Multiple-interval mapping for quantitative trait loci controlling endosperm traits

Endosperm traits are trisomic inheritant and are of great economic importance because they are usually directly related to grain quality. Mapping for quantitative trait loci (QTL) underlying endosperm traits can provide an efficient way to genetically improve grain quality. As the traditional QTL mapping methods (diploid methods) are usually designed for traits under diploid control, they are not the ideal approaches to map endosperm traits because they ignore the triploid nature of endosperm. In this article, a statistical method considering the triploid nature of endosperm (triploid method) is developed on the basis of multiple-interval mapping (MIM) to map for the underlying QTL. The proposed triploid MIM method is derived to broadly use the marker information either from only the maternal plants or from both the maternal plants and their embryos in the backcross and F2 populations for mapping endosperm traits. Due to the use of multiple intervals simultaneously to take multiple QTL into account, the triploid MIM method can provide better detection power and estimation precision, and as shown in this article it is capable of analyzing and searching for epistatic QTL directly as compared to the traditional diploid methods and current triploid methods using only one (or two) interval(s). Several important issues in endosperm trait mapping, such as the relation and differences between the diploid and triploid methods, variance components of genetic variation, and the problems if effects are present and ignored, are also addressed. Simulations are performed to further explore these issues, to investigate the relative efficiency of different experimental designs, and to evaluate the performance of the proposed and current methods in mapping endosperm traits. The MIM-based triploid method can provide a powerful tool to estimate the genetic architecture of endosperm traits and to assist the marker-assisted selection for the improvement of grain quality in crop science. The triploid MIM FORTRAN program for mapping endosperm traits is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

Bayesian mapping of quantitative trait loci for complex binary traits

A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduced variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as multiple QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian statistics are particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitative genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to generate the value of a hypothetical underlying variable (called the liability) and a threshold, which in turn allow the use of existing Bayesian statistics. The reversible jump Markov chain Monte Carlo algorithm is used to simulate the posterior samples of all unknowns, including the number of QTL, the locations and effects of identified QTL, genotypes of each individual at both the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distribution of the number of QTL and the locations and effects of the identified QTL. Utilities of the method are demonstrated using a simulated outbred full-sib family. A computer program written in FORTRAN language is freely available on request.     

Genetic complexity and quantitative trait loci mapping of yeast morphological traits

Functional genomics relies on two essential parameters: the sensitivity of phenotypic measures and the power to detect genomic perturbations that cause phenotypic variations. In model organisms, two types of perturbations are widely used. Artificial mutations can be introduced in virtually any gene and allow the systematic analysis of gene function via mutants fitness. Alternatively, natural genetic variations can be associated to particular phenotypes via genetic mapping. However, the access to genome manipulation and breeding provided by model organisms is sometimes counterbalanced by phenotyping limitations. Here we investigated the natural genetic diversity of Saccharomyces cerevisiae cellular morphology using a very sensitive high-throughput imaging platform. We quantified 501 morphological parameters in over 50,000 yeast cells from a cross between two wild-type divergent backgrounds. Extensive morphological differences were found between these backgrounds. The genetic architecture of the traits was complex, with evidence of both epistasis and transgressive segregation. We mapped quantitative trait loci (QTL) for 67 traits and discovered 364 correlations between traits segregation and inheritance of gene expression levels. We validated one QTL by the replacement of a single base in the genome. This study illustrates the natural diversity and complexity of cellular traits among natural yeast strains and provides an ideal framework for a genetical genomics dissection of multiple traits. Our results did not overlap with results previously obtained from systematic deletion strains, showing that both approaches are necessary for the functional exploration of genomes.     

