While hidden class models of various types arise in many statistical applications, it is often
difficult to establish the identifiability of their parameters. Focusing on models in which there is …

The general Markov model of the evolution of biological sequences along a tree leads to a
parameterization of an algebraic variety. Understanding this variety and the polynomials, …

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 …

Gene trees are evolutionary trees representing the ancestry of genes sampled from multiple
populations. Species trees represent populations of individuals—each with many genes—…

A phylogenetic invariant for a model of biological sequence evolution along a phylogenetic
tree is a polynomial that vanishes on the expected frequencies of base patterns at the …

Species networks generalize the notion of species trees to allow for hybridization or other
lateral gene transfer. Under the network multispecies coalescent model, individual gene trees …

MSCquartets is an R package for species tree hypothesis testing, inference of species trees
and inference of species networks under the Multispecies Coalescent model of incomplete …

Phylogenetic data arising on two possibly different tree topologies might be mixed through
several biological mechanisms, including incomplete lineage sorting or horizontal gene …

We consider the evolution of phylogenetic gene trees along phylogenetic species networks,
according to the network multispecies coalescent process, and introduce a new network …

Inference of evolutionary trees and rates from biological sequences is commonly performed
using continuous-time Markov models of character change. The Markov process evolves …