Related papers: The most parsimonious tree for random data
In this paper we investigate an extremal problem on binary phylogenetic trees. Given two such trees $T_1$ and $T_2$, both with leaf-set ${1,2,...,n}$, we are interested in the size of the largest subset $S \subseteq {1,2,...,n}$ of leaves…
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…
Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…
In phylogenetic analysis, for non-molecular data, particularly morphology, parsimony optimization is the most commonly employed approach. In the past and present application of the parsimony principle, extra step numbers have been added…
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…
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…
Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
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…
A fringe subtree of a rooted tree is a subtree consisting of one of the nodes and all its descendants. In this paper, we are specifically interested in the number of non-isomorphic trees that appear in the collection of all fringe subtrees…
In this thesis the properties of two kinds of non-uniform random recursive trees are studied. In the first model weights are assigned to each node, thus altering the attachment probabilities. We will call these trees weighted recursive…
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…
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…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…
Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…
We characterize and study variable importance (VIMP) and pairwise variable associations in binary regression trees. A key component involves the node mean squared error for a quantity we refer to as a maximal subtree. The theory naturally…
Phylogenetic trees are leaf-labelled trees, where the leaves correspond to extant species (taxa), and the internal vertices represent ancestral species. The evolutionary history of a set of species can be explained by more than one…
Phylogenetic trees describe the evolutionary history of a group of present-day species from a common ancestor. These trees are typically reconstructed from aligned DNA sequence data. In this paper we analytically address the following…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…