# John A. Rhodes

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 ofâ€¦ (More)
[3] David F. Anderson, An efficient finite difference method for parameter sensitivities of continuous time markov chains, Submitted. Available on arxiv.org at Error analysis of tau-leap simulation methods, to appear in Annals of Applied Probability. [7] David F. Anderson and Masanori Koyama, Weak error analysis of numerical methods for stochastic models ofâ€¦ (More)
• Journal of mathematical biology
• 2011
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 geneâ€¦ (More)
• Mathematical biosciences
• 2003
A phylogenetic invariant for a model of biological sequence evolution along a phylogenetic tree is a polynomial that vanishes on the expected frequencies of base patterns at the terminal taxa. While the use of these invariants for phylogenetic inference has long been of interest, explicitly constructing such invariants has been problematic. We constructâ€¦ (More)
• Journal of Computational Biology
• 2006
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 ofâ€¦ (More)
• Journal of theoretical biology
• 2011
One approach to estimating a species tree from a collection of gene trees is to first estimate probabilities of clades from the gene trees, and then to construct the species tree from the estimated clade probabilities. While a greedy consensus algorithm, which consecutively accepts the most probable clades compatible with previously accepted clades, can beâ€¦ (More)
• Journal of Computational Biology
• 2013
The multispecies coalescent model describes the generation of gene trees from a rooted metric species tree and thus provides a framework for the inference of species trees from sampled gene trees. We prove that the STAR method of Liu et al. (2009) and generalizations of it, are statistically consistent methods of topological species tree inference underâ€¦ (More)
• IEEE/ACM Transactions on Computational Biologyâ€¦
• 2011
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 ofâ€¦ (More)
• IEEE/ACM transactions on computational biologyâ€¦
• 2016
The NJst method was proposed by Liu and Yu to infer a species tree topology from unrooted topological gene trees. While its statistical consistency under the multispecies coalescent model was established only for a 4-taxon tree, simulations demonstrated its good performance on gene trees inferred from sequences for many taxa. Here we prove the statisticalâ€¦ (More)