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.     

Bayesian joint mapping of quantitative trait loci for Gaussian and categorical characters in line crosses

Methodology for joint mapping of quantitative trait loci (QTL) affecting continuous and binary characters in experimental crosses is presented. The procedure consists of a Bayesian Gaussian-threshold model implemented via Markov chain Monte Carlo, which bypasses bottlenecks due to high-dimensional integrals required in maximum likelihood approaches. The method handles multiple binary traits and multiple QTL. Modeling of ordered categorical traits is discussed as well. Features of the method are illustrated using simulated datasets representing a backcross design, and the data are analyzed using mixed-trait and single-trait models. The mixed-trait analysis provides greater detection power of a QTL than a single-trait analysis when the QTL affects two or more traits. The number of QTL inferred in the mixed-trait analysis does not pertain to a specific trait, but the roles of each QTL on specific traits can be assessed from estimates of its effects. The impacts of varying incidence level and sample size on the mixed-trait QTL mapping analysis are investigated as well.     

Methodologies for segregation analysis and QTL mapping in plants

Most characters of biological interest and economic importance are quantitative traits. To uncover the genetic architecture of quantitative traits, two approaches have become popular in China. One is the establishment of an analytical model for mixed major-gene plus polygenes inheritance and the other the discovery of quantitative trait locus (QTL). Here we review our progress employing these two approaches. First, we proposed joint segregation analysis of multiple generations for mixed major-gene plus polygenes inheritance. Second, we extended the multilocus method of Lander and Green (1987), Jiang and Zeng (1997) to a more generalized approach. Our methodology handles distorted, dominant and missing markers, including the effect of linked segregation distortion loci on the estimation of map distance. Finally, we developed several QTL mapping methods. In the Bayesian shrinkage estimation (BSE) method, we suggested a method to test the significance of QTL effects and studied the effect of the prior distribution of the variance of QTL effect on QTL mapping. To reduce running time, a penalized maximum likelihood method was adopted. To mine novel genes in crop inbred lines generated in the course of normal crop breeding work, three methods were introduced. If a well-documented genealogical history of the lines is available, two-stage variance component analysis and multi-QTL Haseman-Elston regression were suggested; if unavailable, multiple loci in silico mapping was proposed.     

Using molecular markers to map multiple quantitative trait loci: models for backcross,recombinant inbred,and doubled haploid progeny

Summary To maximize parameter estimation efficiency and statistical power and to estimate epistasis, the parameters of multiple quantitative trait loci (QTLs) must be simultaneously estimated. If multiple QTL affect a trait, then estimates of means of QTL genotypes from individual locus models are statistically biased. In this paper, I describe methods for estimating means of QTL genotypes and recombination frequencies between marker and quantitative trait loci using multilocus backcross, doubled haploid, recombinant inbred, and testcross progeny models. Expected values of marker genotype means were defined using no double or multiple crossover frequencies and flanking markers for linked and unlinked quantitative trait loci. The expected values for a particular model comprise a system of nonlinear equations that can be solved using an interative algorithm, e.g., the Gauss-Newton algorithm. The solutions are maximum likelihood estimates when the errors are normally distributed. A linear model for estimating the parameters of unlinked quantitative trait loci was found by transforming the nonlinear model. Recombination frequency estimators were defined using this linear model. Certain means of linked QTLs are less efficiently estimated than means of unlinked QTLs.     

A Simple Regression-Based Method to Map Quantitative Trait Loci Underlying Function-Valued Phenotypes

Most statistical methods for quantitative trait loci (QTL) mapping focus on a single phenotype. However, multiple phenotypes are commonly measured, and recent technological advances have greatly simplified the automated acquisition of numerous phenotypes, including function-valued phenotypes, such as growth measured over time. While methods exist for QTL mapping with function-valued phenotypes, they are generally computationally intensive and focus on single-QTL models. We propose two simple, fast methods that maintain high power and precision and are amenable to extensions with multiple-QTL models using a penalized likelihood approach. After identifying multiple QTL by these approaches, we can view the function-valued QTL effects to provide a deeper understanding of the underlying processes. Our methods have been implemented as a package for R, funqtl.     

A comparison between methods for linkage disequilibrium fine mapping of quantitative trait loci

We present a maximum likelihood method for mapping quantitative trait loci that uses linkage disequilibrium information from single and multiple markers. We made paired comparisons between analyses using a single marker, two markers and six markers. We also compared the method to single marker regression analysis under several scenarios using simulated data. In general, our method outperformed regression (smaller mean square error and confidence intervals of location estimate) for quantitative trait loci with dominance effects. In addition, the method provides estimates of the frequency and additive and dominance effects of the quantitative trait locus.     

