Connected populations for detecting quantitative trait loci and testing for epistasis: an application in maize

Quantitative trait loci (QTL) detection experiments have often been restricted to large biallelic populations. Use of connected multiparental crosses has been proposed to increase the genetic variability addressed and to test for epistatic interactions between QTL and the genetic background. We present here the results of a QTL detection performed on six connected F₂ populations of 150 F_2:3 families each, derived from four maize inbreds and evaluated for three traits of agronomic interest. The QTL detection was carried out by composite interval mapping on each population separately, then on the global design either by taking into account the connections between populations or not. Epistatic interactions between loci and with the genetic background were tested. Taking into account the connections between populations increased the number of QTL detected and the accuracy of QTL position estimates. We detected many epistatic interactions, particularly for grain yield QTL (R ² increase of 9.6%). Use of connections for the QTL detection also allowed a global ranking of alleles at each QTL. Allelic relationships and epistasis both contribute to the lack of consistency for QTL positions observed among populations, in addition to the limited power of the tests. The potential benefit of assembling favorable alleles by marker-assisted selection are discussed.     

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.     

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.     

Power of tests for QTL detection using replicated progenies derived from a diallel cross

In crop species, most QTL (quantitative trait loci) mapping strategies use segregating populations derived from an initial cross between two lines. However, schemes including more than two parents could also be used. We propose an approach using a high-density restriction fragment length polymorphism (RFLP) map established on six F ₂ populations derived from diallel crosses among four inbred lines and the phenotypic performances of two types of replicated progenies (F ₃ and topcross). The QTL is supposed to be on the marker locus considered. Three linear model tests for the detection of QTL effects (T ₁, T ₂ and T ₃) are described and their power studied for the two types of progeny. T ₁ tests the global genetic effects of the QTL (additivity and dominance) and T ₂ tests only additive effects assuming dominance is absent when it could exist. The models of these two tests assume that the main effects of QTL alleles are constant in different genetic backgrounds. The additive model of test T ₃ considers the six F ₂ populations independently, and T ₃ is the equivalent of the classical mean comparison test if we neglect dominance; it uses only contrasts between the homozygote marker classes. The results show that T ₂ is much more powerful than T ₃. The power of T ₁ and T ₂ depends on the relative sizes of the additive and dominance effects, and their comparison is not easy to establish. Nevertheless, T ₂ seems to be the more powerful in most situations, indicating that it is often more interesting to ignore dominance when testing for a QTL effect. For a given size of genetic effects, the power is affected by the total number of individuals genotyped in F ₂ and the recombination rate between the marker locus and the putative QTL. The approach presented in this paper has some drawbacks but could be easily generalized to other sizes of diallels and different progeny types.     

Mapping,genetic effects,and epistatic interaction of two bacterial canker resistance QTLs from<Emphasis Type="Italic"> Lycopersicon hirsutum</Emphasis>

Two quantitative trait loci (QTL) from Lycopersicon hirsutum, Rcm 2.0 and Rcm 5.1, control resistance to Clavibacter michiganensis subsp. michiganensis (Cmm). To precisely map both loci, we applied interval mapping techniques to 1,056 individuals in three populations exhibiting F₂ segregation. Based on a 1-LOD confidence interval, Rcm 2.0 mapped to a 14.9-cM interval on chromosome 2 and accounted for 25.7–34.0% of the phenotypic variation in disease severity. Rcm 5.1 mapped to a 4.3-cM interval on chromosome 5 and accounted for 25.8–27.9% of the phenotypic variation. Progeny testing of recombinant plants narrowed the QTL location for Rcm 2.0 to a 4.4-cM interval between TG537-TG091 and to a 2.2-cM interval between CT202-TG358 for Rcm 5.1. A population of 750 individuals exhibiting F₂ segregation was used to detect epistasis between both loci using ANOVA and orthogonal contrasts (P=0.027), suggesting that resistance was determined by additive gene action and an additive-by-additive epistatic interaction. A partial diallel mating design was used to confirm epistasis, advance superior genotypes, randomize genetic backgrounds, and create recombination opportunities. This crossing scheme created a more balanced population (n=112) containing the nine F₂ genotypic classes. Parents in the diallel were selected from the previous population based on resistance, genotype at the Rcm 2.0 and Rcm 5.1 loci, and horticultural traits. A replicated trial using the diallel population confirmed additive-by-additive epistasis (P<0.0001). These results validate the gene action, intra -locus interaction, and map position of two loci controlling resistance to Cmm.Communicated by G. Wenzel     

