Related papers: Counting Tree-Child Networks and Their Subclasses

Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…

Evolutionary histories for species that cross with one another or exchange genetic material can be represented by leaf-labelled, directed graphs called phylogenetic networks. A major challenge in the burgeoning area of phylogenetic networks…

A classic problem in computational biology is constructing a phylogenetic tree given a set of distances between n species. In most cases, a tree structure is too constraining. We consider a circular split network, a generalization of a tree…

Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains…

Reconstructing the tree of life from molecular sequences is a fundamental problem in computational biology. Modern data sets often contain a large number of genes, which can complicate the reconstruction problem due to the fact that…

Predicting horizontal gene transfers often requires comparative sequence data, but recent work has shown that character-based approaches could also be useful for this task. Notably, perfect transfer networks (PTN) explain the character…

Staged tree models are a discrete generalization of Bayesian networks. We show that these form curved exponential families and derive their natural parameters, sufficient statistic, and cumulant-generating function as functions of their…

Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of non-treelike evolutionary events, like recombination, hybridization, or lateral gene transfer. In a recent series of papers devoted to the…

The constant rate birth--death process is a popular null model for speciation and extinction. If one removes extinct and non-sampled lineages, this process induces `reconstructed trees' which describe the relationship between extant…

Phylogenetic trees are often constructed by using a metric on the set of taxa that label the leaves of the tree. While there are a number of methods for constructing a tree using a given metric, such trees will only display the metric if 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 -- splitting into new populations or species. The coalescent…

The presence of reticulate evolutionary events in phylogenies turn phylogenetic trees into phylogenetic networks. These events imply in particular that there may exist multiple evolutionary paths from a non-extant species to an extant one,…

Arboreal networks are a generalization of rooted trees, defined by keeping the tree-like structure, but dropping the requirement for a single root. Just as the class of cographs is precisely the class of undirected graphs that can be…

Tree containment problem is a fundamental problem in phylogenetic study, as it is used to verify a network model. It asks whether a given network contain a subtree that resembles a binary tree. The problem is NP-complete in general, even in…

A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…

The genealogy at a single locus of a constant size $N$ population in equilibrium is given by the well-known Kingman's coalescent. When considering multiple loci under recombination, the ancestral recombination graph encodes the genealogies…

The evolutionary relationships between species are typically represented in the biological literature by rooted phylogenetic trees. However, a tree fails to capture ancestral reticulate processes, such as the formation of hybrid species or…

The mathematical analysis of random phylogenetic networks via analytic and algorithmic methods has received increasing attention in the past years. In the present work we introduce branching process methods to their study. This approach…

Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes and species are…

Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…