Time Clustered Sampling Can Inflate the Inferred Substitution Rate in Foot-And-Mouth Disease Virus Analyses

With the emergence of analytical software for the inference of viral evolution, a number of studies have focused on estimating important parameters such as the substitution rate and the time to the most recent common ancestor (t _MRCA) for rapidly evolving viruses. Coupled with an increasing abundance of sequence data sampled under widely different schemes, an effort to keep results consistent and comparable is needed. This study emphasizes commonly disregarded problems in the inference of evolutionary rates in viral sequence data when sampling is unevenly distributed on a temporal scale through a study of the foot-and-mouth (FMD) disease virus serotypes SAT 1 and SAT 2. Our study shows that clustered temporal sampling in phylogenetic analyses of FMD viruses will strongly bias the inferences of substitution rates and t _MRCA because the inferred rates in such data sets reflect a rate closer to the mutation rate rather than the substitution rate. Estimating evolutionary parameters from viral sequences should be performed with due consideration of the differences in short-term and longer-term evolutionary processes occurring within sets of temporally sampled viruses, and studies should carefully consider how samples are combined.     

A statistical characterization of consistent patterns of human immunodeficiency virus evolution within infected patients

Within-patient HIV populations evolve rapidly because of a high mutation rate, short generation time, and strong positive selection pressures. Previous studies have identified "consistent patterns" of viral sequence evolution. Just before HIV infection progresses to AIDS, evolution seems to slow markedly, and the genetic diversity of the viral population drops. This evolutionary slowdown could be caused either by a reduction in the average viral replication rate or because selection pressures weaken with the collapse of the immune system. The former hypothesis (which we denote "cellular exhaustion") predicts a simultaneous reduction in both synonymous and nonsynonymous evolution, whereas the latter hypothesis (denoted "immune relaxation") predicts that only nonsynonymous evolution will slow. In this paper, we present a set of statistical procedures for distinguishing between these alternative hypotheses using DNA sequences sampled over the course of infection. The first component is a new method for estimating evolutionary rates that takes advantage of the temporal information in longitudinal DNA sequence samples. Second, we develop a set of probability models for the analysis of evolutionary rates in HIV populations in vivo. Application of these models to both synonymous and nonsynonymous evolution affords a comparison of the cellular-exhaustion and immune-relaxation hypotheses. We apply the procedures to longitudinal data sets in which sequences of the env gene were sampled over the entire course of infection. Our analyses (1) statistically confirm that an evolutionary slowdown occurs late in infection, (2) strongly support the immune-relaxation hypothesis, and (3) indicate that the cessation of nonsynonymous evolution is associated with disease progression.     

A coalescent-based estimator of admixture from DNA sequences

A variety of estimators have been developed to use genetic marker information in inferring the admixture proportions (parental contributions) of a hybrid population. The majority of these estimators used allele frequency data, ignored molecular information that is available in markers such as microsatellites and DNA sequences, and assumed that mutations are absent since the admixture event. As a result, these estimators may fail to deliver an estimate or give rather poor estimates when admixture is ancient and thus mutations are not negligible. A previous molecular estimator based its inference of admixture proportions on the average coalescent times between pairs of genes taken from within and between populations. In this article I propose an estimator that considers the entire genealogy of all of the sampled genes and infers admixture proportions from the numbers of segregating sites in DNA sequence samples. By considering the genealogy of all sequences rather than pairs of sequences, this new estimator also allows the joint estimation of other interesting parameters in the admixture model, such as admixture time, divergence time, population size, and mutation rate. Comparative analyses of simulated data indicate that the new coalescent estimator generally yields better estimates of admixture proportions than the previous molecular estimator, especially when the parental populations are not highly differentiated. It also gives reasonably accurate estimates of other admixture parameters. A human mtDNA sequence data set was analyzed to demonstrate the method, and the analysis results are discussed and compared with those from previous studies.     

