Related papers: Trinets encode orchard phylogenetic networks

Phylogenetic (i.e. leaf-labeled) trees play a fundamental role in evolutionary research. A typical problem is to reconstruct such trees from data like DNA alignments (whose columns are often referred to as characters), and a simple…

In this paper we give a sufficient and necessary condition for two rooted trees with the same plucking polynomial. Furthermore, we give a criteria for a sequence of non-negative integers to be realized as a rooted tree.

Polyploidization is an evolutionary process by which a species acquires multiple copies of its complete set of chromosomes. The reticulate nature of the signal left behind by it means that phylogenetic networks offer themselves as a…

We provide an $\Omega(n\log n) $ lower bound and an $O(n^2)$ upper bound for the smallest size of rooted binary trees (a.k.a. phylogenetic tree shapes), which are universal for rooted binary trees with $n$ leaves, i.e., contain all of them…

It was recently observed by de Vienne et al. that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on…

We study the problem of finding a temporal hybridization network for a set of phylogenetic trees that minimizes the number of reticulations. First, we introduce an FPT algorithm for this problem on an arbitrary set of $m$ binary trees with…

Background. The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set $L$ is known to be solvable in linear time.…

We consider the following basic problem in phylogenetic tree construction. Let $\mathcal{P} = \{T_1, \ldots, T_k\}$ be a collection of rooted phylogenetic trees over various subsets of a set of species. The tree compatibility problem asks…

Rooted binary phylogenetic networks are extensions of rooted binary trees, adding reticulation nodes that are designed to represent evolutionary processes that involve hybridization events. Enumerative combinatorics studies have counted…

Network reconstruction lies at the heart of phylogenetic research. Two well studied classes of phylogenetic networks include tree-child networks and level-$k$ networks. In a tree-child network, every non-leaf node has a child that is a tree…

Phylogenetic networks are rooted directed acyclic graphs that represent evolutionary relationships between species whose past includes reticulation events such as hybridisation and horizontal gene transfer. To search the space of…

Phylogenetic networks are an important way to represent evolutionary histories that involve reticulations such as hybridization or horizontal gene transfer, yet fundamental questions such as how many networks there are that satisfy certain…

A compacted binary tree is a directed acyclic graph encoding a binary tree in which common subtrees are factored and shared, such that they are represented only once. We show that the number of compacted binary trees of size $n$ grows…

Combining a set of phylogenetic trees into a single phylogenetic network that explains all of them is a fundamental challenge in evolutionary studies. Existing methods are computationally expensive and can either handle only small numbers…

Recently much attention has been devoted to the construction of phylogenetic networks which generalize phylogenetic trees in order to accommodate complex evolutionary processes. Here we present an efficient, practical algorithm for…

Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…

Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs are computationally efficient as they perform inference along one…

Construction of phylogenetic trees has traditionally focused on binary trees where all species appear on leaves, a problem for which numerous efficient solutions have been developed. Certain application domains though, such as viral…

Tree alignment graphs (TAGs) provide an intuitive data structure for storing phylogenetic trees that exhibits the relationships of the individual input trees and can potentially account for nested taxonomic relationships. This paper…

The inference of phylogenetic networks, which model complex evolutionary processes including hybridization and gene flow, remains a central challenge in evolutionary biology. Until now, statistically consistent inference methods have been…