Testing statistical hypothesis on random trees and applications to the protein classification problem

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov--Smirnov-type goodness-of-fit test proposed by Balding et al. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford--Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton--Watson related processes.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS218 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A phylogeny of birds based on over 1,500 loci collected by target enrichment and high-throughput sequencing

Evolutionary relationships among birds in Neoaves, the clade comprising the vast majority of avian diversity, have vexed systematists due to the ancient, rapid radiation of numerous lineages. We applied a new phylogenomic approach to resolve relationships in Neoaves using target enrichment (sequence capture) and high-throughput sequencing of ultraconserved elements (UCEs) in avian genomes. We collected sequence data from UCE loci for 32 members of Neoaves and one outgroup (chicken) and analyzed data sets that differed in their amount of missing data. An alignment of 1,541 loci that allowed missing data was 87% complete and resulted in a highly resolved phylogeny with broad agreement between the Bayesian and maximum-likelihood (ML) trees. Although results from the 100% complete matrix of 416 UCE loci were similar, the Bayesian and ML trees differed to a greater extent in this analysis, suggesting that increasing from 416 to 1,541 loci led to increased stability and resolution of the tree. Novel results of our study include surprisingly close relationships between phenotypically divergent bird families, such as tropicbirds (Phaethontidae) and the sunbittern (Eurypygidae) as well as between bustards (Otididae) and turacos (Musophagidae). This phylogeny bolsters support for monophyletic waterbird and landbird clades and also strongly supports controversial results from previous studies, including the sister relationship between passerines and parrots and the non-monophyly of raptorial birds in the hawk and falcon families. Although significant challenges remain to fully resolving some of the deep relationships in Neoaves, especially among lineages outside the waterbirds and landbirds, this study suggests that increased data will yield an increasingly resolved avian phylogeny.Comment: 30 pages, 1 table, 4 figures, 1 supplementary table, 3 supplementary figure