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Activity Number:
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38
- Inference, Optimization, and Computation on Discrete Structures
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Type:
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Invited
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Date/Time:
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Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
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Sponsor:
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IMS
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Abstract #316661
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Title:
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Statistical Summaries of Unlabeled Evolutionary Trees
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Author(s):
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Samyak Rajanala* and Julia A. Palacios
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Companies:
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Stanford University and Stanford University
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Keywords:
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binary trees;
evolutionary trees;
summarising trees;
unlabeled trees;
frechet;
combinatorial optimisation
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Abstract:
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Rooted and ranked binary trees are mathematical objects of great importance used to model hierarchical data and evolutionary relationships with applications in many fields including evolutionary biology and genetic epidemiology. Bayesian phylogenetic inference usually explore the posterior distribution of trees via MCMC methods, but assessing uncertainty and summarizing distributions or samples of such trees remains challenging. While labelled phylogenetic trees have been extensively studied, relatively less literature exists for unlabelled trees which are increasingly useful. We exploit recently proposed metrics of unlabelled ranked binary trees and genealogies (equipped with branch lengths) to define the Frechet mean and variance as summaries of these tree distributions. We provide an efficient combinatorial optimization algorithm for computing the Frechet mean from a sample of or distribution on unlabelled ranked tree shapes and unlabelled ranked genealogies. We show the applicability of our summary statistics for studying popular tree distributions and for comparing the SARS-CoV-2 evolutionary trees across different locations during the COVID-19 epidemic in 2020.
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Authors who are presenting talks have a * after their name.
