A novel approach for choosing summary statistics in approximate Bayesian computation

The choice of summary statistics is a crucial step in approximate Bayesian computation (ABC). Since statistics are often not sufficient, this choice involves a trade-off between loss of information and reduction of dimensionality. The latter may increase the efficiency of ABC. Here, we propose an approach for choosing summary statistics based on boosting, a technique from the machine-learning literature. We consider different types of boosting and compare them to partial least-squares regression as an alternative. To mitigate the lack of sufficiency, we also propose an approach for choosing summary statistics locally, in the putative neighborhood of the true parameter value. We study a demographic model motivated by the reintroduction of Alpine ibex (Capra ibex) into the Swiss Alps. The parameters of interest are the mean and standard deviation across microsatellites of the scaled ancestral mutation rate (θ(anc) = 4N(e)u) and the proportion of males obtaining access to matings per breeding season (ω). By simulation, we assess the properties of the posterior distribution obtained with the various methods. According to our criteria, ABC with summary statistics chosen locally via boosting with the L(2)-loss performs best. Applying that method to the ibex data, we estimate θ(anc)≈ 1.288 and find that most of the variation across loci of the ancestral mutation rate u is between 7.7 × 10(-4) and 3.5 × 10(-3) per locus per generation. The proportion of males with access to matings is estimated as ω≈ 0.21, which is in good agreement with recent independent estimates.

History of expansion and anthropogenic collapse in a top marine predator of the Black Sea estimated from genetic data

Two major ecological transitions marked the history of the Black Sea after the last Ice Age. The first was the postglacial transition from a brackish-water to a marine ecosystem dominated by porpoises and dolphins once this basin was reconnected back to the Mediterranean Sea (ca. 8,000 y B.P.). The second occurred during the past decades, when overfishing and hunting activities brought these predators close to extinction, having a deep impact on the structure and dynamics of the ecosystem. Estimating the extent of this decimation is essential for characterizing this ecosystem's dynamics and for formulating restoration plans. However, this extent is poorly documented in historical records. We addressed this issue for one of the main Black Sea predators, the harbor porpoise, using a population genetics approach. Analyzing its genetic diversity using an approximate Bayesian computation approach, we show that only a demographic expansion (at most 5,000 y ago) followed by a contemporaneous population collapse can explain the observed genetic data. We demonstrate that both the postglacial settlement of harbor porpoises in the Black Sea and the recent anthropogenic activities have left a clear footprint on their genetic diversity. Specifically, we infer a strong population reduction (~90%) that occurred within the past 5 decades, which can therefore clearly be related to the recent massive killing of small cetaceans and to the continuing incidental catches in commercial fisheries. Our study thus provides a quantitative assessment of these demographically catastrophic events, also showing that two separate historical events can be inferred from contemporary genetic data.

Balancing selection at the tomato RCR3 Guardee gene family maintains variation in strength of pathogen defense

Coevolution between hosts and pathogens is thought to occur between interacting molecules of both species. This results in the maintenance of genetic diversity at pathogen antigens (or so-called effectors) and host resistance genes such as the major histocompatibility complex (MHC) in mammals or resistance (R) genes in plants. In plant-pathogen interactions, the current paradigm posits that a specific defense response is activated upon recognition of pathogen effectors via interaction with their corresponding R proteins. According to the "Guard-Hypothesis," R proteins (the "guards") can sense modification of target molecules in the host (the "guardees") by pathogen effectors and subsequently trigger the defense response. Multiple studies have reported high genetic diversity at R genes maintained by balancing selection. In contrast, little is known about the evolutionary mechanisms shaping the guardee, which may be subject to contrasting evolutionary forces. Here we show that the evolution of the guardee RCR3 is characterized by gene duplication, frequent gene conversion, and balancing selection in the wild tomato species Solanum peruvianum. Investigating the functional characteristics of 54 natural variants through in vitro and in planta assays, we detected differences in recognition of the pathogen effector through interaction with the guardee, as well as substantial variation in the strength of the defense response. This variation is maintained by balancing selection at each copy of the RCR3 gene. Our analyses pinpoint three amino acid polymorphisms with key functional consequences for the coevolution between the guardee (RCR3) and its guard (Cf-2). We conclude that, in addition to coevolution at the "guardee-effector" interface for pathogen recognition, natural selection acts on the "guard-guardee" interface. Guardee evolution may be governed by a counterbalance between improved activation in the presence and prevention of auto-immune responses in the absence of the corresponding pathogen.

