Quantitative trait loci mapping in F(2) crosses between outbred lines

We develop a mixed-model approach for QTL analysis in crosses between outbred lines that allows for QTL segregation within lines as well as for differences in mean QTL effects between lines. We also propose a method called "segment mapping" that is based in partitioning the genome in a series of segments. The expected change in mean according to percentage of breed origin, together with the genetic variance associated with each segment, is estimated using maximum likelihood. The method also allows the estimation of differences in additive variances between the parental lines. Completely fixed random and mixed models together with segment mapping are compared via simulation. The segment mapping and mixed-model behaviors are similar to those of classical methods, either the fixed or random models, under simple genetic models (a single QTL with alternative alleles fixed in each line), whereas they provide less biased estimates and have higher power than fixed or random models in more complex situations, i.e., when the QTL are segregating within the parental lines. The segment mapping approach is particularly useful to determining which chromosome regions are likely to contain QTL when these are linked.     

THE MIXED-MODEL ANALYSIS OF VARIANCE APPLIED TO QUANTITATIVE GENETICS: BIOLOGICAL MEANING OF THE PARAMETERS

The mixed-model factorial analysis of variance has been used in many recent studies in evolutionary quantitative genetics. Two competing formulations of the mixed-model ANOVA are commonly used, the “Scheffe” model and the “SAS” model; these models differ in both their assumptions and in the way in which variance components due to the main effect of random factors are defined. The biological meanings of the two variance component definitions have often been unappreciated, however. A full understanding of these meanings leads to the conclusion that the mixed-model ANOVA could have been used to much greater effect by many recent authors. The variance component due to the random main effect under the two-way SAS model is the covariance in true means associated with a level of the random factor (e.g., families) across levels of the fixed factor (e.g., environments). Therefore the SAS model has a natural application for estimating the genetic correlation between a character expressed in different environments and testing whether it differs from zero. The variance component due to the random main effect under the two-way Scheffe model is the variance in marginal means (i.e., means over levels of the fixed factor) among levels of the random factor. Therefore the Scheffe model has a natural application for estimating genetic variances and heritabilities in populations using a defined mixture of environments. Procedures and assumptions necessary for these applications of the models are discussed. While exact significance tests under the SAS model require balanced data and the assumptions that family effects are normally distributed with equal variances in the different environments, the model can be useful even when these conditions are not met (e.g., for providing an unbiased estimate of the across-environment genetic covariance). Contrary to statements in a recent paper, exact significance tests regarding the variance in marginal means as well as unbiased estimates can be readily obtained from unbalanced designs with no restrictive assumptions about the distributions or variance-covariance structure of family effects.     

