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The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov…
Evolutionary models used for describing molecular sequence variation suppose that at a non-recombining genomic segment, sequences share ancestry that can be represented as a genealogy--a rooted, binary, timed tree, with tips corresponding…
Mixed-effects models are among the most commonly used statistical methods for the exploration of multispecies data. In recent years, also Joint Species Distribution Models and Generalized Linear Latent Variale Models have gained in…
Phylogenetic networks are an extension of phylogenetic trees which are used to represent evolutionary histories in which reticulation events (such as recombination and hybridization) have occurred. A central question for such networks is…
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…
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…
Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…
The reconstruction of a species phylogeny from genomic data faces two significant hurdles: 1) the trees describing the evolution of each individual gene--i.e., the gene trees--may differ from the species phylogeny and 2) the molecular…
Recently there have been several attempts to provide a whole set of generators of the ideal of the algebraic variety associated to a phylogenetic tree evolving under an algebraic model. These algebraic varieties have been proven to be…
Bayesian phylogenetics is vital for understanding evolutionary dynamics, and requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric…
Traditional Quartet Puzzling algorithms use maximum likelihood methods to reconstruct quartet trees, and a puzzling algorithm to combine these quartets into a tree for the full collection of $n$ taxa. We propose a variation of Quartet…
Traditionally, phylogeny and sequence alignment are estimated separately: first estimate a multiple sequence alignment and then infer a phylogeny based on the sequence alignment estimated in the previous step. However, uncertainty in the…
Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…
Phylogenetically decisive collections of taxon sets have the property that if trees are chosen for each of their elements, as long as these trees are compatible, the resulting supertree is unique. This means that as long as the trees…
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,…
Phylogenetic networks play an important role in evolutionary biology as, other than phylogenetic trees, they can be used to accommodate reticulate evolutionary events such as horizontal gene transfer and hybridization. Recent research has…
Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…
Terraces are potentially large sets of trees with precisely the same likelihood or parsimony score, which can be induced by missing sequences in partitioned multi-locus phylogenetic data matrices. The set of trees on a terrace can be…
Discovering the latent structure from many observed variables is an important yet challenging learning task. Existing approaches for discovering latent structures often require the unknown number of hidden states as an input. In this paper,…
There is a long tradition of the axiomatic study of consensus methods in phylogenetics that satisfy certain desirable properties. One recently-introduced property is associative stability, which is desirable because it confers a…