Uncertainty in phylogenetic tree estimates

Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly model the multivariate uncertainty of tree estimates. We consider both the cases where uncertainty information arises extrinsically (through covariate information) and intrinsically (through the tree estimates themselves). The importance of accounting for tree uncertainty in tree space is demonstrated in two case studies. In the first instance, differences between gene trees are small relative to their uncertainties, while in the second, the differences are relatively large. Our main goal is visualization of tree uncertainty, and we demonstrate advantages of our method with respect to reproducibility, speed and preservation of topological differences compared to visualization based on multidimensional scaling. The proposal highlights that phylogenetic trees are estimated in an extremely high-dimensional space, resulting in uncertainty information that cannot be discarded. Most importantly, it is a method that allows biologists to diagnose whether differences between gene trees are biologically meaningful, or due to uncertainty in estimation.Comment: Final version accepted to Journal of Computational and Graphical Statistic

Combining Prior Information for the Prediction of Transcription Factor Binding Sites

Despite the fact that each cell in an organism has the same genetic information, it is possible that cells fundamentally differ in their function. The molecular basis for the functional diversity of cells is governed by biochemical processes that regulate the expression of genes. Key to this regulatory process are proteins called transcription factors that recognize and bind specific DNA sequences of a few nucleotides. Here we tackle the problem of identifying the binding sites of a given transcription factor. The prediction of binding preferences from the structure of a transcription factor is still an unsolved problem. For that reason, binding sites are commonly identified by searching for overrepresented sites in a given collection of nucleotide sequences. Such sequences might be known regulatory regions of genes that are assumed to be coregulated, or they are obtained from so-called ChIP-seq experiments that identify approximately the sites that were bound by a given transcription factor. In both cases, the observed nucleotide sequences are much longer than the actual binding sites and computational tools are required to uncover the actual binding preferences of a factor. Aggravated by the fact that transcription factors recognize not only a single nucleotide sequence, the search for overrepresented patterns in a given collection of sequences has proven to be a challenging problem. Most computational methods merely relied on the given set of sequences, but additional information is required in order to make reliable predictions. Here, this information is obtained by looking at the evolution of nucleotide sequences. For that reason, each nucleotide sequence in the observed data is augmented by its orthologs, i.e. sequences from related species where the same transcription factor is present. By constructing multiple sequence alignments of the orthologous sequences it is possible to identify functional regions that are under selective pressure and therefore appear more conserved than others. The processing of the additional information exerted by ortholog sequences relies on a phylogenetic tree equipped with a nucleotide substitution model that not only carries information about the ancestry, but also about the expected similarity of functional sites. As a result, a Bayesian method for the identification of transcription factor binding sites is presented. The method relies on a phylogenetic tree that agrees with the assumptions of the nucleotide substitution process. Therefore, the problem of estimating phylogenetic trees is discussed first. The computation of point estimates relies on recent developments in Hadamard spaces. Second, the statistical model is presented that captures the enrichment and conservation of binding sites and other functional regions in the observed data. The performance of the method is evaluated on ChIP-seq data of transcription factors, where the binding preferences have been estimated in previous studies

Review Paper: The Shape of Phylogenetic Treespace

Trees are a canonical structure for representing evolutionary histories. Many popular criteria used to infer optimal trees are computationally hard, and the number of possible tree shapes grows super-exponentially in the number of taxa. The underlying structure of the spaces of trees yields rich insights that can improve the search for optimal trees, both in accuracy and in running time, and the analysis and visualization of results. We review the past work on analyzing and comparing trees by their shape as well as recent work that incorporates trees with weighted branch lengths