A Kolmogorov-Smirnov test for the molecular clock based on Bayesian ensembles of phylogenies

Author(s)

Antoneli, Fernando ^{[1, 2]} ; Passos, Fernando M. ^{[3, 2]} ; Lopes, Luciano R. ^{[1, 2]} ; Briones, Marcelo R. S. ^{[1, 2]}

Affiliation

^[1] Univ Fed Sao Paulo, Escola Paulista Med, Dept Informat Saude, Sao Paulo, SP - Brazil

^[2] Univ Fed Sao Paulo, UNIFESP, Escola Paulista Med, Lab Gen Evolut & Biocomplexidade, Rua Pedro Toledo, Sao Paulo, SP - Brazil

^[3] Univ Sao Paulo, Fac Ciencias Farmaceut, Dept Anal Clin & Toxicol, Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: PLoS One; v. 13, n. 1 JAN 4 2018.
• Web of Science Citations: 1

Abstract

Divergence date estimates are central to understand evolutionary processes and depend, in the case of molecular phylogenies, on tests of molecular clocks. Here we propose two non-parametric tests of strict and relaxed molecular clocks built upon a framework that uses the empirical cumulative distribution (ECD) of branch lengths obtained from an ensemble of Bayesian trees and well known non-parametric (one-sample and two-sample) Kolmogorov-Smirnov (KS) goodness-of-fit test. In the strict clock case, the method consists in using the one-sample Kolmogorov-Smirnov (KS) test to directly test if the phylogeny is clock-like, in other words, if it follows a Poisson law. The ECD is computed from the discretized branch lengths and the parameter. of the expected Poisson distribution is calculated as the average branch length over the ensemble of trees. To compensate for the auto-correlation in the ensemble of trees and pseudo-replication we take advantage of thinning and effective sample size, two features provided by Bayesian inference MCMC samplers. Finally, it is observed that tree topologies with very long or very short branches lead to Poisson mixtures and in this case we propose the use of the two-sample KS test with samples from two continuous branch length distributions, one obtained from an ensemble of clock-constrained trees and the other from an ensemble of unconstrained trees. Moreover, in this second form the test can also be applied to test for relaxed clock models. The use of a statistically equivalent ensemble of phylogenies to obtain the branch lengths ECD, instead of one consensus tree, yields considerable reduction of the effects of small sample size and provides a gain of power. (AU)

• FAPESP's process: 13/07838-0 - Mitochondrial microdiversity of Candida albicans and its implications in hospital-acquired infections and patterns of mitochondrial genome macroevolution
• Grantee: Marcelo Ribeiro da Silva Briones
• Support type: Regular Research Grants
• FAPESP's process: 15/50315-3 - Geometry and Dynamics between Ohio and São Paulo
• Grantee: Paolo Piccione
• Support type: Regular Research Grants