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For a given species tree, ancestral configurations are the gene lineages which can be present at a node of the species tree over the set of all gene trees. Root ancestral configurations are the ancestral configurations which are present at the root. They play an important role in a (standard) algorithm for computing probabilities of gene trees that have evolved within the given species tree. In particular, their number is a measure for the complexity of this algorithm. In this talk, we give background, review recent results about the number of ancestral configurations and root ancestral configurations for matching species and gene trees under the uniform and Yule Harding model, and explain our recent refinements of these results which concern moments and limit laws. The talk is based on joint work with F. Disanto (University of Pisa), A. R. Paningbatan (University of the Philippines Diliman), C.-Y. Huang (National Chiao Tung University), and N. A. Rosenberg (Stanford University).

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更多資訊 https://web.math.nccu.edu.tw/mfuchs/comp-meth-ICIAM.pdf