Multi-QTL mapping for quantitative traits using distorted markers

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

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.

Regression interval mapping and multiple interval mapping are compared with regard to mapping linked quantitative trait loci (QTL) in inbred-line cross experiments. For that purpose, a simulation study was performed using genetic models with two linked QTL. Data were simulated for F(2) populations of different sizes and with all QTL and marker alleles fixed for alternative alleles in the parental lines. The criteria for comparison are power of QTL identification and the accuracy of the QTL position and effect estimates. Further, the estimates of the relative QTL variance are assessed. There are distinct differences in the QTL position estimates between the two methods. Multiple interval mapping tends to be more powerful as compared to regression interval mapping. Multiple interval mapping further leads to more accurate QTL position and QTL effect estimates. The superiority increased with wider marker intervals and larger population sizes. If QTL are in repulsion, the differences between the two methods are very pronounced. For both methods, the reduction of the marker interval size from 10 to 5 cM increases power and greatly improves QTL parameter estimates. This contrasts with findings in the literature for single QTL scenarios, where a marker density of 10 cM is generally considered as sufficient. The use of standard (asymptotic) statistical theory for the computation of the standard errors of the QTL position and effect estimates proves to give much too optimistic standard errors for regression interval mapping as well as for multiple interval mapping.

Multiple-trait analysis typically employs models that associate a quantitative trait locus (QTL) with all of the traits. As a result, statistical power for QTL detection may not be optimal if the QTL contributes to the phenotypic variation in only a small proportion of the traits. Excluding QTL effects that contribute little to the test statistic can improve statistical power. In this article, we show that an optimal power can be achieved when the number of QTL effects is best estimated, and that a stringent criterion for QTL effect selection may improve power when the number of QTL effects is small but can reduce power otherwise. We investigate strategies for excluding trivial QTL effects, and propose a method that improves statistical power when the number of QTL effects is relatively small, and fairly maintains the power when the number of QTL effects is large. The proposed method first uses resampling techniques to determine the number of nontrivial QTL effects, and then selects QTL effects by the backward elimination procedure for significance test. We also propose a method for testing QTL-trait associations that are desired for biological interpretation in applications. We validate our methods using simulations and Arabidopsis thaliana transcript data.

A method was derived to estimate effects of quantitative trait loci (QTL) using incomplete genotype information in large outbreeding populations with complex pedigrees. The method accounts for background genes by estimating polygenic effects. The basic equations used are very similar to the usual linear mixed model equations for polygenic models, and segregation analysis was used to estimate the probabilities of the QTL genotypes for each animal. Method R was used to estimate the polygenic heritability simultaneously with the QTL effects. Also, initial allele frequencies were estimated. The method was tested in a simulated data set of 10,000 animals evenly distributed over 10 generations, where 0, 400 or 10,000 animals were genotyped for a candidate gene. In the absence of selection, the bias of the QTL estimates was < 2%. Selection biased the estimate of the Aa genotype slightly, when zero animals were genotyped. Estimates of the polygenic heritability were 0.251 and 0.257, in absence and presence of selection, respectively, while the simulated value was 0.25. Although not tested in this study, marker information could be accommodated by adjusting the transmission probabilities of the genotypes from parent to offspring according to the marker information. This renders a QTL mapping study in large multi-generation pedigrees possible.

Validation of a quantitative trait locus (QTL) for outcrossing perennial plants is rarely reported due to complexity of plausible genetic models and reliance on field designs already available. Here, a particular marker-QTL haplotype exerted a large, positive effect on height for Pinus taeda and its origin could be traced to a founder, GP(3), in a three-generation QTL pedigree. To validate this QTL effect, we used an extended GP(3)-based pedigree. In the validation cross, each of the 46 offspring was clonally propagated from developing seeds using somatic embryogenesis technology. Subsequent analyses were conducted separately for seedlings and for other somatic emblings. For seedlings, the original QTL effect could not be fully validated. For somatic emblings, a strong negative QTL effect was detected in the validation cross; some evidence from another cross-supported the original positive QTL effect. From this part of the analysis, three distinct marker-QTL haplotypes at a single locus could be inferred. Validating QTL haplotypes in readily available field tests was feasible despite the genetic model complexity inherent to outcrossing long-lived perennials.

In a previous study on maize (Zea mays, L.) several quantitative trait loci (QTL) showing high dominance-additive ratio for agronomic traits were identified in a population of recombinant inbred lines derived from B73 × H99. For four of these mapped QTL, namely 3.05, 4.10, 7.03 and 10.03 according to their chromosome and bin position, families of near-isogenic lines (NILs) were developed, i.e., couples of homozygous lines nearly identical except for the QTL region that is homozygote either for the allele provided by B73 or by H99. For two of these QTL (3.05 and 4.10) the NILs families were produced in two different genetic backgrounds. The present research was conducted in order to: (i) characterize these QTL by estimating additive and dominance effects; (ii) investigate if these effects can be affected by genetic background, inbreeding level and environmental growing conditions (low vs. high plant density). The six NILs’ families were tested across three years and in three Experiments at different inbreeding levels as NILs per se and their reciprocal crosses (Experiment 1), NILs crossed to related inbreds B73 and H99 (Experiment 2) and NILs crossed to four unrelated inbreds (Experiment 3). Experiment 2 was conducted at two plant densities (4.5 and 9.0 plants m-2). Results of Experiments 1 and 2 confirmed previous findings as to QTL effects, with dominance-additive ratio superior to 1 for several traits, especially for grain yield per plant and its component traits; as a tendency, dominance effects were more pronounced in Experiment 1. The QTL effects were also confirmed in Experiment 3. The interactions involving QTL effects, families and plant density were generally negligible, suggesting a certain stability of the QTL. Results emphasize the importance of dominance effects for these QTL, suggesting that they might deserve further studies, using NILs’ families and their crosses as base materials.

