Modeling the velocity of evolving lineages and predicting dispersal patterns.

Accurate estimation of the dispersal velocity or speed of evolving organisms is no mean feat. In fact, existing probabilistic models in phylogeography or spatial population genetics generally do not provide an adequate framework to define velocity in a relevant manner. For instance, the very concept of instantaneous speed simply does not exist under one of the most popular approaches that models the evolution of spatial coordinates as Brownian trajectories running along a phylogeny [30]. Here, we introduce a new family of models - the so-called "Phylogenetic Integrated Velocity" (PIV) models - that use Gaussian processes to explicitly model the velocity of evolving lineages instead of focusing on the fluctuation of spatial coordinates over time. We describe the properties of these models and show an increased accuracy of velocity estimates compared to previous approaches. Analyses of West Nile virus data in the U.S.A. indicate that PIV models provide sensible predictions of the dispersal of evolving pathogens at a one-year time horizon. These results demonstrate the feasibility and relevance of predictive phylogeography in monitoring epidemics in time and space.

On the connections between the spatial Lambda-Fleming-Viot model and other processes for analysing geo-referenced genetic data.

The introduction of the spatial Lambda-Fleming-Viot model (ΛV) in population genetics was mainly driven by the pioneering work of Alison Etheridge, in collaboration with Nick Barton and Amandine Véber about ten years ago (Barton et al., 2010; Barton et al., 2013). The ΛV model provides a sound mathematical framework for describing the evolution of a population of related individuals along a spatial continuum. It alleviates the "pain in the torus" issue with Wright and Malécot's isolation by distance model and is sampling consistent, making it a tool of choice for statistical inference. Yet, little is known about the potential connections between the ΛV and other stochastic processes generating trees and the spatial coordinates along the corresponding lineages. This work focuses on a version of the ΛV whereby lineages move rapidly over small distances. Using simulations, we show that the induced ΛV tree-generating process is well approximated by a birth-death model. Our results also indicate that Brownian motions modelling the movements of lines of descent along birth-death trees do not generally provide a good approximation of the ΛV due to habitat boundaries effects that play an increasingly important role in the long run. Accounting for habitat boundaries through reflected Brownian motions considerably increases the similarity to the ΛV model however. Finally, we describe efficient algorithms for fast simulation of the backward and forward in time versions of the ΛV model.

How fast are viruses spreading in the wild?

Genomic data collected from viral outbreaks can be exploited to reconstruct the dispersal history of viral lineages in a two-dimensional space using continuous phylogeographic inference. These spatially explicit reconstructions can subsequently be used to estimate dispersal metrics allowing to unveil the dispersal dynamics and evaluate the capacity to spread among hosts. Heterogeneous sampling intensity of genomic sequences can however impact the accuracy of dispersal insights gained through phylogeographic inference. In our study, we implement a simulation framework to evaluate the robustness of three dispersal metrics - a lineage dispersal velocity, a diffusion coefficient, and an isolation-by-distance signal metric - to the sampling effort. Our results reveal that both the diffusion coefficient and isolation-by-distance signal metrics appear to be robust to the number of samples considered for the phylogeographic reconstruction. We then use these two dispersal metrics to compare the dispersal pattern and capacity of various viruses spreading in animal populations. Our comparative analysis reveals a broad range of isolation-by-distance patterns and diffusion coefficients mostly reflecting the dispersal capacity of the main infected host species but also, in some cases, the likely signature of rapid and/or long-distance dispersal events driven by human-mediated movements through animal trade. Overall, our study provides key recommendations for the lineage dispersal metrics to consider in future studies and illustrates their application to compare the spread of viruses in various settings.

Rate of coalescence of lineage pairs in the Spatial Λ-Fleming-Viot process.

We revisit the Spatial Λ-Fleming-Viot process introduced in Barton and Kelleher (2010). Particularly, we are interested in the time T0 to the most recent common ancestor for two lineages. We distinguish between the cases where the process acts on the two-dimensional plane and on a finite rectangle. Utilizing a differential equation linking T0 with the physical distance between the lineages, we arrive at computationally efficient and reasonably accurate approximation schemes for both cases. Furthermore, our analysis enables us to address the question of whether the genealogical process of the model "comes down from infinity", which has been partly answered before in Véber and Wakolbinger (2015).

