An algorithm for constructing principal geodesics in phylogenetic treespace

TL;DR

This paper introduces a stochastic algorithm to construct principal geodesics in treespace, enabling better summarization and visualization of phylogenetic tree samples by capturing their most variable features.

Contribution

It presents a novel stochastic method for identifying principal geodesics in treespace, improving on previous approaches for analyzing phylogenetic tree samples.

Findings

Successfully constructed principal geodesics for experimental data

Demonstrated improved insights over previous methods

Provided a freely available Java package for implementation

Abstract

Most phylogenetic analyses result in a sample of trees, but summarizing and visualizing these samples can be challenging. Consensus trees often provide limited information about a sample, and so methods such as consensus networks, clustering and multidimensional scaling have been developed and applied to tree samples. This paper describes a stochastic algorithm for constructing a principal geodesic or line through treespace which is analogous to the first principal component in standard Principal Components Analysis. A principal geodesic summarizes the most variable features of a sample of trees, in terms of both tree topology and branch lengths, and it can be visualized as an animation of smoothly changing trees. The algorithm performs a stochastic search through parameter space for a geodesic which minimises the sum of squared projected distances of the data points. This procedure aims to identify the globally optimal principal geodesic, though convergence to locally optimal geodesics is possible. The methodology is illustrated by constructing principal geodesics for experimental and simulated data sets, demonstrating the insight into samples of trees that can be gained and how the method improves on a previously published approach. A java package called GeoPhytter for constructing and visualising principal geodesics is freely available from www.ncl.ac.uk/~ntmwn/geophytter.