Mapping Environment-Specific Quantitative Trait Loci

Environment-specific quantitative trait loci (QTL) refer to QTL that express differently in different environments, a phenomenon called QTL-by-environment (Q × E) interaction. Q × E interaction is a difficult problem extended from traditional QTL mapping. The mixture model maximum-likelihood method is commonly adopted for interval mapping of QTL, but the method is not optimal in handling QTL interacting with environments. We partitioned QTL effects into main and interaction effects. The main effects are represented by the means of QTL effects in all environments and the interaction effects are represented by the variances of the QTL effects across environments. We used the Markov chain Monte Carlo (MCMC) implemented Bayesian method to estimate both the main and the interaction effects. The residual error covariance matrix was modeled using the factor analytic covariance structure. A simulation study showed that the factor analytic structure is robust and can handle other structures as special cases. The method was also applied to Q × E interaction mapping for the yield trait of barley. Eight markers showed significant main effects and 18 markers showed significant Q × E interaction. The 18 interacting markers were distributed across all seven chromosomes of the entire genome. Only 1 marker had both the main and the Q × E interaction effects. Each of the other markers had either a main effect or a Q × E interaction effect but not both.GENOTYPE-BY-ENVIRONMENT (G × E) interaction is a very important phenomenon in quantitative genetics. With the advanced molecular technology and statistical methods for quantitative trait loci (QTL) mapping (Lander and Botstein 1989; Jansen 1993; Zeng 1994), G × E interaction analysis has shifted to QTL-by-environment (Q × E) interaction. In the early stage of QTL mapping, almost all statistical methods were developed in a single environment (Paterson et al. 1991; Stuber et al. 1992). Data from different environments were analyzed separately and the conclusions were drawn from the separate analyses of QTL across environments. These methods do not consider the correlation of data under different environments and thus may not extract maximum information from the data. Composite interval mapping for multiple traits can be used for Q × E interaction if different traits are treated as the same trait measured in different environments (Jiang and Zeng 1995). This multivariate composite interval mapping approach makes good use of all data simultaneously and increases statistical power of QTL detection and accuracy of the estimated QTL positions. However, the number of parameters of this method increases dramatically as the number of environments increases. Therefore, the method may not be applied when the number of environments is large. Several other models have been proposed to solve the problem of a large number of environments (Jansen et al. 1995; Beavis and Keim 1996; Romagosa et al. 1996). These methods were based on some special situations and assumptions. One typical assumption was independent errors or constant variances across environments. These assumptions are often violated in real QTL mapping experiments.Earlier investigators realized the problem and adopted the mixed-model methodology to solve the problem (Piepho 2000; Boer et al. 2007). Under the mixed-model framework, people can choose which model effects are random and which are fixed. The mixed-model methodology is very flexible, leading to an easy way to model genetic and environmental correlation between environments using a suitable error structure. Piepho (2000) proposed a mixed model to detect QTL main effect across environments. Similar to the composite interval mapping analysis, his model incorporated one putative QTL and a few cofactors. The Q × E effects in the model were assumed to be random, which greatly reduced the number of estimated parameters. However, the fact that only one QTL is included in the model means that Piepho''s (2000) model remains a single-QTL model rather than a multivariate model. Boer et al. (2007) proposed a step-by-step mixed-model approach to detecting QTL main effects, Q × E interaction effects, and QTL responses to specific environmental covariates. In the final step, Boer et al. (2007) rewrote the model to include all QTL in a multiple-QTL model and reestimated their effects.In this study, we extended the Bayesian shrinkage method (Xu 2003) to map Q × E interaction effects of QTL. In the original study (Xu 2003), we treated each marker as a putative QTL and used the shrinkage method to simultaneously estimate marker effects of the entire genome. In the multiple-environment case, we can still use this approach to simultaneously evaluate marker effects under multiple environments but we can further partition the marker effects into main and Q × E interaction effects. For any particular marker, the mean of the marker effects represents the main effect and the variance of the marker effects represents the Q × E interaction effect for that marker. Under the Bayesian framework, we assigned a normal prior with zero mean and an unknown variance to each marker main effect and a multivariate normal prior with zero vector mean and homogeneous diagonal variance–covariance matrix to the Q × E interaction effects of each maker. In multiple environments, the structure of the error terms might be very complicated since we need to consider the correlation of the same genotype under different environments. In our analysis, we used different variance–covariance structures to model the error terms. The simplest case was the homogeneous diagonal matrix, and the most complex choice was an unstructured matrix. We also used a heterogeneous diagonal matrix whose parameters are somewhere between the two models. Finally, we considered several factor analytic models. The reason to use the factor analytic structure is that it can separate genetic effects into common effects and environment-specific effects. In addition, the factor analytic structure is parsimonious and thus can substantially reduce the computational burden of the mixed-model analyses.     

