MOTIVATION: Large-scale genotype datasets can help track the dispersal patterns of epidemiological outbreaks and predict the geographic origins of individuals. Such genetically-based geographic assignments also show a range of possible applications in forensics for profiling both victims and criminals, and in wildlife management, where poaching hotspot areas can be located. They, however, require fast and accurate statistical methods to handle the growing amount of genetic information made available from genotype arrays and next-generation sequencing technologies. RESULTS: We introduce a novel statistical method for geopositioning individuals of unknown origin from genotypes. Our method is based on a geostatistical model trained with a dataset of georeferenced genotypes. Statistical inference under this model can be implemented within the theoretical framework of Integrated Nested Laplace Approximation, which represents one of the major recent breakthroughs in statistics, as it does not require Monte Carlo simulations. We compare the performance of our method and an alternative method for geospatial inference, SPA in a simulation framework. We highlight the accuracy and limits of continuous spatial assignment methods at various scales by analyzing genotype datasets from a diversity of species, including Florida Scrub-jay birds Aphelocoma coerulescens, Arabidopsis thaliana and humans, representing 41-197,146 SNPs. Our method appears to be best suited for the analysis of medium-sized datasets (a few tens of thousands of loci), such as reduced-representation sequencing data that become increasingly available in ecology. AVAILABILITY AND IMPLEMENTATION: http://www2.imm.dtu.dk/∼gigu/Spasiba/ CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: In a series of recent papers, Tess, a computer program based on the concept of hidden Markov random field, has been proposed to infer the number and locations of panmictic population units from the genotypes and spatial locations of these individuals. The method seems to be of broad appeal as it is conceptually much simpler than other competing methods and it has been reported by its authors to be fast and accurate. However, this methodology is not grounded in a formal statistical inference method and seems to rely to a large extent on arbitrary choices regarding the parameters used. The present article is an investigation of the accuracy of this method and an attempt to assess whether recent results reported on the basis of this method are genuine features of the genetic process or artefacts of the method. METHOD: I analyse simulated data consisting of populations at Hardy-Weinberg and linkage equilibrium and also data simulated under a scenario of isolation-by-distance at mutation-migration-drift equilibrium. Arabidopsis thaliana data previously analysed with this method are also reconsidered. RESULTS: Using the Tess program under the no-admixture model to analyse data consisting of several genuine HWLE populations with individuals of pure ancestries leads to highly inaccurate results; Using the Tess program under the admixture model to analyse data consisting of a continuous isolation-by-distance population leads to the inference of spurious HWLE populations whose number and features depend on the parameters used. Results previously reported about the A.thaliana using Tess seem to a large extent to be artefacts of the statistical methodology used. The findings go beyond population clustering models and can be an help to design more efficient algorithms based on graphs. AVAILABILITY: The data analysed in the present article are available from http://folk.uio.no/gillesg/Bioinformatics-HMRF.

The Deviance Information Criterion (DIC) has been originally introduced in the context of generalized linear models, and DeIorio and Robert (2002) and Celeux et al. (2006) pointed out some potential inconsistencies in the definition of the DIC for other families of models. However, Francois et al. (2008) do not give any information about there definition of the DIC to estimate the number of clusters. By doing so, they do not comply with the ‘long tradition in statistics’ consisting in giving a minimum of details to allow reproducible research. Chen et al. (2007) suggest to estimate the number of clusters by maximizing the likelihood. The maximum taken by the likelihood being an increasing function of the maximum number of clusters allowed in the model, this practice obviously does not have a ‘well-defined background in statistics’. Chen et al. (2007), Francois et al. (2008) and Durand et al. (2009) recommend to manipulate the neighbourhood graph (including by removing edges or by adding ‘dummy individuals)’ at the user's convenience. This practice does not have any ‘background’ or ‘tradition’ in any field of Science whatsoever. The reference to the book of Gelman et al. (2004) is irrelevant in all these contexts. The recommendations about the choice of Kmax have never been clear in the various references about TESS. In their present reanalysis, the authors recommend to test several values of Kmax and to look for a plateau by a visual check of the outputs for the various runs. This criterion is subjective and opens a new door to manipulations. It would be interesting to know how such visual checks should be performed in intensive analyses [e.g. Rosenberg et al. (2005) involving 367 200 MCMC runs]. I also note that TESS was advertised in Chen et al. (2007) to be fast but the question is now raised as to what remains of this claim if the users have to perform runs for dozens of combinations of parameters and cumbersome visual comparisons. Moreover, this reanalysis does not address at all the issue of spurious populations inferred by TESS for datasets consisting of a single cluster (Table C of Supplementary Material) and the choice of the interaction parameter ψ. The reference to Patterson et al. (2006) seems irrelevant in this context as IBD data have no reason to consist of several recently diverged populations in general. Besides, the number of clusters detected by TESS was found to be highly sensitive to the choice of ψ and Kmax and did not seem to relate to a number of eigenvalues (which is fixed by nature). Novembre and Stephens (2008) do not discuss clustering models but they warned clearly against misinterpretation of spatial patterns in terms of demographic history. This point was missed by Francois et al. (2008) and Durand et al. (2009) do not clarify what the users are supposed to learn about their data under a pattern of IBD by using TESS. This new analysis give results different from my reanalysis and from Francois et al. (2008) and does not clarify at all how version changes and choice of parameters interplay to give estimated values of K varying between 1 and 4. The various theoretical references given by Durand et al. in their reply are a smoke screen and do not address the concerns one might have against TESS. They chose not to mention (i) results for five-island data with FST < 0.03 and (ii) results for data consisting of a single cluster (where TESS proved to perform particularly poorly). This choice speaks for itself. Point (i) is particularly striking if one reminds that TESS was advertised as a program suitable to deal with extremely low differentiation (Chen et al., 2007). Durand et al. do not say a word about the choice of the interaction parameter ψ which is now the elephant in the TESS room. Users that are willing to use TESS can either (i) use the default value 0.6 and be exposed to a high inaccuracy that can be seen in Table C of the Supplementary Material, (ii) experiment different values and get inconsistent results as discussed by Johansson et al. (2008), Cullingham et al. (2009) and Quéméré et al. (2009), (iii) try to tune ψ in such a way that the output of TESS matches the output of another clustering software or (iv) contact the TESS authors for ad hoc suggestions (Fedy et al., 2009). The claims by Durand et al. that ‘TESS is based on highly validated methods’ and that ‘criticisms are not based on strong evidence’ are not supported by scientific argumentation. Conflict of Interest: none declared.

