Related papers: The algebraic $\alpha$-Ford tree under evolution

Species trees represent the historical divergences of populations or species, while gene trees trace the ancestry of individual gene copies sampled within those populations. In cases involving rapid speciation, gene trees with topologies…

Phylogenetics is the study of the evolutionary relationships between organisms. One of the main challenges in the field is to take biological data for a group of organisms and to infer an evolutionary tree, a graph that represents these…

We apply the theory of markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies. We consider the Cavender-Farris-Neyman model of evolution on trees, where all the inner…

In the last decade, some algebraic tools have been successfully applied to phylogenetic reconstruction. These tools are mainly based on the knowledge of equations describing algebraic varieties associated to phylogenetic trees evolving…

We compare the phylogenetic tensors for various trees and networks for two, three and four taxa. If the probability spaces between one tree or network and another are not identical then there will be phylogenetic tensors that could have…

Distance-based approaches in phylogenetics such as Neighbor-Joining are a fast and popular approach for building trees. These methods take pairs of sequences from them construct a value that, in expectation, is additive under a stochastic…

A large class of phylogenetic networks can be obtained from trees by the addition of horizontal edges between the tree edges. These networks are called tree based networks. Reticulation-visible networks and child-sibling networks are all…

Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the…

We consider the decentralized binary hypothesis testing problem on trees of bounded degree and increasing depth. For a regular tree of depth t and branching factor k>=2, we assume that the leaves have access to independent and identically…

We introduce a new phylogenetic reconstruction algorithm which, unlike most previous rigorous inference techniques, does not rely on assumptions regarding the branch lengths or the depth of the tree. The algorithm returns a forest which is…

This article investigates combinatorial properties of non-ambiguous trees. These objects we define may be seen either as binary trees drawn on a grid with some constraints, or as a subset of the tree-like tableaux previously defined by…

The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately…

Phylogenetic networks are leaf-labelled directed acyclic graphs that are used to describe non-treelike evolutionary histories and are thus a generalization of phylogenetic trees. The hybridization number of a phylogenetic network is the sum…

We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…

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…

We consider the phylogenetic tree model in which every node of the tree is observed and binary and the transitions are given by the same matrix on each edge of the tree. We are able to compute the Grobner basis and Markov basis of the toric…

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…

When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a…

Many discrete mathematics problems in phylogenetics are defined in terms of the relative labeling of pairs of leaf-labeled trees. These relative labelings are naturally formalized as tanglegrams, which have previously been an object of…

We propose the following simple stochastic model for phylogenetic trees. New types are born and die according to a birth and death chain. At each birth we associate a fitness to the new type sampled from a fixed distribution. At each death…