High throughput analyses of epistasis for swine body dimensions and organ weights

High throughput analyses were performed to detect epistatic QTL in 17 body dimension and organ weight traits from a large F₂ pig population derived from a White Duroc and Erhualian intercross. The analyses used a nested test framework to handle multiple tests and a combined search algorithm to map epistatic QTL with empirical genome‐wide thresholds derived via prior permutation. Alternative statistical models (e.g. including vs. excluding carcass weight as a covariate) were tested to develop an in‐depth understanding of the role of epistasis in these kinds of traits. Epistasis signals were detected in only two or three traits under each statistical model studied. The interaction component of each pair of epistatic QTL explained a small proportion (0.7 to 2.1%) of the phenotypic variance in general. About half of the detected epistatic QTL pairs involved one of the two major QTL on porcine chromosomes 7 and 4. In those traits, the Erhualian allele consistently increased the phenotypes for the chromosome 7 QTL but decreased them for the chromosome 4 QTL. Models including carcass weight as covariate detected epistasis in body dimension traits whereas those excluding carcass weight found epistasis in organ weight traits. In addition, the epistasis results suggested that a QTL on chromosome 14 could be important for a number of organ weight traits. Using the high‐throughput analysis tool to examine different statistical models was essential for the generation of a complete picture of epistasis in a whole category of traits.     

Bayesian model choice and search strategies for mapping interacting quantitative trait Loci

Most complex traits of animals, plants, and humans are influenced by multiple genetic and environmental factors. Interactions among multiple genes play fundamental roles in the genetic control and evolution of complex traits. Statistical modeling of interaction effects in quantitative trait loci (QTL) analysis must accommodate a very large number of potential genetic effects, which presents a major challenge to determining the genetic model with respect to the number of QTL, their positions, and their genetic effects. In this study, we use the methodology of Bayesian model and variable selection to develop strategies for identifying multiple QTL with complex epistatic patterns in experimental designs with two segregating genotypes. Specifically, we develop a reversible jump Markov chain Monte Carlo algorithm to determine the number of QTL and to select main and epistatic effects. With the proposed method, we can jointly infer the genetic model of a complex trait and the associated genetic parameters, including the number, positions, and main and epistatic effects of the identified QTL. Our method can map a large number of QTL with any combination of main and epistatic effects. Utility and flexibility of the method are demonstrated using both simulated data and a real data set. Sensitivity of posterior inference to prior specifications of the number and genetic effects of QTL is investigated.     

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.     

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.     

Epistasis for fitness-related quantitative traits in Arabidopsis thaliana grown in the field and in the greenhouse

The extent to which epistasis contributes to adaptation, population differentiation, and speciation is a long-standing and important problem in evolutionary genetics. Using recombinant inbred (RI) lines of Arabidopsis thaliana grown under natural field conditions, we have examined the genetic architecture of fitness-correlated traits with respect to epistasis; we identified both single-locus additive and two-locus epistatic QTL for natural variation in fruit number, germination, and seed length and width. For fruit number, we found seven significant epistatic interactions, but only two additive QTL. For seed germination, length, and width, there were from two to four additive QTL and from five to eight epistatic interactions. The epistatic interactions were both positive and negative. In each case, the magnitude of the epistatic effects was roughly double that of the effects of the additive QTL, varying from -41% to +29% for fruit number and from -5% to +4% for seed germination, length, and width. A number of the QTL that we describe participate in more than one epistatic interaction, and some loci identified as additive also may participate in an epistatic interaction; the genetic architecture for fitness traits may be a network of additive and epistatic effects. We compared the map positions of the additive and epistatic QTL for germination, seed width, and seed length from plants grown in both the field and the greenhouse. While the total number of significant additive and epistatic QTL was similar under the two growth conditions, the map locations were largely different. We found a small number of significant epistatic QTL x environment effects when we tested directly for them. Our results support the idea that epistatic interactions are an important part of natural genetic variation and reinforce the need for caution in comparing results from greenhouse-grown and field-grown plants.     

Simultaneous mapping of epistatic QTL in DU6i × DBA/2 mice

We have mapped epistatic quantitative trait loci (QTL) in an F₂ cross between DU6i × DBA/2 mice. By including these epistatic QTL and their interaction parameters in the genetic model, we were able to increase the genetic variance explained substantially (8.8%–128.3%) for several growth and body composition traits. We used an analysis method based on a simultaneous search for epistatic QTL pairs without assuming that the QTL had any effect individually. We were able to detect several QTL that could not be detected in a search for marginal QTL effects because the epistasis cancelled out the individual effects of the QTL. In total, 23 genomic regions were found to contain QTL affecting one or several of the traits and eight of these QTL did not have significant individual effects. We identified 44 QTL pairs with significant effects on the traits, and, for 28 of the pairs, an epistatic QTL model fit the data significantly better than a model without interactions. The epistatic pairs were classified by the significance of the epistatic parameters in the genetic model, and visual inspection of the two-locus genotype means identified six types of related genotype–phenotype patterns among the pairs. Five of these patterns resembled previously published patterns of QTL interactions.     

