Imputing phylogenetic trees using tropical polytopes over the space of phylogenetic trees

TL;DR

This paper introduces a novel tropical geometry-based method for imputing missing parts of phylogenetic trees, leveraging tropical polytopes to improve accuracy in gene tree reconstruction.

Contribution

It proposes a new approach using tropical polytopes for phylogenetic tree imputation, extending classical linear regression concepts into tropical geometry.

Findings

Guaranteed RF distance bound of four from ground truth

Method performs well on simulated data

Utilizes tropical convex hulls for phylogenetic inference

Abstract

When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a sample of gene trees. In this short paper we propose a novel method to infer a missing part of a phylogenetic tree using an analogue of a classical linear regression in the setting of tropical geometry. In our approach, we consider a tropical polytope, a convex hull with respect to the tropical metric closest to the data points. We show a condition that we can guarantee that an estimated tree from our method has at most four Robinson-Foulds (RF) distance from the ground truth and computational experiments with simulated data show our method works well.