ABC: a useful Bayesian tool for the analysis of population data

Inferring the historical demography of southern African cheetahs (Acinonyx jubatus) using Bayesian analyses of molecular genetic data

The contemporary genetic diversity of the cheetah (Acinonyx jubatus) has been the focus of several studies, which have revealed very low levels of variation. Different hypotheses have been proposed to explain this pattern of low diversity, and require additional scrutiny. Here, we used published microsatellite data and coalescence-based analytical methods to explore the historical demography of the largest free-ranging cheetah population, aiming to assess whether present-day diversity may have been impacted by a historical demographic decline. Our results support the hypothesis of a historical (and most likely gradual) demographic decline over the past ~10,000 years, leading to a present-day N e ranging from 700 to 1,600 individuals. This decline was likely induced by climate-driven vegetational shifts affecting habitat suitability and possibly also interspecies interactions with prey and competitors. These results help clarify the demographic history of cheetahs in southern Africa and its impact on the current genetic diversity of this population.

Harbor porpoise losing its edge: Genetic time series suggests a rapid population decline in Iberian waters over the last 30 years

Impact of climate change is expected to be especially noticeable at the edges of a species' distribution, where they meet suboptimal habitat conditions. In Mauritania and Iberia, two genetically differentiated populations of harbor porpoises (Phocoena phocoena) form an ecotype adapted to local upwelling conditions and distinct from other ecotypes further north on the NE Atlantic continental shelf and in the Black Sea. By analyzing the evolution of mitochondrial genetic variation in the Iberian population between two temporal cohorts (1990-2002 vs. 2012-2015), we report a substantial decrease in genetic diversity. Phylogenetic analyses including neighboring populations identified two porpoises in southern Iberia carrying a divergent haplotype closely related to those from the Mauritanian population, yet forming a distinct lineage. This suggests that Iberian porpoises may not be as isolated as previously thought, indicating possible dispersion from Mauritania or an unknown population in between, but none from the northern ecotype. Demo-genetic scenario testing by approximate Bayesian computation showed that the rapid decline in the Iberian mitochondrial diversity was not simply due to the genetic drift of a small population, but models support instead a substantial decline in effective population size, possibly resulting from environmental stochasticity, prey depletion, or acute fishery bycatches. These results illustrate the value of genetics time series to inform demographic trends and emphasize the urgent need for conservation measures to ensure the viability of this small harbor porpoise population in Iberian waters.

Effective population size of Culex quinquefasciatus under insecticide-based vector management and following Hurricane Harvey in Harris County, Texas

Introduction: Culex quinquefasciatus is a mosquito species of significant public health importance due to its ability to transmit multiple pathogens that can cause mosquito-borne diseases, such as West Nile fever and St. Louis encephalitis. In Harris County, Texas, Cx. quinquefasciatus is a common vector species and is subjected to insecticide-based management by the Harris County Public Health Department. However, insecticide resistance in mosquitoes has increased rapidly worldwide and raises concerns about maintaining the effectiveness of vector control approaches. This concern is highly relevant in Texas, with its humid subtropical climate along the Gulf Coast that provides suitable habitat for Cx. quinquefasciatus and other mosquito species that are known disease vectors. Therefore, there is an urgent and ongoing need to monitor the effectiveness of current vector control programs. Methods: In this study, we evaluated the impact of vector control approaches by estimating the effective population size of Cx. quinquefasciatus in Harris County. We applied Approximate Bayesian Computation to microsatellite data to estimate effective population size. We collected Cx. quinquefasciatus samples from two mosquito control operation areas; 415 and 802, during routine vector monitoring in 2016 and 2017. No county mosquito control operations were applied at area 415 in 2016 and 2017, whereas extensive adulticide spraying operations were in effect at area 802 during the summer of 2016. We collected data for eighteen microsatellite markers for 713 and 723 mosquitoes at eight timepoints from 2016 to 2017 in areas 415 and 802, respectively. We also investigated the impact of Hurricane Harvey's landfall in the Houston area in August of 2017 on Cx. quinquefasciatus population fluctuation. Results: We found that the bottleneck scenario was the most probable historical scenario describing the impact of the winter season at area 415 and area 802, with the highest posterior probability of 0.9167 and 0.4966, respectively. We also detected an expansion event following Hurricane Harvey at area 802, showing a 3.03-fold increase in 2017. Discussion: Although we did not detect significant effects of vector control interventions, we found considerable influences of the winter season and a major hurricane on the effective population size of Cx. quinquefasciatus. The fluctuations in effective population size in both areas showed a significant seasonal pattern. Additionally, the significant population expansion following Hurricane Harvey in 2017 supports the necessity for post-hurricane vector-control interventions.