Analysis of the overdispersed clock in the short-term evolution of hepatitis C virus: Using the E1/E2 gene sequences to infer infection dates in a single source outbreak

The assumption of a molecular clock for dating events from sequence information is often frustrated by the presence of heterogeneity among evolutionary rates due, among other factors, to positively selected sites. In this work, our goal is to explore methods to estimate infection dates from sequence analysis. One such method, based on site stripping for clock detection, was proposed to unravel the clocklike molecular evolution in sequences showing high variability of evolutionary rates and in the presence of positive selection. Other alternatives imply accommodating heterogeneity in evolutionary rates at various levels, without eliminating any information from the data. Here we present the analysis of a data set of hepatitis C virus (HCV) sequences from 24 patients infected by a single individual with known dates of infection. We first used a simple criterion of relative substitution rate for site removal prior to a regression analysis. Time was regressed on maximum likelihood pairwise evolutionary distances between the sequences sampled from the source individual and infected patients. We show that it is indeed the fastest evolving sites that disturb the molecular clock and that these sites correspond to positively selected codons. The high computational efficiency of the regression analysis allowed us to compare the site-stripping scheme with random removal of sites. We demonstrate that removing the fast-evolving sites significantly increases the accuracy of estimation of infection times based on a single substitution rate. However, the time-of-infection estimations improved substantially when a more sophisticated and computationally demanding Bayesian method was used. This method was used with the same data set but keeping all the sequence positions in the analysis. Consequently, despite the distortion introduced by positive selection on evolutionary rates, it is possible to obtain quite accurate estimates of infection dates, a result of especial relevance for molecular epidemiology studies.     

The inference of stepwise changes in substitution rates using serial sequence samples.

It is frequently true that molecular sequences do not evolve in a strictly clocklike manner. Instead, substitution rate may vary for a number of reasons, including changes in selection pressure and effective population size, as well as changes in mean generation time. Here we present two new methods for estimating stepwise changes in substitution rates when serially sampled molecular sequences are available. These methods are based on multiple rates with dated tips (MRDT) models and allow different rates to be estimated for different intervals of time. These intervals may correspond to the sampling intervals or to a priori--defined intervals that are not coincident with the times the serial samples are obtained. Two methods for obtaining estimates of multiple rates are described. The first is an extension of the phylogeny-based maximum-likelihood estimation procedure introduced by Rambaut. The second is a new parameterization of the pairwise distance least-squares procedure used by Drummond and Rodrigo. The utility of these methods is demonstrated on a genealogy of HIV sequences obtained at five different sampling times from a single patient over a period of 34 months.     

Application of iterative soft thresholding for fast reconstruction of NMR data non-uniformly sampled with multidimensional Poisson Gap scheduling

The fast Fourier transformation has been the gold standard for transforming data from time to frequency domain in many spectroscopic methods, including NMR. While reliable, it has as a drawback that it requires a grid of uniformly sampled data points. This needs very long measuring times for sampling in multidimensional experiments in all indirect dimensions uniformly and even does not allow reaching optimal evolution times that would match the resolution power of modern high-field instruments. Thus, many alternative sampling and transformation schemes have been proposed. Their common challenges are the suppression of the artifacts due to the non-uniformity of the sampling schedules, the preservation of the relative signal amplitudes, and the computing time needed for spectra reconstruction. Here we present a fast implementation of the Iterative Soft Thresholding approach (istHMS) that can reconstruct high-resolution non-uniformly sampled NMR data up to four dimensions within a few hours and make routine reconstruction of high-resolution NUS 3D and 4D spectra convenient. We include a graphical user interface for generating sampling schedules with the Poisson-Gap method and an estimation of optimal evolution times based on molecular properties. The performance of the approach is demonstrated with the reconstruction of non-uniformly sampled medium and high-resolution 3D and 4D protein spectra acquired with sampling densities as low as 0.8%. The method presented here facilitates acquisition, reconstruction and use of multidimensional NMR spectra at otherwise unreachable spectral resolution in indirect dimensions.     

Towards the phylogeny of the Curculionoidea (Coleoptera): Reconstructions from mitochondrial and nuclear ribosomal DNA sequences

With about 60,000 described species, Curculionoidea represent the most species-rich superfamily in the animal kingdom. The immense diversity apparently creates difficulties in the reconstruction of the phylogenetic relationships. Independent morphological studies have led to very different classifications. This study is based on molecular data from two independent molecular sources, the 16S and 18S rDNA. Sensitivity analyses were conducted for the sequence alignment (gap costs were varied) as well as the phylogenetic reconstruction algorithms and some of their parameters. The higher-level relationships reconstructed within Curculionoidea are sensitive to alignment and reconstruction method. Nemonychidae or Oxycorynidae+Belidae were found to be sister to all remaining Curculionoidea in many analyses. The 16S rDNA sequence data (obtained from 157 species) corroborate many tribes and genera as monophyletic. It is observed that the phylogenetic reconstruction of genera with specific genetic features such as polyploidy and parthenogenetic reproduction is difficult in weevils. The curculionid subfamily Lixinae appears monophyletic. A new monophylum consisting of Entiminae, Hyperinae, Cyclominae, Myllorhinus plus possibly the Cossoninae is distinguished and we call it Entiminae s.l. For most other subfamilies and families homoplasy concealed the phylogenetic signal (due to saturation of the 16S sequences), or the species sampling was insufficient, although our sampling scheme was rather broad. We observed that although data from one source can easily be misleading (16S) or hardly informative (18S), the combination of the two independent data sets can result in useful information for such a speciose group of organisms. Our study represents the most thorough analysis of molecular sequence data of the Curculionoidea to date and although the phylogenetic results appear less stable than expected, they reflect the information content of these sequence data realistically and thus contribute to the total knowledge about the phylogeny of the Curculionoidea.     

