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.     

Extremely elongated tomato fruit controlled by four quantitative trait loci with epistatic interactions

Cultivated tomato (Lycopersicon esculentum) encompass a wide range of fruit shape and size variants. This variation can be used to genetically dissect the molecular basis of ovary and fruit morphology. The cultivar Long John displays an extremely elongated fruit phenotype, while the wild relative Lycopersicon pimpinellifolium LA1589 produces fruit that are nearly perfect spheres, typical of wild tomatoes. Quantitative trait mapping of an F2 population between Long John and LA1589 revealed four fruit shape QTLs, located on chromosomes 2, 3, 7 and 11. The primary role of the fruit shape QTL located on chromosome 7, ljfs7, is to control pericarp elongation. The primary role of the fruit shape QTLs on chromosome 2, 3 and 11 (ljfs2, ljfs3 and ljfs11, respectively) is to control pear shape, measured as the eccentricity index. QTL map position and the effect of the loci on fruit shape suggested that ljfs2 and ljfs7 are allelic to the well-studied fruit shape loci ovate and sun, respectively. ljfs3 and ljfs11 map near the previously identified, but less characterized, fruit shape loci fs3.2 and fs11.1, respectively. This result suggests that most of the variation in tomato fruit shape is controlled by a few major QTLs. Although eccentricity and pericarp elongation were largely controlled by independent growth processes, significant interactions were detected between all four fruit shape loci in the control of eccentricity. This indicates that the three eccentricity loci, ljfs2, ljfs3 and ljfs11, epistatically control the same developmental process, while ljfs7 had a pleiotropic effect on eccentricity. Received: 27 March 2001 / Accepted: 7 May 2001     

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.     

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.     

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     

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.     

Genotype-environment interactions at quantitative trait loci affecting inflorescence development in Arabidopsis thaliana

Phenotypic plasticity and genotype-environment interactions (GEI) play a prominent role in plant morphological diversity and in the potential functional capacities of plant life-history traits. The genetic basis of plasticity and GEI, however, is poorly understood in most organisms. In this report, inflorescence development patterns in Arabidopsis thaliana were examined under different, ecologically relevant photoperiod environments for two recombinant inbred mapping populations (Ler x Col and Cvi x Ler) using a combination of quantitative genetics and quantitative trait locus (QTL) mapping. Plasticity and GEI were regularly observed for the majority of 13 inflorescence traits. These observations can be attributable (at least partly) to variable effects of specific QTL. Pooled across traits, 12/44 (27.3%) and 32/62 (51.6%) of QTL exhibited significant QTL x environment interactions in the Ler x Col and Cvi x Ler lines, respectively. These interactions were attributable to changes in magnitude of effect of QTL more often than to changes in rank order (sign) of effect. Multiple QTL x environment interactions (in Cvi x Ler) clustered in two genomic regions on chromosomes 1 and 5, indicating a disproportionate contribution of these regions to the phenotypic patterns observed. High-resolution mapping will be necessary to distinguish between the alternative explanations of pleiotropy and tight linkage among multiple genes.     

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/).     

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.     

Identification of quantitative trait loci controlling symptom development during viral infection in Arabidopsis thaliana

In compatible interactions between plants and viruses that result in systemic infection, symptom development is a major phenotypic trait. However, host determinants governing this trait are mostly unknown, and the mechanisms underlying it are still poorly understood. In a previous study on the Arabidopsis thaliana-Plum pox virus (PPV) pathosystem, we showed a large degree of variation in symptom development among susceptible accessions. In particular, Cvi-1 (Cape Verde islands) accumulates viral particules but remains symptomless, Col-0 (Columbia) sometimes shows weak symptoms compared with Ler (Landsberg erecta), which always shows severe symptoms. Genetic analyses of Col x Ler and Cvi x Ler F2 and recombinant inbred line (RIL) populations suggested that symptom development as well as viral accumulation traits are polygenic and quantitative. Three of the symptom quantitative trait loci (QTL) identified could be confirmed in near-isogenic lines, including PSI1 (PPV symptom induction 1), which was identified on the distal part of chromosome 1 in both RIL populations. With respect to viral accumulation, several factors have been detected and, interestingly, in the Col x Ler population, two out of three viral accumulation QTL colocalized with loci controlling symptom development, although correlation analysis showed weak linearity between symptom severity and virus accumulation. In addition, in the Cvi x Ler RIL population, a digenic recessive determinant controlling PPV infection was identified.     