Deep Learning in Population Genetics

Population genetics is transitioning into a data-driven discipline thanks to the availability of large-scale genomic data and the need to study increasingly complex evolutionary scenarios. With likelihood and Bayesian approaches becoming either intractable or computationally unfeasible, machine learning, and in particular deep learning, algorithms are emerging as popular techniques for population genetic inferences. These approaches rely on algorithms that learn non-linear relationships between the input data and the model parameters being estimated through representation learning from training data sets. Deep learning algorithms currently employed in the field comprise discriminative and generative models with fully connected, convolutional, or recurrent layers. Additionally, a wide range of powerful simulators to generate training data under complex scenarios are now available. The application of deep learning to empirical data sets mostly replicates previous findings of demography reconstruction and signals of natural selection in model organisms. To showcase the feasibility of deep learning to tackle new challenges, we designed a branched architecture to detect signals of recent balancing selection from temporal haplotypic data, which exhibited good predictive performance on simulated data. Investigations on the interpretability of neural networks, their robustness to uncertain training data, and creative representation of population genetic data, will provide further opportunities for technological advancements in the field.

Variability, skipped breeding and heavy-tailed dynamics in an Antarctic seabird

The population dynamics of many colonially breeding seabirds are characterized by large interannual fluctuations that cannot be explained by environmental conditions alone. This variation may be particularly confounded by the use of skipped breeding by seabirds as a life-history strategy, which directly impacts the number of breeding pairs and may affect the accuracy of breeding abundance as a metric of population health. Additionally, large fluctuations in time series may suggest that the underlying population dynamics are heavy tailed, allowing for a higher likelihood of extreme events than expected under Gaussian dynamics. Here, we investigated the effect of demography on time series for abundance of the Adélie penguin Pygoscelis adeliae and explored the occurrence of heavy-tailed dynamics in observed Adélie time series. We focus this study on the Adélie penguin as it is an important bellwether species long used to track the impacts of climate change and fishing on the Southern Ocean ecosystem and shares life-history traits with many colonial seabirds. We quantified the impacts of demographic rates, including skipped breeding, on time series of Adélie abundance simulated using an age-structured model. We also used observed time series of Adélie breeding abundance at all known Antarctic colonies to classify distributions for abundance as Gaussian or non-Gaussian heavy tailed. We then identified the cause of such heavy-tailed dynamics in simulated time series and linked these to spatial patterns in Adélie food resource variability. We found that breeding propensity drives observed breeding fluctuations more than any other vital rate, with high variability in skipped breeding decoupling true abundance from observed breeding abundance. We also found several Antarctic regions characterized by heavy-tailed dynamics in abundance. These regions were often also characterized by high variability in zooplankton availability. In simulated time series, heavy-tailed dynamics were strongly linked to high variability in adult survival. Our results illustrate that stochastic variability in abundance dynamics, particularly the presence of variable rates of skipped breeding, can challenge our interpretation of fluctuations in abundance through time and obscure the relationship between key environmental drivers and population abundance.

Prevalence and Adaptive Impact of Introgression

Alleles that introgress between species can influence the evolutionary and ecological fate of species exposed to novel environments. Hybrid offspring of different species are often unfit, and yet it has long been argued that introgression can be a potent force in evolution, especially in plants. Over the last two decades, genomic data have increasingly provided evidence that introgression is a critically important source of genetic variation and that this additional variation can be useful in adaptive evolution of both animals and plants. Here, we review factors that influence the probability that foreign genetic variants provide long-term benefits (so-called adaptive introgression) and discuss their potential benefits. We find that introgression plays an important role in adaptive evolution, particularly when a species is far from its fitness optimum, such as when they expand their range or are subject to changing environments.

Using approximate Bayesian inference for a "steps and turns" continuous-time random walk observed at regular time intervals

The study of animal movement is challenging because movement is a process modulated by many factors acting at different spatial and temporal scales. In order to describe and analyse animal movement, several models have been proposed which differ primarily in the temporal conceptualization, namely continuous and discrete time formulations. Naturally, animal movement occurs in continuous time but we tend to observe it at fixed time intervals. To account for the temporal mismatch between observations and movement decisions, we used a state-space model where movement decisions (steps and turns) are made in continuous time. That is, at any time there is a non-zero probability of making a change in movement direction. The movement process is then observed at regular time intervals. As the likelihood function of this state-space model turned out to be intractable yet simulating data is straightforward, we conduct inference using different variations of Approximate Bayesian Computation (ABC). We explore the applicability of this approach as a function of the discrepancy between the temporal scale of the observations and that of the movement process in a simulation study. Simulation results suggest that the model parameters can be recovered if the observation time scale is moderately close to the average time between changes in movement direction. Good estimates were obtained when the scale of observation was up to five times that of the scale of changes in direction. We demonstrate the application of this model to a trajectory of a sheep that was reconstructed in high resolution using information from magnetometer and GPS devices. The state-space model used here allowed us to connect the scales of the observations and movement decisions in an intuitive and easy to interpret way. Our findings underscore the idea that the time scale at which animal movement decisions are made needs to be considered when designing data collection protocols. In principle, ABC methods allow to make inferences about movement processes defined in continuous time but in terms of easily interpreted steps and turns.

