Wu, XiaoweiKimmel, Marek2013-03-152013-03-152013Wu, Xiaowei and Kimmel, Marek. "Modeling neutral evolution using an in nite-allele Markov branching process." <i>International Journal of Stochastic Analysis,</i> 2013, (2013) Hindawi: http://dx.doi.org/10.1155/2013/963831.https://hdl.handle.net/1911/70685We 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.engThis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Journal articleMarkov branching processin finite alleles modelfrequency spectrumhttp://dx.doi.org/10.1155/2013/963831