Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective

Abstract

Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. As data objects, they are characterized by the challenges associated with “big data,” as well as the complication that their discrete geometric structure results in a non-Euclidean phylogenetic tree space, which poses computational and statistical limitations. We propose and study a novel framework based on tropical geometry and discuss its implications in the statistical analysis of evolutionary biological processes represented by phylogenetic trees. Our setting exhibits analytic, geometric, and topological properties that are desirable for theoretical studies in probability and statistics, as well as increased computational efficiency over the current state-of-the-art. We demonstrate our approach on seasonal influenza data.

Qiwen Kang
Qiwen Kang
Graduate Student
Bo Lin
Bo Lin
Visiting Assistant Professor

My research interests include mathematical biology, tropical geometry and combinatorics.

Anthea Monod
Anthea Monod
Lecturer (Assistant Professor with tenure)
Ruriko Yoshida
Ruriko Yoshida
Associate Professor

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