The Gibbs and split–merge sampler for population mixture analysis from genetic data with incomplete baselines

Abstract

Although population mixtures often include contributions from novel populations as well as from baseline populations previously sampled, unlabeled mixture individuals can be separated to their sources from genetic data. A Gibbs and split-merge Markov chain Monte Carlo sampler is described for successively partitioning a genetic mixture sample into plausible subsets of individuals from each of the baseline and extra-baseline populations present. The subsets are selected to satisfy the Hardy-Weinberg and linkage equilibrium conditions expected for large, panmictic populations. The number of populations present can be inferred from the distribution for counts of subsets per partition drawn by the sampler. To further summarize the sampler's output, co-assignment probabilities of mixture individuals to the same subsets are computed from the partitions and are used to construct a binary tree of their relatedness. The tree graphically displays the clusters of mixture individuals together with a quantitative measure of the evidence supporting their various separate and common sources. The methodology is applied to several simulated and real data sets to illustrate its use and demonstrate the sampler's superior performance.Résumé : Bien que les mélanges de populations contiennent des contributions des nouvelles populations en plus de celles des populations originales déjà échantillonnées, les individus non identifiés du mélange peuvent être séparés en fonction de leur source par leurs caractéristiques génétiques. Nous décrivons un échantillonneur de Gibbs de type Monte Carlo avec procédure de séparation-regroupement par chaînes de Markov qui sépare successivement un échantil-lon contenant un mélange génétique en sous-ensembles plausibles d'individus à la fois de la population d'origine et des populations additionnelles présentes. Les sous-ensembles sont sélectionnés de manière à satisfaire aux exigences de l'équilibre Hardy-Weinberg et de l'équilibre de liaison attendus dans de grandes populations panmictiques. Le nombre de populations présentes peut être estimé à partir de la distribution des nombres de sous-ensembles par partition retirés par l'échantillonneur. Afin de mieux résumer le produit de l'échantillonneur, les probabilités d'attribution conjointe des individus du mélange aux mêmes sous-ensembles sont calculées à partir des partitions et elles servent à construire un arbre binaire de leur degré de parenté. L'arbre représente graphiquement les groupements d'individus du mélange de même qu'une mesure quantitative des données qui appuient leurs différentes sources séparées et communes. Nous appliquons la méthodologie à plusieurs ensembles de données réelles et simulées afin d'en illustrer l'utilisation et de démontrer la performance supérieure de cet échantillonneur.[Traduit par la Rédaction] Pella and Masuda 596

Genetic mixed-stock analysis of Atlantic herring populations in a mixed feeding area

“…In contrast to simulated mixtures, real mixed samples may contain individuals originating from unsampled, genetically differentiated populations. Estimation errors associated with occurrence of mixture individuals from unsampled baselines were initially addressed by Smouse et al (1990) and Pella & Masuda (2006) who suggested that the problem may be reduced when unsampled populations have some genetic similarity with populations in the baseline, as is expected under isolation-by-distance. Although our baselines were expected to comprise samples from all major population components in the area, the distribution of herring spawning sites is more or less continuous in the study area, and we are unlikely to have sampled all genetically distinct components contributing to mixed samples.…”

Inference of Population Structure Under a Dirichlet Process Model

“…More recently, Pella and Masuda (2006) applied a Dirichlet process prior to the problem of identifying population structure. Importantly, the Dirichlet process prior allows both the assignment of individuals to populations and the number of populations to be random variables; the number of populations, then, can in principle be estimated.…”

“…Importantly, the Dirichlet process prior allows both the assignment of individuals to populations and the number of populations to be random variables; the number of populations, then, can in principle be estimated. The method of Pella and Masuda (2006) is similar to one proposed by Dawson and Belkhir (2001). Dawson and Belkhir (2001) propose both a maximum-likelihood and a Bayesian approach to infer the assignments of individuals to populations.…”

Joint Inference of Population Assignment and Demographic History

“…It is shown that joint estimates of assignment and demographic history are possible, including estimation of population phylogeny for samples from three populations. The new method is compared to results of a widely used assignment method, using simulated and published empirical data sets.T HE assignment of individuals to populations is a common population genetic application (Paetkau et al 1995;Rannala and Mountain 1997;Pritchard et al 2000;Dawson and Belkhir 2001;Corander et al 2003;Baudouin et al 2004;Guillot et al 2005;François et al 2006;Pella and Masuda 2006;Wu et al 2006;Huelsenbeck and Andolfatto 2007;Zhang 2008;Reeves and Richards 2009). Most methods assume random mating within populations and free recombination between loci to find population assignments that minimize the amount of departure from Hardy-Weinberg equilibrium (HWE) and linkage equilibrium (LE) within populations.…”