Mapping of quantitative trait loci controlling adaptive traits in coastal Douglas fir. III. Quantitative trait loci-by-environment interactions

Quantitative trait loci (QTL) were mapped in the woody perennial Douglas fir (Pseudotsuga menziesii var. menziesii [Mirb.] Franco) for complex traits controlling the timing of growth initiation and growth cessation. QTL were estimated under controlled environmental conditions to identify QTL interactions with photoperiod, moisture stress, winter chilling, and spring temperatures. A three-generation mapping population of 460 cloned progeny was used for genetic mapping and phenotypic evaluations. An all-marker interval mapping method was used for scanning the genome for the presence of QTL and single-factor ANOVA was used for estimating QTL-by-environment interactions. A modest number of QTL were detected per trait, with individual QTL explaining up to 9.5% of the phenotypic variation. Two QTL-by-treatment interactions were found for growth initiation, whereas several QTL-by-treatment interactions were detected among growth cessation traits. This is the first report of QTL interactions with specific environmental signals in forest trees and will assist in the identification of candidate genes controlling these important adaptive traits in perennial plants.     

Identification for quantitative trait loci controlling grain shattering in rice

Seed shattering is an important factor causing loss of grain yield before and during rice harvest. In the present study, the quantitative trait loci regarding shattering scale, breaking tensile strength (BTS) and abscission layer (AL), the parameters evaluating seed shattering habit by hand gripping, a digital force gauge and observation on AL, respectively, were identified by using an doubled haploid line (DHL) population from a cross between a loose-shattering type Tongil variety, ‘Samgang’, and a moderately difficult shattering japonica variety, ‘Nagdong’. Eight QTLs consisted in four QTLs for shattering scale, two QTLs for AL, each one QTL for pulling and bending strength were detected on six chromosomes, respectively. Among them, Qss1 with flanking markers RM6696 and RM476 explained 31% of phenotype variation in shattering scale. Furthermore, two new QTLs controlling shattering habit, Qss5-2 and Qal5-1, were located on chromosome 5 at the interval 5028–5037 and 5021-RM289. They explained 10% and 12% of phenotype variations, respectively. A total of eleven digenic epistatic loci were identified for four parameters. The identification of QTLs affecting seed shattering habits is favorable to thoroughly dissect the genetic mechanism of the shattering habit and to apply for marker-assisted selection in rice breeding system of specific regions.     

Mapping of quantitative trait loci controlling barley flour pasting properties

Pasting properties are important characteristics of barley starch from a processing standpoint. A shorter time to peak viscosity and lower pasting temperature are favorable to both malting and food processing. This study was conducted to identify quantitative trait loci (QTLs) determining pasting properties of barley flour using a doubled haploid population of 177 lines from the cross between six-rowed Yerong and two-rowed Franklin. Yerong is a feed barley with a longer time to peak viscosity and a higher pasting temperature than the other parent Franklin which is a malting barley. Field trials were conducted in three different sites/years. Seven different parameters representing the pasting properties were measured using a Rapid Visco-analyser (RVA). DH lines showed significant differences in all seven parameters in most of the sites/years. For example, the pasting temperature of different DH lines ranged from 73.8 to 89.5 in 2006/2007 MTP field trial. Twenty one QTLs were associated with flour pasting properties. These QTLs were distributed on 11 chromosome regions. Genetic variance explained by these QTLs varies from 4.4 to 15.2%. The most important QTLs controlling the time to peak viscosity and pasting temperature were located on 1H, 2H, 3H and 7H. Results showed that some of the pasting properties can be effectively selected by the combination of several molecular markers.     

Identifying regions of the wheat genome controlling seed development by mapping expression quantitative trait loci

Statistical methods established for the genetic analysis of quantitative traits can be applied to gene expression data. Quantitative trait locus (QTL) analysis can associate the expression of genes or groups of genes with particular genomic regions, and thereby identify regions regulating gene expression. A segregating population of 41 doubled haploid (DH) lines from the hard red spring wheat cross RL4452 x 'AC Domain' was used to map expression level polymorphisms. This population had previously been mapped with microsatellites, and includes a full QTL analysis for agronomic and seed quality traits. Expression analysis on mRNA from developing seed grown in two field locations was conducted on 39 of the 41 DH lines using the Affymetrix GeneChip Wheat Genome Array. Analysis of the hybridization intensity identified 1484 Affymetrix probe sets in the first location and 10,280 probe sets in the second location, where the hybridization intensity varied significantly between genotypes of the population. A common set of 1455 probe sets differing in intensity between genotypes in both locations was used for mapping, and 542 QTLs were identified that each mapped to a single chromosome interval, illustrating that major gene expression QTLs could be found in wheat. Genomic regions corresponding to multiple gene expression QTLs were identified. Comparison of expression mapping data with physical mapping of wheat expressed sequence tag (EST) sequences using rice synteny, as well as logarithm of odds (LOD) score analysis, showed that both cis- and trans-acting expression QTLs were present. Chromosomes 1D and 4B may contain significant trans-regulatory regions in this population.     