Bayesian mapping of genomewide interacting quantitative trait loci for ordinal traits

Development of statistical methods and software for mapping interacting QTL has been the focus of much recent research. We previously developed a Bayesian model selection framework, based on the composite model space approach, for mapping multiple epistatic QTL affecting continuous traits. In this study we extend the composite model space approach to complex ordinal traits in experimental crosses. We jointly model main and epistatic effects of QTL and environmental factors on the basis of the ordinal probit model (also called threshold model) that assumes a latent continuous trait underlies the generation of the ordinal phenotypes through a set of unknown thresholds. A data augmentation approach is developed to jointly generate the latent data and the thresholds. The proposed ordinal probit model, combined with the composite model space framework for continuous traits, offers a convenient way for genomewide interacting QTL analysis of ordinal traits. We illustrate the proposed method by detecting new QTL and epistatic effects for an ordinal trait, dead fetuses, in a F(2) intercross of mice. Utility and flexibility of the method are also demonstrated using a simulated data set. Our method has been implemented in the freely available package R/qtlbim, which greatly facilitates the general usage of the Bayesian methodology for genomewide interacting QTL analysis for continuous, binary, and ordinal traits in experimental crosses.     

Selective genotyping to detect quantitative trait loci affecting multiple traits: interval mapping analysis

 Segregating quantitative trait loci can be detected via linkage to genetic markers. By selectively genotyping individuals with extreme phenotypes for the quantitative trait, the power per individual genotyped is increased at the expense of the power per individual phenotyped, but linear-model estimates of the quantitative-locus effect will be biased. The properties of single- and multiple-trait maximum-likelihood estimates of quantitative-loci parameters derived from selectively genotyped samples were investigated using Monte-Carlo simulations of backcross populations. All individuals with trait records were included in the analyses. All quantitative-locus parameters and the residual correlation were unbiasedly estimated by multiple-trait maximum-likelihood methodology. With single-trait maximum-likelihood, unbiased estimates for quantitative-locus effect and location, and the residual variance, were obtained for the trait under selection, but biased estimates were derived for a correlated trait that was analyzed separately. When an effect of the QTL was simulated only on the trait under selection, a “ghost” effect was also found for the correlated trait. Furthermore, if an effect was simulated only for the correlated trait, then the statistical power was less than that obtained with a random sample of equal size. With multiple-trait analyses, the power of quantitative-trait locus detection was always greater with selective genotyping. Received: 23 February 1998 / Accepted: 15 May 1998     

The efficiency of mapping of quantitative trait loci using cofactor analysis in half-sib design

This simulation study was designed to study the power and type I error rate in QTL mapping using cofactor analysis in half-sib designs. A number of scenarios were simulated with different power to identify QTL by varying family size, heritability, QTL effect and map density, and three threshold levels for cofactor were considered. Generally cofactor analysis did not increase the power of QTL mapping in a half-sib design, but increased the type I error rate. The exception was with small family size where the number of correctly identified QTL increased by 13% when heritability was high and 21% when heritability was low. However, in the same scenarios the number of false positives increased by 49% and 45% respectively. With a liberal threshold level of 10% for cofactor combined with a low heritability, the number of correctly identified QTL increased by 14% but there was a 41% increase in the number of false positives. Also, the power of QTL mapping did not increase with cofactor analysis in scenarios with unequal QTL effect, sparse marker density and large QTL effect (25% of the genetic variance), but the type I error rate tended to increase. A priori, cofactor analysis was expected to have higher power than individual chromosome analysis especially in experiments with lower power to detect QTL. Our study shows that cofactor analysis increased the number of false positives in all scenarios with low heritability and the increase was up to 50% in low power experiments and with lower thresholds for cofactors.     

