相关论文: Mean and Variance of Phylogenetic Trees
Bayesian inference is now a leading technique for reconstructing phylogenetic trees from aligned sequence data. In this short note, we formally show that the maximum posterior tree topology provides a statistically consistent estimate of a…
Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC)…
In this paper we present a new way to understand the timing of branching events in phylogenetic trees. Our method explicitly considers the relative timing of diversification events between sister clades; as such it is complimentary to…
Consider a tree $T=(V,E)$ with root $\circ$ and edge length function $\ell:E\to\mathbb{R}_+$. The phylogenetic covariance matrix of $T$ is the matrix $C$ with rows and columns indexed by $L$, the leaf set of $T$, with entries…
Inferring evolutionary histories (phylogenetic trees) has important applications in biology, criminology and public health. However, phylogenetic trees are complex mathematical objects that reside in a non-Euclidean space, which complicates…
Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site…
Phylogenomics, even more so than traditional phylogenetics, needs to represent the uncertainty in evolutionary trees due to systematic error. Here we illustrate the analysis of genome-scale alignments of yeast, using robust measures of the…
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…
We study the temporal dynamics of the first two empirical moments of Brownian traits on phylogenetic trees. For a fixed tree, we characterize the distributions of their empirical mean and empirical variance across all lineages extant at any…
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…
The Frechet mean or barycenter generalizes the idea of averaging in spaces where pairwise addition is not well-defined. In general metric spaces, the Frechet sample mean is not a consistent estimator of the theoretical Frechet mean. For…
This short note provides a simple formal proof of a folklore result in statistical phylogenetics concerning the convergence of bootstrap support for a tree and its edges.
We answer two questions raised by Bryant, Francis and Steel in their work on consensus methods in phylogenetics. Consensus methods apply to every practical instance where it is desired to aggregate a set of given phylogenetic trees (say,…
We propose a new space of phylogenetic trees which we call wald space. The motivation is to develop a space suitable for statistical analysis of phylogenies, but with a geometry based on more biologically principled assumptions than…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
Variational inference is a popular method for estimating model parameters and conditional distributions in hierarchical and mixed models, which arise frequently in many settings in the health, social, and biological sciences. Variational…
Phylogenies are commonly used to represent the evolutionary relationships between species, and often these phylogenies are equipped with edge lengths that indicate degrees of evolutionary difference. Given such a phylogeny, a popular…
As demonstrated in our previous work on ${\boldsymbol T}_{4}$, the space of phylogenetic trees with four leaves, the global, as well as the local, topological structure of the space plays an important role in the non-classical limiting…
A number of methods have been developed to infer differential rates of species diversification through time and among clades using time-calibrated phylogenetic trees. However, we lack a general framework that can delineate and quantify…
Phylogenetic diversity is a popular measure for quantifying the biodiversity of a collection $Y$ of species, while phylogenetic diversity indices provide a way to apportion phylogenetic diversity to individual species. Typically, for some…