Obtaining maximal concatenated phylogenetic data sets from large sequence databases

To improve the accuracy of tree reconstruction, phylogeneticists are extracting increasingly large multigene data sets from sequence databases. Determining whether a database contains at least k genes sampled from at least m species is an NP-complete problem. However, the skewed distribution of sequences in these databases permits all such data sets to be obtained in reasonable computing times even for large numbers of sequences. We developed an exact algorithm for obtaining the largest multigene data sets from a collection of sequences. The algorithm was then tested on a set of 100,000 protein sequences of green plants and used to identify the largest multigene ortholog data sets having at least 3 genes and 6 species. The distribution of sizes of these data sets forms a hollow curve, and the largest are surprisingly small, ranging from 62 genes by 6 species, to 3 genes by 65 species, with more symmetrical data sets of around 15 taxa by 15 genes. These upper bounds to sequence concatenation have important implications for building the tree of life from large sequence databases.     

Inferences from tip‐calibrated phylogenies: a review and a practical guide

Molecular dating of phylogenetic trees is a growing discipline using sequence data to co‐estimate the timing of evolutionary events and rates of molecular evolution. All molecular‐dating methods require converting genetic divergence between sequences into absolute time. Historically, this could only be achieved by associating externally derived dates obtained from fossil or biogeographical evidence to internal nodes of the tree. In some cases, notably for fast‐evolving genomes such as viruses and some bacteria, the time span over which samples were collected may cover a significant proportion of the time since they last shared a common ancestor. This situation allows phylogenetic trees to be calibrated by associating sampling dates directly to the sequences representing the tips (terminal nodes) of the tree. The increasing availability of genomic data from ancient DNA extends the applicability of such tip‐based calibration to a variety of taxa including humans, extinct megafauna and various microorganisms which typically have a scarce fossil record. The development of statistical models accounting for heterogeneity in different aspects of the evolutionary process while accommodating very large data sets (e.g. whole genomes) has allowed using tip‐dating methods to reach inferences on divergence times, substitution rates, past demography or the age of specific mutations on a variety of spatiotemporal scales. In this review, we summarize the current state of the art of tip dating, discuss some recent applications, highlight common pitfalls and provide a ‘how to’ guide to thoroughly perform such analyses.     

Bayesian coalescent inference of past population dynamics from molecular sequences

We introduce the Bayesian skyline plot, a new method for estimating past population dynamics through time from a sample of molecular sequences without dependence on a prespecified parametric model of demographic history. We describe a Markov chain Monte Carlo sampling procedure that efficiently samples a variant of the generalized skyline plot, given sequence data, and combines these plots to generate a posterior distribution of effective population size through time. We apply the Bayesian skyline plot to simulated data sets and show that it correctly reconstructs demographic history under canonical scenarios. Finally, we compare the Bayesian skyline plot model to previous coalescent approaches by analyzing two real data sets (hepatitis C virus in Egypt and mitochondrial DNA of Beringian bison) that have been previously investigated using alternative coalescent methods. In the bison analysis, we detect a severe but previously unrecognized bottleneck, estimated to have occurred 10,000 radiocarbon years ago, which coincides with both the earliest undisputed record of large numbers of humans in Alaska and the megafaunal extinctions in North America at the beginning of the Holocene.     