Accounting for spatial sampling patterns in Bayesian phylogeography.

Statistical phylogeography provides useful tools to characterize and quantify the spread of organisms during the course of evolution. Analyzing georeferenced genetic data often relies on the assumption that samples are preferentially collected in densely populated areas of the habitat. Deviation from this assumption negatively impacts the inference of the spatial and demographic dynamics. This issue is pervasive in phylogeography. It affects analyses that approximate the habitat as a set of discrete demes as well as those that treat it as a continuum. The present study introduces a Bayesian modeling approach that explicitly accommodates for spatial sampling strategies. An original inference technique, based on recent advances in statistical computing, is then described that is most suited to modeling data where sequences are preferentially collected at certain locations, independently of the outcome of the evolutionary process. The analysis of georeferenced genetic sequences from the West Nile virus in North America along with simulated data shows how assumptions about spatial sampling may impact our understanding of the forces shaping biodiversity across time and space.

EvoLaps: a web interface to visualize continuous phylogeographic reconstructions.

BACKGROUND: Phylogeographic reconstructions serve as a basis to understand the spread and evolution of pathogens. Visualization of these reconstructions often lead to complex graphical representations which are difficult to interpret. RESULT: We present EvoLaps, a user-friendly web interface to visualize phylogeographic reconstructions based on the analysis of latitude/longitude coordinates with various clustering levels. EvoLaps also produces transition diagrams that provide concise and easy to interpret summaries of phylogeographic reconstructions. CONCLUSION: The main contribution of EvoLaps is to assemble known numerical and graphical methods/tools into a user-friendly interface dedicated to the visualization and edition of evolutionary scenarios based on continuous phylogeographic reconstructions. EvoLaps is freely usable at www.evolaps.org .

Sampling bias and model choice in continuous phylogeography: Getting lost on a random walk.

Phylogeographic inference allows reconstruction of past geographical spread of pathogens or living organisms by integrating genetic and geographic data. A popular model in continuous phylogeography-with location data provided in the form of latitude and longitude coordinates-describes spread as a Brownian motion (Brownian Motion Phylogeography, BMP) in continuous space and time, akin to similar models of continuous trait evolution. Here, we show that reconstructions using this model can be strongly affected by sampling biases, such as the lack of sampling from certain areas. As an attempt to reduce the effects of sampling bias on BMP, we consider the addition of sequence-free samples from under-sampled areas. While this approach alleviates the effects of sampling bias, in most scenarios this will not be a viable option due to the need for prior knowledge of an outbreak's spatial distribution. We therefore consider an alternative model, the spatial Λ-Fleming-Viot process (ΛFV), which has recently gained popularity in population genetics. Despite the ΛFV's robustness to sampling biases, we find that the different assumptions of the ΛFV and BMP models result in different applicabilities, with the ΛFV being more appropriate for scenarios of endemic spread, and BMP being more appropriate for recent outbreaks or colonizations.

Rivers and landscape ecology of a plant virus, Rice yellow mottle virus along the Niger Valley.

To investigate the spread of Rice yellow mottle virus (RYMV) along the Niger River, regular sampling of virus isolates was conducted along 500 km of the Niger Valley in the Republic of Niger and was complemented by additional sampling in neighbouring countries in West Africa and Central Africa. The spread of RYMV into and within the Republic of Niger was inferred as a continuous process using a Bayesian statistical framework applied previously to reconstruct its dispersal history in West Africa, East Africa, and Madagascar. The spatial resolution along this section of the Niger River was the highest implemented for RYMV and possibly for any plant virus. We benefited from the results of early field surveys of the disease for the validation of the phylogeographic reconstruction and from the well-documented history of rice cultivation changes along the Niger River for their interpretation. As a prerequisite, the temporal signal of the RYMV data sets was revisited in the light of recent methodological advances. The role of the hydrographic network of the Niger Basin in RYMV spread was examined, and the link between virus population dynamics and the extent of irrigated rice was assessed. RYMV was introduced along the Niger River in the Republic of Niger in the early 1980s from areas to the southwest of the country where rice was increasingly grown. Viral spread was triggered by a major irrigation scheme made of a set of rice perimeters along the river valley. The subsequent spatial and temporal host continuity and the inoculum build-up allowed for a rapid spread of RYMV along the Niger River, upstream and downstream, over hundreds of kilometres, and led to the development of severe epidemics. There was no evidence of long-distance dissemination of the virus through natural water. Floating rice in the main meanders of the Middle Niger did not contribute to virus dispersal from West Africa to Central Africa. RYMV along the Niger River is an insightful example of how agricultural intensification favours pathogen emergence and spread.

