Identifying quantitative trait locus by genetic background interactions in association studies

Association studies are designed to identify main effects of alleles across a potentially wide range of genetic backgrounds. To control for spurious associations, effects of the genetic background itself are often incorporated into the linear model, either in the form of subpopulation effects in the case of structure or in the form of genetic relationship matrices in the case of complex pedigrees. In this context epistatic interactions between loci can be captured as an interaction effect between the associated locus and the genetic background. In this study I developed genetic and statistical models to tie the locus by genetic background interaction idea back to more standard concepts of epistasis when genetic background is modeled using an additive relationship matrix. I also simulated epistatic interactions in four-generation randomly mating pedigrees and evaluated the ability of the statistical models to identify when a biallelic associated locus was epistatic to other loci. Under additive-by-additive epistasis, when interaction effects of the associated locus were quite large (explaining 20% of the phenotypic variance), epistasis was detected in 79% of pedigrees containing 320 individuals. The epistatic model also predicted the genotypic value of progeny better than a standard additive model in 78% of simulations. When interaction effects were smaller (although still fairly large, explaining 5% of the phenotypic variance), epistasis was detected in only 9% of pedigrees containing 320 individuals and the epistatic and additive models were equally effective at predicting the genotypic values of progeny. Epistasis was detected with the same power whether the overall epistatic effect was the result of a single pairwise interaction or the sum of nine pairwise interactions, each generating one ninth of the epistatic variance. The power to detect epistasis was highest (94%) at low QTL minor allele frequency, fell to a minimum (60%) at minor allele frequency of about 0.2, and then plateaued at about 80% as alleles reached intermediate frequencies. The power to detect epistasis declined when the linkage disequilibrium between the DNA marker and the functional polymorphism was not complete.     

QTL detection power of multi-parental RIL populations in Arabidopsis thaliana

A major goal of today's biology is to understand the genetic basis of quantitative traits. This can be achieved by statistical methods that evaluate the association between molecular marker variation and phenotypic variation in different types of mapping populations. The objective of this work was to evaluate the statistical power of quantitative trait loci (QTL) detection of various multi-parental mating designs, as well as to assess the reasons for the observed differences. Our study was based on an empirical data of 20 Arabidopsis thaliana accessions, which have been selected to capture the maximum genetic diversity. The examined mating designs differed strongly with respect to the statistical power to detect QTL. We observed the highest power to detect QTL for the diallel cross with random mating design. The results of our study suggested that performing sibling mating within subpopulations of joint-linkage mapping populations has the potential to considerably increase the power for QTL detection. Our results, however, revealed that using designs in which more than two parental alleles segregate in each subpopulation increases the power even more.     

Both additivity and epistasis control the genetic variation for fruit quality traits in tomato

The effect of a gene involved in the variation of a quantitative trait may change due to epistatic interactions with the overall genetic background or with other genes through digenic interactions. The classical populations used to map quantitative trait loci (QTL) are poorly efficient to detect epistasis. To assess the importance of epistasis in the genetic control of fruit quality traits, we compared 13 tomato lines having the same genetic background except for one to five chromosome fragments introgressed from a distant line. Six traits were assessed: fruit soluble solid content, sugar content and titratable acidity, fruit weight, locule number and fruit firmness. Except for firmness, a large part of the variation of the six traits was under additive control, but interactions between QTL leading to epistasis effects were common. In the lines cumulating several QTL regions, all the significant epistatic interactions had a sign opposite to the additive effects, suggesting less than additive epistasis. Finally the re-examination of the segregating population initially used to map the QTL confirmed the extent of epistasis, which frequently involved a region where main effect QTL have been detected in this progeny or in other studies.     

