Mapping and analysis of quantitative trait loci in experimental populations

Simple statistical methods for the study of quantitative trait loci (QTL), such as analysis of variance, have given way to methods that involve several markers and high-resolution genetic maps. As a result, the mapping community has been provided with statistical and computational tools that have much greater power than ever before for studying and locating multiple and interacting QTL. Apart from their immediate practical applications, the lessons learnt from this evolution of QTL methodology might also be generally relevant to other types of functional genomics approach that are aimed at the dissection of complex phenotypes, such as microarray assessment of gene expression.     

QTL‐seq: rapid mapping of quantitative trait loci in rice by whole genome resequencing of DNA from two bulked populations

The majority of agronomically important crop traits are quantitative, meaning that they are controlled by multiple genes each with a small effect (quantitative trait loci, QTLs). Mapping and isolation of QTLs is important for efficient crop breeding by marker‐assisted selection (MAS) and for a better understanding of the molecular mechanisms underlying the traits. However, since it requires the development and selection of DNA markers for linkage analysis, QTL analysis has been time‐consuming and labor‐intensive. Here we report the rapid identification of plant QTLs by whole‐genome resequencing of DNAs from two populations each composed of 20–50 individuals showing extreme opposite trait values for a given phenotype in a segregating progeny. We propose to name this approach QTL‐seq as applied to plant species. We applied QTL‐seq to rice recombinant inbred lines and F₂ populations and successfully identified QTLs for important agronomic traits, such as partial resistance to the fungal rice blast disease and seedling vigor. Simulation study showed that QTL‐seq is able to detect QTLs over wide ranges of experimental variables, and the method can be generally applied in population genomics studies to rapidly identify genomic regions that underwent artificial or natural selective sweeps.     

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.     

Interval mapping of quantitative trait loci with selective DNA pooling data

Selective DNA pooling is an efficient method to identify chromosomal regions that harbor quantitative trait loci (QTL) by comparing marker allele frequencies in pooled DNA from phenotypically extreme individuals. Currently used single marker analysis methods can detect linkage of markers to a QTL but do not provide separate estimates of QTL position and effect, nor do they utilize the joint information from multiple markers. In this study, two interval mapping methods for analysis of selective DNA pooling data were developed and evaluated. One was based on least squares regression (LS-pool) and the other on approximate maximum likelihood (ML-pool). Both methods simultaneously utilize information from multiple markers and multiple families and can be applied to different family structures (half-sib, F2 cross and backcross). The results from these two interval mapping methods were compared with results from single marker analysis by simulation. The results indicate that both LS-pool and ML-pool provided greater power to detect the QTL than single marker analysis. They also provide separate estimates of QTL location and effect. With large family sizes, both LS-pool and ML-pool provided similar power and estimates of QTL location and effect as selective genotyping. With small family sizes, however, the LS-pool method resulted in severely biased estimates of QTL location for distal QTL but this bias was reduced with the ML-pool.     

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.     

Mapping quantitative trait loci in complex pedigrees: a two-step variance component approach

There is a growing need for the development of statistical techniques capable of mapping quantitative trait loci (QTL) in general outbred animal populations. Presently used variance component methods, which correctly account for the complex relationships that may exist between individuals, are challenged by the difficulties incurred through unknown marker genotypes, inbred individuals, partially or unknown marker phases, and multigenerational data. In this article, a two-step variance component approach that enables practitioners to routinely map QTL in populations with the aforementioned difficulties is explored. The performance of the QTL mapping methodology is assessed via its application to simulated data. The capacity of the technique to accurately estimate parameters is examined for a range of scenarios.     

