Related papers: Information geometry for phylogenetic trees
Evolutionary relationships between species are represented by phylogenetic trees, but these relationships are subject to uncertainty due to the random nature of evolution. A geometry for the space of phylogenetic trees is necessary in order…
Phylogenetic trees summarize evolutionary relationships. The Billera-Holmes-Vogtmann (BHV) space for comparing phylogenetic trees has many elegant mathematical properties, but it does not encompass trees with differing leaf sets. To…
The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…
Phylogenetic trees summarize evolutionary relationships between organisms, and tools to analyze collections of phylogenetic trees enable contrasts between different genes' ancestry. The BHV metric space has enabled the analysis of…
The phylogenetic tree space introduced by Billera, Holmes, and Vogtmann (BHV tree space) is a CAT(0) continuous space that represents trees with edge weights with an intrinsic geodesic distance measure. The geodesic distance measure unique…
Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths…
Inferential summaries of tree estimates are useful in the setting of evolutionary biology, where phylogenetic trees have been built from DNA data since the 1960's. In bioinformatics, psychometrics and data mining, hierarchical clustering…
Computational inference of dated evolutionary histories relies upon various hypotheses about RNA, DNA, and protein sequence mutation rates. Using mutation rates to infer these dated histories is referred to as molecular clock assumption.…
Phylogenetic trees provide a fundamental representation of evolutionary relationships, yet the combinatorial explosion of possible tree topologies renders inference computationally challenging. Classical approaches to characterizing tree…
Phylogenetic inference-the derivation of a hypothesis for the common evolutionary history of a group of species- is an active area of research at the intersection of biology, computer science, mathematics, and statistics. One assumes the…
There are several tools available to infer phylogenetic trees, which depict the evolutionary relationships among biological entities such as viral and bacterial strains in infectious outbreaks, or cancerous cells in tumor progression trees.…
A classic problem in computational biology is constructing a phylogenetic tree given a set of distances between n species. In most cases, a tree structure is too constraining. We consider a circular split network, a generalization of a tree…
Ultrametric matrices are a class of covariance matrices that arise in latent tree models. As a parameter space in a statistical model, the set of ultrametric matrices is neither convex nor a smooth manifold. Focus in the literature has…
Phylogenetics is now fundamental in life sciences, providing insights into the earliest branches of life and the origins and spread of epidemics. However, finding suitable phylogenies from the vast space of possible trees remains…
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.…
Recently, an elegant approach in phylogenetics was introduced by Billera-Holmes-Vogtmann that allows a systematic comparison of different evolutionary histories using the metric geometry of tree spaces. In many problem settings one…
Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. They are also objects of interest in pure mathematics, such as algebraic geometry and combinatorics, due to their discrete geometry.…
We present two algorithms for computing the geodesic distance between phylogenetic trees in tree space, as introduced by Billera, Holmes, and Vogtmann (2001). We show that the possible combinatorial types of shortest paths between two trees…
Nested (or reconciled) phylogenetic trees model co-evolutionary systems in which one evolutionary history is embedded within another. We introduce a geometric framework for such systems by defining $\sigma$-space, a moduli space of fully…
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…