypothesis testing for process parameters. In addition, for a class of special IAMBP with birth and death offspring distribution, we show that the mean of its limiting frequency spectrum has an explicit form in terms of the hypergeometric function. We also derive an asymptotic expression for convergence rate to the limit. Simulations are used to illustrate the results for the birth and death process

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