A model-based Bayesian estimation of the rate of evolution of VNTR loci in Mycobacterium tuberculosis

Variable numbers of tandem repeats (VNTR) typing is widely used for studying the bacterial cause of tuberculosis. Knowledge of the rate of mutation of VNTR loci facilitates the study of the evolution and epidemiology of Mycobacterium tuberculosis. Previous studies have applied population genetic models to estimate the mutation rate, leading to estimates varying widely from around to per locus per year. Resolving this issue using more detailed models and statistical methods would lead to improved inference in the molecular epidemiology of tuberculosis. Here, we use a model-based approach that incorporates two alternative forms of a stepwise mutation process for VNTR evolution within an epidemiological model of disease transmission. Using this model in a Bayesian framework we estimate the mutation rate of VNTR in M. tuberculosis from four published data sets of VNTR profiles from Albania, Iran, Morocco and Venezuela. In the first variant, the mutation rate increases linearly with respect to repeat numbers (linear model); in the second, the mutation rate is constant across repeat numbers (constant model). We find that under the constant model, the mean mutation rate per locus is (95% CI: ,)and under the linear model, the mean mutation rate per locus per repeat unit is (95% CI: ,). These new estimates represent a high rate of mutation at VNTR loci compared to previous estimates. To compare the two models we use posterior predictive checks to ascertain which of the two models is better able to reproduce the observed data. From this procedure we find that the linear model performs better than the constant model. The general framework we use allows the possibility of extending the analysis to more complex models in the future.

Genetically typing the bacterium responsible for tuberculosis is useful for understanding the evolutionary and epidemiological characteristics of the disease. Typing methods based on variable number tandem repeat (VNTR) loci are increasingly being used. These loci, which are composed of repeated units, mutate by increasing or decreasing in the number of these repeats. Knowledge of the mutation rate of molecular markers facilitates the epidemiological interpretation of the observed genetic variation in a sample of bacterial isolates. Few studies have examined the rate of mutation at these markers and estimates to date have varied considerably. To address this problem we develop a stochastic model of evolution of these markers and then estimate their mutation rate using approximate Bayesian computation. We examine two alternative forms of the mutation process. The observed data are from four published data sets of tuberculosis bacterial isolates sampled in Albania, Iran, Morocco and Venezuela. We find that these markers have fairly high rates of mutation compared with estimates from previous studies.

Cape buffalo mitogenomics reveals a Holocene shift in the African human-megafauna dynamics

Africa is unique among the continents in having maintained an extraordinarily diverse and prolific megafauna spanning the Pleistocene-Holocene epochs. Little is known about the historical dynamics of this community and even less about the reasons for its unique persistence to modern times. We sequenced complete mitochondrial genomes from 43 Cape buffalo (Syncerus caffer caffer) to infer the demographic history of this large mammal. A combination of Bayesian skyline plots, simulations and Approximate Bayesian Computation (ABC) were used to distinguish population size dynamics from the confounding effect of population structure and identify the most probable demographic scenario. Our analyses revealed a late Pleistocene expansion phase concurrent with the human expansion between 80 000 and 10 000 years ago, refuting an adverse ecological effect of Palaeolithic humans on this quarry species, but also showed that the buffalo subsequently declined during the Holocene. The distinct two-phased dynamic inferred here suggests that a major ecological transition occurred in the Holocene. The timing of this transition coincides with the onset of drier conditions throughout tropical Africa following the Holocene Optimum (∼9000-5000 years ago), but also with the explosive growth in human population size associated with the transition from the Palaeolithic to the Neolithic cultural stage. We evaluate each of these possible causal factors and their potential impact on the African megafauna, providing the first systematic assessment of megafauna dynamics on the only continent where large mammals remain abundant.

Reliability of genetic bottleneck tests for detecting recent population declines

The identification of population bottlenecks is critical in conservation because populations that have experienced significant reductions in abundance are subject to a variety of genetic and demographic processes that can hasten extinction. Genetic bottleneck tests constitute an appealing and popular approach for determining if a population decline has occurred because they only require sampling at a single point in time, yet reflect demographic history over multiple generations. However, a review of the published literature indicates that, as typically applied, microsatellite-based bottleneck tests often do not detect bottlenecks in vertebrate populations known to have experienced declines. This observation was supported by simulations that revealed that bottleneck tests can have limited statistical power to detect bottlenecks largely as a result of limited sample sizes typically used in published studies. Moreover, commonly assumed values for mutation model parameters do not appear to encompass variation in microsatellite evolution observed in vertebrates and, on average, the proportion of multi-step mutations is underestimated by a factor of approximately two. As a result, bottleneck tests can have a higher probability of 'detecting' bottlenecks in stable populations than expected based on the nominal significance level. We provide recommendations that could add rigor to inferences drawn from future bottleneck tests and highlight new directions for the characterization of demographic history.

