Related papers: Maximum Parsimony on Subsets of Taxa
We examine a mathematical question concerning the reconstruction accuracy of the Fitch algorithm for reconstructing the ancestral sequence of the most recent common ancestor given a phylogenetic tree and sequence data for all taxa under…
In phylogenetic studies, biologists often wish to estimate the ancestral discrete character state at an interior vertex $v$ of an evolutionary tree $T$ from the states that are observed at the leaves of the tree. A simple and fast…
Recurrence formulas are presented for studying the accuracy of the Fitch method for reconstructing the ancestral states in a given phylogenetic tree. As their applications, we analyze the convergence of the accuracy of reconstructing the…
One of the main aims in phylogenetics is the estimation of ancestral sequences based on present-day data like, for instance, DNA alignments. One way to estimate the data of the last common ancestor of a given set of species is to first…
Finding the most parsimonious tree inside a phylogenetic network with respect to a given character is an NP-hard combinatorial optimization problem that for many network topologies is essentially inapproximable. In contrast, if the network…
We consider the problem of inferring an ancestral state from observations at the leaves of a tree, assuming the state evolves along the tree according to a two-state symmetric Markov process. We establish a general branching rate condition…
Applying a method to reconstruct a phylogenetic tree from random data provides a way to detect whether that method has an inherent bias towards certain tree `shapes'. For maximum parsimony, applied to a sequence of random 2-state data, each…
Likelihood-based methods are widely considered the best approaches for reconstructing ancestral states. Although much effort has been made to study properties of these methods, previous works often assume that both the tree topology and…
Tuffley and Steel (1997) proved that Maximum Likelihood and Maximum Parsimony methods in phylogenetics are equivalent for sequences of characters under a simple symmetric model of substitution with no common mechanism. This result has been…
Maximum parsimony is one of the most frequently-discussed tree reconstruction methods in phylogenetic estimation. However, in recent years it has become more and more apparent that phylogenetic trees are often not sufficient to describe…
Estimating phylogenetic trees, which depict the relationships between different species, from aligned sequence data (such as DNA, RNA, or proteins) is one of the main aims of evolutionary biology. However, tree reconstruction criteria like…
Predicting the ancestral sequences of a group of homologous sequences related by a phylogenetic tree has been the subject of many studies, and numerous methods have been proposed to this purpose. Theoretical results are available that show…
The maximum parsimony phylogenetic tree reconstruction problem is NP-hard, presenting a computational bottleneck for classical computing and motivating the exploration of emerging paradigms like quantum computing. To this end, we design…
One of the main aims of phylogenetics is to reconstruct the \enquote{Tree of Life}. In this respect, different methods and criteria are used to analyze DNA sequences of different species and to compare them in order to derive the…
Phylogenetic methods typically rely on an appropriate model of how data evolved in order to infer an accurate phylogenetic tree. For molecular data, standard statistical methods have provided an effective strategy for extracting…
In this paper, we investigate a conjecture by von Haeseler concerning the Maximum Parsimony method for phylogenetic estimation, which was published by the Newton Institute in Cambridge on a list of open phylogenetic problems in 2007. This…
Supertree methods are tree reconstruction techniques that combine several smaller gene trees (possibly on different sets of species) to build a larger species tree. The question of interest is whether the reconstructed supertree converges…
One of the main aims of phylogenetics is the reconstruction of the correct evolutionary tree when data concerning the underlying species set are given. These data typically come in the form of DNA, RNA or protein alignments, which consist…
We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…
Maximum likelihood is one of the most widely used techniques to infer evolutionary histories. Although it is thought to be intractable, a proof of its hardness has been lacking. Here, we give a short proof that computing the maximum…