Bayesian inference of recent migration rates using multilocus genotypes

A new Bayesian method that uses individual multilocus genotypes to estimate rates of recent immigration (over the last several generations) among populations is presented. The method also estimates the posterior probability distributions of individual immigrant ancestries, population allele frequencies, population inbreeding coefficients, and other parameters of potential interest. The method is implemented in a computer program that relies on Markov chain Monte Carlo techniques to carry out the estimation of posterior probabilities. The program can be used with allozyme, microsatellite, RFLP, SNP, and other kinds of genotype data. We relax several assumptions of early methods for detecting recent immigrants, using genotype data; most significantly, we allow genotype frequencies to deviate from Hardy-Weinberg equilibrium proportions within populations. The program is demonstrated by applying it to two recently published microsatellite data sets for populations of the plant species Centaurea corymbosa and the gray wolf species Canis lupus. A computer simulation study suggests that the program can provide highly accurate estimates of migration rates and individual migrant ancestries, given sufficient genetic differentiation among populations and sufficient numbers of marker loci.     

Empirical evaluation of genetic clustering methods using multilocus genotypes from 20 chicken breeds

We tested the utility of genetic cluster analysis in ascertaining population structure of a large data set for which population structure was previously known. Each of 600 individuals representing 20 distinct chicken breeds was genotyped for 27 microsatellite loci, and individual multilocus genotypes were used to infer genetic clusters. Individuals from each breed were inferred to belong mostly to the same cluster. The clustering success rate, measuring the fraction of individuals that were properly inferred to belong to their correct breeds, was consistently approximately 98%. When markers of highest expected heterozygosity were used, genotypes that included at least 8-10 highly variable markers from among the 27 markers genotyped also achieved >95% clustering success. When 12-15 highly variable markers and only 15-20 of the 30 individuals per breed were used, clustering success was at least 90%. We suggest that in species for which population structure is of interest, databases of multilocus genotypes at highly variable markers should be compiled. These genotypes could then be used as training samples for genetic cluster analysis and to facilitate assignments of individuals of unknown origin to populations. The clustering algorithm has potential applications in defining the within-species genetic units that are useful in problems of conservation.     

gerud1.0: a computer program for the reconstruction of parental genotypes from progeny arrays using multilocus DNA data

We have no standard computer algorithm for the reconstruction of parental genotypes from the data generated by molecular studies of progeny arrays. Here I present a computer program that uses the multilocus genotypes of parents and offspring to reconstruct the genotypes of unknown parents contributing gametes to a progeny array for which one parent is known a priori. A second program performs simulations to assess the reliability of the algorithm under various scenarios. These programs will aid scientists engaged in parentage analyses, particularly in species with large clutches.     

Worldwide pattern of multilocus structure in barley determined by discrete log-linear multivariate analyses

Summary Data from the electrophoretic assay for seven enzyme loci of 1,032 accessions of cultivated barley, Hordeum vulgare L., from the USDA world barley collection were analyzed for multilocus structure using discrete log-linear multivariate techniques. Three major steps were involved in the analysis: (i) identification and elimination of terms that have inconsequential effects in multilocus association; (ii) construction of a log-linear model that best describes the complete multilocus structure of the genetic system; and (iii) evaluation of each of the association terms included in the model. The results of analyses of two subsets of loci show that the multilocus genetic system of cultivated barley, including loci located on different chromosomes, is organized into hierarchically structured complexes of loci. Multilocus structure differs in various geographical regions of the world. The structure of barleys from Southwest Asia, the putative center of origin for cultivated barley, is intermediate for both subsets of loci. Differences increased progressively across the Eurasian-African landmasses in each direction with increasing distance from Southwest Asia, with the consequence that the barleys from West Europe, East Asia, and Ethiopia are maximally different from those of Southwest Asia and Middle South Asia.     

New methods employing multilocus genotypes to select or exclude populations as origins of individuals

A new method for assigning individuals of unknown origin to populations, based on the genetic distance between individuals and populations, was compared to two existing methods based on the likelihood of multilocus genotypes. The distribution of the assignment criterion (genetic distance or genotype likelihood) for individuals of a given population was used to define the probability that an individual belongs to the population. Using this definition, it becomes possible to exclude a population as the origin of an individual, a useful extension of the currently available assignment methods. Using simulated data based on the coalescent process, the different methods were evaluated, varying the time of divergence of populations, the mutation model, the sample size, and the number of loci. Likelihood-based methods (especially the Bayesian method) always performed better than distance methods. Other things being equal, genetic markers were always more efficient when evolving under the infinite allele model than under the stepwise mutation model, even for equal values of the differentiation parameter F(st). Using the Bayesian method, a 100% correct assignment rate can be achieved by scoring ca. 10 microsatellite loci (H approximately 0.6) on 30-50 individuals from each of 10 populations when the F(st) is near 0.1.     

