Wu, Xiaowei and Kimmel, Marek. "Modeling neutral evolution using an in nite-allele Markov branching process." International Journal of Stochastic Analysis, 2013, (2013) Hindawi: http://dx.doi.org/10.1155/2013/963831.
We consider an in nite-allele Markov branching process (IAMBP). Our main focus
is the frequency spectrum of this process, i.e., the proportion of alleles having a given
number of copies at a speci ed 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 o spring
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.
Markov branching process; in finite alleles model; frequency spectrum
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