Epistasis and the evolutionary dynamics of measured genotypic values during simulated serial bottlenecks

The evolutionary effects of epistasis have been primarily explored analytically and most empirical studies have utilized yeast, viral and bacterial populations. Empirical analyses in multi‐cellular organisms are rare because of experimental constraints. Here, we report the results of a genome‐wide scan for two‐way epistasis in 16 traits related to body size and composition in F₂ mice from the LG/J by SM/J intercross. We analyze two‐locus genotypic values at quantitative trait loci (QTL), which provides an especially detailed view of epistatic architectures, to evaluate their predicted evolutionary consequences via Monte Carlo simulations. Epistatic profiles vary, but all traits show complicated genetic architectures which are largely hidden in single locus QTL scans. On average, detected epistatic effects are comparable in size to marginal effects. Simulations demonstrate an expected preservation, and often inflation, of heritable variance across several generations of small effective population size for many identified epistatic pairs over a range of starting allele frequencies.     

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.     

Overview of QTL detection in plants and tests for synergistic epistatic interactions

Improvements in the usefulness of QTL analysis arise from better statistical methods applied to the problem, ability to analyze more complex mating designs, and the fitting of less simplified genetic models. Here we review the advantages of different plant mating designs in QTL analysis and conclude that diallel designs have several favorable properties. We then turn to the detection of systematic genome-wide synergistic epistasis. This form of epistasis has important implications from evolutionary (maintenance of sexual reproduction and concealment of cryptic genetic variation) and practical perspectives (response to pyramided favorable alleles). We develop two methods for detecting systematic synergistic epistasis, one based on analyzing interactions between locus effects and predicted individual genotypic values and one based on analyzing pairwise locus interactions. Using the first method we detect synergistic epistasis in a barley and a wheat dataset but not in a maize dataset. We fail to detect synergistic epistasis with the second method. We discuss our results in the light of theoretical questions concerning the mechanisms of synergistic epistasis.     

Quantitative genetics of speciation: additive and non-additive genetic differentiation between <Emphasis Type="Italic">Drosophila madeirensis</Emphasis> and <Emphasis Type="Italic">Drosophila subobscura</Emphasis>

The role of dominance and epistasis in population divergence has been an issue of much debate ever since the neoDarwinian synthesis. One of the best ways to dissect the several genetic components affecting the genetic architecture of populations is line cross analysis. Here we present a study comparing generation means of several life history-traits in two closely related Drosophila species: Drosophila subobscura, D. madeirensis as well as their F ₁ and F ₂ hybrids. This study aims to determine the relative contributions of additive and non-additive genetic parameters to the differentiation of life-history traits between these two species. The results indicate that both negative dominance and epistatic effects are very important in the differentiation of most traits. We end with considerations about the relevance of these findings for the understanding of the role of non-additive effects in speciation.     

QTL analysis reveals context-dependent loci for seed glucosinolate trait in the oilseed <Emphasis Type="Italic">Brassica juncea</Emphasis>: importance of recurrent selection backcross scheme for the identification of ‘true’ QTL

Seed glucosinolate content in Brassica juncea is a complex quantitative trait. A recurrent selection backcross (RSB) method with a doubled haploid (DH) generation interspersing backcross generations was used for the introgression of low glucosinolate alleles from an east European gene pool B. juncea line, Heera into an Indian gene pool variety, Varuna. Phenotypic comparisons among the DH populations derived from early to advanced backcrosses revealed a shift in the mean values for various glucosinolates with the advancement of backcrossing, indicating a change in the selective values of the alleles with change in the genetic background due to the existence of epistasis and context dependencies. QTL mapping for various seed glucosinolates from early (F₁DH) and advanced generation (BC₄DH) populations confirmed the presence of epistasis and context dependency. The common QTL detected in both F₁DH and BC₄DH changed their R ² values from the former to the later generation. Some of the QTL detected in the F₁DH became irrelevant in the BC₄DH population. Further, new QTL were detected in the BC₄DH population for various glucosinolates. A validation study on a population of low glucosinolate DH lines derived from all the backcross generations of the RSB breeding programme revealed that the QTL detected in BC₄DH were the ‘true’ QTL. Using glucosinolate as an example, the study provides strong evidence for the importance of the RSB method for the identification of the ‘true’ QTL which would be significant for marker assisted introgression of a complex quantitative trait whose expression is influenced by epistatic interactions. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Authors N. Ramchiary, N. C. Bisht, V. Gupta, A. Mukhopadhyay and N. Arumugam have contributed equally to this work.     