The analysis of multiple endpoints in clinical trials

Treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall Type I error rate. One option is to select a single primary endpoint for formal statistical inference, but this is not always feasible. Another approach is to apply Bonferroni correction (i.e., multiply each P-value by the total number of endpoints). Its conservatism for correlated endpoints is examined for multivariate normal data. A third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics. Quantitative, binary, and survival endpoints are all considered within this general framework. Two examples are presented and the relative merits of the proposed strategies are discussed.     

Meta-analysis of clinical trials with competing time-to-event endpoints

Recommendations for the analysis of competing risks in the context of randomized clinical trials are well established. Meta-analysis of individual patient data (IPD) is the gold standard for synthesizing evidence for clinical interpretation based on multiple studies. Surprisingly, no formal guidelines have been yet proposed to conduct an IPD meta-analysis with competing risk endpoints. To fill this gap, this work details (i) how to handle the heterogeneity between trials via a stratified regression model for competing risks and (ii) that the usual metrics of inconsistency to assess heterogeneity can readily be employed. Our proposal is illustrated by the re-analysis of a recently published meta-analysis in nasopharyngeal carcinoma, aiming at quantifying the benefit of the addition of chemotherapy to radiotherapy on each competing endpoint.     

Bayesian monitoring of clinical trials with failure-time endpoints

This article presents an aid for monitoring clinical trials with failure-time endpoints based on the Bayesian nonparametric analyses of the data. The posterior distribution is a mixture of Dirichlet processes in the presence of censoring if one assumes a Dirichlet process prior for the survival distribution. Using Gibbs sampling, one can generate random samples from the posterior distribution. With samples from the posterior distributions of treatment-specific survival curves, one can evaluate the current evidence in favor of stopping or continuing the trial based on summary statistics of these survival curves. Because the method is nonparametric, it can easily be used, for example, in situations where hazards cross or are suspected to cross and where relevant clinical decisions might be based on estimating when the integral between the curves might be expected to become positive and in favor of the new but toxic therapy. An example based on an actual trial illustrates the method.     

Inference of bacterial microevolution using multilocus sequence data

We describe a model-based method for using multilocus sequence data to infer the clonal relationships of bacteria and the chromosomal position of homologous recombination events that disrupt a clonal pattern of inheritance. The key assumption of our model is that recombination events introduce a constant rate of substitutions to a contiguous region of sequence. The method is applicable both to multilocus sequence typing (MLST) data from a few loci and to alignments of multiple bacterial genomes. It can be used to decide whether a subset of isolates share common ancestry, to estimate the age of the common ancestor, and hence to address a variety of epidemiological and ecological questions that hinge on the pattern of bacterial spread. It should also be useful in associating particular genetic events with the changes in phenotype that they cause. We show that the model outperforms existing methods of subdividing recombinogenic bacteria using MLST data and provide examples from Salmonella and Bacillus. The software used in this article, ClonalFrame, is available from http://bacteria.stats.ox.ac.uk/.     

Inference of population structure using multilocus genotype data

We describe a model-based clustering method for using multilocus genotype data to infer population structure and assign individuals to populations. We assume a model in which there are K populations (where K may be unknown), each of which is characterized by a set of allele frequencies at each locus. Individuals in the sample are assigned (probabilistically) to populations, or jointly to two or more populations if their genotypes indicate that they are admixed. Our model does not assume a particular mutation process, and it can be applied to most of the commonly used genetic markers, provided that they are not closely linked. Applications of our method include demonstrating the presence of population structure, assigning individuals to populations, studying hybrid zones, and identifying migrants and admixed individuals. We show that the method can produce highly accurate assignments using modest numbers of loci-e.g. , seven microsatellite loci in an example using genotype data from an endangered bird species. The software used for this article is available from http://www.stats.ox.ac.uk/ approximately pritch/home. html.     

