Prediction of identity by descent probabilities from marker-haplotypes

The prediction of identity by descent (IBD) probabilities is essential for all methods that map quantitative trait loci (QTL). The IBD probabilities may be predicted from marker genotypes and/or pedigree information. Here, a method is presented that predicts IBD probabilities at a given chromosomal location given data on a haplotype of markers spanning that position. The method is based on a simplification of the coalescence process, and assumes that the number of generations since the base population and effective population size is known, although effective size may be estimated from the data. The probability that two gametes are IBD at a particular locus increases as the number of markers surrounding the locus with identical alleles increases. This effect is more pronounced when effective population size is high. Hence as effective population size increases, the IBD probabilities become more sensitive to the marker data which should favour finer scale mapping of the QTL. The IBD probability prediction method was developed for the situation where the pedigree of the animals was unknown (i.e. all information came from the marker genotypes), and the situation where, say T, generations of unknown pedigree are followed by some generations where pedigree and marker genotypes are known.     

Mapping quantitative trait loci by genotyping haploid tissues.

Mapping strategies based on a half- or full-sib family design have been developed to map quantitative trait loci (QTL) for outcrossing species. However, these strategies are dependent on controlled crosses where marker-allelic frequency and linkage disequilibrium between the marker and QTL may limit their application. In this article, a maximum-likelihood method is developed to map QTL segregating in an open-pollinated progeny population using dominant markers derived from haploid tissues from single meiotic events. Results from the haploid-based mapping strategy are not influenced by the allelic frequencies of markers and their linkage disequilibria with QTL, because the probabilities of QTL genotypes conditional on marker genotypes of haploid tissues are independent of these population parameters. Parameter estimation and hypothesis testing are implemented via expectation/conditional maximization algorithm. Parameters estimated include the additive effect, the dominant effect, the population mean, the chromosomal location of the QTL in the interval, and the residual variance within the QTL genotypes, plus two population parameters, outcrossing rate and QTL-allelic frequency. Simulation experiments show that the accuracy and power of parameter estimates are affected by the magnitude of QTL effects, heritability levels of a trait, and sample sizes used. The application and limitation of the method are discussed.     

Optimum design of family structure and allocation of resources in association mapping with lines from multiple crosses

Family mapping is based on multiple segregating families and is becoming increasingly popular because of its advantages over population mapping. Athough much progress has been made recently, the optimum design and allocation of resources for family mapping remains unclear. Here, we addressed these issues using a simulation study, resample model averaging and cross-validation approaches. Our results show that in family mapping, the predictive power and the accuracy of quatitative trait loci (QTL) detection depend greatly on the population size and phenotyping intensity. With small population sizes or few test environments, QTL results become unreliable and are hampered by a large bias in the estimation of the proportion of genotypic variance explained by the detected QTL. In addition, we observed that even though good results can be achieved with low marker densities, no plateau is reached with our full marker complement. This suggests that higher quality results could be achieved with greater marker densities or sequence data, which will be available in the near future for many species.     

Detection of quantitative trait loci in outbred populations with incomplete marker data.

Augmentation of marker genotypes for ungenotyped individuals is implemented in a Bayesian approach via the use of Markov chain Monte Carlo techniques. Marker data on relatives and phenotypes are combined to compute conditional posterior probabilities for marker genotypes of ungenotyped individuals. The presented procedure allows the analysis of complex pedigrees with ungenotyped individuals to detect segregating quantitative trait loci (QTL). Allelic effects at the QTL were assumed to follow a normal distribution with a covariance matrix based on known QTL position and identity by descent probabilities derived from flanking markers. The Bayesian approach estimates variance due to the single QTL, together with polygenic and residual variance. The method was empirically tested through analyzing simulated data from a complex granddaughter design. Ungenotyped dams were related to one or more sons or grandsires in the design. Heterozygosity of the marker loci and size of QTL were varied. Simulation results indicated a significant increase in power when ungenotyped dams were included in the analysis.     

Mapping disease genes: family-based association studies.