Quantitative trait loci mapping of phenotypic plasticity and genotype-environment interactions in plant and insect performance

Community genetic studies generally ignore the plasticity of the functional traits through which the effect is passed from individuals to the associated community. However, the ability of organisms to be phenotypically plastic allows them to rapidly adapt to changing environments and plasticity is commonly observed across all taxa. Owing to the fitness benefits of phenotypic plasticity, evolutionary biologists are interested in its genetic basis, which could explain how phenotypic plasticity is involved in the evolution of species interactions. Two current ideas exist: (i) phenotypic plasticity is caused by environmentally sensitive loci associated with a phenotype; (ii) phenotypic plasticity is caused by regulatory genes that simply influence the plasticity of a phenotype. Here, we designed a quantitative trait loci (QTL) mapping experiment to locate QTL on the barley genome associated with barley performance when the environment varies in the presence of aphids, and the composition of the rhizosphere. We simultaneously mapped aphid performance across variable rhizosphere environments. We mapped main effects, QTL × environment interaction (QTL×E), and phenotypic plasticity (measured as the difference in mean trait values) for barley and aphid performance onto the barley genome using an interval mapping procedure. We found that QTL associated with phenotypic plasticity were co-located with main effect QTL and QTL×E. We also located phenotypic plasticity QTL that were located separately from main effect QTL. These results support both of the current ideas of how phenotypic plasticity is genetically based and provide an initial insight into the functional genetic basis of how phenotypically plastic traits may still be important sources of community genetic effects.     

Bayesian mapping of quantitative trait loci under complicated mating designs

Quantitative trait loci (QTL) are easily studied in a biallelic system. Such a system requires the cross of two inbred lines presumably fixed for alternative alleles of the QTL. However, development of inbred lines can be time consuming and cost ineffective for species with long generation intervals and severe inbreeding depression. In addition, restriction of the investigation to a biallelic system can sometimes be misleading because many potentially important allelic interactions do not have a chance to express and thus fail to be detected. A complicated mating design involving multiple alleles mimics the actual breeding system. However, it is difficult to develop the statistical model and algorithm using the classical maximum-likelihood method. In this study, we investigate the application of a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm to QTL mapping under arbitrarily complicated mating designs. We develop the method under a mixed-model framework where the genetic values of founder alleles are treated as random and the nongenetic effects are treated as fixed. With the MCMC algorithm, we first draw the gene flows from the founders to the descendants for each QTL and then draw samples of the genetic parameters. Finally, we are able to simultaneously infer the posterior distribution of the number, the additive and dominance variances, and the chromosomal locations of all identified QTL.     

QTL x environment interactions in rice. I. heading date and plant height

One hundred twenty six doubled-haploid (DH) rice lines were evaluated in nine diverse Asian environments to reveal the genetic basis of genotype × environment interactions (GEI) for plant height (PH) and heading date (HD). A subset of lines was also evaluated in four water-limited environments, where the environmental basis of G × E could be more precisely defined. Responses to the environments were resolved into individual QTL × environment interactions using replicated phenotyping and the mixed linear-model approach. A total of 37 main-effect QTLs and 29 epistatic QTLs were identified. On average, these QTLs were detectable in 56% of the environments. When detected in multiple environments, the main effects of most QTLs were consistent in direction but varied considerably in magnitude across environments. Some QTLs had opposite effects in different environments, particularly in water-limited environments, indicating that they responded to the environments differently. Inconsistent QTL detection across environments was due primarily to non- or weak-expression of the QTL, and in part to significant QTL × environment interaction effects in the opposite direction to QTL main effects, and to pronounced epistasis. QTL × environment interactions were trait- and gene-specific. The greater GEI for HD than for PH in rice were reflected by more environment-specific QTLs, greater frequency and magnitude of QTL × environment interaction effects, and more pronounced epistasis for HD than for PH. Our results demonstrated that QTL × environment interaction is an important property of many QTLs, even for highly heritable traits such as height and maturity. Information about QTL × environment interaction is essential if marker-assisted selection is to be applied to the manipulation of quantitative traits.Communicated by G. Wenzel     

QTL for yield in bioenergy Populus: identifying G×E interactions from growth at three contrasting sites

