Computational Reproducibility of Molecular Phylogenies.

Repeated runs of the same program can generate different molecular phylogenies from identical data sets under the same analytical conditions. This lack of reproducibility of inferred phylogenies casts a long shadow on downstream research employing these phylogenies in areas such as comparative genomics, systematics, and functional biology. We have assessed the relative accuracies and log-likelihoods of alternative phylogenies generated for computer-simulated and empirical data sets. Our findings indicate that these alternative phylogenies reconstruct evolutionary relationships with comparable accuracy. They also have similar log-likelihoods that are not inferior to the log-likelihoods of the true tree. We determined that the direct relationship between irreproducibility and inaccuracy is due to their common dependence on the amount of phylogenetic information in the data. While computational reproducibility can be enhanced through more extensive heuristic searches for the maximum likelihood tree, this does not lead to higher accuracy. We conclude that computational irreproducibility plays a minor role in molecular phylogenetics.

TopHap: rapid inference of key phylogenetic structures from common haplotypes in large genome collections with limited diversity.

MOTIVATION: Building reliable phylogenies from very large collections of sequences with a limited number of phylogenetically informative sites is challenging because sequencing errors and recurrent/backward mutations interfere with the phylogenetic signal, confounding true evolutionary relationships. Massive global efforts of sequencing genomes and reconstructing the phylogeny of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) strains exemplify these difficulties since there are only hundreds of phylogenetically informative sites but millions of genomes. For such datasets, we set out to develop a method for building the phylogenetic tree of genomic haplotypes consisting of positions harboring common variants to improve the signal-to-noise ratio for more accurate and fast phylogenetic inference of resolvable phylogenetic features. RESULTS: We present the TopHap approach that determines spatiotemporally common haplotypes of common variants and builds their phylogeny at a fraction of the computational time of traditional methods. We develop a bootstrap strategy that resamples genomes spatiotemporally to assess topological robustness. The application of TopHap to build a phylogeny of 68 057 SARS-CoV-2 genomes (68KG) from the first year of the pandemic produced an evolutionary tree of major SARS-CoV-2 haplotypes. This phylogeny is concordant with the mutation tree inferred using the co-occurrence pattern of mutations and recovers key phylogenetic relationships from more traditional analyses. We also evaluated alternative roots of the SARS-CoV-2 phylogeny and found that the earliest sampled genomes in 2019 likely evolved by four mutations of the most recent common ancestor of all SARS-CoV-2 genomes. An application of TopHap to more than 1 million SARS-CoV-2 genomes reconstructed the most comprehensive evolutionary relationships of major variants, which confirmed the 68KG phylogeny and provided evolutionary origins of major and recent variants of concern. AVAILABILITY AND IMPLEMENTATION: TopHap is available at https://github.com/SayakaMiura/TopHap. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

TopHap: Rapid inference of key phylogenetic structures from common haplotypes in large genome collections with limited diversity.

MOTIVATION: Building reliable phylogenies from very large collections of sequences with a limited number of phylogenetically informative sites is challenging because sequencing errors and recurrent/backward mutations interfere with the phylogenetic signal, confounding true evolutionary relationships. Massive global efforts of sequencing genomes and reconstructing the phylogeny of SARS-CoV-2 strains exemplify these difficulties since there are only hundreds of phylogenetically informative sites and millions of genomes. For such datasets, we set out to develop a method for building the phylogenetic tree of genomic haplotypes consisting of positions harboring common variants to improve the signal-to-noise ratio for more accurate phylogenetic inference of resolvable phylogenetic features. RESULTS: We present the TopHap approach that determines spatiotemporally common haplotypes of common variants and builds their phylogeny at a fraction of the computational time of traditional methods. To assess topological robustness, we develop a bootstrap resampling strategy that resamples genomes spatiotemporally. The application of TopHap to build a phylogeny of 68,057 genomes (68KG) produced an evolutionary tree of major SARS-CoV-2 haplotypes. This phylogeny is concordant with the mutation tree inferred using the co-occurrence pattern of mutations and recovers key phylogenetic relationships from more traditional analyses. We also evaluated alternative roots of the SARS-CoV-2 phylogeny and found that the earliest sampled genomes in 2019 likely evolved by four mutations of the most recent common ancestor of all SARS-CoV-2 genomes. An application of TopHap to more than 1 million genomes reconstructed the most comprehensive evolutionary relationships of major variants, which confirmed the 68KG phylogeny and provided evolutionary origins of major variants of concern. AVAILABILITY: TopHap is available on the web at https://github.com/SayakaMiura/TopHap . CONTACT: s.kumar@temple.edu.