With recent rapid advances in mapping of the human genome, including highly polymorphic and closely linked markers, studies of marker associations with disease are increasingly relevant for mapping disease genes. The use of nuclear-family data in association studies was initially developed to avoid possible ethnic mismatching between patients and randomly ascertained controls. The parental marker alleles not transmitted to an affected child or never transmitted to an affected sib pair form the so-called AFBAC (affected family-based controls) population. In this paper, the theoretical foundation of the AFBAC method is proved for any single-locus model of disease and for any nuclear family-based ascertainment scheme. In a random-mating population, when there is a marker association with disease, the AFBAC population provides an unbiased estimate of the overall population (control) marker alleles when the recombination fraction (theta) between the marker and disease genes is sufficiently small that it can be taken as zero (theta = 0). With population stratification, only marker associations present in the subpopulations will be detected with family-based analyses. Of more importance, however, is the fact that, when theta not equal to 0, differences between transmitted parental (patient) marker allele frequencies and non- or never-transmitted parental marker allele frequencies (implying a marker association with disease) can only be observed for marker genes linked to a disease gene (theta < 1/2). Thus, associations of unlinked marker loci with disease at the population level, caused by population stratification, migration, or admixture, are eliminated. This validates the use of family-based association tests as an appropriate strategy for mapping disease genes.     

Efficient marker-based recurrent selection for multiple quantitative trait loci

We studied the efficiency of recurrent selection based solely on marker genotypes (marker-based selection), in order to increase favourable allele frequency at 50 previously detected quantitative trait loci (QTLs). Two selection procedures were investigated, using computer simulations: (1) Truncation Selection (MTS), in which individuals are ranked based on marker score, and best individuals are selected for recombination; and (2) QTL Complementation Selection (QCS), in which individuals are selected such that their QTL composition complements those individuals already selected. Provided QTL locations are accurate, marker-based selection with a population size of 200 was very effective in rapidly increasing frequencies of favourable QTL alleles. QCS methods were more effective than MTS for improving the mean frequency and fixation of favourable QTL alleles. Marker-based selection was not very sensitive to a reduction in population size, and appears valuable to optimize the use of molecular markers in recurrent selection programmes.     

Bayesian point estimation of quantitative trait loci

In this article, we consider the problem of the estimation of quantitative trait loci (QTL), those chromosomal regions at which genetic information affecting some quantitative trait is encoded. Generally the number of such encoding sites is unknown, and associations between neutral molecular marker genotypes and observed trait phenotypes are sought to locate them. We consider a Bayesian model for simple experimental designs, and discuss the existing approaches to inference for this problem. In particular, we focus on locating positions of the best candidate markers segregating for the trait, a situation which is of primary interest in comparative mapping. We introduce a loss function for estimating both the number of QTL and their location, and we illustrate its application via simulated and real data.     

Power of two and three-generation QTL mapping experiments in an outbred population containing full-sib or half-sib families

QTL mapping experiments involve many animals to be genotyped and performance tested. Consequently, experimental designs need to be optimized to minimize the costs of data collection and genotyping. The present study has analyzed the power and efficiency of experiments with two or three-generation family structures containing full-sib families, half-sib families, or both. The focus was on data from one outbred population because the main interest is to locate genes that can be used for within-line selection. For a two generation experiment more animals had to be typed for marker loci to obtain a certain power than for a three generation experiment. Fewer trait values, however, had to be obtained for a two-generation experiment than for a three-generation experiment. A two or three-generation family structure with full-sib offspring was more efficient than a two or three-generation family structure with half-sib offspring. A family structure with full-sib grand-offspring, however, was less efficient than a family structure with half-sib grand-offspring. For the most efficient family structure each pair of parents had full-sib offspring that were genotyped for the marker. For the most-efficient family structure each full-sib offspring had half-sib grand-offspring for which trait values were obtained. For equal power with a heritability of 0.1 and 100 grand-offspring per full-sib offspring, 30-times less marker typings were required for this most efficient family structure than for a two-generation half-sib structure in which marker genotypes and trait values were obtained for half-sib offspring. The effect of heritability and the type of analysis (single marker or interval analysis) on the efficiency of a family structure is described. The results of this study should help to design QTL mapping experiments in an outbred population.     

Fractioned DNA pooling: a new cost-effective strategy for fine mapping of quantitative trait loci

Selective DNA pooling (SDP) is a cost-effective means for an initial scan for linkage between marker and quantitative trait loci (QTL) in suitable populations. The method is based on scoring marker allele frequencies in DNA pools from the tails of the population trait distribution. Various analytical approaches have been proposed for QTL detection using data on multiple families with SDP analysis. This article presents a new experimental procedure, fractioned-pool design (FPD), aimed to increase the reliability of SDP mapping results, by "fractioning" the tails of the population distribution into independent subpools. FPD is a conceptual and structural modification of SDP that allows for the first time the use of permutation tests for QTL detection rather than relying on presumed asymptotic distributions of the test statistics. For situations of family and cross mapping design we propose a spectrum of new tools for QTL mapping in FPD that were previously possible only with individual genotyping. These include: joint analysis of multiple families and multiple markers across a chromosome, even when the marker loci are only partly shared among families; detection of families segregating (heterozygous) for the QTL; estimation of confidence intervals for the QTL position; and analysis of multiple-linked QTL. These new advantages are of special importance for pooling analysis with SNP chips. Combining SNP microarray analysis with DNA pooling can dramatically reduce the cost of screening large numbers of SNPs on large samples, making chip technology readily applicable for genomewide association mapping in humans and farm animals. This extension, however, will require additional, nontrivial, development of FPD analytical tools.     