Populus is a genus of fast growing trees that may be suitable as a bioenergy crop grown in short rotation, but understanding the genetic nature of yield and genotype interactions with the environment is critical in developing new high-yield genotypes for wide-scale planting. In the present study, 210 genotypes from an F₂ population (Family 331; POP1) derived from a cross between Populus trichocarpa 93-968 and P. deltoides ILL-129 were grown in southern UK, central France and northern Italy. The performance of POP1, based upon first- and second-year main stem traits and biomass production, improved from northern to southern Europe. Trees at the Italian site produced the highest mean biomass ranging from 0.77 to 18.06 oven-dried tonnes (ODT) ha⁻¹ year⁻¹, and the UK site produced the lowest mean biomass ranging from 0.18 to 10.31 ODT ha⁻¹ year⁻¹. Significant genotype × environment interactions were seen despite heritability values across sites being moderate to high. Using a pseudo-testcross analysis, 37 quantitative trait loci (QTL) were identified for the maternal parent and 45 for the paternal parent for eight stem and biomass traits across the three sites. High genetic correlations between traits suggested that collocating QTL could be inferred as a single pleiotropic QTL, reducing the number of unique QTL to 23 and 24 for the maternal and paternal parent, respectively. Additive genetic effects were seen to differ significantly for eight QTL on the maternal map and 20 on the paternal map across sites. An additive main effects and multiplicative interaction analysis was carried out to obtain stability parameters for each trait. These parameters were mapped as QTL, and collocation to trait QTL was accessed. Two of the eight stability QTL collocate to trait QTL on the maternal map, and 8 of the 20 stability QTL collocate to trait QTL on the paternal map, suggesting that a regulatory gene model is prevalent over an allele sensitivity model for stem trait stability across these environments.     

Genetic control of soybean seed isoflavone content: importance of statistical model and epistasis in complex traits

A major objective for geneticists is to decipher genetic architecture of traits associated with agronomic importance. However, a majority of such traits are complex, and their genetic dissection has been traditionally hampered not only by the number of minor-effect quantitative trait loci (QTL) but also by genome-wide interacting loci with little or no individual effect. Soybean (Glycine max [L.] Merr.) seed isoflavonoids display a broad range of variation, even in genetically stabilized lines that grow in a fixed environment, because their synthesis and accumulation are affected by many biotic and abiotic factors. Due to this complexity, isoflavone QTL mapping has often produced conflicting results especially with variable growing conditions. Herein, we comparatively mapped soybean seed isoflavones genistein, daidzein, and glycitein by using several of the most commonly used mapping approaches: interval mapping, composite interval mapping, multiple interval mapping and a mixed-model based composite interval mapping. In total, 26 QTLs, including many novel regions, were found bearing additive main effects in a population of RILs derived from the cross between Essex and PI 437654. Our comparative approach demonstrates that statistical mapping methodologies are crucial for QTL discovery in complex traits. Despite a previous understanding of the influence of additive QTL on isoflavone production, the role of epistasis is not well established. Results indicate that epistasis, although largely dependent on the environment, is a very important genetic component underlying seed isoflavone content, and suggest epistasis as a key factor causing the observed phenotypic variability of these traits in diverse environments.     

Genetics of phenotypic plasticity: QTL analysis in barley, Hordeum vulgare

Phenotypic plasticity is the variation in phenotypic traits produced by a genotype in different environments. In contrast, environmental canalization is defined as the insensitivity of a genotype's phenotype to variation in environments. Despite the extensive literature on the evolutionary significance and potential genetic mechanisms driving plasticity and canalization, few studies tried to unravel the genetic basis of this phenomenon. Using both simulations and real data from barley (Hordeum vulgare), we used QTL mapping to obtain insights into the genetics of phenotypic plasticity. We explored two ways of quantifying phenotypic plasticity, namely the phenotypic variance across environments and the Finlay-Wilkinson's regression slope. Each relates to a different concept of stability. Through QTL detection with real and simulated data, we show that each measure of plasticity detects specific types of plasticity QTL. Most of the plasticity QTLs were detected in the data set with the lowest number of environments. All plasticity QTL co-located with loci showing QTL x E interaction and there were no QTL that only affected plasticity. The number of environments that are considered and their homogeneity is a key to interpret the genetic control of phenotypic plasticity. Regulatory pathways of plasticity may vary from one set of environments to another due to unique features of each environment. Therefore, with an increasing number of environments, it may become impossible to detect a single 'consistent' regulatory pathway for all environments.     