Rates and Rocks: Strengths and Weaknesses of Molecular Dating Methods.

I present here an in-depth, although non-exhaustive, review of two topics in molecular dating. Clock models, which describe the evolution of the rate of evolution, are considered first. Some of the shortcomings of popular approaches-uncorrelated clock models in particular-are presented and discussed. Autocorrelated models are shown to be more reasonable from a biological perspective. Some of the most recent autocorrelated models also rely on a coherent treatment of instantaneous and average substitution rates while previous models are based on implicit approximations. Second, I provide a brief overview of the processes involved in collecting and preparing fossil data. I then review the main techniques that use this data for calibrating the molecular clock. I argue that, in its current form, the fossilized birth-death process relies on assumptions about the mechanisms underlying fossilization and the data collection process that may negatively impact the date estimates. Node-dating approaches make better use of the data available, even though they rest on paleontologists' intervention to prepare raw fossil data. Altogether, this study provides indications that may help practitioners in selecting appropriate methods for molecular dating. It will also hopefully participate in defining the contour of future methodological developments in the field.

Accounting for Calibration Uncertainty: Bayesian Molecular Dating as a "Doubly Intractable" Problem.

This study introduces a new Bayesian technique for molecular dating that explicitly accommodates for uncertainty in the phylogenetic position of calibrated nodes derived from the analysis of fossil data. The proposed approach thus defines an adequate framework for incorporating expert knowledge and/or prior information about the way fossils were collected in the inference of node ages. Although it belongs to the class of "node-dating" approaches, this method shares interesting properties with "tip-dating" techniques. Yet, it alleviates some of the computational and modeling difficulties that hamper tip-dating approaches. The influence of fossil data on the probabilistic distribution of trees is the crux of the matter considered here. More specifically, among all the phylogenies that a tree model (e.g., the birth-death process) generates, only a fraction of them "agree" with the fossil data. Bayesian inference under the new model requires taking this fraction into account. However, evaluating this quantity is difficult in practice. A generic solution to this issue is presented here. The proposed approach relies on a recent statistical technique, the so-called exchange algorithm, dedicated to drawing samples from "doubly intractable" distributions. A small example illustrates the problem of interest and the impact of uncertainty in the placement of calibration constraints in the phylogeny given fossil data. An analysis of land plant sequences and multiple fossils further highlights the pertinence of the proposed approach.

HIV-1 full-genome phylogenetics of generalized epidemics in sub-Saharan Africa: impact of missing nucleotide characters in next-generation sequences.