Independent domestication events in the blue-cheese fungus Penicillium roqueforti

Domestication provides an excellent framework for studying adaptive divergence. Using population genomics and phenotypic assays, we reconstructed the domestication history of the blue cheese mould Penicillium roqueforti. We showed that this fungus was domesticated twice independently. The population used in Roquefort originated from an old domestication event associated with weak bottlenecks and exhibited traits beneficial for pre‐industrial cheese production (slower growth in cheese and greater spore production on bread, the traditional multiplication medium). The other cheese population originated more recently from the selection of a single clonal lineage, was associated with all types of blue cheese worldwide except Roquefort, and displayed phenotypes more suited for industrial cheese production (high lipolytic activity, efficient cheese cavity colonization ability and salt tolerance). We detected genomic regions affected by recent positive selection and putative horizontal gene transfers. This study sheds light on the processes of rapid adaptation and raises questions about genetic resource conservation.

see also the Perspective by Brigida Gallone, Jan Steensels and Kevin J. Verstrepen.

Approximate Bayesian estimation of coevolutionary arms races

Exaggerated traits involved in species interactions have long captivated the imagination of evolutionary biologists and inspired the durable metaphor of the coevolutionary arms race. Despite decades of research, however, we have only a handful of examples where reciprocal coevolutionary change has been rigorously established as the cause of trait exaggeration. Support for a coevolutionary mechanism remains elusive because we lack generally applicable tools for quantifying the intensity of coevolutionary selection. Here we develop an approximate Bayesian computation (ABC) approach for estimating the intensity of coevolutionary selection using population mean phenotypes of traits mediating interspecific interactions. Our approach relaxes important assumptions of a previous maximum likelihood approach by allowing gene flow among populations, variable abiotic environments, and strong coevolutionary selection. Using simulated data, we show that our ABC method accurately infers the strength of coevolutionary selection if reliable estimates are available for key background parameters and ten or more populations are sampled. Applying our approach to the putative arms race between the plant Camellia japonica and its seed predatory weevil, Curculio camelliae, provides support for a coevolutionary hypothesis but fails to preclude the possibility of unilateral evolution. Comparing independently estimated selection gradients acting on Camellia pericarp thickness with values simulated by our model reveals a correlation between predicted and observed selection gradients of 0.941. The strong agreement between predicted and observed selection gradients validates our method.

Exome Resequencing Reveals Evolutionary History, Genomic Diversity, and Targets of Selection in the Conifers Pinus taeda and Pinus elliottii

Loblolly pine (Pinus taeda) and slash pine (Pinus elliottii) are ecologically and economically important pine species that dominate many forest ecosystems in the southern United States, but like all conifers, the study of their genetic diversity and demographic history has been hampered by their large genome size. A small number of studies mainly based on candidate-gene sequencing have been reported for P. taeda to date, whereas none are available for P. elliottii. Targeted exome resequencing has recently enabled population genomics studies for conifers, approach used here to assess genomic diversity, signatures of selection, population structure, and demographic history of P. elliottii and P. taeda. Extensive similarities were revealed between these species: both species feature rapid linkage disequilibrium decay and high levels of genetic diversity. Moreover, genome-wide positive correlations for measures of genetic diversity between the species were also observed, likely due to shared structural genomic constraints. Also, positive selection appears to be targeting a common set of genes in both pines. Demographic history differs between both species, with only P. taeda being affected by a dramatic bottleneck during the last glacial period. The ability of P. taeda to recover from a dramatic reduction in population size while still retaining high levels of genetic diversity shows promise for other pines facing environmental stressors associated with climate change, indicating that these too may be able to adapt successfully to new future conditions even after a drastic population size contraction.

Projected population-wide impact of antiretroviral therapy-linked isoniazid preventive therapy in a high-burden setting

OBJECTIVE

Both isoniazid preventive therapy (IPT) and antiretroviral therapy (ART) reduce tuberculosis risk in individuals living with HIV. We sought to estimate the broader, population-wide impact of providing a pragmatically implemented 12-month IPT regimen to ART recipients in a high-burden community.

DESIGN

Dynamic transmission model of a tuberculosis (TB)-HIV epidemic, calibrated to site-specific, historical epidemiologic and clinical trial data from Khayelitsha, South Africa.

METHODS

We projected the 5-year impact of delivering a 12-month IPT regimen community-wide to 85% of new ART initiators and 15%/year of those already on ART, accounting for IPT-attributable reductions in TB infection, progression, and transmission. We also evaluated scenarios of continuously-delivered IPT, ongoing ART scale-up, and lower tuberculosis incidence.

RESULTS

Under historical (early 2010) ART coverage, this ART-linked IPT intervention prevented one tuberculosis case per 18 [95% credible interval (CrI) 11-29] people treated. It lowered TB incidence by a projected 23% (95% CrI 14-30%) among people receiving ART, and by 5.2% (95% CrI 2.9-8.7%) in the total population. Continuous IPT reduced the number needed to treat to prevent one case of TB to 10 (95% CrI 7-16), though it required 74% more person-years of therapy (95% CrI 64-94%) to prevent one TB case, relative to 12-month therapy. Under expanding ART coverage, the tuberculosis incidence reduction achieved by 12-month IPT grew to 7.6% (95% CrI 4.3-12.6%). Effect sizes were similar in a simulated setting of lower TB incidence.

