Related papers: Diversity, disparity, and evolutionary rate estima…
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…
One of the classical questions in evolutionary biology is how evolutionary processes are coupled at the gene and species level. With this motivation, we compare the topological properties (mainly the depth scaling, as a characterization of…
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…
An early burst of speciation followed by a subsequent slowdown in the rate of diversification is commonly inferred from molecular phylogenies. This pattern is consistent with some verbal theory of ecological opportunity and adaptive…
In a deterministic or random tree, a notion of ancestral diversity can be defined as follows. Sample independently $n$ groups of $k$ leaves and count the number $N_n(k)$ of distinct most recent common ancestors of each of the groups. As $n$…
Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…
A simple way to model phenotypic evolution is to assume that after splitting, the trait values of the sister species diverge as independent Brownian motions. Relying only on a prior distribution for the underlying species tree (conditioned…
Phylogenetic diversity indices are commonly used to rank the elements in a collection of species or populations for conservation purposes. The derivation of these indices is typically based on some quantitative description of the…
Rooted bifurcating trees are mathematical objects used to model evolutionary relationships and arise naturally in both coalescent theory and phylogenetics. Recent numerical representations of tree topologies, known as F-matrices, allow for…
We introduce two models for multi-type random trees motivated by studies of trait dependence in the evolution of species. Our discrete time model, the multi-type ERM tree, is a generalization of Markov propagation models on a random tree…
Comparative biologists are often interested in inferring covariation between multiple biological traits sampled across numerous related taxa. To properly study these relationships, we must control for the shared evolutionary history of the…
A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree…
The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies…
Species richness varies widely across the tree of life, and there is great interest in identifying ecological, geographic, and other factors that affect rates of species proliferation. Recent methods for explicitly modeling the…
Phylogenetic inference, grounded in molecular evolution models, is essential for understanding the evolutionary relationships in biological data. Accounting for the uncertainty of phylogenetic tree variables, which include tree topologies…
Phylogenetic networks are used to represent the evolutionary history of species. They are versatile when compared to traditional phylogenetic trees, as they capture more complex evolutionary events such as hybridization and horizontal gene…
A phylogenetic variety is an algebraic variety parameterized by a statistical model of the evolution of biological sequences along a tree. Understanding this variety is an important problem in the area of algebraic statistics with…
A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct…
Inference of evolutionary trees and rates from biological sequences is commonly performed using continuous-time Markov models of character change. The Markov process evolves along an unknown tree while observations arise only from the tips…
Phylogenetic networks are increasingly used in evolutionary biology to represent the history of species that have undergone reticulate events such as horizontal gene transfer, hybrid speciation and recombination. One of the most fundamental…