Assessing Rapid Relaxed-Clock Methods for Phylogenomic Dating.

Rapid relaxed-clock dating methods are frequently applied to analyze phylogenomic data sets containing hundreds to thousands of sequences because of their accuracy and computational efficiency. However, the relative performance of different rapid dating methods is yet to be compared on the same data sets, and, thus, the power and pitfalls of selecting among these approaches remain unclear. We compared the accuracy, bias, and coverage probabilities of RelTime, treePL, and least-squares dating time estimates by applying them to analyze computer-simulated data sets in which evolutionary rates varied extensively among branches in the phylogeny. RelTime estimates were consistently more accurate than the other two, particularly when evolutionary rates were autocorrelated or shifted convergently among lineages. The 95% confidence intervals (CIs) around RelTime dates showed appropriate coverage probabilities (95% on average), but other methods produced rather low coverage probabilities because of overly narrow CIs of time estimates. Overall, RelTime appears to be a more efficient method for estimating divergence times for large phylogenies.

Data-driven speciation tree prior for better species divergence times in calibration-poor molecular phylogenies.

MOTIVATION: Precise time calibrations needed to estimate ages of species divergence are not always available due to fossil records' incompleteness. Consequently, clock calibrations available for Bayesian dating analyses can be few and diffused, i.e. phylogenies are calibration-poor, impeding reliable inference of the timetree of life. We examined the role of speciation birth-death (BD) tree prior on Bayesian node age estimates in calibration-poor phylogenies and tested the usefulness of an informative, data-driven tree prior to enhancing the accuracy and precision of estimated times. RESULTS: We present a simple method to estimate parameters of the BD tree prior from the molecular phylogeny for use in Bayesian dating analyses. The use of a data-driven birth-death (ddBD) tree prior leads to improvement in Bayesian node age estimates for calibration-poor phylogenies. We show that the ddBD tree prior, along with only a few well-constrained calibrations, can produce excellent node ages and credibility intervals, whereas the use of an uninformative, uniform (flat) tree prior may require more calibrations. Relaxed clock dating with ddBD tree prior also produced better results than a flat tree prior when using diffused node calibrations. We also suggest using ddBD tree priors to improve the detection of outliers and influential calibrations in cross-validation analyses.These results have practical applications because the ddBD tree prior reduces the number of well-constrained calibrations necessary to obtain reliable node age estimates. This would help address key impediments in building the grand timetree of life, revealing the process of speciation and elucidating the dynamics of biological diversification. AVAILABILITY AND IMPLEMENTATION: An R module for computing the ddBD tree prior, simulated datasets and empirical datasets are available at https://github.com/cathyqqtao/ddBD-tree-prior.

An Evolutionary Portrait of the Progenitor SARS-CoV-2 and Its Dominant Offshoots in COVID-19 Pandemic.

