Phase transition in the sample complexity of likelihood-based phylogeny inference

Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical physics and that connection has led to important insights on the theoretical properties of phylogenetic reconstruction algorithms as well as the development of new inference methods. Here, we study maximum likelihood, a classical statistical technique which is perhaps the most widely used in phylogenetic practice because of its superior empirical accuracy. At the theoretical level, except for its consistency, that is, the guarantee of eventual correct reconstruction as the size of the input data grows, much remains to be understood about the statistical properties of maximum likelihood in this context. In particular, the best bounds on the sample complexity or sequence-length requirement of maximum likelihood, that is, the amount of data required for correct reconstruction, are exponential in the number, $n$, of tips---far from known lower bounds based on information-theoretic arguments. Here we close the gap by proving a new upper bound on the sequence-length requirement of maximum likelihood that matches up to constants the known lower bound for some standard models of evolution. More specifically, for the $r$-state symmetric model of sequence evolution on a binary phylogeny with bounded edge lengths, we show that the sequence-length requirement behaves logarithmically in $n$ when the expected amount of mutation per edge is below what is known as the Kesten-Stigum threshold. In general, the sequence-length requirement is polynomial in $n$. Our results imply moreover that the maximum likelihood estimator can be computed efficiently on randomly generated data provided sequences are as above.Comment: To appear in Probability Theory and Related Field

Consistency and convergence rate of phylogenetic inference via regularization

It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the gene sequences alone to accurately reconstruct the correct "gene tree." Although the gene tree may deviate from the "species tree" due to a variety of genetic processes, in the absence of evidence to the contrary it is parsimonious to assume that they agree. A common statistical approach in these situations is to develop a likelihood penalty to incorporate such additional information. Recent studies using simulation and empirical data suggest that a likelihood penalty quantifying concordance with a species tree can significantly improve the accuracy of gene tree reconstruction compared to using sequence data alone. However, the consistency of such an approach has not yet been established, nor have convergence rates been bounded. Because phylogenetics is a non-standard inference problem, the standard theory does not apply. In this paper, we propose a penalized maximum likelihood estimator for gene tree reconstruction, where the penalty is the square of the Billera-Holmes-Vogtmann geodesic distance from the gene tree to the species tree. We prove that this method is consistent, and derive its convergence rate for estimating the discrete gene tree structure and continuous edge lengths (representing the amount of evolution that has occurred on that branch) simultaneously. We find that the regularized estimator is "adaptive fast converging," meaning that it can reconstruct all edges of length greater than any given threshold from gene sequences of polynomial length. Our method does not require the species tree to be known exactly; in fact, our asymptotic theory holds for any such guide tree.Comment: 34 pages, 5 figures. To appear on The Annals of Statistic

DM-PhyClus: A Bayesian phylogenetic algorithm for infectious disease transmission cluster inference

Background. Conventional phylogenetic clustering approaches rely on arbitrary cutpoints applied a posteriori to phylogenetic estimates. Although in practice, Bayesian and bootstrap-based clustering tend to lead to similar estimates, they often produce conflicting measures of confidence in clusters. The current study proposes a new Bayesian phylogenetic clustering algorithm, which we refer to as DM-PhyClus, that identifies sets of sequences resulting from quick transmission chains, thus yielding easily-interpretable clusters, without using any ad hoc distance or confidence requirement. Results. Simulations reveal that DM-PhyClus can outperform conventional clustering methods, as well as the Gap procedure, a pure distance-based algorithm, in terms of mean cluster recovery. We apply DM-PhyClus to a sample of real HIV-1 sequences, producing a set of clusters whose inference is in line with the conclusions of a previous thorough analysis. Conclusions. DM-PhyClus, by eliminating the need for cutpoints and producing sensible inference for cluster configurations, can facilitate transmission cluster detection. Future efforts to reduce incidence of infectious diseases, like HIV-1, will need reliable estimates of transmission clusters. It follows that algorithms like DM-PhyClus could serve to better inform public health strategies

Metagenomic sequencing unravels gene fragments with phylogenetic signatures of O2-tolerant NiFe membrane-bound hydrogenases in lacustrine sediment

Many promising hydrogen technologies utilising hydrogenase enzymes have been slowed by the fact that most hydrogenases are extremely sensitive to O2. Within the group 1 membrane-bound NiFe hydrogenase, naturally occurring tolerant enzymes do exist, and O2 tolerance has been largely attributed to changes in iron–sulphur clusters coordinated by different numbers of cysteine residues in the enzyme’s small subunit. Indeed, previous work has provided a robust phylogenetic signature of O2 tolerance [1], which when combined with new sequencing technologies makes bio prospecting in nature a far more viable endeavour. However, making sense of such a vast diversity is still challenging and could be simplified if known species with O2-tolerant enzymes were annotated with information on metabolism and natural environments. Here, we utilised a bioinformatics approach to compare O2-tolerant and sensitive membrane-bound NiFe hydrogenases from 177 bacterial species with fully sequenced genomes for differences in their taxonomy, O2 requirements, and natural environment. Following this, we interrogated a metagenome from lacustrine surface sediment for novel hydrogenases via high-throughput shotgun DNA sequencing using the Illumina™ MiSeq platform. We found 44 new NiFe group 1 membrane-bound hydrogenase sequence fragments, five of which segregated with the tolerant group on the phylogenetic tree of the enzyme’s small subunit, and four with the large subunit, indicating de novo O2-tolerant protein sequences that could help engineer more efficient hydrogenases

Ghost-tree: creating hybrid-gene phylogenetic trees for diversity analyses.

BackgroundFungi play critical roles in many ecosystems, cause serious diseases in plants and animals, and pose significant threats to human health and structural integrity problems in built environments. While most fungal diversity remains unknown, the development of PCR primers for the internal transcribed spacer (ITS) combined with next-generation sequencing has substantially improved our ability to profile fungal microbial diversity. Although the high sequence variability in the ITS region facilitates more accurate species identification, it also makes multiple sequence alignment and phylogenetic analysis unreliable across evolutionarily distant fungi because the sequences are hard to align accurately. To address this issue, we created ghost-tree, a bioinformatics tool that integrates sequence data from two genetic markers into a single phylogenetic tree that can be used for diversity analyses. Our approach starts with a "foundation" phylogeny based on one genetic marker whose sequences can be aligned across organisms spanning divergent taxonomic groups (e.g., fungal families). Then, "extension" phylogenies are built for more closely related organisms (e.g., fungal species or strains) using a second more rapidly evolving genetic marker. These smaller phylogenies are then grafted onto the foundation tree by mapping taxonomic names such that each corresponding foundation-tree tip would branch into its new "extension tree" child.ResultsWe applied ghost-tree to graft fungal extension phylogenies derived from ITS sequences onto a foundation phylogeny derived from fungal 18S sequences. Our analysis of simulated and real fungal ITS data sets found that phylogenetic distances between fungal communities computed using ghost-tree phylogenies explained significantly more variance than non-phylogenetic distances. The phylogenetic metrics also improved our ability to distinguish small differences (effect sizes) between microbial communities, though results were similar to non-phylogenetic methods for larger effect sizes.ConclusionsThe Silva/UNITE-based ghost tree presented here can be easily integrated into existing fungal analysis pipelines to enhance the resolution of fungal community differences and improve understanding of these communities in built environments. The ghost-tree software package can also be used to develop phylogenetic trees for other marker gene sets that afford different taxonomic resolution, or for bridging genome trees with amplicon trees.Availabilityghost-tree is pip-installable. All source code, documentation, and test code are available under the BSD license at https://github.com/JTFouquier/ghost-tree