Lineage-specific mapping of quantitative trait loci

We present an approach for quantitative trait locus (QTL) mapping, termed as ‘lineage-specific QTL mapping'', for inferring allelic changes of QTL evolution along with branches in a phylogeny. We describe and analyze the simplest case: by adding a third taxon into the normal procedure of QTL mapping between pairs of taxa, such inferences can be made along lineages to a presumed common ancestor. Although comparisons of QTL maps among species can identify homology of QTLs by apparent co-location, lineage-specific mapping of QTL can classify homology into (1) orthology (shared origin of QTL) versus (2) paralogy (independent origin of QTL within resolution of map distance). In this light, we present a graphical method that identifies six modes of QTL evolution in a three taxon comparison. We then apply our model to map lineage-specific QTLs for inbreeding among three taxa of yellow monkey-flower: Mimulus guttatus and two inbreeders M. platycalyx and M. micranthus, but critically assuming outcrossing was the ancestral state. The two most common modes of homology across traits were orthologous (shared ancestry of mutation for QTL alleles). The outbreeder M. guttatus had the fewest lineage-specific QTL, in accordance with the presumed ancestry of outbreeding. Extensions of lineage-specific QTL mapping to other types of data and crosses, and to inference of ancestral QTL state, are discussed.     

Selection bias in quantitative trait loci mapping

A simulation study was performed to see whether selection affected quantitative trait loci (QTL) mapping. Populations under random selection, under selection among full-sib families, and under selection within a full-sib family were simulated each with heritability of 0.3, 0.5, and 0.7. They were analyzed with the marker spacing of 10 cM and 20 cM. The accuracy for QTL detection decreased for the populations under selection within full-sib family. Estimates of QTL effects and positions differed (P < .05) from their input values. The problems could be ignored when mapping a QTL for the populations under selection among full-sib families. A large heritability helped reduction of such problems. When the animals were selected within a full-sib family, the QTL was detected for the populations with heritability of 0.5 or larger using the marker spacing of 10 cM, and with heritability of 0.7 using the marker spacing of 20 cM. This study implied that when selection was introduced, the accuracy for QTL detection decreased and the estimates of QTL effects were biased. A caution was warranted on the decision of data (including selected animals to be genotyped) for QTL mapping.     

Bayesian LASSO for quantitative trait loci mapping

The mapping of quantitative trait loci (QTL) is to identify molecular markers or genomic loci that influence the variation of complex traits. The problem is complicated by the facts that QTL data usually contain a large number of markers across the entire genome and most of them have little or no effect on the phenotype. In this article, we propose several Bayesian hierarchical models for mapping multiple QTL that simultaneously fit and estimate all possible genetic effects associated with all markers. The proposed models use prior distributions for the genetic effects that are scale mixtures of normal distributions with mean zero and variances distributed to give each effect a high probability of being near zero. We consider two types of priors for the variances, exponential and scaled inverse-chi(2) distributions, which result in a Bayesian version of the popular least absolute shrinkage and selection operator (LASSO) model and the well-known Student's t model, respectively. Unlike most applications where fixed values are preset for hyperparameters in the priors, we treat all hyperparameters as unknowns and estimate them along with other parameters. Markov chain Monte Carlo (MCMC) algorithms are developed to simulate the parameters from the posteriors. The methods are illustrated using well-known barley data.     

Sib mating designs for mapping quantitative trait loci

The power to separate the variance of a quantitative trait locus (QTL) from the polygenic variance is determined by the variability of genes identical by descent (IBD) at the QTL. This variability may increase with inbreeding. Selfing, the most extreme form of inbreeding, increases the variability of the IBD value shared by siblings, and thus has a higher efficiency for QTL mapping than random mating. In self-incompatible organisms, sib mating is the closest form of inbreeding. Similar to selfing, sib mating may also increase the power of QTL detection relative to random mating. In this study, we develop an IBD-based method under sib mating designs for QTL mapping. The efficiency of sib mating is then compared with random mating. Monte Carlo simulations show that sib mating designs notably increase the power for QTL detection. When power is intermediate, the power to detect a QTL using full-sib mating is, on average, 7% higher than under random mating. In addition, the IBD-based method proposed in this paper can be used to combine data from multiple families. As a result, the estimated QTL parameters can be applied to a wide statistical inference space relating to the entire reference population. This revised version was published online in July 2006 with corrections to the Cover Date.     

