Mapping quantitative trait loci with epistatic effects

Epistatic variance can be an important source of variation for complex traits. However, detecting epistatic effects is difficult primarily due to insufficient sample sizes and lack of robust statistical methods. In this paper, we develop a Bayesian method to map multiple quantitative trait loci (QTLs) with epistatic effects. The method can map QTLs in complicated mating designs derived from the cross of two inbred lines. In addition to mapping QTLs for quantitative traits, the proposed method can even map genes underlying binary traits such as disease susceptibility using the threshold model. The parameters of interest are various QTL effects, including additive, dominance and epistatic effects of QTLs, the locations of identified QTLs and even the number of QTLs. When the number of QTLs is treated as an unknown parameter, the dimension of the model becomes a variable. This requires the reversible jump Markov chain Monte Carlo algorithm. The utility of the proposed method is demonstrated through analysis of simulation data.     

Mapping of epistatic quantitative trait loci in four-way crosses

Four-way crosses (4WC) involving four different inbred lines often appear in plant and animal commercial breeding programs. Direct mapping of quantitative trait loci (QTL) in these commercial populations is both economical and practical. However, the existing statistical methods for mapping QTL in a 4WC population are built on the single-QTL genetic model. This simple genetic model fails to take into account QTL interactions, which play an important role in the genetic architecture of complex traits. In this paper, therefore, we attempted to develop a statistical method to detect epistatic QTL in 4WC population. Conditional probabilities of QTL genotypes, computed by the multi-point single locus method, were used to sample the genotypes of all putative QTL in the entire genome. The sampled genotypes were used to construct the design matrix for QTL effects. All QTL effects, including main and epistatic effects, were simultaneously estimated by the penalized maximum likelihood method. The proposed method was confirmed by a series of Monte Carlo simulation studies and real data analysis of cotton. The new method will provide novel tools for the genetic dissection of complex traits, construction of QTL networks, and analysis of heterosis.     

Mapping epistatic quantitative trait loci with one-dimensional genome searches

The discovery of epistatically interacting QTL is hampered by the intractability and low power to detect QTL in multidimensional genome searches. We describe a new method that maps epistatic QTL by identifying loci of high QTL by genetic background interaction. This approach allows detection of QTL involved not only in pairwise but also higher-order interaction, and does so with one-dimensional genome searches. The approach requires large populations derived from multiple related inbred-line crosses as is more typically available for plants. Using maximum likelihood, the method contrasts models in which QTL allelic values are either nested within, or fixed over, populations. We apply the method to simulated doubled-haploid populations derived from a diallel among three inbred parents and illustrate the power of the method to detect QTL of different effect size and different levels of QTL by genetic background interaction. Further, we show how the method can be used in conjunction with standard two-locus QTL detection models that use two-dimensional genome searches and find that the method may double the power to detect first-order epistasis.     

Quantitative trait loci controlling plant architectural traits in cotton

Cotton plant architecture is an important characteristic influencing the suitability of specific cotton varieties in cultivation, fiber yield and quality. However, complex multigenic relationships and substantial genotype–environment interaction underlie plant architecture, and will hinder the efficient improvement of these traits in conventional cotton breeding programs. An enhanced understanding of the molecular-genetic regulation of plant morphological developmental can aid in the modification of agronomically relevant traits. In this study, an interspecific Gossypium hirsutum and Gossypium barbadense BC₁ population was used to identify QTL associated with plant architectural traits. Twenty-six single QTL were identified for seven plant architecture traits. The phenotypic variation explained by an individual QTL ranged from 9.56% to 44.57%. In addition, 11 epistatic QTL for fruit branch angle (FBA), plant height (PH), main-stem leaf size (MLS), and fruiting branch internode length (FBI) explained 2.28–15.34% of the phenotypic variation in these traits. The majority of the interactions (60%) occurred between markers linked to QTL influencing the same traits. The QTL detected in this study are expected to be valuable in future breeding programs to develop cultivars exhibiting desirable cotton architecture.     

Mapping quantitative trait loci for traits defined as ratios

Many traits are defined as ratios of two quantitative traits. Methods of QTL mapping for regular quantitative traits are not optimal when applied to ratios due to lack of normality for traits defined as ratios. We develop a new method of QTL mapping for traits defined as ratios. The new method uses a special linear combination of the two component traits, and thus takes advantage of the normal property of the new variable. Simulation study shows that the new method can substantially increase the statistical power of QTL detection relative to the method which treats ratios as regular quantitative traits. The new method also outperforms the method that uses Box-Cox transformed ratio as the phenotype. A real example of QTL mapping for relative growth rate in soybean demonstrates that the new method can detect more QTL than existing methods of QTL mapping for traits defined as ratios.     