Selection on QTL and complex traits in complex environments

Understanding genetic variation for complex traits in heterogeneous environments is a fundamental problem in biology. In this issue of Molecular Ecology, Fournier‐Level et al. ( 2013 ) analyse quantitative trait loci (QTL) influencing ecologically important phenotypes in mapping populations of Arabidopsis thaliana grown in four habitats across its native European range. They used causal modelling to quantify the selective consequences of life history and morphological traits and QTL on components of fitness. They found phenology QTL colocalizing with known flowering time genes as well as novel loci. Most QTL influenced fitness via life history and size traits, rather than QTL having direct effects on fitness. Comparison of phenotypes among environments found no evidence for genetic trade‐offs for phenology or growth traits, but genetic trade‐offs for fitness resulted because flowering time had opposite fitness effects in different environments. These changes in QTL effects and selective consequences may maintain genetic variation among populations.     

Dissecting the genetic basis for the effect of rice chalkiness, amylose content, protein content, and rapid viscosity analyzer profile characteristics on the eating quality of cooked rice using the chromosome segment substitution line population across eight environments

Quantitative trait locus (QTL) mapping and stability analysis were carried out for 16 rice (Oryza sativa L.) quality traits across eight environments, by using a set of chromosome segment substitution lines with 'Asominori' as genetic background. The 16 quality traits include percentage of grain with chalkiness (PGWC), area of chalky endosperm (ACE), amylose content (AC), protein content (PC), peak viscosity, hot paste viscosity, cool paste viscosity, breakdown viscosity (BDV), setback viscosity (SBV), consistency viscosity, cooked-rice luster (LT), scent, tenderness (TD), viscosity, elasticity, and the integrated values of organleptic evaluation (IVOE). A total of 132 additive effect QTLs are detected for the 16 quality straits in the eight environments. Among these QTLs, 56 loci were detected repeatedly in at least three environments. Interestingly, several QTL clusters were observed for multiple quality traits. Especially, one QTL cluster near the G1149 marker on chromosome 8 includes nine QTLs: qPGWC-8, qACE-8, qAC-8, qPC-8a, qBDV-8a, qSBV-8b, qLT-8a, qTD-8a, and qIVOE-8a, which control PGWC, ACE, AC, PC, BDV, SBV, LT, TD, and IVOE, respectively. Moreover, this QTL cluster shows high stability and repeatability in all eight environments. In addition, one QTL cluster was located near the C2340 marker on chromosome 1 and another was detected near the XNpb67 marker on chromosome 2; each cluster contained five loci. Near the C563 marker on chromosome 3, one QTL cluster with four loci was found. Also, there were nine QTL clusters that each had two or three loci; however, their repeatability in different environments was relatively lower, and the genetic contribution rate was relatively smaller. Considering the correlations among all of the 16 quality traits with QTL cluster distributions, we can conclude that the stable and major QTL cluster on chromosome 8 is the main genetic basis for the effect of rice chalkiness, AC, PC, and rapid viscosity analyzer profile characteristics on the eating quality of cooked rice. Consequently, this QTL cluster is a novel gene resource for controlling rice high-quality traits and should be of great significance for research on formation mechanism and molecule improvement of rice quality.     