CONCLUSIONS

IPT in conjunction with ART reduces tuberculosis incidence among those who receive therapy and has additional impact on tuberculosis transmission in the population.

multi-dice: r package for comparative population genomic inference under hierarchical co-demographic models of independent single-population size changes

Population genetic data from multiple taxa can address comparative phylogeographic questions about community-scale response to environmental shifts, and a useful strategy to this end is to employ hierarchical co-demographic models that directly test multi-taxa hypotheses within a single, unified analysis. This approach has been applied to classical phylogeographic data sets such as mitochondrial barcodes as well as reduced-genome polymorphism data sets that can yield 10,000s of SNPs, produced by emergent technologies such as RAD-seq and GBS. A strategy for the latter had been accomplished by adapting the site frequency spectrum to a novel summarization of population genomic data across multiple taxa called the aggregate site frequency spectrum (aSFS), which potentially can be deployed under various inferential frameworks including approximate Bayesian computation, random forest and composite likelihood optimization. Here, we introduce the r package multi-dice, a wrapper program that exploits existing simulation software for flexible execution of hierarchical model-based inference using the aSFS, which is derived from reduced genome data, as well as mitochondrial data. We validate several novel software features such as applying alternative inferential frameworks, enforcing a minimal threshold of time surrounding co-demographic pulses and specifying flexible hyperprior distributions. In sum, multi-dice provides comparative analysis within the familiar R environment while allowing a high degree of user customization, and will thus serve as a tool for comparative phylogeography and population genomics.

Integrating Crop Growth Models with Whole Genome Prediction through Approximate Bayesian Computation

Genomic selection, enabled by whole genome prediction (WGP) methods, is revolutionizing plant breeding. Existing WGP methods have been shown to deliver accurate predictions in the most common settings, such as prediction of across environment performance for traits with additive gene effects. However, prediction of traits with non-additive gene effects and prediction of genotype by environment interaction (G×E), continues to be challenging. Previous attempts to increase prediction accuracy for these particularly difficult tasks employed prediction methods that are purely statistical in nature. Augmenting the statistical methods with biological knowledge has been largely overlooked thus far. Crop growth models (CGMs) attempt to represent the impact of functional relationships between plant physiology and the environment in the formation of yield and similar output traits of interest. Thus, they can explain the impact of G×E and certain types of non-additive gene effects on the expressed phenotype. Approximate Bayesian computation (ABC), a novel and powerful computational procedure, allows the incorporation of CGMs directly into the estimation of whole genome marker effects in WGP. Here we provide a proof of concept study for this novel approach and demonstrate its use with synthetic data sets. We show that this novel approach can be considerably more accurate than the benchmark WGP method GBLUP in predicting performance in environments represented in the estimation set as well as in previously unobserved environments for traits determined by non-additive gene effects. We conclude that this proof of concept demonstrates that using ABC for incorporating biological knowledge in the form of CGMs into WGP is a very promising and novel approach to improving prediction accuracy for some of the most challenging scenarios in plant breeding and applied genetics.

Inferring the demographic history of Drosophila subobscura from nucleotide variation at regions not affected by chromosomal inversions

Drosophila subobscura presents a rich and complex chromosomal inversion polymorphism. It can thus be considered a model system (i) to study the mechanisms originating inversions and how inversions affect the levels and patterns of variation in the inverted regions and (ii) to study adaptation at both the single-gene and chromosomal inversion levels. It is therefore important to infer its demographic history as previous information indicated that its nucleotide variation is not at mutation-drift equilibrium. For that purpose, we sequenced 16 noncoding regions distributed across those parts of the J chromosome not affected by inversions in the studied population and possibly either by other selective events. The pattern of variation detected in these 16 regions is similar to that previously reported within different chromosomal arrangements, suggesting that the latter results would, thus, mainly reflect recent demographic events rather than the partial selective sweep imposed by the origin and frequency increase of inversions. Among the simple demographic models considered in our Approximate Bayesian Computation analysis of variation at the 16 regions, the model best supported by the data implies a population size expansion soon after the penultimate glacial period. This model constitutes a better null model, and it is therefore an important resource for subsequent studies aiming among others to uncover selective events across the species genome. Our results also highlight the importance of introducing the possibility of multiple hits in the coalescent simulations with an outgroup.

Experimentally guided models reveal replication principles that shape the mutation distribution of RNA viruses

Life history theory posits that the sequence and timing of events in an organism's lifespan are fine-tuned by evolution to maximize the production of viable offspring. In a virus, a life history strategy is largely manifested in its replication mode. Here, we develop a stochastic mathematical model to infer the replication mode shaping the structure and mutation distribution of a poliovirus population in an intact single infected cell. We measure production of RNA and poliovirus particles through the infection cycle, and use these data to infer the parameters of our model. We find that on average the viral progeny produced from each cell are approximately five generations removed from the infecting virus. Multiple generations within a single cell infection provide opportunities for significant accumulation of mutations per viral genome and for intracellular selection.

DOI:http://dx.doi.org/10.7554/eLife.03753.001

Viruses with genetic information made up of molecules of RNA can multiply quickly, but not very accurately. This means that many errors, or mutations, occur when the RNA is copied to create new viruses. The advantage of this rapid, but mistake-filled, RNA replication process is that some of the mutations will be beneficial to the virus. This allows viruses to rapidly evolve, for example, to develop resistance against drugs.