Species trees from gene trees: reconstructing Bayesian posterior distributions of a species phylogeny using estimated gene tree distributions

The desire to infer the evolutionary history of a group of species should be more viable now that a considerable amount of multilocus molecular data is available. However, the current molecular phylogenetic paradigm still reconstructs gene trees to represent the species tree. Further, commonly used methods of combining data, such as the concatenation method, are known to be inconsistent in some circumstances. In this paper, we propose a Bayesian hierarchical model to estimate the phylogeny of a group of species using multiple estimated gene tree distributions, such as those that arise in a Bayesian analysis of DNA sequence data. Our model employs substitution models used in traditional phylogenetics but also uses coalescent theory to explain genealogical signals from species trees to gene trees and from gene trees to sequence data, thereby forming a complete stochastic model to estimate gene trees, species trees, ancestral population sizes, and species divergence times simultaneously. Our model is founded on the assumption that gene trees, even of unlinked loci, are correlated due to being derived from a single species tree and therefore should be estimated jointly. We apply the method to two multilocus data sets of DNA sequences. The estimates of the species tree topology and divergence times appear to be robust to the prior of the population size, whereas the estimates of effective population sizes are sensitive to the prior used in the analysis. These analyses also suggest that the model is superior to the concatenation method in fitting these data sets and thus provides a more realistic assessment of the variability in the distribution of the species tree that may have produced the molecular information at hand. Future improvements of our model and algorithm should include consideration of other factors that can cause discordance of gene trees and species trees, such as horizontal transfer or gene duplication.     

Dating the time of viral subtype divergence

Precise dating of viral subtype divergence enables researchers to correlate divergence with geographic and demographic occurrences. When historical data are absent (that is, the overwhelming majority), viral sequence sampling on a time scale commensurate with the rate of substitution permits the inference of the times of subtype divergence. Currently, researchers use two strategies to approach this task, both requiring strong conditions on the molecular clock assumption of substitution rate. As the underlying structure of the substitution rate process at the time of subtype divergence is not understood and likely highly variable, we present a simple method that estimates rates of substitution, and from there, times of divergence, without use of an assumed molecular clock. We accomplish this by blending estimates of the substitution rate for triplets of dated sequences where each sequence draws from a distinct viral subtype, providing a zeroth-order approximation for the rate between subtypes. As an example, we calculate the time of divergence for three genes among influenza subtypes A-H3N2 and B using subtype C as an outgroup. We show a time of divergence approximately 100 years ago, substantially more recent than previous estimates which range from 250 to 3800 years ago.     

Identifying optimal incomplete phylogenetic data sets from sequence databases

We introduce a new method for identifying optimal incomplete data sets from large sequence databases based on the graph theoretic concept of alpha-quasi-bicliques. The quasi-biclique method searches large sequence databases to identify useful phylogenetic data sets with a specified amount of missing data while maintaining the necessary amount of overlap among genes and taxa. The utility of the quasi-biclique method is demonstrated on large simulated sequence databases and on a data set of green plant sequences from GenBank. The quasi-biclique method greatly increases the taxon and gene sampling in the data sets while adding only a limited amount of missing data. Furthermore, under the conditions of the simulation, data sets with a limited amount of missing data often produce topologies nearly as accurate as those built from complete data sets. The quasi-biclique method will be an effective tool for exploiting sequence databases for phylogenetic information and also may help identify critical sequences needed to build large phylogenetic data sets.     

Inferring speciation times under an episodic molecular clock

We extend our recently developed Markov chain Monte Carlo algorithm for Bayesian estimation of species divergence times to allow variable evolutionary rates among lineages. The method can use heterogeneous data from multiple gene loci and accommodate multiple fossil calibrations. Uncertainties in fossil calibrations are described using flexible statistical distributions. The prior for divergence times for nodes lacking fossil calibrations is specified by use of a birth-death process with species sampling. The prior for lineage-specific substitution rates is specified using either a model with autocorrelated rates among adjacent lineages (based on a geometric Brownian motion model of rate drift) or a model with independent rates among lineages specified by a log-normal probability distribution. We develop an infinite-sites theory, which predicts that when the amount of sequence data approaches infinity, the width of the posterior credibility interval and the posterior mean of divergence times form a perfect linear relationship, with the slope indicating uncertainties in time estimates that cannot be reduced by sequence data alone. Simulations are used to study the influence of among-lineage rate variation and the number of loci sampled on the uncertainty of divergence time estimates. The analysis suggests that posterior time estimates typically involve considerable uncertainties even with an infinite amount of sequence data, and that the reliability and precision of fossil calibrations are critically important to divergence time estimation. We apply our new algorithms to two empirical data sets and compare the results with those obtained in previous Bayesian and likelihood analyses. The results demonstrate the utility of our new algorithms.     