QTL mapping of resistance to Fusarium ear rot using a RIL population in maize

Fusarium ear rot is a prevalent disease in maize, reducing grain yields and quality. Resistance breeding is an efficient way to minimize losses caused by the disease. In this study, 187 lines from a RIL population along with the resistant (87-1) and susceptible (Zong 3) parents were planted in Zhengzhou and Beijing with three replications in years 2004 and 2006. Each line was artificially inoculated using the nail-punch method. Significant genotypic variation in response to Fusarium ear rot was detected in both years. Based on a genetic map containing 246 polymorphic SSR markers with average genetic distances of 9.1 cM, the ear-rot resistance QTL were firstly analyzed by composite interval mapping (CIM). Three QTL were detected in both Zhengzhou and Beijing in 2004; and three and four QTL, respectively, were identified in 2006. The resistant parent contributed all resistance QTL. By using composite interval mapping and a mixed model (MCIM), significant epistatic effects on Fusarium ear rot as well as interactions between mapped loci and environments were observed across environments. Two QTL on chromosome 3 (3.04 bin) were consistently identified across all environments by the two methods. The major resistant QTL with the largest effect was flanked by markers umc1025 and umc1742 on chromosome 3 (3.04 bin), explaining 13–22% of the phenotypic variation. The SSR markers closely flanking the major resistance QTL will facilitate marker-assisted selection (MAS) of resistance to Fusarium ear rot in maize breeding programs.     

Mixed-model QTL mapping for kernel hardness and dough strength in bread wheat

Plant breeding data comprise unbalanced phenotypic data for inbreds with complex pedigrees. As traditional methods to map quantitative trait loci (QTL) cannot exploit plant breeding data, an alternative approach is QTL mapping via a mixed-model procedure. Our objective was to validate mixed-model QTL mapping for self-pollinated crops by detecting QTL for kernel hardness and dough strength from data in a bread wheat (Triticum aestivum L.) breeding program. We studied 80 parental and 373 experimental inbreds genotyped for 65 simple sequence repeat (SSR) markers and three candidate loci. The methodology involved three steps: variance component estimation, single-marker analyses, and a final multiple-marker analysis with marker effects treated as fixed effects. Two QTLs for kernel hardness were detected on chromosomes 1A (close to candidate locus GluA3) and 5D (close to candidate locus Ha). Four QTLs were detected for dough strength on chromosomes 1A, 1B, 1D, and 5B. Candidate gene GluA1, which was associated with dough strength, was the only candidate locus found significant. Results were consistent with previously reported markers and QTLs associated with kernel hardness and dough strength. Unlike previous studies that have assumed QTL effects as random, the assumption of fixed marker effects identified the favorable marker alleles to select for. We conclude that the detection of previously mapped QTL validates the usefulness of mixed-model QTL mapping in the context of a plant-breeding program.     

Habitat-specific natural selection at a flowering-time QTL is a main driver of local adaptation in two wild barley populations

Understanding the genetic basis of local adaptation requires insight in the fitness effects of individual loci under natural field conditions. While rapid progress is made in the search for genes that control differences between plant populations, it is typically unknown whether the genes under study are in fact key targets of habitat-specific natural selection. Using a quantitative trait loci (QTL) approach, we show that a QTL associated with flowering-time variation between two locally adapted wild barley populations is an important determinant of fitness in one, but not in the other population's native habitat. The QTL mapped to the same position as a habitat-specific QTL for field fitness that affected plant reproductive output in only one of the parental habitats, indicating that the genomic region is under differential selection between the native habitats. Consistent with the QTL results, phenotypic selection of flowering time differed between the two environments, whereas other traits (growth rate and seed weight) were under selection but experienced no habitat-specific differential selection. This implies the flowering-time QTL as a driver of adaptive population divergence. Our results from phenotypic selection and QTL analysis are consistent with local adaptation without genetic trade-offs in performance across environments, i.e. without alleles or traits having opposing fitness effects in contrasting environments.     