The poliovirus is an RNA virus that can cause paralysis and death in humans. To prevent such infections, scientists have extensively studied the poliovirus and have developed effective vaccines against it that have eliminated the virus from all but a few countries. Because so much is known about the poliovirus and because it has a very simple structure, scientists continue to use the poliovirus as a model to study virus behavior.

One unknown aspect of the poliovirus' behavior is how it replicates after invading a cell. Are all of its RNA copies made from the original viral RNA that first infected the cell, in what is known as a ‘stamping machine’ model? Or do the new copies of the RNA also get copied themselves in a ‘geometric replication mode’ that increases the likelihood of mutations and enables the virus to evolve more rapidly?

Viral RNA molecules are copied by one of the virus's own proteins and so before the viral RNA can be replicated, it must first be translated to form viral proteins. When and where replication begins depends on the concentration of translated proteins around the RNA and so replication tends to begin in particular areas of the cell at different times. Schulte, Draghi et al. used mathematical modeling to create computer simulations of the number of polioviruses in a cell that take into account these time and space constraints. By including random elements in the model, the simulated behavior more accurately follows experimentally recorded data than previously used models.

The results of the model led Schulte, Draghi et al. to conclude that the poliovirus replicates by the ‘geometric mode’; as new copies of the poliovirus RNA are made, each copy goes on to make more copies. This means that in a single infected cell there are multiple generations of RNA, and each generation may undergo distinct mutations that are passed on to the next set of RNA copies. In fact, Schulte, Draghi et al. found that the average virus released from an infected cell is the great-great-great-granddaughter of the original virus that infected the cell. With so many different generations of virus coexisting in a cell, there are a lot of opportunities for new genetic combinations to occur and for viruses to evolve new abilities.

DOI:http://dx.doi.org/10.7554/eLife.03753.002

Back to BaySICS: a user-friendly program for Bayesian Statistical Inference from Coalescent Simulations

Inference of population demographic history has vastly improved in recent years due to a number of technological and theoretical advances including the use of ancient DNA. Approximate Bayesian computation (ABC) stands among the most promising methods due to its simple theoretical fundament and exceptional flexibility. However, limited availability of user-friendly programs that perform ABC analysis renders it difficult to implement, and hence programming skills are frequently required. In addition, there is limited availability of programs able to deal with heterochronous data. Here we present the software BaySICS: Bayesian Statistical Inference of Coalescent Simulations. BaySICS provides an integrated and user-friendly platform that performs ABC analyses by means of coalescent simulations from DNA sequence data. It estimates historical demographic population parameters and performs hypothesis testing by means of Bayes factors obtained from model comparisons. Although providing specific features that improve inference from datasets with heterochronous data, BaySICS also has several capabilities making it a suitable tool for analysing contemporary genetic datasets. Those capabilities include joint analysis of independent tables, a graphical interface and the implementation of Markov-chain Monte Carlo without likelihoods.

A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation

As modeling becomes a more widespread practice in the life sciences and biomedical sciences, researchers need reliable tools to calibrate models against ever more complex and detailed data. Here we present an approximate Bayesian computation (ABC) framework and software environment, ABC-SysBio, which is a Python package that runs on Linux and Mac OS X systems and that enables parameter estimation and model selection in the Bayesian formalism by using sequential Monte Carlo (SMC) approaches. We outline the underlying rationale, discuss the computational and practical issues and provide detailed guidance as to how the important tasks of parameter inference and model selection can be performed in practice. Unlike other available packages, ABC-SysBio is highly suited for investigating, in particular, the challenging problem of fitting stochastic models to data. In order to demonstrate the use of ABC-SysBio, in this protocol we postulate the existence of an imaginary reaction network composed of seven interrelated biological reactions (involving a specific mRNA, the protein it encodes and a post-translationally modified version of the protein), a network that is defined by two files containing 'observed' data that we provide as supplementary information. In the first part of the PROCEDURE, ABC-SysBio is used to infer the parameters of this system, whereas in the second part we use ABC-SysBio's relevant functionality to discriminate between two different reaction network models, one of them being the 'true' one. Although computationally expensive, the additional insights gained in the Bayesian formalism more than make up for this cost, especially in complex problems.

Robust demographic inference from genomic and SNP data

We introduce a flexible and robust simulation-based framework to infer demographic parameters from the site frequency spectrum (SFS) computed on large genomic datasets. We show that our composite-likelihood approach allows one to study evolutionary models of arbitrary complexity, which cannot be tackled by other current likelihood-based methods. For simple scenarios, our approach compares favorably in terms of accuracy and speed with ∂a∂i, the current reference in the field, while showing better convergence properties for complex models. We first apply our methodology to non-coding genomic SNP data from four human populations. To infer their demographic history, we compare neutral evolutionary models of increasing complexity, including unsampled populations. We further show the versatility of our framework by extending it to the inference of demographic parameters from SNP chips with known ascertainment, such as that recently released by Affymetrix to study human origins. Whereas previous ways of handling ascertained SNPs were either restricted to a single population or only allowed the inference of divergence time between a pair of populations, our framework can correctly infer parameters of more complex models including the divergence of several populations, bottlenecks and migration. We apply this approach to the reconstruction of African demography using two distinct ascertained human SNP panels studied under two evolutionary models. The two SNP panels lead to globally very similar estimates and confidence intervals, and suggest an ancient divergence (>110 Ky) between Yoruba and San populations. Our methodology appears well suited to the study of complex scenarios from large genomic data sets.

