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Explore complex discrete probability models used in evolutionary biology through this mathematical lecture that examines the challenges of reconstructing species phylogenies from genomic data. Delve into how genes evolve under various biological phenomena including hybrid speciation, horizontal gene transfer, gene duplication and loss, and incomplete lineage sorting, all modeled using random gene tree distributions based on discrete stochastic processes such as branching processes, coalescent theory, and random rearrangements. Learn how gene trees are estimated from molecular sequences using Markov models on trees, and discover how rigorous analysis of these complex models guides the design of new reconstruction methods with computational and statistical guarantees. Examine recent research results that illustrate both the challenges and opportunities in this interdisciplinary field, with no prior biology background required to follow the mathematical concepts and probabilistic frameworks presented.
