Related papers: A third strike against perfect phylogeny
We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed $k$ no statistically consistent…
We describe the conditions under which a set of continuous variables or characters can be described as an X-tree or a split network. A distance matrix corresponds exactly to a split network or a valued X-tree if, after ordering of the taxa,…
Phylogenetic trees play a key role in the reconstruction of evolutionary relationships. Typically, they are derived from aligned sequence data (like DNA, RNA, or proteins) by using optimization criteria like, e.g., maximum parsimony (MP).…
An evolutionary tree (phylogenetic tree) is a binary, rooted, unordered tree that models the evolutionary history of currently living species in which leaves are labeled by species. In this paper, we investigate the problem of finding the…
The statistical estimation of phylogenies is always associated with uncertainty, and accommodating this uncertainty is an important component of modern phylogenetic comparative analysis. The birth-death polytomy resolver is a method of…
As an alternative to parsimony analyses, stochastic models have been proposed (Lewis, 2001), (Nylander, et al., 2004) for morphological characters, so that maximum likelihood or Bayesian analyses may be used for phylogenetic inference. A…
In phylogenetics, a key problem is to construct evolutionary trees from collections of characters where, for a set X of species, a character is simply a function from X onto a set of states. In this context, a key concept is convexity,…
Several computational problems in phylogenetic reconstruction can be formulated as restrictions of the following general problem: given a formula in conjunctive normal form where the literals are rooted triples, is there a rooted binary…
Phylogenetic networks are increasingly used in evolutionary biology to represent the history of species that have undergone reticulate events such as horizontal gene transfer, hybrid speciation and recombination. One of the most fundamental…
In this paper we investigate mathematical questions concerning the reliability (reconstruction accuracy) of Fitch's maximum parsimony algorithm for reconstructing the ancestral state given a phylogenetic tree and a character. In particular,…
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…
Evolutionary events such as incomplete lineage sorting and lateral gene transfer constitute major problems for inferring species trees from gene trees, as they can sometimes lead to gene trees which conflict with the underlying species…
Phylogenetic inference aims to reconstruct the evolutionary relationships of different species based on genetic (or other) data. Discrete characters are a particular type of data, which contain information on how the species should be…
Recently, the perfect phylogeny model with persistent characters has attracted great attention in the literature. It is based on the assumption that complex traits or characters can only be gained once and lost once in the course of…
Comparative analyses of phylogenetic trees typically require identical taxon sets, however, in practice, trees often include distinct but overlapping taxa. Pruning non-shared leaves discards phylogenetic signal, whereas tree completion can…
An identifying code of a closed-twin-free graph $G$ is a dominating set $S$ of vertices of $G$ such that any two vertices in $G$ have a distinct intersection between their closed neighborhoods and $S$. It was conjectured that there exists…
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, called phylogenetic invariants, which vanish on it, is a…
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…
It follows from a classical result of Jordan that every tree with maximum degree at most $r$ containing a vertex set labeled by $[n]$, has a single-edge cut which separates two subsets $A,B \subset [n]$ for which $\min\{|A|,|B|\} \ge…
Rooted binary perfect phylogenies provide a generalization of rooted binary unlabeled trees in which each leaf is assigned a positive integer value that corresponds in a biological setting to the count of the number of indistinguishable…