Unravelling parasitic nematode natural history using population genetics

The health and economic importance of parasitic nematodes cannot be overstated. Moreover, they offer a complex and diverse array of life strategies, raising a multitude of evolutionary questions. Researchers are applying population genetics to parasitic nematodes in order to disentangle some aspects of their life strategies, improve our knowledge about disease epidemiology, and design control strategies. However, population genetics studies of nematodes have been constrained due to the difficulty in sampling nematodes and developing molecular markers. In this context, new computational and sequencing technologies represent promising tools to investigate population genomics of parasitic, non-model, nematode species in an epidemiological context.

Genetic basis for spontaneous hybrid genome doubling during allopolyploid speciation of common wheat shown by natural variation analyses of the paternal species

The complex process of allopolyploid speciation includes various mechanisms ranging from species crosses and hybrid genome doubling to genome alterations and the establishment of new allopolyploids as persisting natural entities. Currently, little is known about the genetic mechanisms that underlie hybrid genome doubling, despite the fact that natural allopolyploid formation is highly dependent on this phenomenon. We examined the genetic basis for the spontaneous genome doubling of triploid F1 hybrids between the direct ancestors of allohexaploid common wheat (Triticum aestivum L., AABBDD genome), namely Triticumturgidum L. (AABB genome) and Aegilopstauschii Coss. (DD genome). An Ae. tauschii intraspecific lineage that is closely related to the D genome of common wheat was identified by population-based analysis. Two representative accessions, one that produces a high-genome-doubling-frequency hybrid when crossed with a T. turgidum cultivar and the other that produces a low-genome-doubling-frequency hybrid with the same cultivar, were chosen from that lineage for further analyses. A series of investigations including fertility analysis, immunostaining, and quantitative trait locus (QTL) analysis showed that (1) production of functional unreduced gametes through nonreductional meiosis is an early step key to successful hybrid genome doubling, (2) first division restitution is one of the cytological mechanisms that cause meiotic nonreduction during the production of functional male unreduced gametes, and (3) six QTLs in the Ae. tauschii genome, most of which likely regulate nonreductional meiosis and its subsequent gamete production processes, are involved in hybrid genome doubling. Interlineage comparisons of Ae. tauschii's ability to cause hybrid genome doubling suggested an evolutionary model for the natural variation pattern of the trait in which non-deleterious mutations in six QTLs may have important roles. The findings of this study demonstrated that the genetic mechanisms for hybrid genome doubling could be studied based on the intrinsic natural variation that exists in the parental species.

Modelling tree shape and structure in viral phylodynamics

Epidemiological models have highlighted the importance of population structure in the transmission dynamics of infectious diseases. Using HIV-1 as an example of a model evolutionary system, we consider how population structure affects the shape and the structure of a viral phylogeny in the absence of strong selection at the population level. For structured populations, the number of lineages as a function of time is insufficient to describe the shape of the phylogeny. We develop deterministic approximations for the dynamics of tips of the phylogeny over evolutionary time, the number of ‘cherries’, tips that share a direct common ancestor, and Sackin's index, a commonly used measure of phylogenetic imbalance or asymmetry. We employ cherries both as a measure of asymmetry of the tree as well as a measure of the association between sequences from different groups. We consider heterogeneity in infectiousness associated with different stages of HIV infection, and in contact rates between groups of individuals. In the absence of selection, we find that population structure may have relatively little impact on the overall asymmetry of a tree, especially when only a small fraction of infected individuals is sampled, but may have marked effects on how sequences from different subpopulations cluster and co-cluster.

Bayesian computation via empirical likelihood

Approximate Bayesian computation has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the approximate Bayesian computation parameters (summary statistics, distance, tolerance), while being convergent in the number of observations. Furthermore, bypassing model simulations may lead to significant time savings in complex models, for instance those found in population genetics. The Bayesian computation with empirical likelihood algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size. The method is illustrated using several examples, including estimation of standard distributions, time series, and population genetics models.

The effective population size of malaria mosquitoes: large impact of vector control

Malaria vectors in sub-Saharan Africa have proven themselves very difficult adversaries in the global struggle against malaria. Decades of anti-vector interventions have yielded mixed results--with successful reductions in transmission in some areas and limited impacts in others. These varying successes can be ascribed to a lack of universally effective vector control tools, as well as the development of insecticide resistance in mosquito populations. Understanding the impact of vector control on mosquito populations is crucial for planning new interventions and evaluating existing ones. However, estimates of population size changes in response to control efforts are often inaccurate because of limitations and biases in collection methods. Attempts to evaluate the impact of vector control on mosquito effective population size (N(e)) have produced inconclusive results thus far. Therefore, we obtained data for 13-15 microsatellite markers for more than 1,500 mosquitoes representing multiple time points for seven populations of three important vector species--Anopheles gambiae, An. melas, and An. moucheti--in Equatorial Guinea. These populations were exposed to indoor residual spraying or long-lasting insecticidal nets in recent years. For comparison, we also analyzed data from two populations that have no history of organized vector control. We used Approximate Bayesian Computation to reconstruct their demographic history, allowing us to evaluate the impact of these interventions on the effective population size. In six of the seven study populations, vector control had a dramatic impact on the effective population size, reducing N(e) between 55%-87%, the exception being a single An. melas population. In contrast, the two negative control populations did not experience a reduction in effective population size. This study is the first to conclusively link anti-vector intervention programs in Africa to sharply reduced effective population sizes of malaria vectors.