水稻株高上位性效应和ＱＥ互作效应的ＱＴＬ遗传研究

利用基因混合模型的ＱＴＬ定位方法研究了由籼稻品种ＩＲ６４和粳稻品种Ａzucena杂交衍生的ＤＨ群体在４个环境中的ＱＴＬ上位性效应和环境互作效应,结果表明,上位性是数量性状的重要遗传基础,并揭示了上位性的几个重要特点,所有的ＱＴＬ都参与了上位性效应的形成,６４％的ＱＴＬ还具有本身的加性效应,因此传统方法对ＱＴＬ加性效应的估算会由于上位性的影响而有偏,其他３６％的ＱＴＬ没有本身的加性效应,却参与了４８％的上位性互作用,这些位点可能通过诱发和修饰其他位点而起作用,上位性的特点还包括,经常发现了一个ＱＴＬ与多个ＱＴＬ发生互作;大效应的ＱＴＬ也参与上位性互作;上位性互作受环境影响,ＱＴＬ与环境的互效应比ＱＴＬ的主效应更多地被检测到,表明数量性状基因的表达易受环境影响。     

Mapping quantitative trait loci controlling silking date in a diallel cross among four lines of maize

 We describe and apply an interval mapping method for quantitative trait locus (QTL) detection using F₃ and testcross progenies derived from F₂ populations obtained from a diallel cross among four elite lines of maize. Linear model-based procedures were used for the test and estimation of putative QTL effects together with genetic interactions including epistasis. We mapped QTL associated with silking date and explored their genetic effects. Ten QTL were detected, and these explained more than 40% of the phenotypic variance. Most of these QTL had consistent and stable effects among genetic backgrounds and did not show significant epistasis. QTL-by-environment interaction was important for four QTL and was essentially due to changes in magnitude of allelic effects. These results show the efficiency of our method in several genetic situations as well as the power of the diallel design in detecting QTL simultaneously over several populations. Received: 2 September 1996 / Accepted: 20 December 1996     

Using Information Interaction to Discover Epistatic Effects in Complex Diseases

It is widely agreed that complex diseases are typically caused by the joint effects of multiple instead of a single genetic variation. These genetic variations may show stronger effects when considered together than when considered individually, a phenomenon known as epistasis or multilocus interaction. In this work, we explore the applicability of information interaction to discover pairwise epistatic effects related with complex diseases. We start by showing that traditional approaches such as classification methods or greedy feature selection methods (such as the Fleuret method) do not perform well on this problem. We then compare our information interaction method with BEAM and SNPHarvester in artificial datasets simulating epistatic interactions and show that our method is more powerful to detect pairwise epistatic interactions than its competitors. We show results of the application of information interaction method to the WTCCC breast cancer dataset. Our results are validated using permutation tests. We were able to find 89 statistically significant pairwise interactions with a p-value lower than . Even though many recent algorithms have been designed to find epistasis with low marginals, we observed that all (except one) of the SNPs involved in statistically significant interactions have moderate or high marginals. We also report that the interactions found in this work were not present in gene-gene interaction network STRING.     

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.     

SELECTION BIASES THE PREVALENCE AND TYPE OF EPISTASIS ALONG ADAPTIVE TRAJECTORIES

The contribution to an organism's phenotype from one genetic locus may depend upon the status of other loci. Such epistatic interactions among loci are now recognized as fundamental to shaping the process of adaptation in evolving populations. Although little is known about the structure of epistasis in most organisms, recent experiments with bacterial populations have concluded that antagonistic interactions abound and tend to deaccelerate the pace of adaptation over time. Here, we use the NK model of fitness landscapes to examine how natural selection biases the mutations that substitute during evolution based on their epistatic interactions. We find that, even when beneficial mutations are rare, these biases are strong and change substantially throughout the course of adaptation. In particular, epistasis is less prevalent than the neutral expectation early in adaptation and much more prevalent later, with a concomitant shift from predominantly antagonistic interactions early in adaptation to synergistic and sign epistasis later in adaptation. We observe the same patterns when reanalyzing data from a recent microbial evolution experiment. These results show that when the order of substitutions is not known, standard methods of analysis may suggest that epistasis retards adaptation when in fact it accelerates it.     

