Related papers: Tropical Density Estimation of Phylogenetic Trees
We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…
This paper introduces a novel kernel density estimator (KDE) based on the generalised exponential (GE) distribution, designed specifically for positive continuous data. The proposed GE KDE offers a mathematically tractable form that avoids…
Summary: Both theory and empirical evidence indicate that phylogenies (trees) of different genes (loci) do not display precisely matched topologies. This phylogenetic incongruence is attributed to the reticulated evolutionary history of…
Samples of phylogenetic trees arise in a variety of evolutionary and biomedical applications, and the Fr\'echet mean in Billera-Holmes-Vogtmann tree space is a summary tree shown to have advantages over other mean or consensus trees.…
We derive tractable criteria for the consistency of Bayesian tree reconstruction procedures, which constitute a central class of algorithms for inferring common ancestry among DNA sequence samples in phylogenetics. Our results encompass…
It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough…
Phylogenetic trees capture evolutionary relationships among species and reflect the forces that shaped them. While many studies rely on branch length information, the topology of phylogenetic trees (particularly their degree of imbalance)…
Phylogenetic trees elucidate evolutionary relationships among species, but phylogenetic inference remains challenging due to the complexity of combining continuous (branch lengths) and discrete parameters (tree topology). Traditional Markov…
Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…
For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter.…
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…
Phylogenetic networks are a generalization of phylogenetic trees that are used to represent non-tree-like evolutionary histories that arise in organisms such as plants and bacteria, or uncertainty in evolutionary histories. An…
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…
Topological phylogenetic trees can be assigned edge weights in several natural ways, highlighting different aspects of the tree. Here the rooted triple and quartet metrizations are introduced, and applied to formulate novel fast methods of…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
The inference of evolutionary histories is a central problem in evolutionary biology. The analysis of a sample of phylogenetic trees can be conducted in Billera-Holmes-Vogtmann tree space, which is a CAT(0) metric space of phylogenetic…
Phylogenetic networks are necessary to represent the tree of life expanded by edges to represent events such as horizontal gene transfers, hybridizations or gene flow. Not all species follow the paradigm of vertical inheritance of their…
Selective inference is considered for testing trees and edges in phylogenetic tree selection from molecular sequences. This improves the previously proposed approximately unbiased test by adjusting the selection bias when testing many trees…
In this paper, we study the $\alpha$-cluster tree ($\alpha$-tree) under both singular and nonsingular measures. The $\alpha$-tree uses probability contents within a level set to construct a cluster tree so that it is well-defined for…
Bayesian Markov chain Monte Carlo explores tree space slowly, in part because it frequently returns to the same tree topology. An alternative strategy would be to explore tree space systematically, and never return to the same topology. In…