doi: 10.1093/molbev/mst030. Epub 2013 Feb 18.
FUBAR: a fast, unconstrained bayesian approximation for inferring selection
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- PMID:23420840
- PMCID: PMC3670733
- DOI: 10.1093/molbev/mst030
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FUBAR: a fast, unconstrained bayesian approximation for inferring selection
Ben Murrell et al. Mol Biol Evol.2013 May.
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Abstract
Model-based analyses of natural selection often categorize sites into a relatively small number of site classes. Forcing each site to belong to one of these classes places unrealistic constraints on the distribution of selection parameters, which can result in misleading inference due to model misspecification. We present an approximate hierarchical Bayesian method using a Markov chain Monte Carlo (MCMC) routine that ensures robustness against model misspecification by averaging over a large number of predefined site classes. This leaves the distribution of selection parameters essentially unconstrained, and also allows sites experiencing positive and purifying selection to be identified orders of magnitude faster than by existing methods. We demonstrate that popular random effects likelihood methods can produce misleading results when sites assigned to the same site class experience different levels of positive or purifying selection--an unavoidable scenario when using a small number of site classes. Our Fast Unconstrained Bayesian AppRoximation (FUBAR) is unaffected by this problem, while achieving higher power than existing unconstrained (fixed effects likelihood) methods. The speed advantage of FUBAR allows us to analyze larger data sets than other methods: We illustrate this on a large influenza hemagglutinin data set (3,142 sequences). FUBAR is available as a batch file within the latest HyPhy distribution (http://www.hyphy.org), as well as on the Datamonkey web server (http://www.datamonkey.org/).
Figures
The synonymous and nonsynonymous rates (
) are continuous model parameters that vary from one site to another, illustrated by a hypothetical distribution in (A). Typical random effects models, as exemplified by Dual REL (Kosakovsky Pond and Muse 2005) in (B) use a small number of discrete categories to approximate this continuous distribution, allowing the location (represented by the green bars) and the probability mass of the discrete points to vary; a change in the location of a point necessitates a re-evaluation of the phylogenetic likelihood function. FUBAR, in (C), uses a much denser grid of values chosen a priori, relying on the grid density to circumvent the need to move the parameter locations, and on MCMC to sample the weights assigned to each point. Without the need for movable grid lines, FUBAR needs to compute the conditional likelihood associated with each point only once, eliminating the bottleneck hindering traditional random effects models. Note that the uniform grid spacing depicted here is stylized. As the uncertainty in the selection parameters grows with their magnitude, FUBAR uses larger spacing for larger values (see text for details).
) are continuous model parameters that vary from one site to another, illustrated by a hypothetical distribution in (A). Typical random effects models, as exemplified by Dual REL (Kosakovsky Pond and Muse 2005) in (B) use a small number of discrete categories to approximate this continuous distribution, allowing the location (represented by the green bars) and the probability mass of the discrete points to vary; a change in the location of a point necessitates a re-evaluation of the phylogenetic likelihood function. FUBAR, in (C), uses a much denser grid of values chosen a priori, relying on the grid density to circumvent the need to move the parameter locations, and on MCMC to sample the weights assigned to each point. Without the need for movable grid lines, FUBAR needs to compute the conditional likelihood associated with each point only once, eliminating the bottleneck hindering traditional random effects models. Note that the uniform grid spacing depicted here is stylized. As the uncertainty in the selection parameters grows with their magnitude, FUBAR uses larger spacing for larger values (see text for details).
Execution times for FEL and FUBAR as a function of the number of codon sites (top) and number of taxa (bottom).
Site-specific inference under misspecified models. (Top) 100 log-likelihood curves as functions of
for a set of simulated sites (see text for description). Vertical lines indicate the value
under which the sites were simulated, along with the values for the neutral and positive selection site categories (
and
, respectively) used by the M2a model in PAML. The value of the positive selection site category does not match that under which the sites were simulated, due to the presence of other sites under stronger positive selection. The only evidence considered by M2a when classifying a site into the neutral or positive selection category is the value of the likelihood function at
and the value at
. With the peaks of the likelihood functions between these options, the model becomes overconfident, assigning strong evidence either for positive selection (exemplified by the blue curve) or against it (exemplified by the red curve), even when this conclusion is incorrect. (Bottom) Histograms of posterior site-specific probabilities of positive selection calculated for sites simulated under a true
. M2a (left) confidently identifies positive selection in nearly half of these sites, but also incorrectly declares strong evidence against positive selection in half. FUBAR (right) detects most of the sites, and does not claim strong evidence for incorrect conclusions.
for a set of simulated sites (see text for description). Vertical lines indicate the value under which the sites were simulated, along with the values for the neutral and positive selection site categories ( and, respectively) used by the M2a model in PAML. The value of the positive selection site category does not match that under which the sites were simulated, due to the presence of other sites under stronger positive selection. The only evidence considered by M2a when classifying a site into the neutral or positive selection category is the value of the likelihood function at and the value at. With the peaks of the likelihood functions between these options, the model becomes overconfident, assigning strong evidence either for positive selection (exemplified by the blue curve) or against it (exemplified by the red curve), even when this conclusion is incorrect. (Bottom) Histograms of posterior site-specific probabilities of positive selection calculated for sites simulated under a true. M2a (left) confidently identifies positive selection in nearly half of these sites, but also incorrectly declares strong evidence against positive selection in half. FUBAR (right) detects most of the sites, and does not claim strong evidence for incorrect conclusions.
Influenza hemagglutinin analysis. (Top) The H3 phylogeny with 3,142 coding sequences. (Middle) The smoothed histogram of
across H3, with the greatest density at mild purifying selection
, and fewer sites under positive selection
. The notches depict sites with posteriors greater than 0.9 for positive (red) or purifying (blue) selection. (Bottom) The inferred
values mapped to the HA protein (PDB 3ZTJ; Corti et al. 2011), displayed from two viewpoints. Red regions with stronger diversifying selection are likely involved in immune escape. These primarily occur on the “head” of the protein, with mostly purifying selection on the membrane proximal stem. See text for further detail.
across H3, with the greatest density at mild purifying selection, and fewer sites under positive selection. The notches depict sites with posteriors greater than 0.9 for positive (red) or purifying (blue) selection. (Bottom) The inferred values mapped to the HA protein (PDB 3ZTJ; Corti et al. 2011), displayed from two viewpoints. Red regions with stronger diversifying selection are likely involved in immune escape. These primarily occur on the “head” of the protein, with mostly purifying selection on the membrane proximal stem. See text for further detail.Similar articles
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