Post-hoc pattern-oriented testing and tuning of an existing large model: lessons from the field vole

Pattern-oriented modeling (POM) is a general strategy for modeling complex systems. In POM, multiple patterns observed at different scales and hierarchical levels are used to optimize model structure, to test and select sub-models of key processes, and for calibration. So far, POM has been used for developing new models and for models of low to moderate complexity. It remains unclear, though, whether the basic idea of POM to utilize multiple patterns, could also be used to test and possibly develop existing and established models of high complexity. Here, we use POM to test, calibrate, and further develop an existing agent-based model of the field vole (Microtus agrestis), which was developed and tested within the ALMaSS framework. This framework is complex because it includes a high-resolution representation of the landscape and its dynamics, of the individual’s behavior, and of the interaction between landscape and individual behavior. Results of fitting to the range of patterns chosen were generally very good, but the procedure required to achieve this was long and complicated. To obtain good correspondence between model and the real world it was often necessary to model the real world environment closely. We therefore conclude that post-hoc POM is a useful and viable way to test a highly complex simulation model, but also warn against the dangers of over-fitting to real world patterns that lack details in their explanatory driving factors. To overcome some of these obstacles we suggest the adoption of open-science and open-source approaches to ecological simulation modeling.

Impact of sampling schemes on demographic inference: an empirical study in two species with different mating systems and demographic histories

Most species have at least some level of genetic structure. Recent simulation studies have shown that it is important to consider population structure when sampling individuals to infer past population history. The relevance of the results of these computer simulations for empirical studies, however, remains unclear. In the present study, we use DNA sequence datasets collected from two closely related species with very different histories, the selfing species Capsella rubella and its outcrossing relative C. grandiflora, to assess the impact of different sampling strategies on summary statistics and the inference of historical demography. Sampling strategy did not strongly influence the mean values of Tajima's D in either species, but it had some impact on the variance. The general conclusions about demographic history were comparable across sampling schemes even when resampled data were analyzed with approximate Bayesian computation (ABC). We used simulations to explore the effects of sampling scheme under different demographic models. We conclude that when sequences from modest numbers of loci (<60) are analyzed, the sampling strategy is generally of limited importance. The same is true under intermediate or high levels of gene flow (4Nm > 2-10) in models in which global expansion is combined with either local expansion or hierarchical population structure. Although we observe a less severe effect of sampling than predicted under some earlier simulation models, our results should not be seen as an encouragement to neglect this issue. In general, a good coverage of the natural range, both within and between populations, will be needed to obtain a reliable reconstruction of a species's demographic history, and in fact, the effect of sampling scheme on polymorphism patterns may itself provide important information about demographic history.

Investigation of the domestication of common bean (Phaseolus vulgaris) using multilocus sequence data

Multilocus sequence data collected from domesticated and related wild relatives provides a rich source of information on the effect of human selection on the diversity and adaptability of a species to complex environments. To evaluate the domestication history of common bean (Phaseolus vulgaris L.), multilocus sequence data from landraces representing the various races within the Middle American (MA) and Andean gene pools was evaluated. Across 13 loci, nucleotide diversity was similar between landraces and wild germplasm in both gene pools. The diversity data were evaluated using the approximate Bayesian computation approach to test multiple domestication models and estimate population demographic parameters. A model with a single domestication event coupled with bidirectional migration between wild and domesticated genotypes fitted the data better than models consisting of two or three domestication events in each genepool. The effective bottleneck population size was ~50% of the base population in each genepool. The bottleneck began ~8200 and ~8500 years before present and ended at ~6300 and ~7000 years before present in MA and Andean gene pools respectively. Linkage disequilibrium decayed to a greater extent in the MA genepool. Given the (1) geographical adaptation bottleneck in each wild gene pool, (2) a subsequent domestication bottleneck within each gene pool, (3) differentiation into gene-pool specific races and (4) variable extents of linkage disequilibrium, association mapping experiments for common bean would more appropriately be performed within each genepool.