Coalescent patterns for chromosomal inversions in divergent populations

Chromosomal inversions allow genetic divergence of locally adapted populations by reducing recombination between chromosomes with different arrangements. Divergence between populations (or hybridization between species) is expected to leave signatures in the neutral genetic diversity of the inverted region. Quantitative expectations for these patterns, however, have not been obtained. Here, we develop coalescent models of neutral sites linked to an inversion polymorphism in two locally adapted populations. We consider two scenarios of local adaptation: selection on the inversion breakpoints and selection on alleles inside the inversion. We find that ancient inversion polymorphisms cause genetic diversity to depart dramatically from neutral expectations. Other situations, however, lead to patterns that may be difficult to detect; important determinants are the age of the inversion and the rate of gene flux between arrangements. We also study inversions under genetic drift, finding that they produce patterns similar to locally adapted inversions of intermediate age. Our results are consistent with empirical observations, and provide the foundation for quantitative analyses of the roles that inversions have played in speciation.

Recombination rate variation and speciation: theoretical predictions and empirical results from rabbits and mice

Recently diverged taxa may continue to exchange genes. A number of models of speciation with gene flow propose that the frequency of gene exchange will be lower in genomic regions of low recombination and that these regions will therefore be more differentiated. However, several population-genetic models that focus on selection at linked sites also predict greater differentiation in regions of low recombination simply as a result of faster sorting of ancestral alleles even in the absence of gene flow. Moreover, identifying the actual amount of gene flow from patterns of genetic variation is tricky, because both ancestral polymorphism and migration lead to shared variation between recently diverged taxa. New analytic methods have been developed to help distinguish ancestral polymorphism from migration. Along with a growing number of datasets of multi-locus DNA sequence variation, these methods have spawned a renewed interest in speciation models with gene flow. Here, we review both speciation and population-genetic models that make explicit predictions about how the rate of recombination influences patterns of genetic variation within and between species. We then compare those predictions with empirical data of DNA sequence variation in rabbits and mice. We find strong support for the prediction that genomic regions experiencing low levels of recombination are more differentiated. In most cases, reduced gene flow appears to contribute to the pattern, although disentangling the relative contribution of reduced gene flow and selection at linked sites remains a challenge. We suggest fruitful areas of research that might help distinguish between different models.

EggLib: processing, analysis and simulation tools for population genetics and genomics

Background

With the considerable growth of available nucleotide sequence data over the last decade, integrated and flexible analytical tools have become a necessity. In particular, in the field of population genetics, there is a strong need for automated and reliable procedures to conduct repeatable and rapid polymorphism analyses, coalescent simulations, data manipulation and estimation of demographic parameters under a variety of scenarios.

Results

In this context, we present EggLib (Evolutionary Genetics and Genomics Library), a flexible and powerful C++/Python software package providing efficient and easy to use computational tools for sequence data management and extensive population genetic analyses on nucleotide sequence data. EggLib is a multifaceted project involving several integrated modules: an underlying computationally efficient C++ library (which can be used independently in pure C++ applications); two C++ programs; a Python package providing, among other features, a high level Python interface to the C++ library; and the egglib script which provides direct access to pre-programmed Python applications.

Conclusions

EggLib has been designed aiming to be both efficient and easy to use. A wide array of methods are implemented, including file format conversion, sequence alignment edition, coalescent simulations, neutrality tests and estimation of demographic parameters by Approximate Bayesian Computation (ABC). Classes implementing different demographic scenarios for ABC analyses can easily be developed by the user and included to the package. EggLib source code is distributed freely under the GNU General Public License (GPL) from its website http://egglib.sourceforge.net/ where a full documentation and a manual can also be found and downloaded.