Power of different sampling strategies to detect quantitative trait loci variance effects

Summary Many studies have shown that segregating quantitative trait loci (QTL) can be detected via linkage to genetic markers. Power to detect a QTL effect on the trait mean as a function of the number of individuals genotyped for the marker is increased by selectively genotyping individuals with extreme values for the quantitative trait. Computer simulations were employed to study the effect of various sampling strategies on the statistical power to detect QTL variance effects. If only individuals with extreme phenotypes for the quantitative trait are selected for genotyping, then power to detect a variance effect is less than by random sampling. If 0.2 of the total number of individuals genotyped are selected from the center of the distribution, then power to detect a variance effect is equal to that obtained with random selection. Power to detect a variance effect was maximum when 0.2 to 0.5 of the individuals selected for genotyping were selected from the tails of the distribution and the remainder from the center.     

Bayesian shrinkage analysis of quantitative trait Loci for dynamic traits

Many quantitative traits are measured repeatedly during the life of an organism. Such traits are called dynamic traits. The pattern of the changes of a dynamic trait is called the growth trajectory. Studying the growth trajectory may enhance our understanding of the genetic architecture of the growth trajectory. Recently, we developed an interval-mapping procedure to map QTL for dynamic traits under the maximum-likelihood framework. We fit the growth trajectory by Legendre polynomials. The method intended to map one QTL at a time and the entire QTL analysis involved scanning the entire genome by fitting multiple single-QTL models. In this study, we propose a Bayesian shrinkage analysis for estimating and mapping multiple QTL in a single model. The method is a combination between the shrinkage mapping for individual quantitative traits and the Legendre polynomial analysis for dynamic traits. The multiple-QTL model is implemented in two ways: (1) a fixed-interval approach where a QTL is placed in each marker interval and (2) a moving-interval approach where the position of a QTL can be searched in a range that covers many marker intervals. Simulation study shows that the Bayesian shrinkage method generates much better signals for QTL than the interval-mapping approach. We propose several alternative methods to present the results of the Bayesian shrinkage analysis. In particular, we found that the Wald test-statistic profile can serve as a mechanism to test the significance of a putative QTL.     

Multiple interval mapping for quantitative trait loci.

A new statistical method for mapping quantitative trait loci (QTL), called multiple interval mapping (MIM), is presented. It uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. With the MIM approach, the precision and power of QTL mapping could be improved. Also, epistasis between QTL, genotypic values of individuals, and heritabilities of quantitative traits can be readily estimated and analyzed. Using the MIM model, a stepwise selection procedure with likelihood ratio test statistic as a criterion is proposed to identify QTL. This MIM method was applied to a mapping data set of radiata pine on three traits: brown cone number, tree diameter, and branch quality scores. Based on the MIM result, seven, six, and five QTL were detected for the three traits, respectively. The detected QTL individually contributed from approximately 1 to 27% of the total genetic variation. Significant epistasis between four pairs of QTL in two traits was detected, and the four pairs of QTL contributed approximately 10.38 and 14.14% of the total genetic variation. The asymptotic variances of QTL positions and effects were also provided to construct the confidence intervals. The estimated heritabilities were 0.5606, 0.5226, and 0. 3630 for the three traits, respectively. With the estimated QTL effects and positions, the best strategy of marker-assisted selection for trait improvement for a specific purpose and requirement can be explored. The MIM FORTRAN program is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

Genetic mapping of quantitative trait loci for resistance to Haemonchus contortus in sheep

This paper presents results from a mapping experiment to detect quantitative trait loci (QTL) for resistance to Haemonchus contortus infestation in merino sheep. The primary trait analysed was faecal worm egg count in response to artificial challenge at 6 months of age. In the first stage of the experiment, whole genome linkage analysis was used for broad-scale mapping. The animal resource used was a designed flock comprising 571 individuals from four half-sib families. The average marker spacing was about 20 cM. For the primary trait, 11 QTL (as chromosomal/family combinations) were significant at the 5% chromosome-wide level, with allelic substitution effects of between 0.19 and 0.38 phenotypic standard deviation units. In general, these QTL did not have a significant effect on faecal worm egg count recorded at 13 months of age. In the second stage of the experiment, three promising regions (located on chromosomes 1, 3 and 4) were fine-mapped. This involved typing more closely spaced markers on individuals from the designed flock as well as an additional 495 individuals selected from a related population with a deeper pedigree. Analysis was performed using a linkage disequilibrium–linkage approach, under additive, dominant and multiple QTL models. Of these, the multiple QTL model resulted in the most refined QTL positions, with resolutions of <10 cM achieved for two regions. Because of the moderate size of effect of the QTL, and the apparent age and/or immune status specificity of the QTL, it is suggested that a panel of QTL will be required for significant genetic gains to be achieved within industry via marker-assisted selection.     