Multivariate whole genome average interval mapping: QTL analysis for multiple traits and/or environments

A major aim in some plant-based studies is the determination of quantitative trait loci (QTL) for multiple traits or across multiple environments. Understanding these QTL by trait or QTL by environment interactions can be of great value to the plant breeder. A whole genome approach for the analysis of QTL is presented for such multivariate applications. The approach is an extension of whole genome average interval mapping in which all intervals on a linkage map are included in the analysis simultaneously. A random effects working model is proposed for the multivariate (trait or environment) QTL effects for each interval, with a variance-covariance matrix linking the variates in a particular interval. The significance of the variance-covariance matrix for the QTL effects is tested and if significant, an outlier detection technique is used to select a putative QTL. This QTL by variate interaction is transferred to the fixed effects. The process is repeated until the variance-covariance matrix for QTL random effects is not significant; at this point all putative QTL have been selected. Unlinked markers can also be included in the analysis. A simulation study was conducted to examine the performance of the approach and demonstrated the multivariate approach results in increased power for detecting QTL in comparison to univariate methods. The approach is illustrated for data arising from experiments involving two doubled haploid populations. The first involves analysis of two wheat traits, α-amylase activity and height, while the second is concerned with a multi-environment trial for extensibility of flour dough. The method provides an approach for multi-trait and multi-environment QTL analysis in the presence of non-genetic sources of variation.     

Genotype-environment interaction for quantitative trait loci affecting life span in Drosophila melanogaster

The nature of genetic variation for Drosophila longevity in a population of recombinant inbred lines was investigated by estimating quantitative genetic parameters and mapping quantitative trait loci (QTL) for adult life span in five environments: standard culture conditions, high and low temperature, and heat-shock and starvation stress. There was highly significant genetic variation for life span within each sex and environment. In the analysis of variance of life span pooled over sexes and environments, however, the significant genetic variation appeared in the genotype x sex and genotype x environment interaction terms. The genetic correlation of longevity across the sexes and environments was not significantly different from zero in these lines. We estimated map positions and effects of QTL affecting life span by linkage to highly polymorphic roo transposable element markers, using a multiple-trait composite interval mapping procedure. A minimum of 17 QTL were detected; all were sex and/or environment-specific. Ten of the QTL had sexually antagonistic or antagonistic pleiotropic effects in different environments. These data provide support for the pleiotropy theory of senescence and the hypothesis that variation for longevity might be maintained by opposing selection pressures in males and females and variable environments. Further work is necessary to assess the generality of these results, using different strains, to determine heterozygous effects and to map the life span QTL to the level of genetic loci.     

A biplot approach for investigating QTL-by-environment patterns

Due to the universal presence of genotype by environment interactions, understanding the pattern of quantitative trait loci (QTL)-by-environment interactions is a prerequisite for effective marker-assisted selection. In this report, we describe a biplot approach for investigating QTL-by-environment patterns. This approach involves two steps. It starts with a two-way table containing effects of individual QTLs in individual environments for the trait under investigation. This table is decomposed into principal components via singular value decomposition, and the first two principal components are plotted for both QTLs and environments to form a biplot. The resulting QQE biplot contains information on QTL main effects (Q) and QTL-by-environment interactions (QE). A QQE biplot displays the QTL-by-environment patterns and allows visualization of: (1) the magnitude of the effect of a QTL, (2) the average effect of a QTL and its stability across environments, (3) the effects of a QTL in individual environments, (4) the similarity/dissimilarity among QTLs in effect and response to the environments, (5) the similarity/dissimilarity among environments in modulating QTL effects, (6) any differentiation of mega-environments, and (7) the combination of QTL alleles for maximum/minimum expression of the trait for each environment or mega-environment. A case study is provided using the QTL-by-environment two-way table for barley yield.     