Microsatellite genotyping reveals end-Pleistocene decline in mammoth autosomal genetic variation

The last glaciation was a dynamic period with strong impact on the demography of many species and populations. In recent years, mitochondrial DNA sequences retrieved from radiocarbon-dated remains have provided novel insights into the history of Late Pleistocene populations. However, genotyping of loci from the nuclear genome may provide enhanced resolution of population-level changes. Here, we use four autosomal microsatellite DNA markers to investigate the demographic history of woolly mammoths (Mammuthus primigenius) in north-eastern Siberia from before 60 000 years ago up until the species' final disappearance c.4000 years ago. We identified two genetic groups, implying a marked temporal genetic differentiation between samples with radiocarbon ages older than 12 thousand radiocarbon years before present (ka) and those younger than 9ka. Simulation-based analysis indicates that this dramatic change in genetic composition, which included a decrease in individual heterozygosity of approximately 30%, was due to a multifold reduction in effective population size. A corresponding reduction in genetic variation was also detected in the mitochondrial DNA, where about 65% of the diversity was lost. We observed no further loss in genetic variation during the Holocene, which suggests a rapid final extinction event.

Population divergence with or without admixture: selecting models using an ABC approach

Genetic data have been widely used to reconstruct the demographic history of populations, including the estimation of migration rates, divergence times and relative admixture contribution from different populations. Recently, increasing interest has been given to the ability of genetic data to distinguish alternative models. One of the issues that has plagued this kind of inference is that ancestral shared polymorphism is often difficult to separate from admixture or gene flow. Here, we applied an approximate Bayesian computation (ABC) approach to select the model that best fits microsatellite data among alternative splitting and admixture models. We performed a simulation study and showed that with reasonably large data sets (20 loci) it is possible to identify with a high level of accuracy the model that generated the data. This suggests that it is possible to distinguish genetic patterns due to past admixture events from those due to shared polymorphism (population split without admixture). We then apply this approach to microsatellite data from an endangered and endemic Iberian freshwater fish species, in which a clustering analysis suggested that one of the populations could be admixed. In contrast, our results suggest that the observed genetic patterns are better explained by a population split model without admixture.

Does speciation between Arabidopsis halleri and Arabidopsis lyrata coincide with major changes in a molecular target of adaptation?

Ever since Darwin proposed natural selection as the driving force for the origin of species, the role of adaptive processes in speciation has remained controversial. In particular, a largely unsolved issue is whether key divergent ecological adaptations are associated with speciation events or evolve secondarily within sister species after the split. The plant Arabidopsis halleri is one of the few species able to colonize soils highly enriched in zinc and cadmium. Recent advances in the molecular genetics of adaptation show that the physiology of this derived ecological trait involves copy number expansions of the AhHMA4 gene, for which orthologs are found in single copy in the closely related A. lyrata and the outgroup A. thaliana. To gain insight into the speciation process, we ask whether adaptive molecular changes at this candidate gene were contemporary with important stages of the speciation process. We first inferred the scenario and timescale of speciation by comparing patterns of variation across the genomic backgrounds of A. halleri and A. lyrata. Then, we estimated the timing of the first duplication of AhHMA4 in A. halleri. Our analysis suggests that the historical split between the two species closely coincides with major changes in this molecular target of adaptation in the A. halleri lineage. These results clearly indicate that these changes evolved in A. halleri well before industrial activities fostered the spread of Zn- and Cd-polluted areas, and suggest that adaptive processes related to heavy-metal homeostasis played a major role in the speciation process.

Estimation of leaf wetness duration requirements of foliar fungal pathogens with uncertain data-an application to Mycosphaerella nawae

Wetness of the host surface is a critical environmental factor for the development of foliar fungal diseases, but it is difficult to estimate the wetness durations required by pathogens for infection when only few experimental data are available. In this paper, we propose a method to estimate wetness duration requirements of foliar fungal pathogens when precise experimental data are not available. The proposed method is based on approximate Bayesian computation. It only requires lower and upper bounds of wetness duration requirements for one or fewer temperatures. We describe the method, show how to apply it to an infection model, and then present a case study on Mycosphaerella nawae, the causal agent of circular leaf spot of persimmon. In this example, the parameters of a simple infection model were estimated using experimental data found in the literature for the pathogen, and the model was applied to assess the risk in a Spanish area recently affected by the disease. The results showed that the probability of successful infection was higher than 0.5 for 32% of the on-site wetness durations recorded in the affected area. Results obtained with simulated data showed that our method was able to improve the estimation of wetness duration requirement. Given the flexibility of the proposed method, we expect it to become adopted for assessing the risk of introduction of exotic fungal plant pathogens.