Sib mating designs for mapping quantitative trait loci

The power to separate the variance of a quantitative trait locus (QTL) from the polygenic variance is determined by the variability of genes identical by descent (IBD) at the QTL. This variability may increase with inbreeding. Selfing, the most extreme form of inbreeding, increases the variability of the IBD value shared by siblings, and thus has a higher efficiency for QTL mapping than random mating. In self-incompatible organisms, sib mating is the closest form of inbreeding. Similar to selfing, sib mating may also increase the power of QTL detection relative to random mating. In this study, we develop an IBD-based method under sib mating designs for QTL mapping. The efficiency of sib mating is then compared with random mating. Monte Carlo simulations show that sib mating designs notably increase the power for QTL detection. When power is intermediate, the power to detect a QTL using full-sib mating is, on average, 7% higher than under random mating. In addition, the IBD-based method proposed in this paper can be used to combine data from multiple families. As a result, the estimated QTL parameters can be applied to a wide statistical inference space relating to the entire reference population. This revised version was published online in July 2006 with corrections to the Cover Date.     

Design III with Marker Loci

Design III is an experimental design originally proposed by R. E. COMSTOCK and H. F. ROBINSON for estimating genetic variances and the average degree of dominance for quantitative trait loci (QTL) and has recently been extended for mapping QTL. In this paper, we first extend COMSTOCK and ROBINSON's analysis of variance to include linkage, two-locus epistasis and the use of F(3) parents. Then we develop the theory and statistical analysis of orthogonal contrasts and contrast X environment interaction for a single marker locus to characterize the effects of QTL. The methods are applied to the maize data of C. W. STUBER. The analyses strongly suggest that there are multiple linked QTL in many chromosomes for several traits examined. QTL effects are largely environment-independent for grain yield, ear height, plant height and ear leaf area and largely environment dependent for days to tassel, grain moisture and ear number. There is significant QTL epistasis. The results are generally in favor of the hypothesis of dominance of favorable genes to explain the observed heterosis in grain yield and other traits, although epistasis could also play an important role and overdominance at individual QTL level can not be ruled out.     

Efficiency of triple test cross for detecting epistasis with marker information

The triple test cross (TTC) is an experimental design for detecting epistasis and estimating the components of genetic variance for quantitative traits. In this paper, we extend the analysis to include molecular information. The statistical power of the mating design was assessed under a model assuming that a finite number of loci affect the trait in question. Formulae are developed for the analysis with or without marker information relating to the recombination fraction between loci, the genetical properties of quantitative trait controlled by the quantitative trait loci (QTL), the linkage phases of the parents and population size. Application of these formulae showed that the recombination fraction between genes and the magnitude and the types of epistasis have important interactions in their effects on power. The results demonstrate that the TTC may have increased power to detect epistasis when marker information is present. However, the simulation experiments show that the standard deviation of the estimated expected mean square was higher with one marker than that with two, whereas the corresponding value without marker information was the lowest. In addition, we demonstrate that the relative position of QTL and markers and the number of markers can both affect the power of epistatic detection.     

Detection of QTL for flowering time in multiple families of elite maize

Flowering time is a fundamental quantitative trait in maize that has played a key role in the postdomestication process and the adaptation to a wide range of climatic conditions. Flowering time has been intensively studied and recent QTL mapping results based on diverse founders suggest that the genetic architecture underlying this trait is mainly based on numerous small-effect QTL. Here, we used a population of 684 progenies from five connected families to investigate the genetic architecture of flowering time in elite maize. We used a joint analysis and identified nine main effect QTL explaining approximately 50?% of the genotypic variation of the trait. The QTL effects were small compared with the observed phenotypic variation and showed strong differences between families. We detected no epistasis with the genetic background but four digenic epistatic interactions in a full 2-dimensional genome scan. Our results suggest that flowering time in elite maize is mainly controlled by main effect QTL with rather small effects but that epistasis may also contribute to the genetic architecture of the trait.     

