Statistical Phylogenetic Tree Analysis Using Differences of Means

TL;DR

This paper introduces a statistical method for comparing phylogenetic tree distributions to detect significant incongruences, aiding in understanding genome evolution events like horizontal gene transfer.

Contribution

It presents a novel statistical approach using difference of means and kernel embeddings to compare tree distributions, with applications to real biological data and a supporting toolkit.

Findings

Successfully distinguishes gene tree sets under different models

Detects unusual genome evolution events in real datasets

Provides a computational toolkit for phylogenetic analysis

Abstract

We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by the input alignments, instead of comparing point estimations of trees. This statistical approach can be applied to gene tree analysis for example, detecting unusual events in genome evolution such as horizontal gene transfer and reshuffling. Our method uses difference of means to compare two distributions of trees, after embedding trees in a vector space. Bootstrapping alignment columns can then be applied to obtain p-values. To compute distances between means, we employ a "kernel trick" which speeds up distance calculations when trees are embedded in a high-dimensional feature space, e.g. splits or quartets feature space. In this pilot study, first we test our statistical method's ability to distinguish between sets of gene trees generated under coalescence models with species trees of varying dissimilarity. We follow our simulation results with applications to various data sets of gophers and lice, grasses and their endophytes, and different fungal genes from the same genome. A companion toolkit, {\tt Phylotree}, is provided to facilitate computational experiments.