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 for nonlinear epidemiological models using genealogies and time series

Phylodynamics - the field aiming to quantitatively integrate the ecological and evolutionary dynamics of rapidly evolving populations like those of RNA viruses - increasingly relies upon coalescent approaches to infer past population dynamics from reconstructed genealogies. As sequence data have become more abundant, these approaches are beginning to be used on populations undergoing rapid and rather complex dynamics. In such cases, the simple demographic models that current phylodynamic methods employ can be limiting. First, these models are not ideal for yielding biological insight into the processes that drive the dynamics of the populations of interest. Second, these models differ in form from mechanistic and often stochastic population dynamic models that are currently widely used when fitting models to time series data. As such, their use does not allow for both genealogical data and time series data to be considered in tandem when conducting inference. Here, we present a flexible statistical framework for phylodynamic inference that goes beyond these current limitations. The framework we present employs a recently developed method known as particle MCMC to fit stochastic, nonlinear mechanistic models for complex population dynamics to gene genealogies and time series data in a Bayesian framework. We demonstrate our approach using a nonlinear Susceptible-Infected-Recovered (SIR) model for the transmission dynamics of an infectious disease and show through simulations that it provides accurate estimates of past disease dynamics and key epidemiological parameters from genealogies with or without accompanying time series data.

Approximate Bayesian computation reveals the factors that influence genetic diversity and population structure of foxsnakes

Contemporary geographical range and patterns of genetic diversity within species reflect complex interactions between multiple factors acting across spatial and temporal scales, and it is notoriously difficult to disentangle causation. Here, we quantify patterns of genetic diversity and genetic population structure using mitochondrial DNA sequences (101 individuals, cytochrome b) and microsatellites (816 individuals, 12 loci) and use Approximate Bayesian computation methods to test competing models of the demographic history of eastern and western foxsnakes. Our analyses indicate that post-glacial colonization and past population declines, probably caused by the infilling of deciduous forest and cooler temperatures since the mid-Holocene, largely underpin large-scale genetic patterns for foxsnakes. At finer geographical scales, our results point to more recent anthropogenic habitat loss as having accentuated genetic population structure by causing further declines and fragmentation.

MTML-msBayes: approximate Bayesian comparative phylogeographic inference from multiple taxa and multiple loci with rate heterogeneity

Background

MTML-msBayes uses hierarchical approximate Bayesian computation (HABC) under a coalescent model to infer temporal patterns of divergence and gene flow across codistributed taxon-pairs. Under a model of multiple codistributed taxa that diverge into taxon-pairs with subsequent gene flow or isolation, one can estimate hyper-parameters that quantify the mean and variability in divergence times or test models of migration and isolation. The software uses multi-locus DNA sequence data collected from multiple taxon-pairs and allows variation across taxa in demographic parameters as well as heterogeneity in DNA mutation rates across loci. The method also allows a flexible sampling scheme: different numbers of loci of varying length can be sampled from different taxon-pairs.

Results

Simulation tests reveal increasing power with increasing numbers of loci when attempting to distinguish temporal congruence from incongruence in divergence times across taxon-pairs. These results are robust to DNA mutation rate heterogeneity. Estimating mean divergence times and testing simultaneous divergence was less accurate with migration, but improved if one specified the correct migration model. Simulation validation tests demonstrated that one can detect the correct migration or isolation model with high probability, and that this HABC model testing procedure was greatly improved by incorporating a summary statistic originally developed for this task (Wakeley's Ψ_W). The method is applied to an empirical data set of three Australian avian taxon-pairs and a result of simultaneous divergence with some subsequent gene flow is inferred.

Conclusions

To retain flexibility and compatibility with existing bioinformatics tools, MTML-msBayes is a pipeline software package consisting of Perl, C and R programs that are executed via the command line. Source code and binaries are available for download at http://msbayes.sourceforge.net/ under an open source license (GNU Public License).

Evolution and population genetics of exotic and re-emerging pathogens: novel tools and approaches

Given human population growth and accelerated global trade, the rate of emergence of exotic plant pathogens is bound to increase. Understanding the processes that lead to the emergence of new pathogens can help manage emerging epidemics. Novel tools for analyzing population genetic variation can be used to infer the evolutionary history of populations or species, allowing for the unprecedented reconstruction of the demographic history of pathogens. Specifically, recent advances in the application of coalescent, maximum likelihood (ML), and Bayesian methods to population genetic data combined with increasing availability of affordable sequencing and parallel computing have created the opportunity to apply these methods to a broad range of questions regarding the evolution of emerging pathogens. These approaches are particularly powerful when used to test multiple competing hypotheses. We provide several examples illustrating how coalescent analysis provides critical insights into understanding migration pathways as well as processes of divergence, speciation, and recombination.