Kimmel, Marek2011-07-252011-07-252010Wu, Xiaowei. "Branching processes with biological applications." (2010) Diss., Rice University. <a href="https://hdl.handle.net/1911/61992">https://hdl.handle.net/1911/61992</a>.https://hdl.handle.net/1911/61992Branching processes play an important role in models of genetics, molecular biology, microbiology, ecology and evolutionary theory. This thesis explores three aspects of branching processes with biological applications. The first part of the thesis focuses on fluctuation analysis, with the main purpose to estimate mutation rates in microbial populations. We propose a novel estimator of mutation rates, and apply it to a number of Luria-Delbruck type fluctuation experiments in Saccharomyces cerevisiae. Second, we study the extinction of Markov branching processes, and derived theorems for the path to extinction in the critical case, as an extension to Jagers' theory. The third part of the thesis introduces infinite-allele Markov branching processes. As an important non-trivial example, the limiting frequency spectrum for the birth-death process has been derived. Potential application of modeling the proliferation and mutation of human Alu sequences is also discussed.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.StatisticsThesisTHESIS STAT. 2010 WU