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Fast, accurate and simulation-free stochastic mapping - PubMed

  • ️Tue Jan 01 2008

Fast, accurate and simulation-free stochastic mapping

Vladimir N Minin et al. Philos Trans R Soc Lond B Biol Sci. 2008.

Abstract

Mapping evolutionary trajectories of discrete traits onto phylogenies receives considerable attention in evolutionary biology. Given the trait observations at the tips of a phylogenetic tree, researchers are often interested where on the tree the trait changes its state and whether some changes are preferential in certain parts of the tree. In a model-based phylogenetic framework, such questions translate into characterizing probabilistic properties of evolutionary trajectories. Current methods of assessing these properties rely on computationally expensive simulations. In this paper, we present an efficient, simulation-free algorithm for computing two important and ubiquitous evolutionary trajectory properties. The first is the mean number of trait changes, where changes can be divided into classes of interest (e.g. synonymous/non-synonymous mutations). The mean evolutionary reward, accrued proportionally to the time a trait occupies each of its states, is the second property. To illustrate the usefulness of our results, we first employ our simulation-free stochastic mapping to execute a posterior predictive test of correlation between two evolutionary traits. We conclude by mapping synonymous and non-synonymous mutations onto branches of an HIV intrahost phylogenetic tree and comparing selection pressure on terminal and internal tree branches.

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Figures

Figure 1
Figure 1

Sandwich formula illustration. (a) An example phylogenetic tree in which we label internal nodes numerically and two branches b* and b′. We break this tree at nodes 3 and 4 into the subtrees shown in (b). Assuming that the trait states are i and j at nodes 3 and 4, respectively, we mark each subtree by the corresponding quantity needed for calculating the posterior expectation of a mapping summary on branch b*.

Figure 2
Figure 2

Primate trait data. We plot a phylogenetic tree, randomly chosen from the posterior sample, of 60 primate species. Branches of the sampled tree are not drawn to scale, nor is the tree ultrametric. Taxa names and trait values (‘0’, absence; ‘1’, presence; ‘−’, missing) for oestrus advertisement (EA) and multimale mating system (MS) are depicted at the tips of the tree.

Figure 3
Figure 3

Testing coevolution. (a,c) Plots depicting observed (white bars) and predicted (grey bars) distributions of the discrepancy measure for the (a,b) primate and (c,d) simulated data. (b,d) The scatter plots of these distributions.

Figure 4
Figure 4

Time evolution of synonymous and non-synonymous rates. (a) A representative phylogeny of 129 intrahost HIV sequences. The three heat maps depict the marginal posterior densities of the (b) synonymous and (c) non-synonymous rates, and (d) the proportion of non-synonymous mutations over time.

Figure 5
Figure 5

Bimodality of the fraction of non-synonymous mutations. We plot the predicted fraction of non-synonymous mutations computed for terminal (grey bars) and internal (white bars) branches.

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