Density and depth variations of Daphnia multilocus genotypes during a summer period in Lake Maarsseveen

The genotype composition of a Daphnia population complex during a summer period in Lake Maarsseveen (The Netherlands) was determined by allozyme analysis. The depth distribution, diel vertical migration and several parameters of the total population were measured. Young-of-the-year (0⁺) perch (Perca fluviatilis) were caught and species and allozyme types of Daphnia in the perch gut were also analysed. During May 1997, the densities of D. hyalina, D. galeata, the back-cross D. g x h – hyalina and the multilocus allozyme genotypes of the hybrid D. g x h decreased, except one multilocus genotype (MMMF). Total population size decreased and the ratio of females with eggs to those without eggs decreased as well. Food limitation during this clear-water phase in the lake is considered responsible. All genotypes, except MMMF, gradually descended in the water column. This drift is thought to be a reaction to the abundantly present 0⁺ perch or to the kairomones of this fish, although predation on the daphnids was still absent. In June, diel vertical migration started, except again part of the MMMF subpopulation. The other part migrated over a short distance compared with the other taxa and allozyme types. Within two weeks, the upper 5 m of the epilimnion was devoid of Daphnia, and guts of perch were predominantly filled with MMMF. The daphnids in the gut and the lake did not differ in allozyme type composition. By the end of July, population density had increased again. The size and composition of the Daphnia population complex continuously changed during the study period, as did the depth distribution of the components. Different genotypes within the population complex seem to have developed different strategies to cope with starvation and predation and the state at a particular moment can be understood only if past and present factors are considered.     

A new method for estimating effective population sizes from a single sample of multilocus genotypes

Equations for the effective size ( N_e ) of a population were derived in terms of the frequencies of a pair of offspring taken at random from the population being sibs sharing the same one or two parents. Based on these equations, a novel method (called sibship assignment method) was proposed to infer N_e from the sibship frequencies estimated from a sibship assignment analysis, using the multilocus genotypes of a sample of offspring taken at random from a single cohort in a population. Comparative analyses of extensive simulated data and some empirical data clearly demonstrated that the sibship assignment method is much more accurate [measured by the root mean squared error, RMSE, of 1/(2 N_e )] than other methods such as the heterozygote excess method, the linkage disequilibrium method, and the temporal method. The RMSE of 1/(2 N_e ) from the sibship assignment method is typically a small fraction of that from other methods. The new method is also more general and flexible than other methods. It can be applied to populations with nonoverlapping generations of both diploid and haplodiploid species under random or nonrandom mating, using either codominant or dominant markers. It can also be applied to the estimation of N_e for a subpopulation with immigration. With some modification, it could be applied to monoecious diploid populations with self-fertilization, and to populations with overlapping generations.     

Characterization of discrete and continuous modes of visual pattern discrimination

Discrete and continuous modes of visual pattern discrimination performance are analyzed using a model for the investigation of discrete internal pattern representations described in previous papers (Foster, 1980a, b). A simple quantitative criterion is derived to characterize the two kinds of visual discrimination performance. Values predicted by this criterion are then compared with values obtained from experimental data.     

Population history in Arabidopsis halleri using multilocus analysis

A. halleri is a psuedometallophyte with a patchy distribution in Europe and is often spread by human activity. To determine the population history and whether this history is consistent with potential human effects, we surveyed nucleotide variation using 24 loci from 12 individuals in a large A. halleri population. The means of total and silent nucleotide variation (θ_W) are within the range expected for the species. The population genetic neutrality tests Tajima’s D and Wall’s B had significant composite results rejecting panmixia, and Approximate Bayesian Computation analysis revealed that a subdivision model better explained the variation than the standard neutral model, refugia (or admixture), bottleneck or change of population size models. A categorical regression analysis further supports the subdivision model, and under the subdivision model, the neutrality tests are no longer significant. The best support was for two source populations, a situation consistent with the mixing of two populations possibly mediated by human activity. This scenario might limit the genetic diversity and adaptive potential of the population. The non‐neutral population variation described here should be considered in bioinformatic searches for adaptation.     

Bayesian identification of admixture events using multilocus molecular markers

Bayesian statistical methods for the estimation of hidden genetic structure of populations have gained considerable popularity in the recent years. Utilizing molecular marker data, Bayesian mixture models attempt to identify a hidden population structure by clustering individuals into genetically divergent groups, whereas admixture models target at separating the ancestral sources of the alleles observed in different individuals. We discuss the difficulties involved in the simultaneous estimation of the number of ancestral populations and the levels of admixture in studied individuals' genomes. To resolve this issue, we introduce a computationally efficient method for the identification of admixture events in the population history. Our approach is illustrated by analyses of several challenging real and simulated data sets. The software (baps), implementing the methods introduced here, is freely available at http://www.rni.helsinki.fi/~jic/bapspage.html.     