Global sequencing of genomes of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has continued to reveal new genetic variants that are the key to unraveling its early evolutionary history and tracking its global spread over time. Here we present the heretofore cryptic mutational history and spatiotemporal dynamics of SARS-CoV-2 from an analysis of thousands of high-quality genomes. We report the likely most recent common ancestor of SARS-CoV-2, reconstructed through a novel application and advancement of computational methods initially developed to infer the mutational history of tumor cells in a patient. This progenitor genome differs from genomes of the first coronaviruses sampled in China by three variants, implying that none of the earliest patients represent the index case or gave rise to all the human infections. However, multiple coronavirus infections in China and the United States harbored the progenitor genetic fingerprint in January 2020 and later, suggesting that the progenitor was spreading worldwide months before and after the first reported cases of COVID-19 in China. Mutations of the progenitor and its offshoots have produced many dominant coronavirus strains that have spread episodically over time. Fingerprinting based on common mutations reveals that the same coronavirus lineage has dominated North America for most of the pandemic in 2020. There have been multiple replacements of predominant coronavirus strains in Europe and Asia as well as continued presence of multiple high-frequency strains in Asia and North America. We have developed a continually updating dashboard of global evolution and spatiotemporal trends of SARS-CoV-2 spread (http://sars2evo.datamonkey.org/).

Molecular and morphological clocks for estimating evolutionary divergence times.

BACKGROUND: Matrices of morphological characters are frequently used for dating species divergence times in systematics. In some studies, morphological and molecular character data from living taxa are combined, whereas others use morphological characters from extinct taxa as well. We investigated whether morphological data produce time estimates that are concordant with molecular data. If true, it will justify the use of morphological characters alongside molecular data in divergence time inference. RESULTS: We systematically analyzed three empirical datasets from different species groups to test the concordance of species divergence dates inferred using molecular and discrete morphological data from extant taxa as test cases. We found a high correlation between their divergence time estimates, despite a poor linear relationship between branch lengths for morphological and molecular data mapped onto the same phylogeny. This was because node-to-tip distances showed a much higher correlation than branch lengths due to an averaging effect over multiple branches. We found that nodes with a large number of taxa often benefit from such averaging. However, considerable discordance between time estimates from molecules and morphology may still occur as  some intermediate nodes may show large time differences between these two types of data. CONCLUSIONS: Our findings suggest that node- and tip-calibration approaches may be better suited for nodes with many taxa. Nevertheless, we highlight the importance of evaluating the concordance of intrinsic time structure in morphological and molecular data before any dating analysis using combined datasets.

Molecular dating for phylogenies containing a mix of populations and species by using Bayesian and RelTime approaches.

Simultaneous molecular dating of population and species divergences is essential in many biological investigations, including phylogeography, phylodynamics and species delimitation studies. In these investigations, multiple sequence alignments consist of both intra- and interspecies samples (mixed samples). As a result, the phylogenetic trees contain interspecies, interpopulation and within-population divergences. Bayesian relaxed clock methods are often employed in these analyses, but they assume the same tree prior for both inter- and intraspecies branching processes and require specification of a clock model for branch rates (independent vs. autocorrelated rates models). We evaluated the impact of a single tree prior on Bayesian divergence time estimates by analysing computer-simulated data sets. We also examined the effect of the assumption of independence of evolutionary rate variation among branches when the branch rates are autocorrelated. Bayesian approach with coalescent tree priors generally produced excellent molecular dates and highest posterior densities with high coverage probabilities. We also evaluated the performance of a non-Bayesian method, RelTime, which does not require the specification of a tree prior or a clock model. RelTime's performance was similar to that of the Bayesian approach, suggesting that it is also suitable to analyse data sets containing both populations and species variation when its computational efficiency is needed.

An evolutionary portrait of the progenitor SARS-CoV-2 and its dominant offshoots in COVID-19 pandemic.