Quantitative trait loci affecting delta13C and response to differential water availibility in Arabidopsis thaliana

Phenotypic plasticity is an important response mechanism of plants to environmental heterogeneity. Here, we explored the genetic basis of plastic responses of Arabidopsis thaliana to water deficit by experimentally mapping quantitative trait loci (QTL) in two recombinant inbred populations (Cvi x Ler and Ler x Col). We detected genetic variation and significant genotype-by-environment interactions for many traits related to water use. We also mapped 26 QTL, including six for carbon isotope composition (delta13C). Negative genetic correlations between fruit length and fruit production as well as between flowering time and branch production were corroborated by QTL colocalization, suggesting these correlations are due to pleiotropy or physical linkage. Water-limited plants were more apically dominant with greater root:shoot ratios and higher delta13C (higher water-use efficiency) when compared to well-watered plants. Many of the QTL effects for these traits interacted significantly with the irrigation treatment, suggesting that the observed phenotypic plasticity is genetically based. We specifically searched for epistatic (QTL-QTL) interactions using a two-dimensional genome scan, which allowed us to detect epistasis regardless of additive genetic effects. We found several significant QTL-QTL interactions including three that exhibited environmental dependence. These results provide preliminary evidence for proposed genetic mechanisms underlying phenotypic plasticity.     

Epistasis and genotype-environment interaction for quantitative trait loci affecting flowering time in Arabidopsis thaliana

A major goal of evolutionary biology is to understand the genetic architecture of the complex quantitative traits that may lead to adaptations in natural populations. Of particular relevance is the evaluation of the frequency and magnitude of epistasis (gene–gene and gene–environment interaction) as it plays a controversial role in models of adaptation within and among populations. Here, we explore the genetic basis of flowering time in Arabidopsis thaliana using a series of quantitative trait loci (QTL) mapping experiments with two recombinant inbred line (RIL) mapping populations [Columbia (Col) x Landsberg erecta (Ler), Ler x Cape Verde Islands (Cvi)]. We focus on the response of RILs to a series of environmental conditions including drought stress, leaf damage, and apical damage. These data were explicitly evaluated for the presence of epistasis using Bayesian based multiple-QTL genome scans. Overall, we mapped fourteen QTL affecting flowering time. We detected two significant QTL–QTL interactions and several QTL–environment interactions for flowering time in the Ler x Cvi population. QTL–environment interactions were due to environmentally induced changes in the magnitude of QTL effects and their interactions across environments – we did not detect antagonistic pleiotropy. We found no evidence for QTL interactions in the Ler x Col population. We evaluate these results in the context of several other studies of flowering time in Arabidopsis thaliana and adaptive evolution in natural populations.     

Mapping the epistatic network underlying murine reproductive fatpad variation

Genome-wide mapping analyses are now commonplace in many species and several networks of interacting loci have been reported. However, relatively few details regarding epistatic interactions and their contribution to complex trait variation in multicellular organisms are available and the identification of positional candidate loci for epistatic QTL (epiQTL) is hampered, especially in mammals, by the limited genetic resolution inherent in most study designs. Here we further investigate the genetic architecture of reproductive fatpad weight in mice using the F(10) generation of the LG,SM advanced intercross (AI) line. We apply multiple mapping techniques including a single-locus model, locus-specific composite interval mapping (CIM), and tests for multiple QTL per chromosome to the 12 chromosomes known to harbor single-locus QTL (slQTL) affecting obesity in this cross. We also perform a genome-wide scan for pairwise epistasis. Using this combination of approaches we detect 199 peaks spread over all 19 autosomes, which potentially contribute to trait variation including all eight original F(2) loci (Adip1-8), novel slQTL peaks on chromosomes 7 and 9, and several novel epistatic loci. Extensive epistasis is confirmed involving both slQTL confidence intervals (C.I.) as well as regions that show no significant additive or dominance effects. These results provide important new insights into mapping complex genetic architectures and the role of epistasis in complex trait variation.     

