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Phylogenetic trait evolution models allow for the estimation of evolutionary correlations between a set of traits observed in a sample of related organisms. By directly modeling the evolution of the traits along an estimable phylogenetic…
Latent space models for network data characterize each node through a vector of latent features whose pairwise similarities define the edge probabilities among the pairs of nodes. Although this formulation has led to successful…
In evolutionary biology, the speciation history of living organisms is represented graphically by a phylogeny, that is, a rooted tree whose leaves correspond to current species and branchings indicate past speciation events. Phylogenies are…
Phylogenetics, the inference of evolutionary trees from molecular sequence data such as DNA, is an enterprise that yields valuable evolutionary understanding of many biological systems. Bayesian phylogenetic algorithms, which approximate a…
Statistical consistency in phylogenetics has traditionally referred to the accuracy of estimating phylogenetic parameters for a fixed number of species as we increase the number of characters. However, as sequences are often of fixed length…
Simple stochastic models for phylogenetic trees on species have been well studied. But much paleontology data concerns time series or trees on higher-order taxa, and any broad picture of relationships between extant groups requires use of…
Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the (unknown) subset of current species that will still be present at some future time, then this…
Modelling the substitution of nucleotides along a phylogenetic tree is usually done by a hidden Markov process. This allows to define a distribution of characters at the leaves of the trees and one might be able to obtain polynomial…
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…
We propose a model of the evolution of a matrix along a phylogenetic tree, in which transformations affect either entire rows or columns of the matrix. This represents the change of both lexical and phonological aspects of linguistic data,…
There have been many studies to examine whether one trait is correlated with another trait across a group of present-day species (for example, do species with larger brains tend to have longer gestation times. Since the introduction of the…
The goal of branch length estimation in phylogenetic inference is to estimate the divergence time between a set of sequences based on compositional differences between them. A number of software is currently available facilitating branch…
Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the…
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
Covarion models of character evolution describe inhomogeneities in substitution processes through time. In phylogenetics, such models are used to describe changing functional constraints or selection regimes during the evolution of…
We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by the input alignments, instead of comparing…
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…
Phylogenetic trees are widely used to understand the evolutionary history of organisms. Tree shapes provide information about macroevolutionary processes. However, macroevolutionary models are unreliable for inferring the true processes…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…