Genetic mapping of quantitative trait loci for meat quality and muscle metabolic traits in cattle

A whole‐genome scan was carried out in New Zealand and Australia to detect quantitative trait loci (QTL) for live animal and carcass composition traits and meat quality attributes in cattle. Backcross calves (385 heifers and 398 steers) were generated, with Jersey and Limousin backgrounds. The New Zealand cattle were reared and finished on pasture, whilst Australian cattle were reared on grass and finished on grain for at least 180 days. This paper reports on meat quality traits (tenderness measured as shear force at 4–5 ages on two muscles as well as associated traits of meat colour, pH and cooking loss) and a number of metabolic traits. For meat quality traits, 18 significant QTL (P < 0.05), located in nine linkage groups, were detected on a genome‐wise basis, in combined‐sire (seven QTL) or within‐sire analyses (11 QTL). For metabolic traits, 11 significant QTL (P < 0.05), located in eight linkage groups, were detected on a genome‐wise basis, in combined‐sire (five QTL) or within‐sire analyses (six QTL). BTA2 and BTA3 had QTL for both metabolic traits and meat quality traits. Six significant QTL for meat quality and metabolic traits were found at the proximal end of chromosome 2. BTA2 and BTA29 were the most common chromosomes harbouring QTL for meat quality traits; QTL for improved tenderness were associated with Limousin‐derived and Jersey‐derived alleles on these two chromosomes, respectively.     

Application of the false discovery rate to quantitative trait loci interval mapping with multiple traits

Controlling the false discovery rate (FDR) has been proposed as an alternative to controlling the genome-wise error rate (GWER) for detecting quantitative trait loci (QTL) in genome scans. The objective here was to implement FDR in the context of regression interval mapping for multiple traits. Data on five traits from an F2 swine breed cross were used. FDR was implemented using tests at every 1 cM (FDR1) and using tests with the highest test statistic for each marker interval (FDRm). For the latter, a method was developed to predict comparison-wise error rates. At low error rates, FDR1 behaved erratically; FDRm was more stable but gave similar significance thresholds and number of QTL detected. At the same error rate, methods to control FDR gave less stringent significance thresholds and more QTL detected than methods to control GWER. Although testing across traits had limited impact on FDR, single-trait testing was recommended because there is no theoretical reason to pool tests across traits for FDR. FDR based on FDRm was recommended for QTL detection in interval mapping because it provides significance tests that are meaningful, yet not overly stringent, such that a more complete picture of QTL is revealed.     

Bayesian multiple quantitative trait loci mapping for complex traits using markers of the entire genome

A Bayesian methodology has been developed for multiple quantitative trait loci (QTL) mapping of complex binary traits that follow liability threshold models. Unlike most QTL mapping methods where only one or a few markers are used at a time, the proposed method utilizes all markers across the genome simultaneously. The outperformance of our Bayesian method over the traditional single-marker analysis and interval mapping has been illustrated via simulations and real data analysis to identify candidate loci associated with colorectal cancer.     

Marker pair selection for mapping quantitative trait loci

Mapping of quantitative trait loci (QTL) for backcross and F(2) populations may be set up as a multiple linear regression problem, where marker types are the regressor variables. It has been shown previously that flanking markers absorb all information on isolated QTL. Therefore, selection of pairs of markers flanking QTL is useful as a direct approach to QTL detection. Alternatively, selected pairs of flanking markers can be used as cofactors in composite interval mapping (CIM). Overfitting is a serious problem, especially if the number of regressor variables is large. We suggest a procedure denoted as marker pair selection (MPS) that uses model selection criteria for multiple linear regression. Markers enter the model in pairs, which reduces the number of models to be considered, thus alleviating the problem of overfitting and increasing the chances of detecting QTL. MPS entails an exhaustive search per chromosome to maximize the chance of finding the best-fitting models. A simulation study is conducted to study the merits of different model selection criteria for MPS. On the basis of our results, we recommend the Schwarz Bayesian criterion (SBC) for use in practice.     

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/).     