Candidate targets of balancing selection in the genome of Staphylococcus aureus

Signatures of balancing selection can highlight polymorphisms and functions that are important to the long-term fitness of a species. We performed a first genome-wide scan for balancing selection in a bacterial species, Staphylococcus aureus, which is a common cause of serious antimicrobial-resistant infections of humans. Using a sliding window approach, the genomes of 16 strains of S. aureus, including 5 new genome sequences presented here, and 1 outgroup strain of S. epidermidis were scanned for signatures of balancing selection. A total of 195 short windows were investigated based on their extreme values of both Tajima's D (>2.03) and π/K ratios (>0.12) relative to the rest of the genome. To test the unusualness of these windows, an Approximate Bayesian Computation framework was used to select a null demographic model that better accounted for the observed data than did the standard neutral model. A total of 186 windows were demonstrated to be unusual under the null model and, thus, represented candidate loci under balancing selection. These 186 candidate windows were located within 99 candidate genes that were spread across 62 different loci. Nearly all the signal (97.2%) was located within coding sequences; balancing selection on gene regulation apparently occurs through the targeting of global regulators such as agr and gra/aps. The agr locus had some of the strongest signatures of balancing selection, which provides new insight into the causes of diversity at this locus. The list of candidate genes included multiple virulence-associated genes and was significantly enriched for functions in amino acid and inorganic ion transport and metabolism and in defense mechanisms against innate immunity and antimicrobials, highlighting these particular functions as important to the fitness of this pathogen.

Choice of summary statistic weights in approximate Bayesian computation

In this paper, we develop a Genetic Algorithm that can address the fundamental problem of how one should weight the summary statistics included in an approximate Bayesian computation analysis built around an accept/reject algorithm, and how one might choose the tolerance for that analysis. We then demonstrate that using weighted statistics, and a well-chosen tolerance, in such an approximate Bayesian computation approach can result in improved performance, when compared to unweighted analyses, using one example drawn purely from statistics and two drawn from the estimation of population genetics parameters.

Lack of confidence in approximate Bayesian computation model choice

Approximate Bayesian computation (ABC) have become an essential tool for the analysis of complex stochastic models. Grelaud et al. [(2009) Bayesian Anal 3:427-442] advocated the use of ABC for model choice in the specific case of Gibbs random fields, relying on an intermodel sufficiency property to show that the approximation was legitimate. We implemented ABC model choice in a wide range of phylogenetic models in the Do It Yourself-ABC (DIY-ABC) software [Cornuet et al. (2008) Bioinformatics 24:2713-2719]. We now present arguments as to why the theoretical arguments for ABC model choice are missing, because the algorithm involves an unknown loss of information induced by the use of insufficient summary statistics. The approximation error of the posterior probabilities of the models under comparison may thus be unrelated with the computational effort spent in running an ABC algorithm. We then conclude that additional empirical verifications of the performances of the ABC procedure as those available in DIY-ABC are necessary to conduct model choice.

Inference on population history and model checking using DNA sequence and microsatellite data with the software DIYABC (v1.0)

BACKGROUND

Approximate Bayesian computation (ABC) is a recent flexible class of Monte-Carlo algorithms increasingly used to make model-based inference on complex evolutionary scenarios that have acted on natural populations. The software DIYABC offers a user-friendly interface allowing non-expert users to consider population histories involving any combination of population divergences, admixtures and population size changes. We here describe and illustrate new developments of this software that mainly include (i) inference from DNA sequence data in addition or separately to microsatellite data, (ii) the possibility to analyze five categories of loci considering balanced or non balanced sex ratios: autosomal diploid, autosomal haploid, X-linked, Y-linked and mitochondrial, and (iii) the possibility to perform model checking computation to assess the "goodness-of-fit" of a model, a feature of ABC analysis that has been so far neglected.

RESULTS

We used controlled simulated data sets generated under evolutionary scenarios involving various divergence and admixture events to evaluate the effect of mixing autosomal microsatellite, mtDNA and/or nuclear autosomal DNA sequence data on inferences. This evaluation included the comparison of competing scenarios and the quantification of their relative support, and the estimation of parameter posterior distributions under a given scenario. We also considered a set of scenarios often compared when making ABC inferences on the routes of introduction of invasive species to illustrate the interest of the new model checking option of DIYABC to assess model misfit.

CONCLUSIONS

Our new developments of the integrated software DIYABC should be particularly useful to make inference on complex evolutionary scenarios involving both recent and ancient historical events and using various types of molecular markers in diploid or haploid organisms. They offer a handy way for non-expert users to achieve model checking computation within an ABC framework, hence filling up a gap of ABC analysis. The software DIYABC V1.0 is freely available at http://www1.montpellier.inra.fr/CBGP/diyabc.

ABC as a flexible framework to estimate demography over space and time: some cons, many pros

The analysis of genetic variation to estimate demographic and historical parameters and to quantitatively compare alternative scenarios recently gained a powerful and flexible approach: the Approximate Bayesian Computation (ABC). The likelihood functions does not need to be theoretically specified, but posterior distributions can be approximated by simulation even assuming very complex population models including both natural and human-induced processes. Prior information can be easily incorporated and the quality of the results can be analysed with rather limited additional effort. ABC is not a statistical analysis per se, but rather a statistical framework and any specific application is a sort of hybrid between a simulation and a data-analysis study. Complete software packages performing the necessary steps under a set of models and for specific genetic markers are already available, but the flexibility of the method is better exploited combining different programs. Many questions relevant in ecology can be addressed using ABC, but adequate amount of time should be dedicated to decide among alternative options and to evaluate the results. In this paper we will describe and critically comment on the different steps of an ABC analysis, analyse some of the published applications of ABC and provide user guidelines.