The Future of Systematics: Tree-Thinking Without the Tree

Phylogenetic trees are meant to represent the genealogical history of life and apparently derive their justification from the existence of the tree of life and the fact that evolutionary processes are tree-like. However, there are a number of problems for these assumptions. Here it is argued that once we understand the important role that phylogenetic trees play as models which contain idealizations, we can accept these criticisms and deny the reality of the tree while justifying the continued use of trees in phylogenetic theory and preserving nearly all of what defenders of trees have called “the importance of tree-thinking.

Operads and Phylogenetic Trees

We construct an operad $\mathrm{Phyl}$ whose operations are the edge-labelled trees used in phylogenetics. This operad is the coproduct of $\mathrm{Com}$, the operad for commutative semigroups, and $[0,\infty)$, the operad with unary operations corresponding to nonnegative real numbers, where composition is addition. We show that there is a homeomorphism between the space of $n$-ary operations of $\mathrm{Phyl}$ and $\mathcal{T}_n\times [0,\infty)^{n+1}$, where $\mathcal{T}_n$ is the space of metric $n$-trees introduced by Billera, Holmes and Vogtmann. Furthermore, we show that the Markov models used to reconstruct phylogenetic trees from genome data give coalgebras of $\mathrm{Phyl}$. These always extend to coalgebras of the larger operad $\mathrm{Com} + [0,\infty]$, since Markov processes on finite sets converge to an equilibrium as time approaches infinity. We show that for any operad $O$, its coproduct with $[0,\infty]$ contains the operad $W(O)$ constucted by Boardman and Vogt. To prove these results, we explicitly describe the coproduct of operads in terms of labelled trees.Comment: 48 pages, 3 figure

jsPhyloSVG: A Javascript Library for Visualizing Interactive and Vector-Based Phylogenetic Trees on the Web

BackgroundMany software packages have been developed to address the need for generating phylogenetic trees intended for print. With an increased use of the web to disseminate scientific literature, there is a need for phylogenetic trees to be viewable across many types of devices and feature some of the interactive elements that are integral to the browsing experience. We propose a novel approach for publishing interactive phylogenetic trees. Methods/Principal Findings We present a javascript library, jsPhyloSVG, which facilitates constructing interactive phylogenetic trees from raw Newick or phyloXML formats directly within the browser in Scalable Vector Graphics (SVG) format. It is designed to work across all major browsers and renders an alternative format for those browsers that do not support SVG. The library provides tools for building rectangular and circular phylograms with integrated charting. Interactive features may be integrated and made to respond to events such as clicks on any element of the tree, including labels. Conclusions/Significance jsPhyloSVG is an open-source solution for rendering dynamic phylogenetic trees. It is capable of generating complex and interactive phylogenetic trees across all major browsers without the need for plugins. It is novel in supporting the ability to interpret the tree inference formats directly, exposing the underlying markup to data-mining services. The library source code, extensive documentation and live examples are freely accessible at www.jsphylosvg.com

The space of ultrametric phylogenetic trees

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.Comment: Minor changes. This version has been published in JTB. 27 pages, 9 figure