Mapping quantitative trait loci regulating chicken body composition traits

Genome scans were conducted on an F₂ resource population derived from intercross of the White Plymouth Rock with the Silkies Fowl to detect QTL affecting chicken body composition traits. The population was genotyped with 129 microsatellite markers and phenotyped for 12 body composition traits on 238 F₂ individuals from 15 full-sib families. In total, 21 genome-wide QTL were found to be responsible for 11 traits, including two newly studied traits of proventriculus weight and shank girth. Three QTL were genome-wide significant: at 499 c m on GGA1 (explained 3.6% of phenotypic variance, P  < 0.01) and 51 c m on GGA5 (explained 3.3% of phenotypic variance, P  < 0.05) for the shank & claw weight and 502 c m on GGA1 (explained 1.4% of phenotypic variance, P  < 0.05) for wing weight. The QTL on GGA1 seemed to have pleiotropic effects, also affecting gizzard weight at 490 c m , shank girth at 489 c m and intestine length at 481 c m . It is suggested that further efforts be made to understand the possible pleiotropic effects of the QTL on GGA1 and that on GGA5 for two shank-related traits.     

Marker-based mapping of quantitative trait loci using replicated progenies

Summary When heritability of the trait under investigation is low, replicated progenies can bring about a major reduction in the number of individuals that need to be scored for marker genotype in determining linkage between marker loci and quantitative trait loci (QTL). Savings are greatest when heritability of the trait is low, but are much reduced when heritability of the quantitative trait is moderate to high. Required numbers for recombinant inbred lines will be greater than those required for a simple F₂ population when heritabilities are moderate to high and the proportion of recombination between marker locus and quantitative trait locus is substantial.Contribution No. 2613-E of the Agricultural Research Organization, 1989 series     

In silico mapping of quantitative trait loci in maize

Quantitative trait loci (QTL) are most often detected through designed mapping experiments. An alternative approach is in silico mapping, whereby genes are detected using existing phenotypic and genomic databases. We explored the usefulness of in silico mapping via a mixed-model approach in maize (Zea mays L.). Specifically, our objective was to determine if the procedure gave results that were repeatable across populations. Multilocation data were obtained from the 1995–2002 hybrid testing program of Limagrain Genetics in Europe. Nine heterotic patterns comprised 22,774 single crosses. These single crosses were made from 1,266 inbreds that had data for 96 simple sequence repeat (SSR) markers. By a mixed-model approach, we estimated the general combining ability effects associated with marker alleles in each heterotic pattern. The numbers of marker loci with significant effects—37 for plant height, 24 for smut [Ustilago maydis (DC.) Cda.] resistance, and 44 for grain moisture—were consistent with previous results from designed mapping experiments. Each trait had many loci with small effects and few loci with large effects. For smut resistance, a marker in bin 8.05 on chromosome 8 had a significant effect in seven (out of a maximum of 18) instances. For this major QTL, the maximum effect of an allele substitution ranged from 5.4% to 41.9%, with an average of 22.0%. We conclude that in silico mapping via a mixed-model approach can detect associations that are repeatable across different populations. We speculate that in silico mapping will be more useful for gene discovery than for selection in plant breeding programs.     

Accuracy of mapping quantitative trait loci in autogamous species

Summary The development of linkage maps with large numbers of molecular markers has stimulated the search for methods to map genes involved in quantitative traits (QTLs). A promising method, proposed by Lander and Botstein (1989), employs pairs of neighbouring markers to obtain maximum linkage information about the presence of a QTL within the enclosed chromosomal segment. In this paper the accuracy of this method was investigated by computer simulation. The results show that there is a reasonable probability of detecting QTLs that explain at least 5% of the total variance. For this purpose a minimum population of 200 backcross or F₂ individuals is necessary. Both the number of individuals and the relative size of the genotypic effect of the QTL are important factors determining the mapping precision. On the average, a QTL with 5% or 10% explained variance is mapped on an interval of 40 or 20 centiMorgans, respectively. Of course, QTLs with a larger genotypic effect will be located more precisely. It must be noted, however, that the interval length is rather variable.