Mapping quantitative trait loci for longitudinal traits in line crosses

Quantitative traits whose phenotypic values change over time are called longitudinal traits. Genetic analyses of longitudinal traits can be conducted using any of the following approaches: (1) treating the phenotypic values at different time points as repeated measurements of the same trait and analyzing the trait under the repeated measurements framework, (2) treating the phenotypes measured from different time points as different traits and analyzing the traits jointly on the basis of the theory of multivariate analysis, and (3) fitting a growth curve to the phenotypic values across time points and analyzing the fitted parameters of the growth trajectory under the theory of multivariate analysis. The third approach has been used in QTL mapping for longitudinal traits by fitting the data to a logistic growth trajectory. This approach applies only to the particular S-shaped growth process. In practice, a longitudinal trait may show a trajectory of any shape. We demonstrate that one can describe a longitudinal trait with orthogonal polynomials, which are sufficiently general for fitting any shaped curve. We develop a mixed-model methodology for QTL mapping of longitudinal traits and a maximum-likelihood method for parameter estimation and statistical tests. The expectation-maximization (EM) algorithm is applied to search for the maximum-likelihood estimates of parameters. The method is verified with simulated data and demonstrated with experimental data from a pseudobackcross family of Populus (poplar) trees.     

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.     

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.     

Mapping of quantitative trait loci for clinical–chemical traits in swine

Clinical–chemical traits are diagnostic parameters essential for characterization of health and disease in veterinary practice. The traits show significant variability and are under genetic control, but little is known about the fundamental genetic architecture of this variability, especially in swine. We have identified QTL for alkaline phosphatase (ALP), lactate (LAC), bilirubin (BIL), creatinine (CRE) and ionized sodium (Na⁺), potassium (K⁺) and calcium (Ca⁺⁺) from the serum of 139 F₂ pigs from a Meishan/Pietrain family before and after challenge with Sarcocystis miescheriana , a protozoan parasite of muscle. After infection, the pigs passed through three stages representing acute disease, subclinical disease and chronic disease. Forty-two QTL influencing clinical–chemical traits during these different stages were identified on 15 chromosomes. Eleven of the QTL were significant on a genome-wide level; 31 QTL were chromosome-wide significant. QTL showed specific health/disease patterns with respect to the baseline values of the traits as well as the values obtained through the different stages of disease. QTL influencing different traits at different times were found primarily on chromosomes 1, 3, 7 and 14. The most prominent QTL for the investigated clinical–chemical traits mapped to SSC3 and 7. Baseline traits of ALP, LAC, BIL, Ca⁺⁺ and K⁺ were influenced by QTL regions on SSC3, 6, 7, 8 and 13. Single QTL explained up to 21.7% of F₂ phenotypic variance. Our analysis confirms that variation of clinical–chemical traits is associated with multiple chromosomal regions.     

Identification of quantitative trait loci and epistatic interactions for plant height and heading date in rice

Appropriate heading date and plant height are prerequisites for attaining the desired yield level in rice breeding programs. In this study, we analyzed the genetic bases of heading date and plant height at both single- locus and two-locus levels, using a population of 240 F_2:3 families derived from a cross between two elite rice lines. Measurements for the traits were obtained over 2 years in replicated field trials. A linkage map was constructed with 151 polymorphic marker loci, based on which interval mapping was performed using Mapmaker/QTL. The analyses detected six QTLs for plant height and six QTLs for heading date; collectively the QTLs for heading date accounted for a much greater amount of phenotypic variation than did the QTLs for plant height. Two-way analyses of variance, with all possible two-locus combinations, detected large numbers (from 101 to 257) of significant digenic interactions in the 2 years for both traits involving markers distributed in the entire genome; 22 and 39 were simultaneously detected in both years for plant height and heading date, respectively. Each of the interactions individually accounted for only a very small portion of the phenotypic variation. The majority of the significant interactions involved marker loci that did not detect significant effects by single-locus analyses, and many of the QTLs detected by single-locus analyses were involved in epistatic interactions. The results clearly demonstrated the importance of epistatic interactions in the genetic bases of heading date and plant height. Received: 5 May 2001 / Accepted: 3 August 2001     

Mapping epistatic quantitative trait loci underlying endosperm traits using all markers on the entire genome in a random hybridization design

Triploid endosperm is of great economic importance owing to its nutritious quality. Mapping endosperm trait loci (ETL) can provide an efficient way to genetically improve grain quality. However, most triploid ETL mapping methods do not produce unbiased estimates of the two dominant effects of ETL. A random hybridization design is an alternative method that may be used to overcome this problem. However, epistasis has an important role in the dissection of genetic architecture for complex traits. In this study, therefore, an attempt was made to map epistatic ETL (eETL) under a triploid genetic model of endosperm traits in a random hybridization design. The endosperm trait means of random hybrid lines, together with known marker genotype information from their corresponding parental F(2) plants, were used to estimate, efficiently and without bias, the positions and all of the effects of eETL using a penalized maximum likelihood method. The method proposed in this article was verified by a series of Monte Carlo simulation experiments. Results from the simulated studies show that the proposed method provides accurate estimates of eETL parameters with a low false-positive rate and a relatively short running time. This new method enables us to map triploid eETL in the same way as diploid quantitative traits.     

