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 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.     

Analysis of candidate genes underlying two epistatic quantitative trait loci on SSC12 affecting litter size in pig

The previous results from a genome scan for total number of piglets born and number of piglets born alive in a F₂ Iberian by Meishan intercross showed several single and epistatic QTL. One of the most interesting results was obtained for SSC12, where two QTL affecting both traits showed epistatic interaction. In this study, we proposed two genes ( SLC9A3R1 and NOS2 ) as biological and potentially positional candidates underlying these QTL. Both cDNAs were characterized and 23 polymorphisms were detected. A chromosome scan was conducted with 12 markers, plus one SNP in SLC9A3R1 and one in NOS2, covering 110 cM of SSC12. The epistatic QTL (QTL1 at 15 cM and QTL2 at 97 cM) were confirmed, and SLC9A3R1 and NOS2 were mapped around the QTL1 and QTL2 regions respectively. Several SNPs in both genes were tested with standard animal model and marker assisted association tests. The most significant results were obtained with the NOS2 haplotype defined by one missense SNP c.2192C > T (Val to Ala) and a 15 bp duplication at the 3'UTR. This duplication seems to include AU-rich elements, and could be a target site for miRNA, therefore there are statistical and biological indications to consider this haplotype as the potential causal mutation underlying QTL2. SLC9A3R1 results were not conclusive. Although the interaction between the SNPs was not significant, we cannot reject the possibility of interaction of the NOS2 haplotype with other polymorphisms closely linked to the SL9A3R1 SNPs analysed.     

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.     

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.     

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.     

Shared quantitative trait loci underlying the genetic correlation between continuous traits

We review genetic correlations among quantitative traits in light of their underlying quantitative trait loci (QTL). We derive an expectation of genetic correlation from the effects of underlying loci and test whether published genetic correlations can be explained by the QTL underlying the traits. While genetically correlated traits shared more QTL (33%) on average than uncorrelated traits (11%), the actual number of shared QTL shared was small. QTL usually predicted the sign of the correlation with good accuracy, but the quantitative prediction was poor. Approximately 25% of trait pairs in the data set had at least one QTL with antagonistic effects. Yet a significant minority (20%) of such trait pairs have net positive genetic correlations due to such antagonistic QTL 'hidden' within positive genetic correlations. We review the evidence on whether shared QTL represent single pleiotropic loci or closely linked monotropic genes, and argue that strict pleiotropy can be viewed as one end of a continuum of recombination rates where r=0. QTL studies of genetic correlation will likely be insufficient to predict evolutionary trajectories over long time spans in large panmictic populations, but will provide important insights into the trade-offs involved in population and species divergence.     

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.     

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.     

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.     

Experimental designs and statistical methods for mapping quantitative trait loci underlying triploid endosperm traits without maternal genetic variation

Many endosperm traits are related to grain quality in cereal crops. Endosperm traits are mainly controlled by the endosperm genome but may be affected by the maternal genome. Studies have shown that maternal genotypic variation could greatly influence the estimation of the direct effects of quantitative trait loci (QTLs) underlying endosperm traits. In this paper, we propose methods of interval mapping of endosperm QTLs using seeds of F2 or BC1 (an equal mixture of F1 x P1 and F1 x P2 with F1 as the female parent) derived from a cross between 2 pure lines (P1 x P2). The most significant advantage of our experimental designs is that the maternal effects do not contribute to the genetic variation of endosperm traits and therefore the direct effects of endosperm QTLs can be estimated without the influence of maternal effects. In addition, the experimental designs can greatly reduce environmental variation because a few F1 plants grown in a small block of field will produce sufficient F2 or BC1 seeds for endosperm QTL analysis. Simulation studies show that the methods can efficiently detect endosperm QTLs and unbiasedly estimate their positions and effects. The BC1 design is better than the F2 design.     

Mixed linear model approach for mapping quantitative trait loci underlying crop seed traits

The crop seed is a complex organ that may be composed of the diploid embryo, the triploid endosperm and the diploid maternal tissues. According to the genetic features of seed characters, two genetic models for mapping quantitative trait loci (QTLs) of crop seed traits are proposed, with inclusion of maternal effects, embryo or endosperm effects of QTL, environmental effects and QTL-by-environment (QE) interactions. The mapping population can be generated either from double back-cross of immortalized F₂ (IF₂) to the two parents, from random-cross of IF₂ or from selfing of IF₂ population. Candidate marker intervals potentially harboring QTLs are first selected through one-dimensional scanning across the whole genome. The selected candidate marker intervals are then included in the model as cofactors to control background genetic effects on the putative QTL(s). Finally, a QTL full model is constructed and model selection is conducted to eliminate false positive QTLs. The genetic main effects of QTLs, QE interaction effects and the corresponding P-values are computed by Markov chain Monte Carlo algorithm for Gaussian mixed linear model via Gibbs sampling. Monte Carlo simulations were performed to investigate the reliability and efficiency of the proposed method. The simulation results showed that the proposed method had higher power to accurately detect simulated QTLs and properly estimated effect of these QTLs. To demonstrate the usefulness, the proposed method was used to identify the QTLs underlying fiber percentage in an upland cotton IF₂ population. A computer software, QTLNetwork-Seed, was developed for QTL analysis of seed traits.     

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.     

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).     

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.     

Genomic distribution of quantitative trait loci for yield and yield-related traits in common wheat

A major objective of quantitative trait locus(QTL)studies is to find genes/markers that can be used in breeding programs via marker assisted selection(MAS).We surveyed the QTLs for yield and yield related traits and their genomic distributions in common wheat(Triticum aestivum L.)in the available published reports.We then carried out a meta-QTL(MQTL)analysis to identify the major and consistent QTLs for these traits.In total,55 MQTLs were identified,of which 12 significant MQTLs were located on wheat chromosomes 1A,1B,2A,2D,3B,4A,4B,4D and 5A.Our study showed that the genetic control of yield and its components in common wheat involved the important genes such as Rht and Vrn.Furthermore,several significant MQTLs were found in the chromosomal regions corresponding to several rice genomic locations containing important QTLs for yield related traits.Our results demonstrate that meta-QTL analysis is a powerful tool for confirming the major and stable QTLs and refining their chromosomal positions in common wheat,which may be useful for improving the MAS efficiency of yield related traits.     

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     

Genetic mapping of quantitative trait loci controlling fruit size and shape in papaya

Papaya (Carica papaya L.) is a pan-tropical tree that bears fruit exhibiting a wide range of size and shape. Depending on variety and environment, papaya fruit may weigh from 0.2 kg up to 10 kg. Papaya fruit shape is a sex-linked trait ranging from spherical to ovate, cylindrical or pyriform. An F2 mapping population, produced from a cross between the Thai variety Khaek Dum, bearing 1.2 kg, red-fleshed fruit, and variety 2H94, a Hawaii Solo type bearing a 0.2 kg, yellow-fleshed fruit, was used to identify quantitative trait loci (QTLs) that influence papaya fruit characters including weight, diameter, length and shape. Fruit phenotype data, collected from two subpopulations planted in successive growing seasons, showed striking differences by year indicating significant genotype × environment interactions. Fourteen QTL with phenotypic effects ranging from 5 to 23% were identified across six linkage groups (LGs) with clusters of two or more QTL on LGs 02, 03, 07 and 09. These loci contain homologs to the tomato fruit QTL ovate, sun and fw2.2 regulating fruit size and shape. The papaya fruit QTL provide a starting point for dissecting the genetic pathways leading to extreme fruit size and shape and may prove useful for papaya breeders attempting to tailor new varieties to specific consumer markets.