相关论文: Identifiability of 3-Class Jukes-Cantor Mixtures

Identifiability of phylogenetic models is a necessary condition to ensure that the model parameters can be uniquely determined from data. Mixture models are phylogenetic models where the probability distributions in the model are convex…

For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter.…

Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. The…

We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…

In this paper we investigate properties of algebraic varieties representing group-based phylogenetic models. We propose a method of generating many phylogenetic invariants. We prove that we obtain all invariants for any tree for the binary…

Jukes-Cantor model is one of the most meaningful statistical models from a biological perspective. We are interested in computing the algebraic degrees for phylogenetic varieties, which we call phylogenetic degrees, associated to the…

Phylogenetic data arising on two possibly different tree topologies might be mixed through several biological mechanisms, including incomplete lineage sorting or horizontal gene transfer in the case of different topologies, or simply…

Identifiability is a crucial property for a statistical model since distributions in the model uniquely determine the parameters that produce them. In phylogenetics, the identifiability of the tree parameter is of particular interest since…

A phylogenetic variety is an algebraic variety parameterized by a statistical model of the evolution of biological sequences along a tree. Understanding this variety is an important problem in the area of algebraic statistics with…

Complex systems of polynomial equations have to be set up and solved algebraically in order to obtain analytic solutions for maximum likelihood on phylogenetic trees. This has restricted the types of systems previously resolved to the…

Recently there have been several attempts to provide a whole set of generators of the ideal of the algebraic variety associated to a phylogenetic tree evolving under an algebraic model. These algebraic varieties have been proven to be…

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies…

Phylogenetic networks provide a means of describing the evolutionary history of sets of species believed to have undergone hybridization or gene flow during their evolution. The mutation process for a set of such species can be modeled as a…

Distances between sequences based on their $k$-mer frequency counts can be used to reconstruct phylogenies without first computing a sequence alignment. Past work has shown that effective use of k-mer methods depends on 1) model-based…

We study the ChorHendySnir2006 evolutionary model, which consists of a rooted phylogenetic tree with three leaves, subject to the Jukes--Cantor (JC69) molecular evolutionary model and molecular clock. We show that the likelihood function…

We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.

A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…

We provide a logarithmic upper bound for the disentangling number on unordered lists of leaf labeled trees. This results is useful for analyzing phylogenetic mixture models. The proof depends on interpreting multisets of trees as high…

Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…

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…