BACKGROUND: The ascertainment process of molecular markers amounts to disregard loci carrying alleles with low frequencies. This can result in strong biases in inferences under population genetics models if not properly taken into account by the inference algorithm. Attempting to model this censoring process in view of making inference of population structure (i.e.identifying clusters of individuals) brings up challenging numerical difficulties. METHOD: These difficulties are related to the presence of intractable normalizing constants in Metropolis-Hastings acceptance ratios. This can be solved via an Markov chain Monte Carlo (MCMC) algorithm known as single variable exchange algorithm (SVEA). RESULT: We show how this general solution can be implemented for a class of clustering models of broad interest in population genetics that includes the models underlying the computer programs STRUCTURE, GENELAND and GESTE. We also implement the method proposed for a simple example and show that it allows us to reduce the bias substantially. AVAILABILITY: Further details and a computer program implementing the method are available from http://folk.uio.no/gillesg/AscB/.

MOTIVATION: This article considers the problem of estimating population genetic subdivision from multilocus genotype data. A model is considered to make use of genotypes and possibly of spatial coordinates of sampled individuals. A particular attention is paid to the case of low genetic differentiation with the help of a previously described Bayesian clustering model where allele frequencies are assumed to be a priori correlated. Under this model, various problems of inference are considered, in particular the common and difficult, but still unaddressed, situation where the number of populations is unknown. RESULTS: A Markov chain Monte Carlo algorithm and a new post-processing scheme are proposed. It is shown that they significantly improve the accuracy of previously existing algorithms in terms of estimated number of populations and estimated population membership. This is illustrated numerically with data simulated from the prior-likelihood model used in inference and also with data simulated from a Wright-Fisher model. Improvements are also illustrated on a real dataset of eighty-eight wolverines (Gulo gulo) genotyped at 10 microsatellites loci. The interest of the solutions presented here are not specific to any clustering model and are hence relevant to many settings in populations genetics where weakly differentiated populations are assumed or sought. AVAILABILITY: The improvements implemented will be made available in version 3.0.0 of the R package Geneland. Informations on how to get and use the software are available from http://folk.uio.no/gillesg/Geneland.html. SUPPLEMENTARY INFORMATION: http://folk.uio.no/gillesg/CFM/SuppMat.pdf.

Abstract Summary: We introduce a new algorithm to account for the presence of null alleles in inferences of populations clusters from individual multilocus genetic data. We show by simulations that the presence of null alleles can affect the accuracy of inferences if not properly accounted for and that our algorithm improve signficantly their accuracy. Availability: This new algorithm is implemented in the program Geneland. It is freely available under GNU public license as an R package on the Comprehensive R Archive Network. It now includes a fully clickable graphical interface. Informations on how to get the software are available on folk.uio.no/gillesg/Geneland.html Contact: [email protected] Supplementary information: Details on the simulation study are available from folk.uio.no/gillesg/BioInformatics_Geneland