We report the likely most recent common ancestor of SARS-CoV-2 - the coronavirus that causes COVID-19. This progenitor SARS-CoV-2 genome was recovered through a novel application and advancement of computational methods initially developed to reconstruct the mutational history of tumor cells in a patient. The progenitor differs from the earliest coronaviruses sampled in China by three variants, implying that none of the earliest patients represent the index case or gave rise to all the human infections. However, multiple coronavirus infections in China and the USA harbored the progenitor genetic fingerprint in January 2020 and later, suggesting that the progenitor was spreading worldwide as soon as weeks after the first reported cases of COVID-19. Mutations of the progenitor and its offshoots have produced many dominant coronavirus strains, which have spread episodically over time. Fingerprinting based on common mutations reveals that the same coronavirus lineage has dominated North America for most of the pandemic. There have been multiple replacements of predominant coronavirus strains in Europe and Asia and the continued presence of multiple high-frequency strains in Asia and North America. We provide a continually updating dashboard of global evolution and spatiotemporal trends of SARS-CoV-2 spread (http://sars2evo.datamonkey.org/).

Using a GTR+Γ substitution model for dating sequence divergence when stationarity and time-reversibility assumptions are violated.

MOTIVATION: As the number and diversity of species and genes grow in contemporary datasets, two common assumptions made in all molecular dating methods, namely the time-reversibility and stationarity of the substitution process, become untenable. No software tools for molecular dating allow researchers to relax these two assumptions in their data analyses. Frequently the same General Time Reversible (GTR) model across lineages along with a gamma (+Γ) distributed rates across sites is used in relaxed clock analyses, which assumes time-reversibility and stationarity of the substitution process. Many reports have quantified the impact of violations of these underlying assumptions on molecular phylogeny, but none have systematically analyzed their impact on divergence time estimates. RESULTS: We quantified the bias on time estimates that resulted from using the GTR + Γ model for the analysis of computer-simulated nucleotide sequence alignments that were evolved with non-stationary (NS) and non-reversible (NR) substitution models. We tested Bayesian and RelTime approaches that do not require a molecular clock for estimating divergence times. Divergence times obtained using a GTR + Γ model differed only slightly (∼3% on average) from the expected times for NR datasets, but the difference was larger for NS datasets (∼10% on average). The use of only a few calibrations reduced these biases considerably (∼5%). Confidence and credibility intervals from GTR + Γ analysis usually contained correct times. Therefore, the bias introduced by the use of the GTR + Γ model to analyze datasets, in which the time-reversibility and stationarity assumptions are violated, is likely not large and can be reduced by applying multiple calibrations. AVAILABILITY AND IMPLEMENTATION: All datasets are deposited in Figshare: https://doi.org/10.6084/m9.figshare.12594638.

Relative Efficiencies of Simple and Complex Substitution Models in Estimating Divergence Times in Phylogenomics.

The conventional wisdom in molecular evolution is to apply parameter-rich models of nucleotide and amino acid substitutions for estimating divergence times. However, the actual extent of the difference between time estimates produced by highly complex models compared with those from simple models is yet to be quantified for contemporary data sets that frequently contain sequences from many species and genes. In a reanalysis of many large multispecies alignments from diverse groups of taxa, we found that the use of the simplest models can produce divergence time estimates and credibility intervals similar to those obtained from the complex models applied in the original studies. This result is surprising because the use of simple models underestimates sequence divergence for all the data sets analyzed. We found three fundamental reasons for the observed robustness of time estimates to model complexity in many practical data sets. First, the estimates of branch lengths and node-to-tip distances under the simplest model show an approximately linear relationship with those produced by using the most complex models applied on data sets with many sequences. Second, relaxed clock methods automatically adjust rates on branches that experience considerable underestimation of sequence divergences, resulting in time estimates that are similar to those from complex models. And, third, the inclusion of even a few good calibrations in an analysis can reduce the difference in time estimates from simple and complex models. The robustness of time estimates to model complexity in these empirical data analyses is encouraging, because all phylogenomics studies use statistical models that are oversimplified descriptions of actual evolutionary substitution processes.

A new method for inferring timetrees from temporally sampled molecular sequences.

