A statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci

Non-equivalent expression of alleles at a locus results in genomic imprinting. In this article, a statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci (iQTL) underlying complex traits is developed based on experimental crosses of inbred line species in backcross populations. The joint likelihood function is composed of four component likelihood functions with each of them derived from one of four backcross families. The proposed approach models genomic imprinting effect as a probability measure with which one can test the degree of imprinting. Simulation results show that the model is robust for identifying iQTL with various degree of imprinting ranging from no imprinting, partial imprinting to complete imprinting. Under various simulation scenarios, the proposed model shows consistent parameter estimation with reasonable precision and high power in testing iQTL. When a QTL shows Mendelian effect, the proposed model also outperforms traditional Mendelian model. Extension to incorporate maternal effect is also given. The developed model, built within the maximum likelihood framework and implemented with the EM algorithm, provides a quantitative framework for testing and estimating iQTL involved in the genetic control of complex traits.     

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.     

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 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.     

Exponential mapping of quantitative trait loci governing allometric relationships in organisms

Allometric scaling relationships or quarter-power rules, as a universal biological law, can be viewed as having some genetic component, and the particular genes (or quantitative trait loci, QTL) underlying these allometric relationships can be mapped using molecular markers. We develop a mathematical and statistical model for mapping allometric QTL on the basis of nonlinear power functions using Taylors approximation theory. Simulation studies indicate that the QTL position and effect can be estimated using our model, but the estimation precision can be improved from the higher- over lower-order approximation when the sample size used and gene effects are small. The application of our approach in a real example from forest trees leads to successful detection of a QTL governing the allometric relationship between 3rd-year stem height and 3rd-year stem biomass. It is expected that our model will have broad implications for genetic, evolutionary, biomedical and breeding research.     

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     

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.     

An empirical Bayes method for estimating epistatic effects of quantitative trait loci

Summary .   The genetic variance of a quantitative trait is often controlled by the segregation of multiple interacting loci. Linear model regression analysis is usually applied to estimating and testing effects of these quantitative trait loci (QTL). Including all the main effects and the effects of interaction (epistatic effects), the dimension of the linear model can be extremely high. Variable selection via stepwise regression or stochastic search variable selection (SSVS) is the common procedure for epistatic effect QTL analysis. These methods are computationally intensive, yet they may not be optimal. The LASSO (least absolute shrinkage and selection operator) method is computationally more efficient than the above methods. As a result, it has been widely used in regression analysis for large models. However, LASSO has never been applied to genetic mapping for epistatic QTL, where the number of model effects is typically many times larger than the sample size. In this study, we developed an empirical Bayes method (E-BAYES) to map epistatic QTL under the mixed model framework. We also tested the feasibility of using LASSO to estimate epistatic effects, examined the fully Bayesian SSVS, and reevaluated the penalized likelihood (PENAL) methods in mapping epistatic QTL. Simulation studies showed that all the above methods performed satisfactorily well. However, E-BAYES appears to outperform all other methods in terms of minimizing the mean-squared error (MSE) with relatively short computing time. Application of the new method to real data was demonstrated using a barley dataset.     

Mapping quantitative trait loci using molecular marker linkage maps

Summary High-density restriction fragment length polymorphism (RFLP) and allozyme linkage maps have been developed in several plant species. These maps make it technically feasible to map quantitative trait loci (QTL) using methods based on flanking marker genetic models. In this paper, we describe flanking marker models for doubled haploid (DH), recombinant inbred (RI), backcross (BC), F₁ testcross (F₁TC), DH testcross (DHTC), recombinant inbred testcross (RITC), F₂, and F₃ progeny. These models are functions of the means of quantitative trait locus genotypes and recombination frequencies between marker and quantitative trait loci. In addition to the genetic models, we describe maximum likelihood methods for estimating these parameters using linear, nonlinear, and univariate or multivariate normal distribution mixture models. We defined recombination frequency estimators for backcross and F₂ progeny group genetic models using the parameters of linear models. In addition, we found a genetically unbiased estimator of the QTL heterozygote mean using a linear function of marker means. In nonlinear models, recombination frequencies are estimated less efficiently than the means of quantitative trait locus genotypes. Recombination frequency estimation efficiency decreases as the distance between markers decreases, because the number of progeny in recombinant marker classes decreases. Mean estimation efficiency is nearly equal for these methods.     

Mapping quantitative trait loci for seedling vigor in rice using RFLPs

Improving seedling vigor is an important objective of modern rice (Oryza saliva L.) breeding programs. The purpose of this study was to identify and map quantitative trait loci (QTL) underlying seedling vigor-related traits using restriction fragment length polymorphisms (RFLPs). An F₂ population of 204 plants was developed from a cross between a low-vigor japonica cultivar Labelle (LBL) and a high-vigor indica cultivar Black Gora (BG). A linkage map was constructed of 117 markers spanning 1496 Haldane cM and encompassing the 12 rice chromosomes with an average marker spacing of 14 cM. The length of the shoots, roots, coleoptile and mesocotyl were measured on F₃ families in slantboard tests conducted at two temperatures (18° and 25°C). By means of interval analysis, 13 QTLs, each accounting for 7% to 38% of the phenotypic variance, were identified and mapped in the two temperature regimes at a log-likelihood (LOD) threshold of 2.5. Four QTLs controlled shoot length, 2 each controlled root and coleoptile lengths and 5 influenced mesocotyl length. Single-point analysis confirmed the presence of these QTLs and detected additional loci for shoot, root and coleoptile lengths, these latter usually accounting for less than 5% of the phenotypic variation. Only 3 QTLs detected both by interval and singlepoint analyses were expressed under both temperature regimes. Additive, dominant and overdominant modes of gene action were observed. Contrary to what was predicted from parental phenotype, the low-vigor LBL contributed 46% of the positive alleles for shoot, root and coleoptile lengths. Positive alleles from the high-vigor parent BG were identified for increased root, coleoptile and mesocotyl lengths. However, BG contributed alleles with only minor effects for shoot length, the most important determinant of seedling vigor in water-seeded rice, suggesting that it would not be an ideal donor parent for introducing faster shoot growth alleles into temperate japonica cultivars.     