To characterize HIV-1 transmission dynamics in regions where the burden of HIV-1 is greatest, the 'Phylogenetics and Networks for Generalised HIV Epidemics in Africa' consortium (PANGEA-HIV) is sequencing full-genome viral isolates from across sub-Saharan Africa. We report the first 3,985 PANGEA-HIV consensus sequences from four cohort sites (Rakai Community Cohort Study, n=2,833; MRC/UVRI Uganda, n=701; Mochudi Prevention Project, n=359; Africa Health Research Institute Resistance Cohort, n=92). Next-generation sequencing success rates varied: more than 80% of the viral genome from the gag to the nef genes could be determined for all sequences from South Africa, 75% of sequences from Mochudi, 60% of sequences from MRC/UVRI Uganda, and 22% of sequences from Rakai. Partial sequencing failure was primarily associated with low viral load, increased for amplicons closer to the 3' end of the genome, was not associated with subtype diversity except HIV-1 subtype D, and remained significantly associated with sampling location after controlling for other factors. We assessed the impact of the missing data patterns in PANGEA-HIV sequences on phylogeny reconstruction in simulations. We found a threshold in terms of taxon sampling below which the patchy distribution of missing characters in next-generation sequences has an excess negative impact on the accuracy of HIV-1 phylogeny reconstruction, which is attributable to tree reconstruction artifacts that accumulate when branches in viral trees are long. The large number of PANGEA-HIV sequences provides unprecedented opportunities for evaluating HIV-1 transmission dynamics across sub-Saharan Africa and identifying prevention opportunities. Molecular epidemiological analyses of these data must proceed cautiously because sequence sampling remains below the identified threshold and a considerable negative impact of missing characters on phylogeny reconstruction is expected.

Demographic inference under the coalescent in a spatial continuum.

Understanding population dynamics from the analysis of molecular and spatial data requires sound statistical modeling. Current approaches assume that populations are naturally partitioned into discrete demes, thereby failing to be relevant in cases where individuals are scattered on a spatial continuum. Other models predict the formation of increasingly tight clusters of individuals in space, which, again, conflicts with biological evidence. Building on recent theoretical work, we introduce a new genealogy-based inference framework that alleviates these issues. This approach effectively implements a stochastic model in which the distribution of individuals is homogeneous and stationary, thereby providing a relevant null model for the fluctuation of genetic diversity in time and space. Importantly, the spatial density of individuals in a population and their range of dispersal during the course of evolution are two parameters that can be inferred separately with this method. The validity of the new inference framework is confirmed with extensive simulations and the analysis of influenza sequences collected over five seasons in the USA.

Molecular Evolution of the TET Gene Family in Mammals.

Ten-eleven translocation (TET) proteins, a family of Fe(2+)- and 2-oxoglutarate-dependent dioxygenases, are involved in DNA demethylation. They also help regulate various cellular functions. Three TET paralogs have been identified (TET1, TET2, and TET3) in humans. This study focuses on the evolution of mammalian TET genes. Distinct patterns in TET1 and TET2 vs. TET3 were revealed by codon-based tests of positive selection. Results indicate that TET1 and TET2 genes have experienced positive selection more frequently than TET3 gene, and that the majority of codon sites evolved under strong negative selection. These findings imply that the selective pressure on TET3 may have been relaxed in several lineages during the course of evolution. Our analysis of convergent amino acid substitutions also supports the different evolutionary dynamics among TET gene subfamily members. All of the five amino acid sites that are inferred to have evolved under positive selection in the catalytic domain of TET2 are localized at the protein's outer surface. The adaptive changes of these positively selected amino acid sites could be associated with dynamic interactions between other TET-interacting proteins, and positive selection thus appears to shift the regulatory scheme of TET enzyme function.

How well can the exponential-growth coalescent approximate constant-rate birth-death population dynamics?

One of the central objectives in the field of phylodynamics is the quantification of population dynamic processes using genetic sequence data or in some cases phenotypic data. Phylodynamics has been successfully applied to many different processes, such as the spread of infectious diseases, within-host evolution of a pathogen, macroevolution and even language evolution. Phylodynamic analysis requires a probability distribution on phylogenetic trees spanned by the genetic data. Because such a probability distribution is not available for many common stochastic population dynamic processes, coalescent-based approximations assuming deterministic population size changes are widely employed. Key to many population dynamic models, in particular epidemiological models, is a period of exponential population growth during the initial phase. Here, we show that the coalescent does not well approximate stochastic exponential population growth, which is typically modelled by a birth-death process. We demonstrate that introducing demographic stochasticity into the population size function of the coalescent improves the approximation for values of R0 close to 1, but substantial differences remain for large R0. In addition, the computational advantage of using an approximation over exact models vanishes when introducing such demographic stochasticity. These results highlight that we need to increase efforts to develop phylodynamic tools that correctly account for the stochasticity of population dynamic models for inference.