Calculating bootstrap probabilities of phylogeny using multilocus sequence data

Phylogeny estimation is extremely crucial in the study of molecular evolution. The increase in the amount of available genomic data facilitates phylogeny estimation from multilocus sequence data. Although maximum likelihood and Bayesian methods are available for phylogeny reconstruction using multilocus sequence data, these methods require heavy computation, and their application is limited to the analysis of a moderate number of genes and taxa. Distance matrix methods present suitable alternatives for analyzing huge amounts of sequence data. However, the manner in which distance methods can be applied to multilocus sequence data remains unknown. Here, we suggest new procedures to estimate molecular phylogeny using multilocus sequence data and evaluate its significance in the framework of the distance method. We found that concatenation of the multilocus sequence data may result in incorrect phylogeny estimation with an extremely high bootstrap probability (BP), which is due to incorrect estimation of the distances and intentional ignorance of the intergene variations. Therefore, we suggest that the distance matrices for multilocus sequence data be estimated separately and these matrices be subsequently combined to reconstruct phylogeny instead of phylogeny reconstruction using concatenated sequence data. To calculate the BPs of the reconstructed phylogeny, we suggest that 2-stage bootstrap procedures be adopted; in this, genes are resampled followed by resampling of the sequence columns within the resampled genes. By resampling the genes during calculation of BPs, intergene variations are properly considered. Via simulation studies and empirical data analysis, we demonstrate that our 2-stage bootstrap procedures are more suitable than the conventional bootstrap procedure that is adopted after sequence concatenation.     

Identification of endangered Hawaiian ducks (Anas wyvilliana), introduced North American mallards (A. platyrhynchos) and their hybrids using multilocus genotypes

Hawaiian ducks (Anas wyvilliana), or koloa, are endemic to the Hawaiian Islands and are listed as a federal and state endangered species. Hybridization between koloa and introduced mallards (A. platyrhynchos) is believed to be a primary threat to the recovery of koloa. We evaluated the utility of two sets of nuclear markers (microsatellite loci and amplified fragment length polymorphisms) and a variable portion of the mitochondrial DNA control region to distinguish among koloa, mallards, and hybrids. We show that microsatellite and AFLP markers can be used to distinguish between koloa and mallard-koloa hybrids with a high degree of confidence. For all but one of the putative koloa in our sample, the posterior probability of belonging to the koloa category was >0.90. Similarly all but one of the mallard-koloa hybrids were assigned to the hybrid category with posterior probabilities >0.98. Subsets of markers led to poorer resolution among koloa, mallard and hybrid categories. Among a sample of 61 koloa, hybrids and mallards, we found 25 different mtDNA haplotypes, belonging to two groups of haplotypes (A and B) identified previously in mallards and their relatives. All putative koloa samples exhibited group B haplotypes, of which 65% comprised one haplotype, while the rest were divided among four haplotypes. All Hawai’i mallard samples exhibited haplotypes that belonged to group A. Hybrids and California mallards exhibited haplotypes belonging to both groups, but a majority were of group A, suggesting that hybridization may more commonly involve mating between Hawai’i mallard females and koloa males.     

Utility of multilocus genotypes for taxon assignment in stands of closely related European white oaks from Switzerland

Background and Aims

European white oaks (Quercus petraea, Q. pubescens, Q. robur) have long puzzled plant biologists owing to disputed species differentiation. Extensive hybridization or shared ancestry have been proposed as alternative hypotheses to explain why genetic differentiation between these oak species is low. Species delimitation is usually weak and often shows gradual transitions in leaf morphology. Hence, individual identification may be difficult, but remains a critical step for both scientific work and practical management.

Methods

Multilocus genotype data (five nuclear microsatellites) were used from ten Swiss oak stands for taxon identification without a priori grouping of individuals or populations, using model-based Bayesian assignment tests.

Key Results

Three groups best structured the data, indicating that the taxonomical signal was stronger than the spatial signal. Most individuals showed high posterior probabilities for either of three genetic groups that were best circumscribed as taxonomical units. The assignment of a subset of trees, whose taxonomic status had been previously characterized in detail, supported this classification scheme.

Conclusions

Molecular-genetic assignment tests are useful in the identification of species status in critical taxon complexes such as the European white oaks. Such an approach is of practical importance for forest management, e.g. for stand certification or in seed trade to trace the origin of forest products.Key words: Assignment test, Bayesian inference, multilocus genotype, nuclear microsatellites, Quercus sp., species complex