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.     

Mapping quantitative trait loci with dominant markers in four-way crosses

 A common problem in mapping quantitative trait loci (QTLs) is that marker data are often incomplete. This includes missing data, dominant markers, and partially informative markers, arising in outbred populations. Here we briefly present an iteratively re-weighted least square method (IRWLS) to incorporate dominant and missing markers for mapping QTLs in four-way crosses under a heterogeneous variance model. The algorithm uses information from all markers in a linkage group to infer the QTL genotype. Monte Carlo simulations indicate that with half dominant markers, QTL detection is almost as efficient as with all co-dominant markers. However, the precision of the estimated QTL parameters generally decreases as more markers become missing or dominant. Notable differences are observed on the standard deviation of the estimated QTL position for varying levels of marker information content. The method is relatively simple so that more complex models including multiple QTLs or fixed effects can be fitted. Finally, the method can be readily extended to QTL mapping in full-sib families. Received: 16 June 1998 / Accepted: 29 September 1998     

Mapping of quantitative trait loci influencing frost tolerance in Eucalyptus nitens

 Regions of the genome influencing frost tolerance in an outbred family of Eucalyptus nitens have been identified. Two QTLs present on the same linkage group, but located 40 cM apart, were identified using single-factor analysis of variance. The QTLs explained between 7.7 and 10.8% of the phenotypic variation for frost tolerance in this family. Analysis of marker loci linked to the QTLs showed one of them to have a simple mode of action with the effect segregating from the male parent in the family. For the other QTL multiple alleles were identified. This QTL showed segregation from the female parent which gave a positive effect on frost tolerance; however, an allele segregating from the male parent was identified which showed a negative interaction with the allele for increased frost tolerance. Received: 10 May 1997 / Accepted: 2 June 1997     

Mapping of quantitative trait loci controlling adaptive traits in coastal Douglas-fir. II. Spring and fall cold-hardiness

Quantitative trait loci (QTLs) affecting fall and spring cold-hardiness were identified in a three-generation outbred pedigree of coastal Douglas-fir [Pseudotsuga meniziesii (Mirb.) Franco var. menziesii]. Eleven QTLs controlling fall cold-hardiness were detected on four linkage groups, and 15 QTLs controlling spring cold-hardiness were detected on four linkage groups. Only one linkage group contained QTLs for both spring and fall cold-hardiness, and these QTLs tended to map in close proximity to one another. Several QTLs were associated with hardiness in all three shoot tissues assayed in the spring, supporting previous reports that there is synchronization of plant tissues during de-acclimatization. For fall cold-hardiness, co-location of QTLs was not observed for the different tissues assayed, which is consistent with previous reports of less synchronization of hardening in the fall. In several cases, QTLs for spring or fall cold-hardiness mapped to the same location as QTLs controlling spring bud flush. QTL estimations, relative magnitudes of heritabilities, and genetic correlations based on clonal data in this single full-sib family, supports conclusions about the genetic control and relationships among cold-hardiness traits observed in population samples of Douglas-fir in previous studies. Received: 20 July 2000 / Accepted: 19 October 2000     

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.     

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.     

Mapping single-locus and epistatic quantitative trait loci for plant architectural traits in chrysanthemum

Plant architecture is important for chrysanthemum cultivation and breeding. To determine the genetic basis of plant architectural traits in chrysanthemum, a population of 142 F1 plants derived from a cross between the creeping ground-cover chrysanthemum cultivar Yuhualuoying and the erect potted cultivar Aoyunhanxiao was used to detect quantitative trait loci (QTL) associated with plant height, plant width, inter-node length and flower neck length. The broad-sense heritability h _B ² for the four plant architectural traits ranged from 0.33 to 0.83, and transgressive segregation was observed. Single-locus QTL analysis revealed a total of five QTL, accounting for 6.0?C16.1% of the phenotypic variation. Additionally, 11 pairs of epistatic QTL were identified, explaining 3.5?C14.5% of the phenotypic variations. The majority of the interactions detected occurred between background loci. These results indicate that both additive and epistatic effects contribute to phenotypic variation in the plant architecture of chrysanthemum. It is expected that the identified markers associated with the additive QTL and epistatic QTL detected in this study will be of importance in future breeding programs to develop chrysanthemum cultivars exhibiting desirable plant architecture.     

Quantitative trait loci for fertility traits in Finnish Ayrshire cattle

A whole genome scan was carried out to detect quantitative trait loci (QTL) for fertility traits in Finnish Ayrshire cattle. The mapping population consisted of 12 bulls and 493 sons. Estimated breeding values for days open, fertility treatments, maternal calf mortality and paternal non-return rate were used as phenotypic data. In a granddaughter design, 171 markers were typed on all 29 bovine autosomes. Associations between markers and traits were analysed by multiple marker regression. Multi-trait analyses were carried out with a variance component based approach for the chromosomes and trait combinations, which were observed significant in the regression method. Twenty-two chromosome-wise significant QTL were detected. Several of the detected QTL areas were overlapping with milk production QTL previously identified in the same population. Multi-trait QTL analyses were carried out to test if these effects were due to a pleiotropic QTL affecting fertility and milk yield traits or to linked QTL causing the effects. This distinction could only be made with confidence on BTA1 where a QTL affecting milk yield is linked to a pleiotropic QTL affecting days open and fertility treatments.     

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 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.