Reconstructing parental genotypes when testing for linkage in the presence of association

Various family-based association methods have recently been proposed that allow testing for linkage in the presence of linkage disequilibrium between a marker and a disease even if there is only incomplete parental-genotype information. For some families, it may be possible to reconstruct missing parental genotypes from the genotypes of their offspring. Treating such a reconstructed family as if parental genotypes have been typed, however, can introduce bias. The reconstruction-combined transmission/disequilibrium test (RC-TDT) and its X-chromosomal counterpart, XRC-TDT, employ parental-genotype reconstruction and correct for the biases involved in this reconstruction without relying on population marker allele frequencies. For the two tests, exact P values can be obtained by numerically calculating the convolution of the null distributions corresponding to the families in the sample.     

QTL detection with bidirectional and unidirectional selective genotyping: marker-based and trait-based analyses

Selective genotyping of one or both phenotypic extremes of a population can be used to detect linkage between markers and quantitative trait loci (QTL) in situations in which full-population genotyping is too costly or not feasible, or where the objective is to rapidly screen large numbers of potential donors for useful alleles with large effects. Data may be subjected to 'trait-based' analysis, in which marker allele frequencies are compared between classes of progeny defined based on trait values, or to 'marker-based' analysis, in which trait means are compared between progeny classes defined based on marker genotypes. Here, bidirectional and unidirectional selective genotyping were simulated, using population sizes and selection intensities relevant to cereal breeding. Control of Type I error was usually adequate with marker-based analysis of variance or trait-based testing using the normal approximation of the binomial distribution. Bidirectional selective genotyping was more powerful than unidirectional. Trait-based analysis and marker-based analysis of variance were about equally powerful. With genotyping of the best 30 out of 500 lines (6%), a QTL explaining 15% of the phenotypic variance could be detected with a power of 0.8 when tests were conducted at a marker 10 cM from the QTL. With bidirectional selective genotyping, QTL with smaller effects and (or) QTL farther from the nearest marker could be detected. Similar QTL detection approaches were applied to data from a population of 436 recombinant inbred rice lines segregating for a large-effect QTL affecting grain yield under drought stress. That QTL was reliably detected by genotyping as few as 20 selected lines (4.5%). In experimental populations, selective genotyping can reduce costs of QTL detection, allowing larger numbers of potential donors to be screened for useful alleles with effects across different backgrounds. In plant breeding programs, selective genotyping can make it possible to detect QTL using even a limited number of progeny that have been retained after selection.     

QTL Express: mapping quantitative trait loci in simple and complex pedigrees

QTL Express is the first application for Quantitative Trait Locus (QTL) mapping in outbred populations with a web-based user interface. User input of three files containing a marker map, trait data and marker genotypes allows mapping of single or multiple QTL by the regression approach, with the option to perform permutation or bootstrap tests.     

A statistical framework for quantitative trait mapping

We describe a general statistical framework for the genetic analysis of quantitative trait data in inbred line crosses. Our main result is based on the observation that, by conditioning on the unobserved QTL genotypes, the problem can be split into two statistically independent and manageable parts. The first part involves only the relationship between the QTL and the phenotype. The second part involves only the location of the QTL in the genome. We developed a simple Monte Carlo algorithm to implement Bayesian QTL analysis. This algorithm simulates multiple versions of complete genotype information on a genomewide grid of locations using information in the marker genotype data. Weights are assigned to the simulated genotypes to capture information in the phenotype data. The weighted complete genotypes are used to approximate quantities needed for statistical inference of QTL locations and effect sizes. One advantage of this approach is that only the weights are recomputed as the analyst considers different candidate models. This device allows the analyst to focus on modeling and model comparisons. The proposed framework can accommodate multiple interacting QTL, nonnormal and multivariate phenotypes, covariates, missing genotype data, and genotyping errors in any type of inbred line cross. A software tool implementing this procedure is available. We demonstrate our approach to QTL analysis using data from a mouse backcross population that is segregating multiple interacting QTL associated with salt-induced hypertension.     