Mapping QTLs with digenic epistasis under multiple environments and predicting heterosis based on QTL effects

Mixed linear model approach was proposed for mapping QTLs with the digenic epistasis and QTL by environment (QE) interaction as well as additive and dominant effects. Monte Carlo simulations indicated that the proposed method could provide unbiased estimations for both positions and genetic main effects of QTLs, as well as unbiased predictions for QE interaction effects. A method was suggested for predicting heterosis based on individual QTL effects. The immortalized F₂ (IF₂) population constructed by random mating among RI or DH lines is appropriate for mapping QTLs with epistasis and their QE interaction. Based on the models and methodology proposed, we developed a QTL mapping software, QTLMapper 2.0 on the basis of QTLmapper 1.0, which is suitable for analyzing populations of DH, RIL, F₂ and IF₂. Data of thousand grain weight of IF₂ population with 240 lines derived from elite hybrid rice Shanyou 63 were analyzed as a worked example.     

Genome-wide QTL mapping of saltwater tolerance in sibling species of Anopheles (malaria vector) mosquitoes

Although freshwater (FW) is the ancestral habitat for larval mosquitoes, multiple species independently evolved the ability to survive in saltwater (SW). Here, we use quantitative trait locus (QTL) mapping to investigate the genetic architecture of osmoregulation in Anopheles mosquitoes, vectors of human malaria. We analyzed 1134 backcross progeny from a cross between the obligate FW species An. coluzzii, and its closely related euryhaline sibling species An. merus. Tests of 2387 markers with Bayesian interval mapping and machine learning (random forests) yielded six genomic regions associated with SW tolerance. Overlap in QTL regions from both approaches enhances confidence in QTL identification. Evidence exists for synergistic as well as disruptive epistasis among loci. Intriguingly, one QTL region containing ion transporters spans the 2Rop chromosomal inversion that distinguishes these species. Rather than a simple trait controlled by one or a few loci, our data are most consistent with a complex, polygenic mode of inheritance.     

Unraveling epistasis with triple testcross progenies of near-isogenic lines

Libraries of near-isogenic lines (NILs) are a powerful plant genetic resource to map quantitative trait loci (QTL). Nevertheless, QTL mapping with NILs is mostly restricted to genetic main effects. Here we propose a two-step procedure to map additive-by-additive digenic epistasis with NILs. In the first step, a generation means analysis of parents, their F₁ hybrid, and one-segment NILs and their triple testcross (TTC) progenies is used to identify in a one-dimensional scan loci exhibiting QTL-by-background interactions. In a second step, one-segment NILs with significant additive-by-additive background interactions are used to produce particular two-segment NILs to test for digenic epistatic interactions between these segments. We evaluated our approach by analyzing a random subset of a genomewide Arabidopsis thaliana NIL library for growth-related traits. The results of our experimental study illustrated the potential of the presented two-step procedure to map additive-by-additive digenic epistasis with NILs. Furthermore, our findings suggested that additive main effects as well as additive-by-additive digenic epistasis strongly influence the genetic architecture underlying growth-related traits of A. thaliana.     

Estimating the genetic architecture of quantitative traits

Understanding and estimating the structure and parameters associated with the genetic architecture of quantitative traits is a major research focus in quantitative genetics. With the availability of a well-saturated genetic map of molecular markers, it is possible to identify a major part of the structure of the genetic architecture of quantitative traits and to estimate the associated parameters. Multiple interval mapping, which was recently proposed for simultaneously mapping multiple quantitative trait loci (QTL), is well suited to the identification and estimation of the genetic architecture parameters, including the number, genomic positions, effects and interactions of significant QTL and their contribution to the genetic variance. With multiple traits and multiple environments involved in a QTL mapping experiment, pleiotropic effects and QTL by environment interactions can also be estimated. We review the method and discuss issues associated with multiple interval mapping, such as likelihood analysis, model selection, stopping rules and parameter estimation. The potential power and advantages of the method for mapping multiple QTL and estimating the genetic architecture are discussed. We also point out potential problems and difficulties in resolving the details of the genetic architecture as well as other areas that require further investigation. One application of the analysis is to improve genome-wide marker-assisted selection, particularly when the information about epistasis is used for selection with mating.