Detection of quantitative trait loci for seminal root traits in maize (Zea mays L.) seedlings grown under differential phosphorus levels

Suboptimal phosphorus availability is a primary constraint for terrestrial plant growth. Seminal roots play an important role in acquisition of nutrients by plant seedlings. The length and number of seminal roots may be particularly important in acquisition of immobile nutrients such as phosphorus by increasing soil exploration. The objective of this study was to identify quantitative trait loci (QTL) controlling seminal root growth in response to phosphorus stress in maize, and to characterize epistatic interactions among QTL. Seminal root length and number were evaluated in 162 recombinant inbred lines derived from a cross between B73 and Mo17 in seedlings grown in a controlled environment. B73 and Mo17 significantly differed for seminal root length under low phosphorus, but not under adequate phosphorus conditions. Seminal root length of the population grown under low phosphorus ranged from 0 to 79.2 cm with a mean of 32.3 cm; while seminal root length of plants grown under high phosphorus ranged from 0.67 to 59.0 cm with a mean of 23.4 cm. Under low phosphorus, one main-effect QTL was associated with seminal root length and three QTL with seminal root number; under high phosphorus, two QTL with seminal root length and three QTL for seminal root number. These accounted for 11, 25.4, 22.8, and 24.1% of the phenotypic variations for seminal root length and number at low phosphorus, and seminal root length and number at high phosphorus, respectively. Di-genic epistatic loci were detected for seminal root length at low phosphorus (two pairs) seminal root number at low phosphorus (eight pairs), seminal root length at high phosphorus (four pairs), and seminal root number at high phosphorus (two pairs), which accounted for 23.2, 50.6, 32.2, and 20.3% of the total variations, respectively. Seminal root traits observed here were positively yet weakly correlated with shoot biomass in the field under low phosphorus, although no coincident QTL were detected. These results suggest that epistatic interactions are important in controlling genotypic variation associated with seedling seminal root traits.     

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 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.     

Bayesian mapping of genomewide interacting quantitative trait loci for ordinal traits

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

Use of randomization testing to detect multiple epistatic QTLs

Here, we describe a randomization testing strategy for mapping interacting quantitative trait loci (QTLs). In a forward selection strategy, non-interacting QTLs and simultaneously mapped interacting QTL pairs are added to a total genetic model. Simultaneous mapping of epistatic QTLs increases the power of the mapping strategy by allowing detection of interacting QTL pairs where none of the QTL can be detected by their marginal additive and dominance effects. Randomization testing is used to derive empirical significance thresholds for every model selection step in the procedure. A simulation study was used to evaluate the statistical properties of the proposed randomization tests and for which types of epistasis simultaneous mapping of epistatic QTLs adds power. Least squares regression was used for QTL parameter estimation but any other QTL mapping method can be used. A genetic algorithm was used to search for interacting QTL pairs, which makes the proposed strategy feasible for single processor computers. We believe that this method will facilitate the evaluation of the importance at epistatic interaction among QTLs controlling multifactorial traits and disorders.     

Multi-QTL Mapping for Quantitative Traits Using Epistatic Distorted Markers

The interaction between segregation distortion loci (SDL) has been often observed in all kinds of mapping populations. However, little has been known about the effect of epistatic SDL on quantitative trait locus (QTL) mapping. Here we proposed a multi-QTL mapping approach using epistatic distorted markers. Using the corrected linkage groups, epistatic SDL was identified. Then, these SDL parameters were used to correct the conditional probabilities of QTL genotypes, and these corrections were further incorporated into the new QTL mapping approach. Finally, a set of simulated datasets and a real data in 304 mouse F₂ individuals were used to validate the new method. As compared with the old method, the new one corrects genetic distance between distorted markers, and considers epistasis between two linked SDL. As a result, the power in the detection of QTL is higher for the new method than for the old one, and significant differences for estimates of QTL parameters between the two methods were observed, except for QTL position. Among two QTL for mouse weight, one significant difference for QTL additive effect between the above two methods was observed, because epistatic SDL between markers C66 and T93 exists (P = 2.94e-4).     