Novel quantitative trait loci controlling development of experimental autoimmune encephalomyelitis and proportion of lymphocyte subpopulations

The B10.RIII mouse strain (H-2(r)) develops chronic experimental autoimmune encephalomyelitis (EAE) upon immunization with the myelin basic protein 89-101 peptide. EAE was induced and studied in a backcross between B10.RIII and the EAE-resistant RIIIS/J strain (H-2(r)), and a complete genome scan with microsatellite markers was performed. Five loci were significantly linked to different traits and clinical subtypes of EAE on chromosomes 1, 5, 11, 15, and 16, three of the loci having sex specificity. The quantitative trait locus on chromosome 15 partly overlapped with the Eae2 locus, previously identified in crosses between the B10.RIII and RIIIS/J mouse strains. The loci on chromosomes 11 and 16 overlapped with Eae loci identified in other mouse crosses. By analyzing the backcross animals for lymphocyte phenotypes, the proportion of B and T cells in addition to the levels of CD4(+)CD8(-) and CD4(-)CD8(+) T cells and the CD4(+)/CD8(+) ratio in spleen were linked to different loci on chromosomes 1, 2, 3, 5, 6, 11, and 15. On chromosome 16, we found significant linkage to spleen cell proliferation. Several linkages overlapped with the quantitative trait loci for disease phenotypes. The identification of subphenotypes that are linked to the same loci as disease traits could be most useful in the search for candidate genes and biological pathways involved in the pathological process.     

Detection of quantitative trait loci controlling extremely early heading in rice

To clarify the genetic basis of extremely early heading in rice, we conducted quantitative trait locus (QTL) analyses using F₂ populations from two genetically wide cross combinations, Hayamasari/Kasalath (HaF₂) and Hoshinoyume/Kasalath (HoF₂). Hayamasari and Hoshinoyume are extremely early-heading japonica cultivars. Photoperiod sensitivity is completely lost in Hayamasari and weak in Hoshinoyume. Three QTLs, QTL(chr6), QTL(chr7), and QTL(chr8), for days-to-heading (DTH) in HaF₂ were detected on chromosomes 6, 7, and 8, respectively, and QTL(chr6) and QTL(chr7) were detected in HoF₂. On the basis of the chromosomal locations, QTL(chr6), QTL(chr7), and QTL(chr8) may be likely to be Hd1, Hd4, and Hd5, respectively, which had been detected previously as QTLs for DTH in an F₂ population of Nipponbare × Kasalath. Alleles of QTL(chr7) decreased DTH dramatically in both Hayamasari and Hoshinoyume, suggesting that QTL(chr7) has a major role in determining extremely early heading. In addition, allele-specific interactions were detected between QTL(chr6), QTL(chr7) and QTL(chr8). This result suggests that not only allelic differences but also epistatic interactions contribute to extremely early heading. QTL(chr8) was detected in HaF₂, but not in HoF₂, suggesting that it determines the difference in DTH between Hayamasari and Hoshinoyume. A major QTL was also detected in the region of QTL(chr8) in QTL analysis using an F₂ population of Hayamasari × Hoshinoyume. This result supports the idea that QTL(chr8) is a major factor that determines the difference in DTH between Hayamasari and Hoshinoyume, and is involved in photoperiod sensitivity.     

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.     

Identification of quantitative trait loci controlling developmental characteristics of Brassica oleracea L

A segregating population of F₁-derived doubled haploid (DH) lines of Brassica oleracea was used to detect and locate QTLs controlling 27 morphological and developmental traits, including leaf, flowering, axillary bud and stem characters. The population resulted from a cross between two very different B. oleracea crop types, an annual cauliflower and a biennial Brussels sprout. A principal component analysis (PCA), based on line means, allowed all the traits to be grouped into distinct categories according to the first five Principal Components. These were: leaf traits (PC1), flowering traits (PC2), axillary bud traits (PC3 and 5) and stem traits (PC4). Between zero and four putative QTL were located per trait, which individually explained between 6% and 43% of the additive genetic variation, using the multiple-marker regression approach to QTL mapping. For lamina width, bare petiole length and stem length two QTL with opposite effects were detected on the same linkage groups. Intra- and inter-specific comparative mapping using RFLP markers identified a QTL on linkage group O8 accounting for variation in vernalisation, which is probably synonymous with a QTL detected on linkage group N19 of Brassica napus. In addition, a QTL for petiole length detected on O3 of this study appeared to be homologous to a QTL detected on another B. oleracea genetic map (Camargo et al. 1995). Received: 28 March 2001 / Accepted: 25 June 2001