On the Matrix Condition of Phylogenetic Tree. (February 2020)

• Record Type: Journal Article
• Authors: Jhwueng, Dwueng-Chwuan; O'Meara, Brian C
• Is Part Of: Evolutionary bioinformatics online. Volume 16(2020)
• Publication Date: 2020-02
• Subjects: condition number -- phylogenetic tree -- Brownian motion -- phylogenetic comparative analysis -- covariance matrix inversion; Bioinformatics -- Periodicals; Evolutionary computation -- Periodicals; Genetic programming (Computer science) -- Periodicals; Computational Biology; Evolution, Molecular; Bioinformatics; Electronic journals; Periodicals; Fulltext; Internet Resources; Periodicals; Periodicals; 576.8
• DOI: 10.1177/1176934320901721
• Languages: English
• ISSNs: 1176-9343

Abstract

Phylogenetic comparative analyses use trees of evolutionary relationships between species to understand their evolution and ecology. A phylogenetic tree of n taxa can be algebraically transformed into an n by n squared symmetric phylogenetic covariance matrix C where each elementc ij in C represents the affinity between extant species i and extant species j . This matrix C is used internally in several comparative methods: for example, it is often inverted to compute the likelihood of the data under a model. However, if the matrix is ill-conditioned (ie, ifκ, defined by the ratio of the maximum eigenvalue of C to the minimum eigenvalue of C, is too high), this inversion may not be stable, and thus neither will be the calculation of the likelihood or parameter estimates that are based on optimizing the likelihood. We investigate this potential issue and propose several methods to attempt to remedy this issue.