Pathogen timetrees are phylogenies scaled to time. They reveal the temporal history of a pathogen spread through the populations as captured in the evolutionary history of strains. These timetrees are inferred by using molecular sequences of pathogenic strains sampled at different times. That is, temporally sampled sequences enable the inference of sequence divergence times. Here, we present a new approach (RelTime with Dated Tips [RTDT]) to estimating pathogen timetrees based on a relative rate framework underlying the RelTime approach that is algebraic in nature and distinct from all other current methods. RTDT does not require many of the priors demanded by Bayesian approaches, and it has light computing requirements. In analyses of an extensive collection of computer-simulated datasets, we found the accuracy of RTDT time estimates and the coverage probabilities of their confidence intervals (CIs) to be excellent. In analyses of empirical datasets, RTDT produced dates that were similar to those reported in the literature. In comparative benchmarking with Bayesian and non-Bayesian methods (LSD, TreeTime, and treedater), we found that no method performed the best in every scenario. So, we provide a brief guideline for users to select the most appropriate method in empirical data analysis. RTDT is implemented for use via a graphical user interface and in high-throughput settings in the newest release of cross-platform MEGA X software, freely available from http://www.megasoftware.net.

Reliable Confidence Intervals for RelTime Estimates of Evolutionary Divergence Times.

Confidence intervals (CIs) depict the statistical uncertainty surrounding evolutionary divergence time estimates. They capture variance contributed by the finite number of sequences and sites used in the alignment, deviations of evolutionary rates from a strict molecular clock in a phylogeny, and uncertainty associated with clock calibrations. Reliable tests of biological hypotheses demand reliable CIs. However, current non-Bayesian methods may produce unreliable CIs because they do not incorporate rate variation among lineages and interactions among clock calibrations properly. Here, we present a new analytical method to calculate CIs of divergence times estimated using the RelTime method, along with an approach to utilize multiple calibration uncertainty densities in dating analyses. Empirical data analyses showed that the new methods produce CIs that overlap with Bayesian highest posterior density intervals. In the analysis of computer-simulated data, we found that RelTime CIs show excellent average coverage probabilities, that is, the actual time is contained within the CIs with a 94% probability. These developments will encourage broader use of computationally efficient RelTime approaches in molecular dating analyses and biological hypothesis testing.

A Machine Learning Method for Detecting Autocorrelation of Evolutionary Rates in Large Phylogenies.

New species arise from pre-existing species and inherit similar genomes and environments. This predicts greater similarity of the tempo of molecular evolution between direct ancestors and descendants, resulting in autocorrelation of evolutionary rates in the tree of life. Surprisingly, molecular sequence data have not confirmed this expectation, possibly because available methods lack the power to detect autocorrelated rates. Here, we present a machine learning method, CorrTest, to detect the presence of rate autocorrelation in large phylogenies. CorrTest is computationally efficient and performs better than the available state-of-the-art method. Application of CorrTest reveals extensive rate autocorrelation in DNA and amino acid sequence evolution of mammals, birds, insects, metazoans, plants, fungi, parasitic protozoans, and prokaryotes. Therefore, rate autocorrelation is a common phenomenon throughout the tree of life. These findings suggest concordance between molecular and nonmolecular evolutionary patterns, and they will foster unbiased and precise dating of the tree of life.

Theoretical Foundation of the RelTime Method for Estimating Divergence Times from Variable Evolutionary Rates.

RelTime estimates divergence times by relaxing the assumption of a strict molecular clock in a phylogeny. It shows excellent performance in estimating divergence times for both simulated and empirical molecular sequence data sets in which evolutionary rates varied extensively throughout the tree. RelTime is computationally efficient and scales well with increasing size of data sets. Until now, however, RelTime has not had a formal mathematical foundation. Here, we show that the basis of the RelTime approach is a relative rate framework (RRF) that combines comparisons of evolutionary rates in sister lineages with the principle of minimum rate change between evolutionary lineages and their respective descendants. We present analytical solutions for estimating relative lineage rates and divergence times under RRF. We also discuss the relationship of RRF with other approaches, including the Bayesian framework. We conclude that RelTime will be useful for phylogenies with branch lengths derived not only from molecular data, but also morphological and biochemical traits.

