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This lecture explores the challenges and opportunities in reconstructing species phylogenies from genomic data, focusing on complex discrete probability models in evolutionary biology. Learn how biological phenomena like hybrid speciation, horizontal gene transfer, gene duplication, and incomplete lineage sorting create discordant gene histories, and how these can be modeled using discrete stochastic processes including branching processes, the coalescent, and random rearrangements. Discover how Markov models on trees are used to estimate gene trees from molecular sequences, and how rigorous analysis of these complex models can guide the development of reconstruction methods with computational and statistical guarantees. The presentation includes recent research results to illustrate key concepts, and no prior biology background is required to follow the material.
