Title: Inferring Microbial Gene Family Evolution using Duplication-Transfer-Loss Reconciliation: Algorithms and Complexity Major Advisor: Dr. Mukul Bansal Associate Advisors: Dr. Ion Mandoiu, Dr. Yufeng Wu, Dr. Sheida Nabavi Date/Time: Friday, December 1, 2017 at 3:30pm Location: Homer Babbidge Library Class of 1947 Conference Room Reconstructing the evolutionary histories of genes and genomes is an important problem in evolutionary biology and fundamental to our modern understanding of biology. In microbes, gene families evolve through complex evolutionary processes such as speciation, gene duplication, horizontal gene transfer, and gene loss. In the typical formulation of this problem, called DTL reconciliation problem, the goal is to reconcile an input gene tree (gene family phylogeny) to the corresponding rooted species tree by postulating speciation, duplication, transfer, and loss events. In this dissertation proposal, we focus on one of the most important limitations of the DTL reconciliation framework, gene uncertainty, and provide new problem formulations, analyze the computational complexities of the new formulations, and provide FPT algorithms for it.