The space of ultrametric phylogenetic trees. (21st August 2016)

• Record Type: Journal Article
• Authors: Gavryushkin, Alex; Drummond, Alexei J.
• Is Part Of: Journal of theoretical biology. Volume 403(2016)
• Page Start: 197
• Page End: 208
• Publication Date: 2016-08-21
• Subjects: Phylogenetic tree -- Time-tree -- Ultrametric tree -- Phylogenetic inference -- Posterior distribution summary -- Geodesic -- Simplicial complex -- Curvature -- CAT(0); Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2016.05.001
• Languages: English
• ISSNs: 0022-5193

Abstract

Abstract: The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data. Hence the question of statistical consistency of such methods is equivalent to the consistency of the summary of the sample. More generally, statistical consistency is ensured by the tree space used to analyse the sample. In this paper, we consider two standard parameterisations of phylogenetic time-trees used in evolutionary models: inter-coalescent interval lengths and absolute times of divergence events. For each of these parameterisations we introduce a natural metric space on ultrametric phylogenetic trees. We compare the introduced spaces with existing models of tree space and formulate several formal requirements that a metric space on phylogenetic trees must possess in order to be a satisfactory space for statistical analysis, and justify them. We show that only a few known constructions of the space of phylogenetic trees satisfy these requirements. However, our results suggest that these basic requirements are not enough to distinguish between the two metric spaces we introduce and that the choice between metric spaces requires additional properties to be considered. Particularly, that the summary tree minimising the square distance to the trees from the sample might be different for different parameterisations. This suggests that further fundamental insight is needed into the problem of statistical consistency of phylogenetic inference methods. Abstract : Highlights: We introduce two natural metric spaces on ultrametric phylogenetic trees. The mean (summary) tree is different for different parameterisations. Efficient algorithms are given for the intercoalescent-interval parameterisation. Mean trees are unique for the absolute-divergence-time parameterisation. The way a tree is parameterised changes geometry and algorithms dramatically.