title: Efficient representation of uncertainty in multiple sequence alignments using directed acyclic graphs.
abstract: BACKGROUND
  A standard procedure in many areas of bioinformatics is to use a single multiple sequence alignment (MSA) as the basis for various types of analysis. However, downstream results may be highly sensitive to the alignment used, and neglecting the uncertainty in the alignment can lead to significant bias in the resulting inference. In recent years, a number of approaches have been developed for probabilistic sampling of alignments, rather than simply generating a single optimum. However, this type of probabilistic information is currently not widely used in the context of downstream inference, since most existing algorithms are set up to make use of a single alignment.
  
  
  RESULTS
  In this work we present a framework for representing a set of sampled alignments as a directed acyclic graph (DAG) whose nodes are alignment columns; each path through this DAG then represents a valid alignment. Since the probabilities of individual columns can be estimated from empirical frequencies, this approach enables sample-based estimation of posterior alignment probabilities. Moreover, due to conditional independencies between columns, the graph structure encodes a much larger set of alignments than the original set of sampled MSAs, such that the effective sample size is greatly increased.
  
  
  CONCLUSIONS
  The alignment DAG provides a natural way to represent a distribution in the space of MSAs, and allows for existing algorithms to be efficiently scaled up to operate on large sets of alignments. As an example, we show how this can be used to compute marginal probabilities for tree topologies, averaging over a very large number of MSAs. This framework can also be used to generate a statistically meaningful summary alignment; example applications show that this summary alignment is consistently more accurate than the majority of the alignment samples, leading to improvements in downstream tree inference. Implementations of the methods described in this article are available at http://statalign.github.io/WeaveAlign .
authors.affiliation: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, UK. herman@stats.ox.ac.uk.|Division of Mathematical Biology, National Institute of Medical Research,, The Ridgeway, London, NW7 1AA, UK. herman@stats.ox.ac.uk.
authors.forename: Joseph L
authors.initials: JL
authors.lastname: Herman
authors.affiliation: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, UK. novak@stats.ox.ac.uk.
authors.forename: Ádám
authors.initials: Á
authors.lastname: Novák
authors.affiliation: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, UK. rune@lyngsoe.eu.
authors.forename: Rune
authors.initials: R
authors.lastname: Lyngsø
authors.affiliation: Institute of Computer Science and Control, Hungarian Academy of Sciences, Lagymanyosi u. 11., Budapest, 1111, Hungary. adrienn.szabo@sztaki.mta.hu.
authors.forename: Adrienn
authors.initials: A
authors.lastname: Szabó
authors.affiliation: Institute of Computer Science and Control, Hungarian Academy of Sciences, Lagymanyosi u. 11., Budapest, 1111, Hungary. miklosi@renyi.hu.|Department of Stochastics, Rényi Institute, Reáltanoda u. 13-15, Budapest, 1053, Hungary. miklosi@renyi.hu.
authors.forename: István
authors.initials: I
authors.lastname: Miklós
authors.affiliation: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, UK. hein@stats.ox.ac.uk.
authors.forename: Jotun
authors.initials: J
authors.lastname: Hein
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D003196:Computer Graphics; D003198:Computer Simulation; D006801:Humans; D015233:Models, Statistical; D016415:Sequence Alignment / Q000379:methods*; D012984:Software; D035501:Uncertainty