Bayesian model selection for genome-wide epistatic quantitative trait loci analysis

The problem of identifying complex epistatic quantitative trait loci (QTL) across the entire genome continues to be a formidable challenge for geneticists. The complexity of genome-wide epistatic analysis results mainly from the number of QTL being unknown and the number of possible epistatic effects being huge. In this article, we use a composite model space approach to develop a Bayesian model selection framework for identifying epistatic QTL for complex traits in experimental crosses from two inbred lines. By placing a liberal constraint on the upper bound of the number of detectable QTL we restrict attention to models of fixed dimension, greatly simplifying calculations. Indicators specify which main and epistatic effects of putative QTL are included. We detail how to use prior knowledge to bound the number of detectable QTL and to specify prior distributions for indicators of genetic effects. We develop a computationally efficient Markov chain Monte Carlo (MCMC) algorithm using the Gibbs sampler and Metropolis-Hastings algorithm to explore the posterior distribution. We illustrate the proposed method by detecting new epistatic QTL for obesity in a backcross of CAST/Ei mice onto M16i.     

Mapping quantitative trait loci controlling variation in forage quality traits in barley

Barley forage quality has a direct relationship to animal performance, but forage quality traits are often neglected or not accessible to the plant breeders. Doubled haploid lines (145) from the cross Steptoe × Morex were grown in 2 years of trails under irrigated conditions to evaluate the variation in forage quality characteristics, identify quantitative trait loci (QTL) for these traits and determine if variation in forage quality characteristics among barley lines is heritable. Forage quality traits were determined at plant anthesis and at peak forage yield stages. A total of 32 QTL were identified that conditioned forage traits at anthesis stage, and 10 QTLs were identified at peak forage yield. At anthesis, forage traits were highly to moderate heritablely, while at peak forage yield, all traits were weakly heritable, indicating that selection progress for these traits will be effective at early stages of maturity. This research has identified and mapped QTL for barley forage quality and will allow deployment of genes for improved forage quality via marker-assisted selection.     

Bayesian mapping of genome-wide epistatic imprinted loci for quantitative traits

Genomic imprinting, an epigenetic phenomenon of parent-of-origin-specific gene expression, has been widely observed in plants, animals, and humans. To detect imprinting genes influencing quantitative traits, the least squares and maximum likelihood approaches for fitting a single quantitative trait locus (QTL) and Bayesian methods for simultaneously modeling multiple QTL have been adopted, respectively, in various studies. However, most of these studies have only estimated imprinting main effects and thus ignored imprinting epistatic effects. In the presence of extremely complex genomic imprinting architectures, we introduce a Bayesian model selection method to analyze the multiple interacting imprinted QTL (iQTL) model. This approach will greatly enhance the computational efficiency through setting the upper bound of the number of QTLs and performing selective sampling for QTL parameters. The imprinting types of detected main-effect QTLs can be estimated from the Bayes factor statistic formulated by the posterior probabilities for the genetic effects being compared. The performance of the proposed method is demonstrated by several simulation experiments. Moreover, this method is applied to dissect the imprinting genetic architecture for body weight in mouse and fruit weight in tomato. Matlab code for implementing this approach will be available from the authors upon request.     

Mapping quantitative trait loci for bean traits and ovule number in Theobroma cacao L.

Quantitative trait loci (QTL) mapping for bean traits and the number of ovules per ovary was carried out in cocoa (Theobroma cacao L.) using three test-cross progenies derived from crosses between a lower Amazon Forastero male parent (Catongo) and three female parents: one upper Amazon Forastero (IMC78) and two Trinitario (DR1 and S52). RFLP (restriction fragment length polymorphism), microsatellite, and AFLP (amplified fragment lengthpolymorphism) markers were used for mapping. Between one and six QTL for bean traits (length, weight, and shape index) and one and four QTL for the number of ovules per ovary were detected using composite interval mapping (CIM). Individual QTL explained between 5 and 24% of the phenotypic variation. QTL clusters were identified on several chromosomes, but particularly on chromosome 4. QTL related to bean traits were detected in the same region in both Trinitario parents and in a close region in the upper Amazon Forastero parent. In reference to a previous diversity study where alleles specific to Criollo and Forastero genotypes were identified, it was possible to speculate on the putative origin (Criollo or Forastero) of favorable QTL alleles segregating in both Trinitario studied.     