Closed form modeling of evolutionary rates by exponential Brownian functionals.

Accurate estimation of species divergence times from the analysis of genetic sequences relies on probabilistic models of evolution of the rate of molecular evolution. Importantly, while these models describe the sample paths of the substitution rates along a phylogenetic tree, only the (random) average rate can be estimated on each edge. For mathematical convenience, the stochastic nature of these averages is generally ignored. In this article we derive the probabilistic distribution of the average substitution rate assuming a geometric Brownian motion for the sample paths, and we investigate the corresponding error bounds via numerical simulations. In particular we confirm the validity of the gamma approximation proposed in Guindon (Syst Biol 62(1):22-34, 2013) for "small" values of the autocorrelation parameter.

Adaptive evolution of formyl peptide receptors in mammals.

The formyl peptide receptors (FPRs) are a family of chemoattractant receptors with important roles in host defense and the regulation of inflammatory reactions. In humans, three FPR paralogs have been identified (FPR1, FPR2, and FPR3) and may have functionally diversified by gene duplication and adaptive evolution. However, the evolutionary mechanisms operating in the diversification of FPR family genes and the changes in selection pressures have not been characterized to date. Here, we have made a comprehensive evolutionary analysis of FPR genes from mammalian species. Phylogenetic analysis showed that an early duplication was responsible for FPR1 and FPR2/FPR3 splitting, and FPR3 originated from the latest duplication event near the origin of primates. Codon-based tests of positive selection reveal interesting patterns in FPR1 and FPR2 versus FPR3, with the first two genes showing clear evidence of positive selection at some sites while the majority of them evolve under strong negative selection. In contrast, our results suggest that the selective pressure may be relaxed in the FPR3 lineage. Of the six amino acid sites inferred to evolve under positive selection in FPR1 and FPR2, four sites were located in extracellular loops of the protein. The electrostatic potential of the extracellular surface of FPR might be affected more frequently with amino acid substitutions in positively selected sites. Thus, positive selection of FPRs among mammals may reflect a link between changes in the sequence and surface structure of the proteins and is likely to be important in the host's defense against invading pathogens.

Modelling competition and dispersal in a statistical phylogeographic framework.

Competition between organisms influences the processes governing the colonization of new habitats. As a consequence, species or populations arriving first at a suitable location may prevent secondary colonization. Although adaptation to environmental variables (e.g., temperature, altitude, etc.) is essential, the presence or absence of certain species at a particular location often depends on whether or not competing species co-occur. For example, competition is thought to play an important role in structuring mammalian communities assembly. It can also explain spatial patterns of low genetic diversity following rapid colonization events or the "progression rule" displayed by phylogenies of species found on archipelagos. Despite the potential of competition to maintain populations in isolation, past quantitative analyses have largely ignored it because of the difficulty in designing adequate methods for assessing its impact. We present here a new model that integrates competition and dispersal into a Bayesian phylogeographic framework. Extensive simulations and analysis of real data show that our approach clearly outperforms the traditional Mantel test for detecting correlation between genetic and geographic distances. But most importantly, we demonstrate that competition can be detected with high sensitivity and specificity from the phylogenetic analysis of genetic variation in space.

Performance of standard and stochastic branch-site models for detecting positive selection among coding sequences.

The branch-site model is a widely popular approach that accommodates for the lineage- and the site-specific heterogeneity of natural selection regimes among coding sequences. This model relies on prior knowledge of the (foreground) lineage(s) evolving under positive selection at some sites. Unfortunately, such prior information is not always available in practice. A more recent technique (Guindon S, Rodrigo A, Dyer K, Huelsenbeck J. 2004. Modeling the site-specific variation of selection patterns along lineages. Proc Natl Acad Sci USA 101:12957-12962) alleviates this issue by explicitly modeling the variability of selection patterns using a stochastic process. However, the performance of this approach for deciding whether a set of homologous sequences evolved under positive selection at some point has not been assessed yet. This study compares the sensitivity and specificity of tests for positive selection derived from both the standard and the stochastic approaches using extensive simulations. We show that the two methods have low proportions of type I errors, that is, they tend to be conservative when testing the null hypothesis of no positive selection if sequences truly evolve under neutral or negative selection regimes. Also, the standard approach is more powerful than the stochastic one when the prior knowledge on foreground lineages is correct. When this prior is incorrect, however, the stochastic approach outperforms the standard model in a broad range of conditions. Additional comparisons also suggest that the stochastic branch-site method compares favorably with the recently proposed mixed-effects model of evolution of Murrell et al. (Murrell B, Wertheim JO, Moola S, Weighill T, Scheffler K, Pond SLK. 2012. Detecting individual sites subject to episodic diversifying selection. PLoS Genet. 8:e1002764). Altogether, our results show that the standard branch-site model is well suited to confirmatory analyses, whereas the stochastic approach should be preferred over the standard or the mixed-effects ones for exploratory studies.