GENE EFFECTS ON A QUANTITATIVE TRAIT: TWO-LOCUS EPISTATIC EFFECTS MEASURED AT MICROSATELLITE MARKERS AND AT ESTIMATED QTL

Most evolutionarily and agriculturally important traits are affected by many genes (quantitative trait loci, or QTL) of relatively small effect. Usually the genetics of these traits are examined by indirect statistical analysis of the covariance among relatives, rather than by direct analyses. We use new analytical and molecular techniques to examine nonadditive interactions of microsatellite markers and estimated QTL that influence adult body weight in mice. Offspring of a cross between a large inbred mouse strain (LG/J) and a small inbred strain (SM/J) were intercrossed to form a segregating F₂ generation. Using 76 microsatellite markers and 19 estimated QTL, we estimate gene-level epistasis and population-level epistasis for body weight at 10 weeks for 534 F₂ mice. Significant epistasis was found for large numbers of the two locus comparisons using both markers and previously detected QTL. There are many genes segregating for adult body weight in this cross and many of these genes appear to interact epistatically. The discovery of potentially extensive epistasis has important implications for evolutionary models.     

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.     

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.     

Influence of dent corn genetic backgrounds on QTL detection for plant-height traits and their relationships in high-oil maize

QTL mapping for plant-height traits has not been hitherto reported in high-oil maize. A high-oil maize inbred ‘GY220’ was crossed with two dent maize inbreds (‘8984’ and ‘8622’) to generate two connected F_2:3 populations. Four plant-height traits were evaluated in 284 and 265 F_2:3 families. Single-trait QTL mapping and multiple-trait joint QTL mapping was used to detect QTLs for the traits and the genetic relationship between plant height (PH) and two other plant-height traits. A total of 28 QTLs and 12 pairs of digenic interactions among detected QTLs for four traits were detected in the two F_2:3 families. Only one marker was shared between the two populations. Joint analysis of PH with ear height (EH) and PH with top height (TH) detected 32 additional QTLs. Our results showed that QTL detection for PH was dependent on the genetic background of dent corn inbreds. Multiple-trait joint QTL analysis could increase the number of detected QTLs.     

Epistatic QTL pairs associated with meat quality and carcass composition traits in a porcine Duroc × Pietrain population

Background

Quantitative trait loci (QTL) analyses in pig have revealed numerous individual QTL affecting growth, carcass composition, reproduction and meat quality, indicating a complex genetic architecture. In general, statistical QTL models consider only additive and dominance effects and identification of epistatic effects in livestock is not yet widespread. The aim of this study was to identify and characterize epistatic effects between common and novel QTL regions for carcass composition and meat quality traits in pig.

Methods

Five hundred and eighty five F₂ pigs from a Duroc × Pietrain resource population were genotyped using 131 genetic markers (microsatellites and SNP) spread over the 18 pig autosomes. Phenotypic information for 26 carcass composition and meat quality traits was available for all F₂ animals. Linkage analysis was performed in a two-step procedure using a maximum likelihood approach implemented in the QxPak program.

Results

A number of interacting QTL was observed for different traits, leading to the identification of a variety of networks among chromosomal regions throughout the porcine genome. We distinguished 17 epistatic QTL pairs for carcass composition and 39 for meat quality traits. These interacting QTL pairs explained up to 8% of the phenotypic variance.

Conclusions

Our findings demonstrate the significance of epistasis in pigs. We have revealed evidence for epistatic relationships between different chromosomal regions, confirmed known QTL loci and connected regions reported in other studies. Considering interactions between loci allowed us to identify several novel QTL and trait-specific relationships of loci within and across chromosomes.     

控制玉米雄穗分枝数目和雄穗重的主效QTL的定位

利用2套具有共同亲本黄早四且分别含有230个及235个家系的F_2:3群体, 结合2年多点的表型鉴定, 运用完备复合区间作图方法对不同生态环境下(2007-北京、2008-北京、2007-河南、2008-河南、2007-新疆以及2008-新疆)的玉米雄穗分枝数和雄穗重进行QTL定位。同时, 利用基于混合线性模型的QTLNetwork-2.0软件进行基因×环境互作及上位性分析。6个环境下2个群体共检测到51个与雄穗分枝数和雄穗重相关的QTL(Q/H群体32个, Y/H群体19个), 其中包括7个主效QTL, 并在Q/H群体中确定了2个重要的QTL, 即位于7.01bin的Qqtpbn7-1和位于7.02bin的Qqtw7-2。对比2个群体的定位结果, 共挖掘到3个在不同遗传背景下的“一致性”QTL, 这些在不同环境及不同遗传背景下能够稳定存在的QTL可为玉米雄穗相关性状的生产应用以及精细定位提供有价值的参考。     

Contribution of genetic effects to genetic variance components with epistasis and linkage disequilibrium

Background

Cockerham genetic models are commonly used in quantitative trait loci (QTL) analysis with a special feature of partitioning genotypic variances into various genetic variance components, while the F_∞ genetic models are widely used in genetic association studies. Over years, there have been some confusion about the relationship between these two type of models. A link between the additive, dominance and epistatic effects in an F_∞ model and the additive, dominance and epistatic variance components in a Cockerham model has not been well established, especially when there are multiple QTL in presence of epistasis and linkage disequilibrium (LD).

