Olivier François

Approximate Bayesian Computation (ABC) in practice

Understanding the forces that influence natural variation within and among populations has been a major objective of evolutionary biologists for decades. Motivated by the growth in computational power and data complexity, modern approaches to this question make intensive use of simulation methods. Approximate Bayesian Computation (ABC) is one of these methods. Here we review the foundations of ABC, its recent algorithmic developments, and its applications in evolutionary biology and ecology. We argue that the use of ABC should incorporate all aspects of Bayesian data analysis: formulation, fitting, and improvement of a model. ABC can be a powerful tool to make inferences with complex models if these principles are carefully applied.

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.

Spatial Inference of Admixture Proportions and Secondary Contact Zones

Genetic admixture of distinct gene pools is the consequence of complex spatiotemporal processes that could have involved massive migration and local mating during the history of a species. However, current methods for estimating individual admixture proportions lack the incorporation of such a piece of information. Here, we extend Bayesian clustering algorithms by including global trend surfaces and spatial autocorrelation in the prior distribution on individual admixture coefficients. We test our algorithm by using spatially explicit and realistic coalescent simulations of colonization followed by secondary contact. By coupling our multiscale spatial analyses with a Bayesian evaluation of model complexity and fit, we show that the algorithm provides a correct description of smooth clinal variation, while still detecting zones of sharp variation when they are present in the data. We also apply our approach to understand the population structure of the killifish, Fundulus heteroclitus, for which the algorithm uncovers a presumed contact zone in the Atlantic coast of North America.

Bayesian Clustering Using Hidden Markov Random Fields in Spatial Population Genetics

We introduce a new Bayesian clustering algorithm for studying population structure using individually geo-referenced multilocus data sets. The algorithm is based on the concept of hidden Markov random field, which models the spatial dependencies at the cluster membership level. We argue that (i) a Markov chain Monte Carlo procedure can implement the algorithm efficiently, (ii) it can detect significant geographical discontinuities in allele frequencies and regulate the number of clusters, (iii) it can check whether the clusters obtained without the use of spatial priors are robust to the hypothesis of discontinuous geographical variation in allele frequencies, and (iv) it can reduce the number of loci required to obtain accurate assignments. We illustrate and discuss the implementation issues with the Scandinavian brown bear and the human CEPH diversity panel data set.

Applications of landscape genetics in conservation biology: concepts and challenges

Landscape genetics plays an increasingly important role in the management and conservation of species. Here, we highlight some of the opportunities and challenges in using landscape genetic approaches in conservation biology. We first discuss challenges related to sampling design and introduce several recent methodological developments in landscape genetics (analyses based on pairwise relatedness, the application of Bayesian methods, inference from landscape resistance and a shift from population-based to individual-based analyses). We then show how simulations can foster the field of landscape genetics and, finally, elaborate on technical developments in sequencing techniques that will dramatically improve our ability to study genetic variation in wild species, opening up new and unprecedented avenues for genetic analysis in conservation biology.

Testing for Associations between Loci and Environmental Gradients Using Latent Factor Mixed Models

Adaptation to local environments often occurs through natural selection acting on a large number of loci, each having a weak phenotypic effect. One way to detect these loci is to identify genetic polymorphisms that exhibit high correlation with environmental variables used as proxies for ecological pressures. Here, we propose new algorithms based on population genetics, ecological modeling, and statistical learning techniques to screen genomes for signatures of local adaptation. Implemented in the computer program “latent factor mixed model” (LFMM), these algorithms employ an approach in which population structure is introduced using unobserved variables. These fast and computationally efficient algorithms detect correlations between environmental and genetic variation while simultaneously inferring background levels of population structure. Comparing these new algorithms with related methods provides evidence that LFMM can efficiently estimate random effects due to population history and isolation-by-distance patterns when computing gene-environment correlations, and decrease the number of false-positive associations in genome scans. We then apply these models to plant and human genetic data, identifying several genes with functions related to development that exhibit strong correlations with climatic gradients.

Spatially explicit Bayesian clustering models in population genetics.

This article reviews recent developments in Bayesian algorithms that explicitly include geographical information in the inference of population structure. Current models substantially differ in their prior distributions and background assumptions, falling into two broad categories: models with or without admixture. To aid users of this new generation of spatially explicit programs, we clarify the assumptions underlying the models, and we test these models in situations where their assumptions are not met. We show that models without admixture are not robust to the inclusion of admixed individuals in the sample, thus providing an incorrect assessment of population genetic structure in many cases. In contrast, admixture models are robust to an absence of admixture in the sample. We also give statistical and conceptual reasons why data should be explored using spatially explicit models that include admixture.

Demographic history of european populations of Arabidopsis thaliana.

The model plant species Arabidopsis thaliana is successful at colonizing land that has recently undergone human-mediated disturbance. To investigate the prehistoric spread of A. thaliana, we applied approximate Bayesian computation and explicit spatial modeling to 76 European accessions sequenced at 876 nuclear loci. We find evidence that a major migration wave occurred from east to west, affecting most of the sampled individuals. The longitudinal gradient appears to result from the plant having spread in Europe from the east ∼10,000 years ago, with a rate of westward spread of ∼0.9 km/year. This wave-of-advance model is consistent with a natural colonization from an eastern glacial refugium that overwhelmed ancient western lineages. However, the speed and time frame of the model also suggest that the migration of A. thaliana into Europe may have accompanied the spread of agriculture during the Neolithic transition.

Which Random Processes Describe the Tree of Life? A Large-Scale Study of Phylogenetic Tree Imbalance

The explosion of phylogenetic studies not only provides a clear snapshot of biodiversity, but also makes it possible to infer how the diversity has arisen (see for example, Purvis and Hector, 2000; Harvey et al., 1996; Nee et al., 1996; Mace et al., 2003). To this aim, variation in speciation and extinction rates have been investigated through their signatures in the shapes of phylogenetic trees (Mooers and Heard, 1997). This issue is of great importance, as fitting stochastic models to tree data would help to understand underlying macroevolutionary processes. Although the prevailing view is that it does not represent phylogenies so well, the most popular model of phylogenetic trees is a branching process introduced by Yule, in which lineages split at random (Yule, 1924). Here we report the study of one major database of published

Genome scan methods against more complex models: when and how much should we trust them?

The recent availability of next‐generation sequencing (NGS) has made possible the use of dense genetic markers to identify regions of the genome that may be under the influence of selection. Several statistical methods have been developed recently for this purpose. Here, we present the results of an individual‐based simulation study investigating the power and error rate of popular or recent genome scan methods: linear regression, Bayescan, BayEnv and LFMM. Contrary to previous studies, we focus on complex, hierarchical population structure and on polygenic selection. Additionally, we use a false discovery rate (FDR)‐based framework, which provides an unified testing framework across frequentist and Bayesian methods. Finally, we investigate the influence of population allele frequencies versus individual genotype data specification for LFMM and the linear regression. The relative ranking between the methods is impacted by the consideration of polygenic selection, compared to a monogenic scenario. For strongly hierarchical scenarios with confounding effects between demography and environmental variables, the power of the methods can be very low. Except for one scenario, Bayescan exhibited moderate power and error rate. BayEnv performance was good under nonhierarchical scenarios, while LFMM provided the best compromise between power and error rate across scenarios. We found that it is possible to greatly reduce error rates by considering the results of all three methods when identifying outlier loci.