From trajectories to averages: an improved description of the heterogeneity of substitution rates along lineages.

The accuracy and precision of species divergence date estimation from molecular data strongly depend on the models describing the variation of substitution rates along a phylogeny. These models generally assume that rates randomly fluctuate along branches from one node to the next. However, for mathematical convenience, the stochasticity of such a process is ignored when translating these rate trajectories into branch lengths. This study addresses this shortcoming. A new approach is described that explicitly considers the average substitution rates along branches as random quantities, resulting in a more realistic description of the variations of evolutionary rates along lineages. The proposed method provides more precise estimates of the rate autocorrelation parameter as well as divergence times. Also, simulation results indicate that ignoring the stochastic variation of rates along edges can lead to significant overestimation of specific node ages. Altogether, the new approach introduced in this study is a step forward to designing biologically relevant models of rate evolution that are well suited to data sets with dense taxon sampling which are likely to present rate autocorrelation. The computer programme PhyTime, part of the PhyML package and implementing the new approach, is available from http://code.google.com/p/phyml (last accessed 1 August 2012).

Cumulative viral evolutionary changes in chronic hepatitis B virus infection precedes hepatitis B e antigen seroconversion.

OBJECTIVE: To examine viral evolutionary changes and their relationship to hepatitis B e antigen (HBeAg) seroconversion. DESIGN: A matched case-control study of HBeAg seroconverters (n = 8) and non-seroconverters (n = 7) with adequate stored sera before seroconversion was performed. Nested PCR, cloning and sequencing of hepatitis B virus (HBV) precore/core gene was performed. Sequences were aligned using Clustal X2.0, followed by construction of phylogenetic trees using Pebble 1.0. Viral diversity, evolutionary rates and positive selection were then analysed. RESULTS: Baseline HBV quasispecies viral diversity was identical in seroconverters and non-seroconverters 10 years before seroconversion but started to increase approximately 3 years later. Concurrently, precore stop codon (PSC) mutations appeared. Some 2 years later, HBV-DNA declined, together with a dramatic reduction in HBeAg titres. Just before HBeAg seroconversion, seroconverters had HBV-DNA levels 2 log lower (p = 0.008), HBeAg titres 310-fold smaller (p = 0.02), PSC mutations > 25% (p < 0.001), viral evolution 8.1-fold higher (p = 0.01) and viral diversity 2.9-fold higher (p < 0.001), compared to non-seroconverters, with a 9.3-fold higher viral diversity than baseline (p = 0.011). Phylogenetic trees in seroconverters showed clustering of separate time points and longer branch lengths than non-seroconverters (p = 0.01). Positive selection was detected in five of eight seroconverters but none in non-seroconverters (p = 0.026). There was significant negative correlation between viral diversity (rs = -0.60, p < 0.001) and HBV-DNA or HBeAg (rs = -0.58, p = 0.006) levels; and positive correlation with PSC mutations (rs = 0.38, p = 0.009). Over time, the significant positive correlation was viral diversity (rs = 0.65, p < 0.001), while negative correlation was HBV-DNA (rs = -0.627, p < 0.001) and HBeAg levels (rs = -0.512, p =0.015). CONCLUSIONS: Cumulative viral evolutionary changes that precede HBeAg seroconversion provide insights into this event that may have implications for therapy.