Results

In this paper, we further explore the differences and links between the F_∞ and Cockerham models. First, we show that the Cockerham type models are allelic based models with a special modification to correct a confounding problem. Several important moment functions, which are useful for partition of variance components in Cockerham models, are also derived. Next, we discuss properties of the F_∞ models in partition of genotypic variances. Its difference from that of the Cockerham models is addressed. Finally, for a two-locus biallelic QTL model with epistasis and LD between the loci, we present detailed formulas for calculation of the genetic variance components in terms of the additive, dominant and epistatic effects in an F_∞ model. A new way of linking the Cockerham and F_∞ model parameters through their coding variables of genotypes is also proposed, which is especially useful when reduced F_∞ models are applied.

Conclusion

The Cockerham type models are allele-based models with a focus on partition of genotypic variances into various genetic variance components, which are contributed by allelic effects and their interactions. By contrast, the F_∞ regression models are genotype-based models focusing on modeling and testing of within-locus genotypic effects and locus-by-locus genotypic interactions. When there is no need to distinguish the paternal and maternal allelic effects, these two types of models are transferable. Transformation between an F_∞ model's parameters and its corresponding Cockerham model's parameters can be established through a relationship between their coding variables of genotypes. Genetic variance components in terms of the additive, dominance and epistatic genetic effects in an F_∞ model can then be calculated by translating formulas derived for the Cockerham models.

     

Epistasis causes outbreeding depression in eucalypt hybrids

The genetic architecture underlying species differentiation is essential for understanding the mechanisms of speciation and post-zygotic reproductive barriers which exist between species. We undertook line-cross analysis of multiple hybrid (F₁, F₂ and backcrosses) and pure-species populations of two diploid eucalypt species from different subseries, Eucalyptus globulus and Eucalyptus nitens, to unravel the genetic architecture of their differentiation. The populations were replicated on two sites and monitored for growth and survival over a 14-year period. The hybrids exhibited severe outbreeding depression which increased with age. Of the composite additive, dominance and epistatic effects estimated, the additive × additive epistatic component was the most important in determining population divergence in both growth and survival. Significant dominance × dominance epistasis was also detected for survival at several ages. While favourable dominance and, in the case of survival, dominance × dominance epistasis could produce novel gene combinations which enhance hybrid fitness, at the population level, these effects were clearly overridden by adverse additive × additive epistasis which appears to be a major driver of overall outbreeding depression in the hybrid populations. The lack of model fit at older ages suggested that even high-order epistatic interactions may potentially have a significant contribution to outbreeding depression in survival. The estimated composite genetic parameters were generally stable across sites. Our results argue that the development of favourable epistasis is a key mechanism underlying the genetic divergence of eucalypt species, and epistasis is an important mechanism underlying the evolution of post-zygotic reproductive barriers.     

Genetic models to estimate additive and non-additive effects of marker-associated QTL using multiple regression techniques

Summary The development of molecular markers has recently raised expectations for their application in selection programs. However, some questions related to quantitative trait loci (QTL) identification are still unanswered. The objectives of this paper are (1) to develop statistical genetic models for detecting and locating on the genome multi-QTL with additive, dominance and epistatic effects using multiple linear regression analysis in the backcross and F_n generations from the cross of two inbred lines; and (2) to discuss the bias caused by linked and unlinked QTL on the genetic estimates. Non-linear models were developed for different backcross and F_n generations when both epistasis and no epistasis were assumed. Generation analysis of marked progenies is suggested as a way of increasing the number of observations for the estimates without additional cost for molecular scoring. Some groups of progenies can be created in different generations from the same scored individuals. The non-linear models were transformed into approximate multivariate linear models to which combined stepwise and standard regression analysis could be applied. Expressions for the biases of the marker classes from linked QTL were obtained when no epistasis was assumed. When epistasis was assumed, these expressions increased in complexity, and the biases were caused by both linked and unlinked QTL.