QTL fine mapping by measuring and testing for Hardy-Weinberg and linkage disequilibrium at a series of linked marker loci in extreme samples of populations

It has recently been demonstrated that fine-scale mapping of a susceptibility locus for a complex disease can be accomplished on the basis of deviations from Hardy-Weinberg (HW) equilibrium at closely linked marker loci among affected individuals. We extend this theory to fine-scale localization of a quantitative-trait locus (QTL) from extreme individuals in populations, by means of HW and linkage-disequilibrium (LD) analyses. QTL mapping and/or linkage analyses can establish a large genomic region ( approximately 30 cM) that contains a QTL. The QTL can be fine mapped by examination of the degree of deviation from HW and LD at a series of closely linked marker loci. The tests can be performed for samples of individuals belonging to either high or low percentiles of the phenotype distribution or for combined samples of these extreme individuals. The statistical properties (the power and the size) of the tests of this fine-mapping approach are investigated and are compared extensively, under various genetic models and parameters for the QTL and marker loci. On the basis of the results, a two-stage procedure that uses extreme samples and different tests (for HW and LD) is suggested for QTL fine mapping. This two-step procedure is economic and powerful and can accurately narrow a genomic region containing a QTL from approximately 30-1 cM, a range that renders physical mapping feasible for identification of the QTL. In addition, the relationship between parameterizations of complex diseases, by means of penetrance, and those of complex quantitative traits, by means of genotypic values, is outlined. This means that many statistical genetic methods developed for searching for susceptibility loci of complex diseases can be directly adopted and/or extended to QTL mapping for quantitative traits.     

Optimal sampling of a population to determine QTL location, variance, and allelic number

In a population intended for breeding and selection, questions of interest relative to a specific segregating QTL are the variance it generates in the population, and the number and effects of its alleles. One approach to address these questions is to extract several inbreds from the population and use them to generate multiple mapping families. Given random sampling of parents, sampling strategy may be an important factor determining the power of the analysis and its accuracy in estimating QTL variance and allelic number. We describe appropriate multiple-family QTL mapping methodology and apply it to simulated data sets to determine optimal sampling strategies in terms of family number versus family size. Genomes were simulated with seven chromosomes, on which 107 markers and six QTL were distributed. The total heritability was 0.60. Two to ten alleles were segregating at each QTL. Sampling strategies ranged from sampling two inbreds and generating a single family of 600 progeny to sampling 40 inbreds and generating 40 families of 15 progeny each. Strategies involving only one to five families were subject to variation due to the sampling of inbred parents. For QTL where more than two alleles were segregating, these strategies did not sample QTL alleles representative of the original population. Conversely, strategies involving 30 or more parents were subject to variation due to sampling of QTL genotypes within the small families obtained. Given these constraints, greatest QTL detection power was obtained for strategies involving five to ten mapping families. The most accurate estimation of the variance generated by the QTL, however, was obtained with strategies involving 20 or more families. Finally, strategies with an intermediate number of families best estimated the number of QTL alleles. We conclude that no overall optimal sampling strategy exists but that the strategy adopted must depend on the objective.Communicated by P. Langridge     

Development of a near-isogenic line population of Arabidopsis thaliana and comparison of mapping power with a recombinant inbred line population

In Arabidopsis recombinant inbred line (RIL) populations are widely used for quantitative trait locus (QTL) analyses. However, mapping analyses with this type of population can be limited because of the masking effects of major QTL and epistatic interactions of multiple QTL. An alternative type of immortal experimental population commonly used in plant species are sets of introgression lines. Here we introduce the development of a genomewide coverage near-isogenic line (NIL) population of Arabidopsis thaliana, by introgressing genomic regions from the Cape Verde Islands (Cvi) accession into the Landsberg erecta (Ler) genetic background. We have empirically compared the QTL mapping power of this new population with an already existing RIL population derived from the same parents. For that, we analyzed and mapped QTL affecting six developmental traits with different heritability. Overall, in the NIL population smaller-effect QTL than in the RIL population could be detected although the localization resolution was lower. Furthermore, we estimated the effect of population size and of the number of replicates on the detection power of QTL affecting the developmental traits. In general, population size is more important than the number of replicates to increase the mapping power of RILs, whereas for NILs several replicates are absolutely required. These analyses are expected to facilitate experimental design for QTL mapping using these two common types of segregating populations.     