Strategies for genetic mapping of categorical traits

The search for efficient and powerful statistical methods and optimal mapping strategies for categorical traits under various experimental designs continues to be one of the main tasks in genetic mapping studies. Methodologies for genetic mapping of categorical traits can generally be classified into two groups, linear and non-linear models. We develop a method based on a threshold model, termed mixture threshold model to handle ordinal (or binary) data from multiple families. Monte Carlo simulations are done to compare its statistical efficiencies and properties of the proposed non-linear model with a linear model for genetic mapping of categorical traits using multiple families. The mixture threshold model has notably higher statistical power than linear models. There may be an optimal sampling strategy (family size vs number of families) in which genetic mapping reaches its maximal power and minimal estimation errors. A single large-sibship family does not necessarily produce the maximal power for detection of quantitative trait loci (QTL) due to genetic sampling of QTL alleles. The QTL allelic model has a marked impact on efficiency of genetic mapping of categorical traits in terms of statistical power and QTL parameter estimation. Compared with a fixed number of QTL alleles (two or four), the model with an infinite number of QTL alleles and normally distributed allelic effects results in loss of statistical power. The results imply that inbred designs (e.g. F₂ or four-way crosses) with a few QTL alleles segregating or reducing number of QTL alleles (e.g. by selection) in outbred populations are desirable in genetic mapping of categorical traits using data from multiple families. This revised version was published online in July 2006 with corrections to the Cover Date.     

Epistasis between QTLs for bone density variation in Copenhagen × dark agouti F2 rats

The variation in several of the risk factors for osteoporotic fracture, including bone mineral density (BMD), has been shown to be strongly influenced by genetic differences. However, the genetic architecture of BMD is complex in both humans and in model organisms. We previously reported quantitative trait locus (QTL) results for BMD from a genome screen of 828 F2 progeny of Copenhagen and dark agouti rats. These progeny also provide an excellent opportunity to search for epistatic effects, or interaction between genetic loci, that contribute to fracture risk. Microsatellite marker data from a 20-cM genome screen was analyzed along with weight-adjusted bone density (DXA and pQCT) phenotypic data using the R/qtl software package. Genotype and phenotype data were permuted to determine genome-wide significance thresholds for the full model and epistasis (interaction) LOD scores corresponding to an alpha level of 0.01. A novel locus on chromosome 15 and a previously reported chromosome 14 QTL demonstrated a strong epistatic effect on BMD at the femur by DXA (LOD = 5.4). Two novel QTLs on chromosomes 2 and 12 were found to interact to affect total BMD at the femur midshaft by pQCT (LOD = 5.0). These results provide new information regarding the mode of action of previously identified QTL in the rat, as well as identifying novel loci that act in combination with known QTL or with other novel loci to contribute to BMD variation.     

Using a physiological framework for improving the detection of quantitative trait loci related to nitrogen nutrition in <Emphasis Type="Italic">Medicago truncatula</Emphasis>

Medicago truncatula is used as a model plant for exploring the genetic and molecular determinants of nitrogen (N) nutrition in legumes. In this study, our aim was to detect quantitative trait loci (QTL) controlling plant N nutrition using a simple framework of carbon/N plant functioning stemming from crop physiology. This framework was based on efficiency variables which delineated the plant’s efficiency to take up and process carbon and N resources. A recombinant inbred line population (LR4) was grown in a glasshouse experiment under two contrasting nitrate concentrations. At low nitrate, symbiotic N₂ fixation was the main N source for plant growth and a QTL with a large effect located on linkage group (LG) 8 affected all the traits. Significantly, efficiency variables were necessary both to precisely localize a second QTL on LG5 and to detect a third QTL involved in epistatic interactions on LG2. At high nitrate, nitrate assimilation was the main N source and a larger number of QTL with weaker effects were identified compared to low nitrate. Only two QTL were common to both nitrate treatments: a QTL of belowground biomass located at the bottom of LG3 and another one on LG6 related to three different variables (leaf area, specific N uptake and aboveground:belowground biomass ratio). Possible functions of several candidate genes underlying QTL of efficiency variables could be proposed. Altogether, our results provided new insights into the genetic control of N nutrition in M. truncatula. For instance, a novel result for M. truncatula was identification of two epistatic interactions in controlling plant N₂ fixation. As such this study showed the value of a simple conceptual framework based on efficiency variables for studying genetic determinants of complex traits and particularly epistatic interactions.     

Model selection in binary trait locus mapping

Quantitative trait locus (QTL) mapping methodology for continuous normally distributed traits is the subject of much attention in the literature. Binary trait locus (BTL) mapping in experimental populations has received much less attention. A binary trait by definition has only two possible values, and the penetrance parameter is restricted to values between zero and one. Due to this restriction, the infinitesimal model appears to come into play even when only a few loci are involved, making selection of an appropriate genetic model in BTL mapping challenging. We present a probability model for an arbitrary number of BTL and demonstrate that, given adequate sample sizes, the power for detecting loci is high under a wide range of genetic models, including most epistatic models. A novel model selection strategy based upon the underlying genetic map is employed for choosing the genetic model. We propose selecting the "best" marker from each linkage group, regardless of significance. This reduces the model space so that an efficient search for epistatic loci can be conducted without invoking stepwise model selection. This procedure can identify unlinked epistatic BTL, demonstrated by our simulations and the reanalysis of Oncorhynchus mykiss experimental data.     