Fast,scalable generation of high‐quality protein multiple sequence alignments using Clustal Omega

Multiple sequence alignments are fundamental to many sequence analysis methods. Most alignments are computed using the progressive alignment heuristic. These methods are starting to become a bottleneck in some analysis pipelines when faced with data sets of the size of many thousands of sequences. Some methods allow computation of larger data sets while sacrificing quality, and others produce high‐quality alignments, but scale badly with the number of sequences. In this paper, we describe a new program called Clustal Omega, which can align virtually any number of protein sequences quickly and that delivers accurate alignments. The accuracy of the package on smaller test cases is similar to that of the high‐quality aligners. On larger data sets, Clustal Omega outperforms other packages in terms of execution time and quality. Clustal Omega also has powerful features for adding sequences to and exploiting information in existing alignments, making use of the vast amount of precomputed information in public databases like Pfam.     

Testing spatiotemporal hypothesis of bacterial evolution using methicillin-resistant Staphylococcus aureus ST239 genome-wide data within a bayesian framework

Staphylococcus aureus is a common cause of infections that has undergone rapid global spread over recent decades. Formal phylogeographic methods have not yet been applied to the molecular epidemiology of bacterial pathogens because the limited genetic diversity of data sets based on individual genes usually results in poor phylogenetic resolution. Here, we investigated a whole-genome single nucleotide polymorphism (SNP) data set of health care-associated Methicillin-resistant S. aureus sequence type 239 (HA-MRSA ST239) strains, which we analyzed using Markov spatial models that incorporate geographical sampling distributions. The reconstructed timescale indicated a temporal origin of this strain shortly after the introduction of Methicillin, followed by global pandemic spread. The estimate of the temporal origin was robust to the molecular clock, coalescent prior, full/intergenic/synonymous SNP inclusion, and correction for excluded invariant site patterns. Finally, phylogeographic analyses statistically supported the role of human movement in the global dissemination of HA-MRSA ST239, although it was unable to conclusively resolve the location of the root. This study demonstrates that bacterial genomes can indeed contain sufficient evolutionary information to elucidate the temporal and spatial dynamics of transmission. Future applications of this approach to other bacterial strains may provide valuable epidemiological insights that may justify the cost of genome-wide typing.     

Estimating evolution of temporal sequence changes: a practical approach to inferring ancestral developmental sequences and sequence heterochrony

Developmental biology often yields data in a temporal context. Temporal data in phylogenetic systematics has important uses in the field of evolutionary developmental biology and, in general, comparative biology. The evolution of temporal sequences, specifically developmental sequences, has proven difficult to examine due to the highly variable temporal progression of development. Issues concerning the analysis of temporal sequences and problems with current methods of analysis are discussed. We present here an algorithm to infer ancestral temporal sequences, quantify sequence heterochronies, and estimate pseudoreplicate consensus support for sequence changes using Parsimov-based genetic inference [PGi]. Real temporal developmental sequence data sets are used to compare PGi with currently used approaches, and PGi is shown to be the most efficient, accurate, and practical method to examine biological data and infer ancestral states on a phylogeny. The method is also expandable to address further issues in developmental evolution, namely modularity.     

Inference of population genetic parameters from an irregular time series of seasonal influenza virus sequences

Basic summary statistics that quantify the population genetic structure of influenza virus are important for understanding and inferring the evolutionary and epidemiological processes. However, the sampling dates of global virus sequences in the last several decades are scattered nonuniformly throughout the calendar. Such temporal structure of samples and the small effective size of viral population hampers the use of conventional methods to calculate summary statistics. Here, we define statistics that overcome this problem by correcting for the sampling-time difference in quantifying a pairwise sequence difference. A simple linear regression method jointly estimates the mutation rate and the level of sequence polymorphism, thus providing an estimate of the effective population size. It also leads to the definition of Wright’s F_ST for arbitrary time-series data. Furthermore, as an alternative to Tajima’s D statistic or the site-frequency spectrum, a mismatch distribution corrected for sampling-time differences can be obtained and compared between actual and simulated data. Application of these methods to seasonal influenza A/H3N2 viruses sampled between 1980 and 2017 and sequences simulated under the model of recurrent positive selection with metapopulation dynamics allowed us to estimate the synonymous mutation rate and find parameter values for selection and demographic structure that fit the observation. We found that the mutation rates of HA and PB1 segments before 2007 were particularly high and that including recurrent positive selection in our model was essential for the genealogical structure of the HA segment. Methods developed here can be generally applied to population genetic inferences using serially sampled genetic data.