Genealogical methods for multitype branching processes with applications in biology

Biological populations are naturally organized into lineages of reproducing particles. Multitype branching processes are a probabilistic description of such systems. Historically, branching process models have been used to study the extinction and the long term growth of populations. This thesis develops new methods for analyzing samples drawn from branching processes. The main results are methods to analyze the genealogy of individuals randomly sampled from the process. The genealogical analysis applies to a novel problems arising in molecular biology. The main application in the thesis involves mutations which arise in Polymerase Chain Reaction (PCR) experiments. By modeling the PCR procedure with a branching process, inferences can be made regarding diversity in the PCR products