Guerre des sexes chez une fourmi : reproduction clonale des mâles et des reines

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Reliable ABC model choice via random forests

Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques. We propose a novel approach based on a machine learning tool named random forests to conduct selection among the highly complex models covered by ABC algorithms. We thus modify the way Bayesian model selection is both understood and operated, in that we rephrase the inferential goal as a classification problem, first predicting the model that best fits the data with random forests and postponing the approximation of the posterior probability of the predicted MAP for a second stage also relying on random forests. Compared with earlier implementations of ABC model choice, the ABC random forest approach offers several potential improvements: (i) it often has a larger discriminative power among the competing models, (ii) it is more robust against the number and choice of statistics summarizing the data, (iii) the computing effort is drastically reduced (with a gain in computation efficiency of at least fifty), and (iv) it includes an approximation of the posterior probability of the selected model. The call to random forests will undoubtedly extend the range of size of datasets and complexity of models that ABC can handle. We illustrate the power of this novel methodology by analyzing controlled experiments as well as genuine population genetics datasets. The proposed methodologies are implemented in the R package abcrf available on the CRAN.Comment: 39 pages, 15 figures, 6 table

Bayesian computation via empirical likelihood

Approximate Bayesian computation (ABC) 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 ABC 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 BCel 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.Comment: 21 pages, 12 figures, revised version of the previous version with a new titl

ABC random forests for Bayesian parameter inference

This preprint has been reviewed and recommended by Peer Community In Evolutionary Biology (http://dx.doi.org/10.24072/pci.evolbiol.100036). Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian inference for models associated with intractable likelihood functions. Most ABC implementations require the preliminary selection of a vector of informative statistics summarizing raw data. Furthermore, in almost all existing implementations, the tolerance level that separates acceptance from rejection of simulated parameter values needs to be calibrated. We propose to conduct likelihood-free Bayesian inferences about parameters with no prior selection of the relevant components of the summary statistics and bypassing the derivation of the associated tolerance level. The approach relies on the random forest methodology of Breiman (2001) applied in a (non parametric) regression setting. We advocate the derivation of a new random forest for each component of the parameter vector of interest. When compared with earlier ABC solutions, this method offers significant gains in terms of robustness to the choice of the summary statistics, does not depend on any type of tolerance level, and is a good trade-off in term of quality of point estimator precision and credible interval estimations for a given computing time. We illustrate the performance of our methodological proposal and compare it with earlier ABC methods on a Normal toy example and a population genetics example dealing with human population evolution. All methods designed here have been incorporated in the R package abcrf (version 1.7) available on CRAN.Comment: Main text: 24 pages, 6 figures Supplementary Information: 14 pages, 5 figure

Anarchy in the UK: Detailed genetic analysis of worker reproduction in a naturally occurring British anarchistic honeybee, Apis mellifera, colony using DNA microsatellites

Anarchistic behaviour is a very rare phenotype of honeybee colonies. In an anarchistic colony, many workers’ sons are reared in the presence of the queen. Anarchy has previously been described in only two Australian colonies. Here we report on a first detailed genetic analysis of a British anarchistic colony. Male pupae were present in great abundance above the queen excluder, which was clearly indicative of extensive worker reproduction and is the hallmark of anarchy. Seventeen microsatellite loci were used to analyse these male pupae, allowing us to address whether all the males were indeed workers’ sons, and how many worker patrilines and individual workers produced them. In the sample, 95 of 96 of the males were definitely workers’ sons. Given that ≈ 1% of workers’ sons were genetically indistinguishable from queen’s sons, this suggests that workers do not move any queen-laid eggs between the part of the colony where the queen is present to the area above the queen excluder which the queen cannot enter. The colony had 16 patrilines, with an effective number of patrilines of 9.85. The 75 males that could be assigned with certainty to a patriline came from 7 patrilines, with an effective number of 4.21. They were the offspring of at least 19 workers. This is in contrast to the two previously studied Australian naturally occurring anarchist colonies, in which most of the workers’ sons were offspring of one patriline. The high number of patrilines producing males leads to a low mean relatedness between laying workers and males of the colony. We discuss the importance of studying such colonies in the understanding of worker policing and its evolution

Chloroplast microsatellites: measures of genetic diversity and the effect of homoplasy

Chloroplast microsatellites have been widely used in population genetic studies of conifers in recent years. However, their haplotype configurations suggest that they could have high levels of homoplasy, thus limiting the power of these molecular markers. A coalescent-based computer simulation was used to explore the influence of homoplasy on measures of genetic diversity based on chloroplast microsatellites. The conditions of the simulation were defined to fit isolated populations originating from the colonization of one single haplotype into an area left available after a glacial retreat. Simulated data were compared with empirical data available from the literature for a species of Pinus that has expanded north after the Last Glacial Maximum. In the evaluation of genetic diversity, homoplasy was found to have little influence on Nei's unbiased haplotype diversity (H(E)) while Goldstein's genetic distance estimates (D2sh) were much more affected. The effect of the number of chloroplast microsatellite loci for evaluation of genetic diversity is also discussed

Inferring introduction routes of invasive species using approximate Bayesian computation on microsatellite data

Determining the routes of introduction provides not only information about the history of an invasion process, but also information about the origin and construction of the genetic composition of the invading population. It remains difficult, however, to infer introduction routes from molecular data because of a lack of appropriate methods. We evaluate here the use of an approximate Bayesian computation (ABC) method for estimating the probabilities of introduction routes of invasive populations based on microsatellite data. We considered the crucial case of a single source population from which two invasive populations originated either serially from a single introduction event or from two independent introduction events. Using simulated datasets, we found that the method gave correct inferences and was robust to many erroneous beliefs. The method was also more efficient than traditional methods based on raw values of statistics such as assignment likelihood or pairwise F(ST). We illustrate some of the features of our ABC method, using real microsatellite datasets obtained for invasive populations of the western corn rootworm, Diabrotica virgifera virgifera. Most computations were performed with the DIYABC program (http://www1.montpellier.inra.fr/CBGP/diyabc/)

Likelihood-free model choice

Fan, and Beaumont (2017). Beyond exposing the potential pitfalls of ABC approximations to posterior probabilities, the review emphasizes mostly the solution proposed by [25] on the use of random forests for aggregating summary statistics and for estimating the posterior probability of the most likely model via a secondary random forest