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Phylogenies provide a useful way to understand the evolutionary history of genetic samples, and data sets with more than a thousand taxa are becoming increasingly common, notably with viruses e. Dating ancestral events is one of the first, essential goals with such data. However, current sophisticated probabilistic approaches struggle to handle data sets of this size. Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley-Fitch molecular-clock model. We show that this model is robust to uncorrelated violations of the molecular clock. Our algorithms apply to serial data, where the tips of the tree have been sampled through times. They estimate the substitution rate and the dates of all ancestral nodes.

On that date, the World Health Organization WHO declared a pandemic, and the end of the pandemic was declared in August for details, see Christman et al. Molecular epidemiology studies on this virus were performed at an early stage of the epidemic, using strains collected between 30 March and 12 July Lemey et al.

These studies indicated that this virus has a high evolutionary rate of 4. To our knowledge, no other molecular dating study has been published on a more comprehensive set of strains sampled over a longer time period.

The strains used here were collected worldwide between 13 March and 9 June see Online Appendix Supplementary Table S5 for further details. As many sequences were identical but collected at different time points, we retained for each set of identical sequences only one exemplar with a sampling date equal to the average of the dates of the corresponding strains. Note that grouping identical sequences does not impact phylogeny inference identical sequences are separated by branches of length zero but accelerates the computations and is consistent with our dating model which has difficulty in dealing with branches of length zero but different dates at both extremities see Eqs.

However, this simplification was not used with BEAST, which handles such data due to its coalescent, population genetics model. To run our dating algorithms, we first have to infer a phylogenetic tree.

For both methods we analyzed the ingroup sequences only and considered both the outgroup-based rooted tree, and the unrooted tree obtained by root removal. To improve computational efficiency, the tree topology was kept constant and equal to the topology inferred using the original data set; only the branch lengths were re-estimated from the bootstrap samples.

We compared the same methods as in the previous sections, using the same options. Two independent MCMC chains were used per model, with a minimum of million generations each, sampling every 10, generations. The first 25 million generations in each run were discarded as burn-in, and the Highest Posterior Density statistics for each parameter were calculated over a posterior sample of states using Tracer 1.

Moreover, as we observed a strong discrepancy between BEAST and the other methods regarding substitution rate estimations see belowwe also launched BEAST with the cleaned data set where identical sequences were grouped taxaand using the PhyML rooted tree topology which was kept constant all along the computations, solely sampling the branch lengths and model parameters.

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However, the time to build trees has to be accounted for, especially when bootstraps are used. To get a good posterior sample of time resolved Bayesian phylogenetic trees with the sequences requires running BEAST for a minimum of 20 d, using at least million MCMC generations at approximately 2 h per million generations.

Note: Time is expressed in seconds, except otherwise specified.

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With bootstrap samples, only the branch lengths were reoptimized; the tree topology was kept constant and equal to the topology inferred using the original alignment.

We see little difference Fig. This strongly suggests using FastME when the focus is on rates and dates, at least for large data sets, as it is several orders of magnitude faster than PhyML.

Moreover, both tree building and dating are then consistently based on similar distance-based approaches. The box plots represent the median, maximum, minimum, Regarding rate estimation Fig. QPD also shows relatively large intervals, likely due to the fact that it has to infer the tree root and is thus subject to more variability and possible rooting errors.

We also observed similar discrepancies between both approaches on other biological data sets results not shown.

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However, the gap here was so large that we ran BEAST with the cleaned data set and the fixed PhyML rooted tree topology that was used with other approaches. The reasons for these findings are still unclear. Such calculations in a Bayesian setting could simply be too heavy, thus supporting the use of simpler PAML-like approaches for estimating dates and rates from fixed rooted tree topologies.

This date is compatible with Rambaut and HolmesLemey et al. The latter show more variability, larger confidence intervals, and tend to produce older date estimates, around the beginning of these intervals and dates, however, are still statistically compatible with those of other methods.

Again this larger variability is likely explained by the difficulty of tree rooting.

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Regarding substitution rate estimation, we observe a large discrepancy between distance-based methods and BEAST, when used in the usual way estimating all parameters, including the tree topology and its root.

However, with the fixed rooted tree topology, BEAST estimates of the substitution rate become similar to those of distance-based approaches. We have described very fast algorithms to estimate rates and dates from serial data.

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These algorithms are based on a Gaussian noise, least-squares model, simplifying the Langley and Fitch's Poisson model implemented in the r8s package Sanderson We showed that this model should be robust to uncorrelated violations of the molecular clock, and our simulation results confirm this theoretical prediction.

LD uses a pure linear algebra approach, while QPD accounts for temporal precedence constraints, which appears to be important with real data. Given an input tree with dated tips, our algorithms provide the user with estimates of the substitution rate, the root date and the dates of all internal tree nodes, a task that is not achieved by RTT also based on a simple, least-squares approach, but not able to date internal nodes.

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Our algorithms can be used to root the input tree when no outgroup is available, a feature that is not available in the r8s implementation of LF, and would be time consuming in the Poisson setting. Consequently, LD and QPD are also new fast, practical methods for tree rooting, which represent an alternative to the standard midpoint and minimum-variance approaches.