RelTime Relaxes the Strict Molecular Clock throughout the Phylogeny.

The RelTime method estimates divergence times when evolutionary rates vary among lineages. Theoretical analyses show that RelTime relaxes the strict molecular clock throughout a molecular phylogeny, and it performs well in the analyses of empirical and computer simulated data sets in which evolutionary rates are variable. Lozano-Fernandez et al. (2017) found that the application of RelTime to one metazoan data set (Erwin et al. 2011) produced equal rates for several ancient lineages, which led them to speculate that RelTime imposes a strict molecular clock for deep animal divergences. RelTime does not impose a strict molecular clock. The pattern observed by Lozano-Fernandez et al. (2017) was a result of the use of an option to assign the same rate to lineages in RelTime when the rates are not statistically significantly different. The median rate difference was 5% for many deep metazoan lineages for the Erwin et al. (2011) data set, so the rate equality was not rejected. In fact, RelTime analyses with and without the option to test rate differences produced very similar time estimates. We also found that the Bayesian time estimates vary widely depending on the root priors assigned, and that the use of less restrictive priors produces Bayesian divergence times that are concordant with those from RelTime for the Erwin et al. (2011) data set. Therefore, it is prudent to discuss Bayesian estimates obtained under a range of priors in any discourse about molecular dating, including method comparisons.

Fast and Accurate Estimates of Divergence Times from Big Data.

Ongoing advances in sequencing technology have led to an explosive expansion in the molecular data available for building increasingly larger and more comprehensive timetrees. However, Bayesian relaxed-clock approaches frequently used to infer these timetrees impose a large computational burden and discourage critical assessment of the robustness of inferred times to model assumptions, influence of calibrations, and selection of optimal data subsets. We analyzed eight large, recently published, empirical datasets to compare time estimates produced by RelTime (a non-Bayesian method) with those reported by using Bayesian approaches. We find that RelTime estimates are very similar to Bayesian approaches, yet RelTime requires orders of magnitude less computational time. This means that the use of RelTime will enable greater rigor in molecular dating, because faster computational speeds encourage more extensive testing of the robustness of inferred timetrees to prior assumptions (models and calibrations) and data subsets. Thus, RelTime provides a reliable and computationally thrifty approach for dating the tree of life using large-scale molecular datasets.

Expressional analysis of immunoglobulin D in cattle (Bos taurus), a large domesticated ungulate.

For decades, it has remained unknown whether artiodactyls, such as cattle, pigs, and sheep, express immunoglobulin D (IgD), although the δ gene was identified in these species nearly 10 years ago. By developing a mouse anti-bovine IgD heavy chain monoclonal antibody (13C2), we show that secreted bovine IgD was present mainly as a monomer in serum and was heavily glycosylated by N-linked saccharides. Nonetheless, IgD was detectable in some but not all of the Holstein cattle examined. Membrane-bound IgD was detected in the spleen by western blotting. Flow cytometric analysis demonstrated that IgD-positive B cells constituted a much lower percentage of B cells in the bovine spleen (∼6.8% of total B cells), jejunal Peyer's patches (∼0.8%), and peripheral blood leukocytes (∼1.2%) than in humans and mice. Furthermore, IgD-positive B cells were almost undetectable in bovine bone marrow and ileal Peyer's patches. We also demonstrated that the bovine δ gene can be expressed via class switch recombination. Accordingly, bovine δ germline transcription, which involves an Iδ exon and is highly homologous to Iµ, was confirmed. However, we could not identify an Iδ promoter, despite bovine Eµ demonstrating both enhancer and promoter activity. This study has answered a long-standing question in cattle B cell biology and significantly contributes to our understanding of B cell development in this species.