Interactions between markers can be caused by the dominance effect of quantitative trait loci

F₂ populations are commonly used in genetic studies of animals and plants. For simplicity, most quantitative trait locus or loci (QTL) mapping methods have been developed on the basis of populations having two distinct genotypes at each polymorphic marker or gene locus. In this study, we demonstrate that dominance can cause the interactions between markers and propose an inclusive linear model that includes marker variables and marker interactions so as to completely control both additive and dominance effects of QTL. The proposed linear model is the theoretical basis for inclusive composite-interval QTL mapping (ICIM) for F₂ populations, which consists of two steps: first, the best regression model is selected by stepwise regression, which approximately identifies markers and marker interactions explaining both additive and dominance variations; second, the interval mapping approach is applied to the phenotypic values adjusted by the regression model selected in the first step. Due to the limited mapping population size, the large number of variables, and multicollinearity between variables, coefficients in the inclusive linear model cannot be accurately determined in the first step. Interval mapping is necessary in the second step to fine tune the QTL to their true positions. The efficiency of including marker interactions in mapping additive and dominance QTL was demonstrated by extensive simulations using three QTL distribution models with two population sizes and an actual rice F₂ population.     

Bayesian methods for quantitative trait loci mapping based on model selection: approximate analysis using the Bayesian information criterion.

We describe an approximate method for the analysis of quantitative trait loci (QTL) based on model selection from multiple regression models with trait values regressed on marker genotypes, using a modification of the easily calculated Bayesian information criterion to estimate the posterior probability of models with various subsets of markers as variables. The BIC-delta criterion, with the parameter delta increasing the penalty for additional variables in a model, is further modified to incorporate prior information, and missing values are handled by multiple imputation. Marginal probabilities for model sizes are calculated, and the posterior probability of nonzero model size is interpreted as the posterior probability of existence of a QTL linked to one or more markers. The method is demonstrated on analysis of associations between wood density and markers on two linkage groups in Pinus radiata. Selection bias, which is the bias that results from using the same data to both select the variables in a model and estimate the coefficients, is shown to be a problem for commonly used non-Bayesian methods for QTL mapping, which do not average over alternative possible models that are consistent with the data.     

Power and precision of alternate methods for linkage disequilibrium mapping of quantitative trait loci

Linkage disequilibrium (LD) analysis in outbred populations uses historical recombinations to detect and fine map quantitative trait loci (QTL). Our objective was to evaluate the effect of various factors on power and precision of QTL detection and to compare LD mapping methods on the basis of regression and identity by descent (IBD) in populations of limited effective population size (N(e)). An 11-cM region with 6-38 segregating single-nucleotide polymorphisms (SNPs) and a central QTL was simulated. After 100 generations of random mating with N(e) of 50, 100, or 200, SNP genotypes and phenotypes were generated on 200, 500, or 1000 individuals with the QTL explaining 2 or 5% of phenotypic variance. To detect and map the QTL, phenotypes were regressed on genotypes or (assumed known) haplotypes, in comparison with the IBD method. Power and precision to detect QTL increased with sample size, marker density, and QTL effect. Power decreased with N(e), but precision was affected little by N(e). Single-marker regression had similar or greater power and precision than other regression models, and was comparable to the IBD method. Thus, for rapid initial screening of samples of adequate size in populations in which drift is the primary force that has created LD, QTL can be detected and mapped by regression on SNP genotypes without recovering haplotypes.     

Performance of single nucleotide polymorphisms versus haplotypes for genome-wide association analysis in barley

Genome-wide association studies (GWAS) may benefit from utilizing haplotype information for making marker-phenotype associations. Several rationales for grouping single nucleotide polymorphisms (SNPs) into haplotype blocks exist, but any advantage may depend on such factors as genetic architecture of traits, patterns of linkage disequilibrium in the study population, and marker density. The objective of this study was to explore the utility of haplotypes for GWAS in barley (Hordeum vulgare) to offer a first detailed look at this approach for identifying agronomically important genes in crops. To accomplish this, we used genotype and phenotype data from the Barley Coordinated Agricultural Project and constructed haplotypes using three different methods. Marker-trait associations were tested by the efficient mixed-model association algorithm (EMMA). When QTL were simulated using single SNPs dropped from the marker dataset, a simple sliding window performed as well or better than single SNPs or the more sophisticated methods of blocking SNPs into haplotypes. Moreover, the haplotype analyses performed better 1) when QTL were simulated as polymorphisms that arose subsequent to marker variants, and 2) in analysis of empirical heading date data. These results demonstrate that the information content of haplotypes is dependent on the particular mutational and recombinational history of the QTL and nearby markers. Analysis of the empirical data also confirmed our intuition that the distribution of QTL alleles in nature is often unlike the distribution of marker variants, and hence utilizing haplotype information could capture associations that would elude single SNPs. We recommend routine use of both single SNP and haplotype markers for GWAS to take advantage of the full information content of the genotype data.