Mapping quantitative trait loci affecting chicken body size traits via genome scanning

Body size traits reflect the condition of body development, are always mentioned when a breed is described, and are also targets in breeding programmes. In chicken, there are several reports focused on body size traits, such as shank length, tibia length or bone traits. However, no study was carried out on chest width (CW), chest depth (CD), body slope length (BL) and head width (HW) traits. In this study, genome scans were conducted on an F₂ resource population (238 F₂ individuals from 15 full‐sib families derived from an intercross of the White Plymouth Rock with the Silkies Fowl) to identify quantitative trait loci (QTL) associated with CW, CD, BL and HW from 7 to 12 weeks of age. In total, 21 significant or suggestive QTL were found that affected four body size traits. Four QTL reached 1% genome‐wide significance level: at 297 cM on GGA3 (associated with CW at 9 weeks of age), between 155 and 184 cM on GGA1 (affecting BL traits at 9 and 10 weeks of age), at 22 cM on GGA2 (related with BL traits at 12 weeks of age) and at 36 cM on GGA1 (for HW trait at 8 weeks of age).     

Mapping quantitative trait loci affecting female reproductive traits on porcine chromosome 8

An understanding of the genetic control of porcine female reproductive performance would offer the opportunity to utilize natural variation and improve selective breeding programs through marker-assisted selection. The Chinese Meishan is one of the most prolific pig breeds known, farrowing three to five more viable piglets per litter than the European Large White breed. This difference in prolificacy is attributed to the Meishan's superior prenatal survival levels. The present study utilized a three-generation cross in which the founder grandparental animals were purebred Meishan and Large White pigs in a scan for quantitative trait loci (QTL) on porcine chromosome 8 (SSC8) associated with reproductive performance. Reproductive traits, including number of corpora lutea (ovulation rate), teat number, litter size, and prenatal survival, were recorded for as many as 220 F2 females. Putative QTL for the related traits of litter size and prenatal survival were identified at the distal end of the long arm of SSC8. A physiological candidate gene, SPP1, was found to lie within the 95% confidence interval of these QTL. A suggestive QTL for teat number was revealed on the short arm of SSC8. The present study demonstrates, to our knowledge, the first independent confirmation of QTL for fecundity on SSC8, and these QTL regions provide a crucial starting point in the search for the causal genetic variants.     

Bayesian quantitative trait loci mapping for multiple traits

Most quantitative trait loci (QTL) mapping experiments typically collect phenotypic data on multiple correlated complex traits. However, there is a lack of a comprehensive genomewide mapping strategy for correlated traits in the literature. We develop Bayesian multiple-QTL mapping methods for correlated continuous traits using two multivariate models: one that assumes the same genetic model for all traits, the traditional multivariate model, and the other known as the seemingly unrelated regression (SUR) model that allows different genetic models for different traits. We develop computationally efficient Markov chain Monte Carlo (MCMC) algorithms for performing joint analysis. We conduct extensive simulation studies to assess the performance of the proposed methods and to compare with the conventional single-trait model. Our methods have been implemented in the freely available package R/qtlbim (http://www.qtlbim.org), which greatly facilitates the general usage of the Bayesian methodology for unraveling the genetic architecture of complex traits.     

Mapping quantitative trait loci in oligogenic models

We discuss strategies for mapping quantitative trait loci with emphasis on certain issues of study design that have recently received attention: e.g. genotyping only selected pedigrees and the comparative value of large pedigrees versus sib pairs. We use a standard variance components model and a parametrization of the genetic effects in which the 'segregation' parameters are locally orthogonal to the 'linkage' parameters. This permits simple explicit expressions for the expectation of the score statistic, which we use to compare the power of different strategies. We also discuss robustness of the score statistic.     

Mapping quantitative trait loci in tetraploid populations

Knowledge of quantitative trait locus (QTL) mapping in polyploids is almost void, albeit many exquisite strategies of QTL mapping have been proposed and extensive investigations have been carried out in diploid animals and plants. In this paper we develop a simple algorithm which uses an iteratively reweighted least square method to map QTLs in tetraploid populations. The method uses information from all markers in a linkage group to infer the probability distribution of QTL genotype under the assumption of random chromosome segregation. Unlike QTL mapping in diploid species, here we estimate and test the compound 'gametic effect', which consists of the composite 'genic effect' of alleles and higher-order gene interactions. The validity and efficiency of the proposed method are investigated through simulation studies. Results show that the method can successfully locate QTLs and separates different sources (e.g. additive and dominance) of variance components contributed by the QTLs.