Mapping QTLs with epistatic effects and QTL×environment interactions by mixed linear model approaches

A new methodology based on mixed linear models was developed for mapping QTLs with digenic epistasis and QTL×environment (QE) interactions. Reliable estimates of QTL main effects (additive and epistasis effects) can be obtained by the maximum-likelihood estimation method, while QE interaction effects (additive×environment interaction and epistasis×environment interaction) can be predicted by the-best-linear-unbiased-prediction (BLUP) method. Likelihood ratio and t statistics were combined for testing hypotheses about QTL effects and QE interactions. Monte Carlo simulations were conducted for evaluating the unbiasedness, accuracy, and power for parameter estimation in QTL mapping. The results indicated that the mixed-model approaches could provide unbiased estimates for both positions and effects of QTLs, as well as unbiased predicted values for QE interactions. Additionally, the mixed-model approaches also showed high accuracy and power in mapping QTLs with epistatic effects and QE interactions. Based on the models and the methodology, a computer software program (QTLMapper version 1.0) was developed, which is suitable for interval mapping of QTLs with additive, additive×additive epistasis, and their environment interactions. Received: 23 October 1998 / Accepted: 11 May 1999     

Unifying Genetic Canalization,Genetic Constraint,and Genotype-by-Environment Interaction: QTL by Genomic Background by Environment Interaction of Flowering Time in Boechera stricta

Natural populations exhibit substantial variation in quantitative traits. A quantitative trait is typically defined by its mean and variance, and to date most genetic mapping studies focus on loci altering trait means but not (co)variances. For single traits, the control of trait variance across genetic backgrounds is referred to as genetic canalization. With multiple traits, the genetic covariance among different traits in the same environment indicates the magnitude of potential genetic constraint, while genotype-by-environment interaction (GxE) concerns the same trait across different environments. While some have suggested that these three attributes of quantitative traits are different views of similar concepts, it is not yet clear, however, whether they have the same underlying genetic mechanism. Here, we detect quantitative trait loci (QTL) influencing the (co)variance of phenological traits in six distinct environments in Boechera stricta, a close relative of Arabidopsis. We identified nFT as the QTL altering the magnitude of phenological trait canalization, genetic constraint, and GxE. Both the magnitude and direction of nFT''s canalization effects depend on the environment, and to our knowledge, this reversibility of canalization across environments has not been reported previously. nFT''s effects on trait covariance structure (genetic constraint and GxE) likely result from the variable and reversible canalization effects across different traits and environments, which can be explained by the interaction among nFT, genomic backgrounds, and environmental stimuli. This view is supported by experiments demonstrating significant nFT by genomic background epistatic interactions affecting phenological traits and expression of the candidate gene, FT. In contrast to the well-known canalization gene Hsp90, the case of nFT may exemplify an alternative mechanism: Our results suggest that (at least in traits with major signal integrators such as flowering time) genetic canalization, genetic constraint, and GxE may have related genetic mechanisms resulting from interactions among major QTL, genomic backgrounds, and environments.     

Multi-environment analysis and improved mapping of a yield-related QTL on chromosome 3B of wheat

Improved mapping, multi-environment quantitative trait loci (QTL) analysis and dissection of allelic effects were used to define a QTL associated with grain yield, thousand grain weight and early vigour on chromosome 3BL of bread wheat (Triticum aestivum L.) under abiotic stresses. The QTL had pleiotropic effects and showed QTL x environment interactions across 21 diverse environments in Australia and Mexico. The occurrence and the severity of water deficit combined with high temperatures during the growing season affected the responsiveness of this QTL, resulting in a reversal in the direction of allelic effects. The influence of this QTL can be substantial, with the allele from one parent (RAC875) increasing grain yield by up to 12.5 % (particularly in environments where both heat and drought stress occurred) and the allele from the other parent (Kukri) increasing grain yield by up to 9 % in favourable environments. With the application of additional markers and the genotyping of additional recombinant inbred lines, the genetic map in the QTL region was refined to provide a basis for future positional cloning.