Computer simulations show that the accuracy of our algorithms is better than RTT's, and just slightly behind LF's with rooted trees. Compared to BEAST, our algorithms combined with standard tree building methods have a similar or better accuracy in estimating the substitution rate, while regarding dates the results depend very much on the presence of an outgroup and the way BEAST is used, estimating all parameters including the tree topology and its root, or using a fixed rooted tree topology.

Globally, we did not observe any obvious limitation of our algorithms compared to BEAST, with simulated as well as real data sets. Moreover, our results clearly show the importance of having an accurate root position, a difficult goal when no outgroup is available and with relaxed realistic molecular clock. Our algorithms require quasi linear computing times with rooted trees, as a function of nthe number of leaves. With unrooted trees, the computing time is nearly quadratic in n.

This is obtained with complex algorithms, exploiting the closeness between least-squares and linear algebra; we also exploit the tree structure which makes it possible to design fast recursive procedures.

This speed is important for current applications of phylogenetics. In Mourad et al. Our approach could be developed in several directions. First, we currently use a bootstrap approach to obtain confidence intervals, which is possible due to the speed of the algorithms, but still slow. Much faster approaches could be designed, for example, using the second derivative of the log-likelihood least-squares function. Second, we have described here the application of these algorithms to serial phylogenies with dated tips; easy adaptations should make it possible to use the very same approach to deal with phylogenies with time calibration points, attaching dated tips to ancestral nodes and using intervals constraints to account for ancestral date uncertainty.

Last, an important direction is to implement fast methods that are able to cope with more complex, correlated molecular clock models, typically combining the least-squares framework with penalized criteria, similar to Sandersonor using some of our algorithmic solutions to deal with multi-normal approximations of the likelihood function Thorne et al.

Akerborg O. Sennblad B. Lagergren J. Birth-death prior on phylogeny and speed dating. BMC Evol. Google Scholar. Arvestad L. Simultaneous Bayesian gene tree reconstruction and reconciliation analysis. PNAS 14 : - Ayres D. Darling A.

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Zwickl D. Beerli P. Holder M. Lewis P. Huelsenbeck J. Ronquist F. Swofford D. Cummings M. Rambaut A. Suchard M. BEAGLE: an application programming interface and high-performance computing library for statistical phylogenetics. Battistuzzi F. Filipski A. Hedges S. Kumar S. Performance of relaxed-clock methods in estimating evolutionary divergence times and their credibility intervals. Bello G.

Passaes C. Lorete R.

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Matos Almeida S. Medeiros R. Alencastro P. Morgado M.

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AIDS 22 : - Bertsekas D. Nonlinear programming. Cambridge, MA : Athena Scientific. Google Preview.

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Boyd S. Vandenberghe L. Convex optimization, Chapter Cambridge : Cambridge University Press. Britton T. Anderson C. Jacquet D.

Author notes

Lundqvist S. Bremer K. Estimating divergence times in large phylogenetic trees. Christman M. Kedwaii A. Donis R. Pandemic H1N1 virus revisited: an evolutionary retrospective.

Desper R. Gascuel O. Fast and accurate phylogeny reconstruction algorithms based on the minimum-evolution principle. Douzery E. Delsuc F. Stanhope M. Huchon D. Local molecular clocks in three nuclear genes: divergence times for rodents and other mammals and incompatibility among fossil calibrations. Doyon J.

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Ranwez V. Daubin V. Berry V. Models, algorithms and programs for phylogeny reconciliation. Drummond A. Rodrigo A. Reconstruction genealogies of serial samples under the assumption of a molecular clock using serial-sample UPGMA.

Pybus O. Forsberg R. Measurably evolving populations. Trends Ecol. Inference of viral evolutionary rates from molecular sequences. Phillips M. Relaxed phylogenetics and dating with confidence. PLoS Biol. Xie D. Felsenstein J. Cladistics 5 : - Fitch W. Margoliash E. Construction of phylogenetic trees.

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perhaps shall simply

Unifying the epidemiological and evolutionary dynamics of pathogens. Guindon S. Bayesian estimation of divergence times from large sequence alignments. A simple, fast and accurate algorithm to infer large phylogenies by maximum-likelihood.

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Fast and dating

Lefort V. Anisimova M. Hordijk W. New algorithms and methods to estimate maximum-likelihood phylogenies: assessing the performance of PhyML 3. Hedge J. Lycett S. Real-time characterization of the molecular epidemiology of an influenza pandemic. The timetree of life. New York : Oxford University Press. Jetz W.

They move to wherever they are told throughout the country. They talk to strangers about Jesus. But perhaps one of the most shocking things they do is give up dating for an entire year. All first year missionaries fast from romantic relationships for one year. No dating. No flirting. No handholding.

No mentally stalking someone who has caught their attention So why would a young adult in perhaps the prime of their search for their future mate temporally give up dating? And why am I going to suggest that you do the same? Freedom to love. Sounds backwards right? Read on. You vow never again to order anything of importance online and hop in line at the local coffee shop. In this scenario, were you free? I say not really. Instead of you being in control of the espresso, the espresso was in control of you.

And for those who are not currently dating, this fact can turn into something they just have to obsess about. I call that a pretty undesirable side effect. Sounds a lot like our espresso, huh?

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