Statistics Seminar: Jayasval -- General Markov Models for Nucleotide Sequence Evolution

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     *           UNIVERSITY OF SYDNEY            *
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     *     SCHOOL OF MATHEMATICS & STATISTICS    *
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     *       STATISTICS SEMINAR SERIES - 2007    *
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            *       SEMINAR NOTICE     *
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    General Markov Models for Nucleotide Sequence Evolution

                     Vivek Jayaswal                     

                 (University of Sydney)


   Friday, 14 September, 2007, 2pm Carslaw 373

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The aim of many molecular phylogenetics studies is to infer the most
probable sequence of gene evolution. The order in which the genes
evolve gives rise to a branching pattern referred to as the tree
topology. In addition to the tree topology, phylogeneticists are
interested in estimating the rate of evolution along the individual
branches and these are modeled as Markov processes. Under the
assumption that the nucleotide sites within a gene are independent
and identically distributed (iid), the most general model is the one
proposed by Barry and Hartigan (Stat Sci., 1987:191-210). Since the
iid assumption is often violated by real data sets, we generalize
the Barry and Hartigan model by relaxing the assumption of identical
distribution. We achieve this by allowing a site to be either
variable or invariant (BH+I model) and by allowing the variable
sites to evolve at k different rates (BHk+I model). We use the
maximum-likelihood method to estimate the parameters for the new
models and apply these models to real and simulated data sets. We
show that these models satisfy the constraint of internal
consistency; a necessary condition for analyzing evolutionary trees
where the last common ancestor is unknown. We use the BH+I model to
analyze a bacterial data set where most of the existing models
(including those that allow non-identical distribution of sites)
fail due to lack of stationarity and homogeneity. We use parametric
bootstrap to (a) show that the data are consistent with the BH+I
model and (b) determine the tree topology that best explains the
observed data. Finally, we briefly discuss the $BH_{k}+I$ model.

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