Linkage disequilibrium fine mapping of quantitative trait loci: A simulation study

Recently, the use of linkage disequilibrium (LD) to locate genes which affect quantitative traits (QTL) has received an increasing interest, but the plausibility of fine mapping using linkage disequilibrium techniques for QTL has not been well studied. The main objectives of this work were to (1) measure the extent and pattern of LD between a putative QTL and nearby markers in finite populations and (2) investigate the usefulness of LD in fine mapping QTL in simulated populations using a dense map of multiallelic or biallelic marker loci. The test of association between a marker and QTL and the power of the test were calculated based on single-marker regression analysis. The results show the presence of substantial linkage disequilibrium with closely linked marker loci after 100 to 200 generations of random mating. Although the power to test the association with a frequent QTL of large effect was satisfactory, the power was low for the QTL with a small effect and/or low frequency. More powerful, multi-locus methods may be required to map low frequent QTL with small genetic effects, as well as combining both linkage and linkage disequilibrium information. The results also showed that multiallelic markers are more useful than biallelic markers to detect linkage disequilibrium and association at an equal distance.     

Maximum Likelihood Mapping of Quantitative Trait Loci Using Full-Sib Families

A maximum likelihood method is presented for the detection of quantitative trait loci (QTL) using flanking markers in full-sib families. This method incorporates a random component for common family effects due to additional QTL or the environment. Simulated data have been used to investigate this method. With a fixed total number of full sibs power of detection decreased substantially with decreasing family size. Increasing the number of alleles at the marker loci (i.e., polymorphism information content) and decreasing the interval size about the QTL increased power. Flanking markers were more powerful than single markers. In testing for a linked QTL the test must be made against a model which allows for between family variation (i.e., including an unlinked QTL or a between family variance component) or the test statistic may be grossly inflated. Mean parameter estimates were close to the simulated values in all situations when fitting the full model (including a linked QTL and common family effect). If the common family component was omitted the QTL effect was overestimated in data in which additional genetic variance was simulated and when compared with an unlinked QTL model there was reduced power. The test statistic curves, reflecting the likelihood of the QTL at each position along the chromosome, have discontinuities at the markers caused by adjacent pairs of markers providing different amounts of information. This must be accounted for when using flanking markers to search for a QTL in an outbred population.     

Novel linkage mapping approach using DNA pooling in human and animal genetics. II. Detection of quantitative traits loci in dairy cattle

Selective DNA pooling is an advanced methodology for linkage mapping of quantitative trait loci (QTL) in farm animals. The principle is based on densitometric estimates of marker allele frequency in pooled DNA samples of phenotypically extreme individuals from half-sib, backcross and F(2) experimental designs in farm animals. This methodology provides a rapid and efficient analysis of a large number of individuals with short tandem repeat markers that are essential to detect QTL through the genome - wide searching approach. Several strategies involving whole genome scanning with a high statistical power have been developed for systematic search to detect the quantitative traits loci and linked loci of complex traits. In recent studies, greater success has been achieved in mapping several QTLs in Israel-Holstein cattle using selective DNA pooling. This paper outlines the currently emerged novel strategies of linkage mapping to identify QTL based on selective DNA pooling with more emphasis on its theoretical pre-requisite to detect linked QTLs, applications, a general theory for experimental half-sib designs, the power of statistics and its feasibility to identify genetic markers linked QTL in dairy cattle. The study reveals that the application of selective DNA pooling in dairy cattle can be best exploited in the genome-wide detection of linked loci with small and large QTL effects and applied to a moderately sized half-sib family of about 500 animals.     

High Resolution of Quantitative Traits into Multiple Loci via Interval Mapping

A very general method is described for multiple linear regression of a quantitative phenotype on genotype [putative quantitative trait loci (QTLs) and markers] in segregating generations obtained from line crosses. The method exploits two features, (a) the use of additional parental and F(1) data, which fixes the joint QTL effects and the environmental error, and (b) the use of markers as cofactors, which reduces the genetic background noise. As a result, a significant increase of QTL detection power is achieved in comparison with conventional QTL mapping. The core of the method is the completion of any missing genotypic (QTL and marker) observations, which is embedded in a general and simple expectation maximization (EM) algorithm to obtain maximum likelihood estimates of the model parameters. The method is described in detail for the analysis of an F(2) generation. Because of the generality of the approach, it is easily applicable to other generations, such as backcross progenies and recombinant inbred lines. An example is presented in which multiple QTLs for plant height in tomato are mapped in an F(2) progeny, using additional data from the parents and their F(1) progeny.     

