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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. We establish tree identifiability for a number of phylogenetic models, including a covarion model and a variety of… (More)

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 process, which models ancestry of gene copies within populations, is often used to model the probability distribution of gene… (More)

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 problem within the broader area of Algebraic Statistics. For an arbitrary trivalent tree, we determine the full ideal of… (More)

- Elizabeth S Allman, C, Ecile Ané, John A Rhodes, Allman
- 2007

Inference of evolutionary trees and rates from biological sequences is commonly performed using continuous-time Markov models of character change. The Markov process evolves along an unknown tree while observations arise only from the tips of the tree. Rate heterogeneity is present in most real data sets and is accounted for by the use of flexible mixture… (More)

The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov process on a tree. For statistical use it is important to know if the model is identifiable; can both the tree topology… (More)

Though algebraic geometry over C is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and larger rank. Here we focus on the n × n × n tensors of rank n over C, which has as a dense subset the orbit of a single tensor under a natural group action. We construct polynomial… (More)

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 different substitution processes on characters in the case of the same topology. Recent work on a 2-state symmetric model of… (More)

Covarion models of character evolution describe inhomogeneities in substitution processes through time. In phylogenetics, such models are used to describe changing functional constraints or selection regimes during the evolution of biological sequences. In this work the identifiability of such models for generic parameters on a known phylogenetic tree is… (More)

Changing base composition during the evolution of biological sequences can mislead some of the phylogenetic inference techniques in current use. However, detecting whether such a process has occurred may be difficult, since convergent evolution may lead to similar base frequencies emerging from different lineages. To study this situation, algebraic models… (More)

- Elizabeth S Allman, Sonja Petrovi´c, John A Rhodes, Seth Sullivant
- 2009

— 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 different substitution processes on characters in the case of the same topology. Recent work on a 2-state symmetric model… (More)