Genetical Genomics of Behavior: A Novel Chicken Genomic Model for Anxiety Behavior

The identification of genetic variants responsible for behavioral variation is an enduring goal in biology, with wide-scale ramifications, ranging from medical research to evolutionary theory on personality syndromes. Here, we use for the first time a large-scale genetical genomics analysis in the brains of chickens to identify genes affecting anxiety as measured by an open field test. We combine quantitative trait locus (QTL) analysis in 572 individuals and expression QTL (eQTL) analysis in 129 individuals from an advanced intercross between domestic chickens and Red Junglefowl. We identify 10 putative quantitative trait genes affecting anxiety behavior. These genes were tested for an association in the mouse Heterogeneous Stock anxiety (open field) data set and human GWAS data sets for bipolar disorder, major depressive disorder, and schizophrenia. Although comparisons between species are complex, associations were observed for four of the candidate genes in mice and three of the candidate genes in humans. Using a multimodel approach we have therefore identified a number of putative quantitative trait genes affecting anxiety behavior, principally in chickens but also with some potentially translational effects as well. This study demonstrates that chickens are an excellent model organism for the genetic dissection of behavior.     

Optimum spacing of genetic markers for determining linkage between marker loci and quantitative trait loci

The cost of experiments aimed at determining linkage between marker loci and quantitative trait loci (QTL) was investigated as a function of marker spacing and number of individuals scored. It was found that for a variety of experimental designs, fairly wide marker spacings (ca. 50 cM) are optimum or close to optimum for initial studies of marker-QTL linkage, in the sense of minimizing overall cost of the experiment. Thus, even when large numbers of more or less evenly spaced markers are available, it will not always be cost effective to make full utilization of this capacity. This is particularly true when costs of rearing and trait evaluation per individual scored are low, as when marker data are obtained on individuals raised and evaluated for quantitative traits as part of existing programs. When costs of rearing and trait evaluation per individual scored are high, however, as in human family data collection carried out primarily for subsequent marker — QTL analyses, or when plants or animals are raised specifically for purposes of marker — QTL linkage experiments, optimum spacing may be rather narrow. It is noteworthy that when marginal costs of additional markers or individuals are constant, total resources allocated to a given experiment will determine total number of individuals sampled, but not the optimal marker spacing.     

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.     

Improving quantitative trait loci mapping resolution in experimental crosses by the use of genotypically selected samples

One of the key factors contributing to the success of a quantitative trait locus (QTL) mapping experiment is the precision with which QTL positions can be estimated. We show, using simulations, that QTL mapping precision for an experimental cross can be increased by the use of a genotypically selected sample of individuals rather than an unselected sample of the same size. Selection is performed using a previously described method that optimizes the complementarity of the crossover sites within the sample. Although the increase in precision is accompanied by a decrease in QTL detection power at markers distant from QTL, only a modest increase in marker density is needed to obtain equivalent power over the whole map. Selected samples also show a slight reduction in the number of false-positive QTL. We find that two features of selected samples independently contribute to these effects: an increase in the number of crossover sites and increased evenness in crossover spacing. We provide an empirical formula for crossover enrichment in selected samples that is useful in experimental design and data analysis. For QTL studies in which the phenotyping is more of a limiting factor than the generation of individuals and the scoring of genotypes, selective sampling is an attractive strategy for increasing genome-wide QTL map resolution.