Interval mapping of quantitative trait loci for time-to-event data with the proportional hazards mixture cure model

Interval mapping using normal mixture models has been an important tool for analyzing quantitative traits in experimental organisms. When the primary phenotype is time-to-event, it is natural to use survival models such as Cox's proportional hazards model instead of normal mixtures to model the phenotype distribution. An extra challenge for modeling time-to-event data is that the underlying population may consist of susceptible and nonsusceptible subjects. In this article, we propose a semiparametric proportional hazards mixture cure model which allows missing covariates. We discuss applications to quantitative trait loci (QTL) mapping when the primary trait is time-to-event from a population of mixed susceptibility. This model can be used to characterize QTL effects on both susceptibility and time-to-event distribution, and to estimate QTL location. The model can naturally incorporate covariate effects of other risk factors. Maximum likelihood estimates for the parameters in the model as well as their corresponding variance estimates can be obtained numerically using an EM-type algorithm. The proposed methods are assessed by simulations under practical settings and illustrated using a real data set containing survival times of mice after infection with Listeria monocytogenes. An extension to multiple intervals is also discussed.     

Mapping multiple Quantitative Trait Loci by Bayesian classification

We developed a classification approach to multiple quantitative trait loci (QTL) mapping built upon a Bayesian framework that incorporates the important prior information that most genotypic markers are not cotransmitted with a QTL or their QTL effects are negligible. The genetic effect of each marker is modeled using a three-component mixture prior with a class for markers having negligible effects and separate classes for markers having positive or negative effects on the trait. The posterior probability of a marker's classification provides a natural statistic for evaluating credibility of identified QTL. This approach performs well, especially with a large number of markers but a relatively small sample size. A heat map to visualize the results is proposed so as to allow investigators to be more or less conservative when identifying QTL. We validated the method using a well-characterized data set for barley heading values from the North American Barley Genome Mapping Project. Application of the method to a new data set revealed sex-specific QTL underlying differences in glucose-6-phosphate dehydrogenase enzyme activity between two Drosophila species. A simulation study demonstrated the power of this approach across levels of trait heritability and when marker data were sparse.     

Cross-validation in association mapping and its relevance for the estimation of QTL parameters of complex traits

Association mapping has become a widely applied genomic approach to identify quantitative trait loci (QTL) and dissect the genetic architecture of complex traits. However, approaches to assess the quality of the obtained QTL results are lacking. We therefore evaluated the potential of cross-validation in association mapping based on a large sugar beet data set. Our results show that the proportion of the population that should be used as estimation and validation sets, respectively, depends on the size of the mapping population. Generally, a fivefold cross-validation, that is, 20% of the lines as independent validation set, appears appropriate for commonly used population sizes. The predictive power for the proportion of genotypic variance explained by QTL was overestimated by on average 38% indicating a strong bias in the estimated QTL effects. The cross-validated predictive power ranged between 4 and 50%, which are more realistic estimates of this parameter for complex traits. In addition, QTL frequency distributions can be used to assess the precision of QTL position estimates and the robustness of the detected QTL. In summary, cross-validation can be a valuable tool to assess the quality of QTL parameters in association mapping.     

STAIRS: a new genetic resource for functional genomic studies of Arabidopsis

Many biologically and economically important traits in plants and animals are quantitative/multifactorial, being controlled by several quantitative trait loci (QTL). QTL are difficult to locate accurately by conventional methods using molecular markers in segregating populations, particularly for traits of low heritability or for QTL with small effects. In order to resolve this, large (often unrealistically large) populations are required. In this paper we present an alternative approach using a specially developed resource of lines that facilitate QTL location first to a particular chromosome, then to successively smaller regions within a chromosome (< or = 0.5 cM) by means of simple comparisons among a few lines. This resource consists of "Stepped Aligned Inbred Recombinant Strains" (STAIRS) plus single whole Chromosome Substitution Strains (CSSs). We explain the analytical power of STAIRS and illustrate their construction and use with Arabidopsis thaliana, although the principles could be applied to many organisms. We were able to locate flowering QTL at the top of chromosome 3 known to contain several potential candidate genes.     

