Fast and Robust Characterization of Time-Heterogeneous Sequence Evolutionary Processes Using Substitution Mapping

et al. (2012) Fast and Robust Characterization of Time-Heterogeneous Sequence Evolutionary Processes Using Substitution Mapping. PLoS ONE 7(3): e33852. doi:10.1371/journal.pone.0033852 Fast and Robust Characterization of Time- Heterogeneous Sequence Evolutionary Processes Using Substitution Mapping Jonathan Romiguier 0 Emeric Figuet 0 Nicolas Galtier 0 Emmanuel J. P. Douzery 0 Bastien Boussau 0 Julien Y. Dutheil 0 Vincent Ranwez 0 David Liberles, University of Wyoming, United States of America 0 1 Institut des Sciences de l'Evolution de Montpellier, CNRS-Universite Montpellier 2, Montpellier, France, 2 Laboratoire de Biome trie et Biologie Evolutive, CNRS-Universite Lyon 1, Villeurbanne, France, 3 Unite Mixte de Recherche Ame lioration ge ne tique et adaptation des plantes me diterrane ennes et tropicales, Montpellier SupAgro, Montpellier, France, 4 Department of Integrative Biology, University of California , Berkeley, California , United States of America Genes and genomes do not evolve similarly in all branches of the tree of life. Detecting and characterizing the heterogeneity in time, and between lineages, of the nucleotide (or amino acid) substitution process is an important goal of current molecular evolutionary research. This task is typically achieved through the use of non-homogeneous models of sequence evolution, which being highly parametrized and computationally-demanding are not appropriate for large-scale analyses. Here we investigate an alternative methodological option based on probabilistic substitution mapping. The idea is to first reconstruct the substitutional history of each site of an alignment under a homogeneous model of sequence evolution, then to characterize variations in the substitution process across lineages based on substitution counts. Using simulated and published datasets, we demonstrate that probabilistic substitution mapping is robust in that it typically provides accurate reconstruction of sequence ancestry even when the true process is heterogeneous, but a homogeneous model is adopted. Consequently, we show that the new approach is essentially as efficient as and extremely faster than (up to 25 000 times) existing methods, thus paving the way for a systematic survey of substitution process heterogeneity across genes and lineages. - . These authors contributed equally to this work. Mapping the history of nucleotide or amino-acid changes onto the evolutionary history of a gene, as depicted by a phylogenetic tree, is of central interest to researchers in molecular evolution. This procedure, called mutation or substitution mapping, is useful for characterizing the molecular evolutionary processes of DNA and protein sequences, and their variations across sites and lineages. Substitution mapping has been successfully applied to study various aspects of molecular evolution, including coevolution [1], [2], selective constraints in proteins [3], deviations from the molecular clock hypothesis [4], and changes in selective regimes [5]. Beyond this, substitution mapping has also enabled the implementation of a number of models that were otherwise intractable [6],[7]. Over the past 10 years, several inference methods have been developed to achieve substitution mapping. Formally, the problem is to identify, for every site in a sequence alignment, the kinds of character changes that occurred, and their location in the underlying phylogeny. So a substitution mapping method would take an alignment and a tree as input and return, as output, an estimate of the number/nature of substitutions that have occurred, for each site of the alignment and each branch of the tree. The naive substitution mapping procedure [8] involves first reconstructing all ancestral sequences at each node of the phylogenetic tree. Secondly, for each site, one substitution is mapped on a branch when two different states are observed for this site at the two extremities of the branch. The main drawback of such an approach is that it overlooks the uncertainty of the ancestral sequence inference. Two improved mapping methods have been proposed: Bayesian Mutational Mapping (BMM, [9]) and Probabilistic Substitution Mapping (PSM, [1],[10]). They both use Markov chains to model the substitution process and account for the uncertainty in the ancestral states [11], [12]. BMM is a procedure that generates a substitution scenario compatible with the data, together with its associated likelihood. This procedure was not designed to produce human-readable substitution maps, but rather to integrate a statistic of interest over the set of possible substitution maps. Because it is a sampling procedure, BMM is fairly computer-expensive, although some more stable or efficient samplers have been proposed lately [13], [14], [15]. PSM is an analytical procedure, which computes the probability distribution of the number of substitutions that occurred at each site of the alignment and each branch of the phylogenetic tree. Dutheil et al 2005 [1] report how to compute the mean number of total substitutions per branch and site, but it is also possible to compute higher-order moments of the distribution, or distinguish between different types of substitutions ([14],[15] and the present study). PSM is a maximum likelihood solution of BMM for some particular statistics (the mean of the branch and site-specific distributions of the expected number of substitutions in the case of Dutheil et al 2005 [1]) and is therefore quite fast to compute for a given tree and substitution model, which is a significant advantage with respect to the increasing amount of molecular data provided by high-throughput sequencing. In addition, the relative simplicity and computer efficiency of substitution mapping procedures have promoted them for use in several analyses (e.g. [16]). They have been shown to facilitate parameter estimation of complex models when used within expectation-maximization procedures [17]. Adequate statistics based on substitution maps could therefore serve as straight-forward descriptors of molecular evolution that can be used as proxies for more complex ones. One of the major advantages of substitution mapping is its power to detect and characterize time-heterogeneous processes, i.e. processes that vary across branches of the tree. Such variations, when identified, can be linked to variations in selective pressure (e.g. [18]) and mutation/fixation biases (e.g. [19]), or linked to macroscopic features of species such as effective population size (e.g. [20], [21]), ecological preferences [22] or life-history traits [23]. To detect heterogeneous processes, explicit models of nonhomogeneous sequence evolution have been implemented in the maximum-likelihood or Bayesian frameworks [22], [24], [25], [26]. However, these parameter-rich models could lead to overparametrization issues and are computationally demanding, so their usage is limited to relatively small subsets of the large amounts of (...truncated)