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.     

Epistatic pleiotropy and the genetic architecture of covariation within early and late-developing skull trait complexes in mice

The role of epistasis as a source of trait variation is well established, but its role as a source of covariation among traits (i.e., as a source of "epistatic pleiotropy") is rarely considered. In this study we examine the relative importance of epistatic pleiotropy in producing covariation within early and late-developing skull trait complexes in a population of mice derived from an intercross of the Large and Small inbred strains. Significant epistasis was found for several pairwise combinations of the 21 quantitative trait loci (QTL) affecting early developing traits and among the 20 QTL affecting late-developing traits. The majority of the epistatic effects were restricted to single traits but epistatic pleiotropy still contributed significantly to covariances. Because of their proportionally larger effects on variances than on covariances, epistatic effects tended to reduce within-group correlations of traits and reduce their overall degree of integration. The expected contributions of single-locus and two-locus epistatic pleiotropic QTL effects to the genetic covariance between traits were analyzed using a two-locus population genetic model. The model demonstrates that, for single-locus or epistatic pleiotropy to contribute to trait covariances in the study population, both traits must show the same pattern of single-locus or epistatic effects. As a result, a large number of the cases where loci show pleiotropic effects do not contribute to the covariance between traits in this population because the loci show a different pattern of effect on the different traits. In general, covariance patterns produced by single-locus and epistatic pleiotropy predicted by the model agreed well with actual values calculated from the QTL analysis. Nearly all single-locus and epistatic pleiotropic effects contributed positive components to covariances between traits, suggesting that genetic integration in the skull is achieved by a complex combination of pleiotropic effects.     

Detection of two QTL on chicken chromosome 14 for keyhole lymphet heamocyanin

A keyhole lymphet heamocyanin is an antigen which triggers Th1 type of immune response. A QTL for a primary immune response towards keyhole lymphet heamocyanin has been detected on chicken chromosome 14 in three populations. The results from the most recent population were inconsistent and varied depending on the applied QTL detection model. The major goal of the current study was the reanalysis of this data using a 2 QTL model. Additionally, in order to provide more accurate estimates of QTL effects and positions, epistasis between the QTL was considered as a potential important contributor to quantitative traits. Four statistical models were assumed: M1: A model assuming marginal additive effects of two QTL; M2: A model assuming marginal and epistatic additive effects of two QTL; M3: A model assuming marginal additive and dominance effects of two QTL; M4: A model assuming marginal additive and dominance effects of two QTL and all possible pairwise epistases. Two QTL with significant additive and dominance effects were detected on chicken chromosome 14 using model M3. One QTL was detected at 63 cM between MCW0123 and ROS0005, another at 76 cM between ROS0005 and MCW0225/NTN2Lsts1 (FDR = 0.0051). Modelling only additive effects resulted in a significantly worse fit. On the other hand, including epistatic effects did not improve fit significantly. The current study confirms previous reports of the QTL location on GGA14. A notable finding of this study is recognition of two closely related QTL for a keyhole lymphet heamocyanin response at the distal part of chicken chromosome 14.     

The use of a genetic algorithm for simultaneous mapping of multiple interacting quantitative trait loci

Here we describe a general method for improving computational efficiency in simultaneous mapping of multiple interacting quantitative trait loci (QTL). The method uses a genetic algorithm to search for QTL in the genome instead of an exhaustive enumerative ("step-by-step") search. It can be used together with any method of QTL mapping based on a genomic search, since it only provides a more efficient way to search the genome for QTL. The computational demand decreases by a factor of approximately 130 when using genetic algorithm-based mapping instead of an exhaustive enumerative search for two QTL in a genome size of 2000 cM using a resolution of 1 cM. The advantage of using a genetic algorithm increases further for larger genomes, higher resolutions, and searches for more QTL. We show that a genetic algorithm-based search has efficiency higher than or equal to a search method conditioned on previously identified QTL for all epistatic models tested and that this efficiency is comparable to that of an exhaustive search for multiple QTL. The genetic algorithm is thus a powerful and computationally tractable alternative to the exhaustive enumerative search for simultaneous mapping of multiple interacting QTL. The use of genetic algorithms for simultaneous mapping of more than two QTL and for determining empirical significance thresholds using permutation tests is also discussed.