家畜抗性等级性状的QTL定位方法

在广义线性模型的框架内模拟研究了家畜抗性等级性状的QTL定位方法,QTL参数的估计采用最大似然方法,比较了阈模型方法与一般线性方法的QTL定位效率,并对影响等级性状QTL定位效率的主要因素（QTL效应、性状的遗传力）进行了模拟研究,实验设计为多个家系的女儿设计,资源群体大小为500头。研究结果表明：在QTL位置参数估计及检验功效方面,阈模型方法具有一定的优势,对抗性等级性状QTL定位的功效也高于线性方法。另外,性状遗传力和QTL效应的大小对QTL定位的准确度也有直接的影响,随着性状遗传力QTL效应的     

Detecting Marker-Qtl Linkage and Estimating Qtl Gene Effect and Map Location Using a Saturated Genetic Map

A simulation study was carried out on a backcross population in order to determine the effect of marker spacing, gene effect and population size on the power of marker-quantitative trait loci (QTL) linkage experiments and on the standard error of maximum likelihood estimates (MLE) of QTL gene effect and map location. Power of detecting a QTL was virtually the same for a marker spacing of 10 cM as for an infinite number of markers and was only slightly decreased for marker spacing of 20 or even 50 cM. The advantage of using interval mapping as compared to single-marker analysis was slight. ``Resolving power' of a marker-QTL linkage experiment was defined as the 95% confidence interval for the QTL map location that would be obtained when scoring an infinite number of markers. It was found that reducing marker spacing below the resolving power did not add appreciably to narrowing the confidence interval. Thus, the 95% confidence interval with infinite markers sets the useful marker spacing for estimating QTL map location for a given population size and estimated gene effect.     

A simple and rapid method for calculating identity-by-descent matrices using multiple markers

A fast, partly recursive deterministic method for calculating Identity-by-Descent (IBD) probabilities was developed with the objective of using IBD in Quantitative Trait Locus (QTL) mapping. The method combined a recursive method for a single marker locus with a method to estimate IBD between sibs using multiple markers. Simulated data was used to compare the deterministic method developed in the present paper with a stochastic method (LOKI) for precision in estimating IBD probabilities and performance in the task of QTL detection with the variance component approach. This comparison was made in a variety of situations by varying family size and degree of polymorphism among marker loci. The following were observed for the deterministic method relative to MCMC: (i) it was an order of magnitude faster; (ii) its estimates of IBD probabilities were found to agree closely, even though it does not extract information when haplotypes are not known with certainty; (iii) the shape of the profile for the QTL test statistic as a function of location was similar, although the magnitude of the test statistic was slightly smaller; and (iv) the estimates of QTL variance was similar. It was concluded that the method proposed provided a rapid means of calculating the IBD matrix with only a small loss in precision, making it an attractive alternative to the use of stochastic MCMC methods. Furthermore, developments in marker technology providing denser maps would enhance the relative advantage of this method.     

A Model Selection Approach for the Identification of Quantitative Trait Loci in Experimental Crosses, Allowing Epistasis

The identification of quantitative trait loci (QTL) and their interactions is a crucial step toward the discovery of genes responsible for variation in experimental crosses. The problem is best viewed as one of model selection, and the most important aspect of the problem is the comparison of models of different sizes. We present a penalized likelihood approach, with penalties on QTL and pairwise interactions chosen to control false positive rates. This extends the work of Broman and Speed to allow for pairwise interactions among QTL. A conservative version of our penalized LOD score provides strict control over the rate of extraneous QTL and interactions; a more liberal criterion is more lenient on interactions but seeks to maintain control over the rate of inclusion of false loci. The key advance is that one needs only to specify a target false positive rate rather than a prior on the number of QTL and interactions. We illustrate the use of our model selection criteria as exploratory tools; simulation studies demonstrate reasonable power to detect QTL. Our liberal criterion is comparable in power to two Bayesian approaches.     

Mapping quantitative trait loci underlying triploid endosperm traits

Endosperm, which is derived from two polar nuclei fusing with one sperm, is a triploid tissue in cereals. Endosperm tissue determines the grain quality of cereals. Improving grain quality is one of the important breeding objectives in cereals. However, current statistical methods for mapping quantitative trait loci (QTL) under diploid genetic control have not been effective for dealing with endosperm traits because of the complexity of their triploid inheritance. In this paper, we derive for the first time the conditional probabilities of F(3) endosperm QTL genotypes given different flanking marker genotypes in F(2) plants. Using these probabilities, we develop a multiple linear regression method implemented via the iteratively reweighted least-squares (IRWLS) algorithm and a maximum likelihood method (ML) implemented via the expectation-maximization (EM) algorithm to map QTL underlying endosperm traits. We use the mean value of endosperm traits of F(3) seeds as the dependent variable and the expectations of genotypic indicators for additive and dominance effect of a putative QTL flanked by a pair of markers as independent variables for IRWLS mapping. However, if an endosperm trait is measured quantitatively using a single endosperm sample, the ML mapping method can be used to separate the two dominance effects. Efficiency of the methods is verified through extensive Monte Carlo simulation studies. Results of simulation show that the proposed methods provide accurate estimates of both the QTL effects and locations with very high statistical power. With these methods, we are now ready to map endosperm traits, as we can for regular quantitative trait under diploid control.