A multiple marker least squares approach is presented for the analysis of a single three-generation pedigree for quantitative trait locus (QTL) characterisation. It is an extension of the approach by Haley et al. (1994) to the situation where grandparents cannot be assumed to be homozygous at QTLs for the trait of interest. The method is applied to the analysis of wood specific gravity in loblolly pine (Pinus taeda L.). Within a similar framework, a series of preliminary analyses are carried out, followed by a more detailed search of the genome for one or more QTLs. The preliminary analyses provide information about whether the contribution from each linkage group appears to be polygenic, localised to a small region (e.g. a single QTL) or oligogenic (i.e. several QTLs). Significance levels are obtained using a permutation test that uses the observed phenotypes and marker genotypes. The conclusion of these analyses is that in this pedigree single QTLs with very large effect on wood specific gravity do not appear to be segregating, although there is evidence for QTLs with small effect. Finally, in order to assess the potential power of this pedigree, we simulated QTLs within the framework of the actual marker data. As expected, QTL effects would need to be large to be reliably detected in this study, and the power to detect QTLs varies at different positions in the genome depending on the level of information in the local markers.

Mendelian inheritance can ensure equal segregation of alleles from parents to offspring, which provides fundamental basis for genetics and molecular biology. Segregation distortion (SD) leads to preferential transmission of certain alleles from generation to generation. Such violation of Mendelian genetic principle is often accompanied by reproductive isolation and eventually speciation. Although SD is observed in a wide range of species from plants to animals, genome-wide dissection of such biased transmission of gametes is rare. Using nine inter-subspecific rice crosses, a genome-wide screen for SD loci is performed, which reveals 61 single-locus quantitative trait loci and 194 digenic interactions showing distorted transmission ratio, among which 24 new SD loci are identified. Biased transmission of alleles is observed in all nine crosses, suggesting that SD exists extensively in rice populations. 72.13% distorted regions are repeatedly detected in multiple populations, and the most prevalent SD hotspot that observed in eight populations is mapped to chromosome 3. Xian alleles are transmitted at higher frequencies than geng alleles in inter-subspecific crosses, which change the genetic composition of the rice populations. Epistatic interaction contributes significantly to the deviation of Mendelian segregation at the whole-genome level in rice, which is distinct from that in animals. These results provide an extensive archive for investigating the genetic basis of SD in rice, which have significant implications in understanding the reproductive isolation and formation of inter-subspecific barriers during the evolution.

BackgroundVariance component (VC) models are commonly used for Quantitative Trait Loci (QTL) mapping in outbred populations. Here, the QTL effect is given as a random effect and a critical part of the model is the relationship between the phenotypic values and the random effect. In the traditional VC model, each individual has a unique QTL effect and the relationship between these random effects is given as a covariance structure (known as the identity-by-descent (IBD) matrix).ResultsWe present an alternative notation of the variance component model, where the elements of the random effect are independent base generation allele effects and sampling term effects. The relationship between the phenotypic vales and the random effect is given by an incidence matrix, which results in a novel, but statistically equivalent, version of the traditional VC model. A general algorithm to estimate this incidence matrix is presented. Since the model is given in terms of base generation allele effects and sampling term effects, these effects can be estimated separately using best linear unbiased prediction (BLUP). From simulated data, we showed that biallelic QTL effects could be accurately clustered using the BLUP obtained from our model notation when markers are fully informative, and that the accuracy increased with the size of the QTL effect. We also developed a measure indicating whether a base generation marker homozygote is a QTL heterozygote or not, by comparing the variances of the sampling term BLUP and the base generation allele BLUP. A ratio greater than one gives strong support for a QTL heterozygote.ConclusionWe developed a simple presentation of the VC QTL model for identification of base generation allele effects in QTL linkage analysis. The base generation allele effects and sampling term effects were separated in our model notation. This clarifies the assumptions of the model and should also enhance the development of genome scan methods.

Strategies for mapping quantitative trait (QT) loci (QTL) need special studies in species where inbred lines cannot easily be obtained. We propose the detection of QTL with schemes including several full-sib families and study here the efficiency of such schemes — diallel, factorial, cyclic or single-pair mating designs — for a varying number of parents, on the basis of the power of tests for QTL detection. We considered a single, fully informative marker completely linked to the QTL. The tests proposed for QTL detection are based on linear additive models. The results show that for a given number of parents, in given conditions, the mating design has no effect on power. It increases as the total number of individuals genotyped increases. The number of parents affects the power of QTL detection insofar as the effect of substituting QT alleles varies from one parent to another and as some parents can be homozygous at the QTL: with only two parents QTL detection is often less powerful than with more parents. The size of the genetic effects that can be detected with a given power decreases as the number of parents increases from two to six and is quite stable for more than six parents. If QTL heterozygote frequency in the base population is high enough (greater than 0.2) mating designs with six parents should give a good sample of variance attributable to QTL and allow the detection of QTL with reasonable power.

Grain yield (GY) is a direct function of its components and these traits to being less complex and highly correlated with yield. The objectives of this study were to map Quantitative Trait Loci (QTL) for GY and its components in maize lines and GY in their testcrosses, to verify its congruence and the possibility to select testcrosses from the predict means of the lines by using markers information. Two hundred and fifty-six S1 lines derived from the cross L-08-05F × L-14-04B of tropical germplasm and the testcrosses of these lines with two testers were evaluated in six environments. The traits analysed in the lines were GY, prolificacy, ear height and diameter, number of rows per ear and kernels per row, kernel depth, grain weight, and GY in the testcrosses. QTL were mapped in the lines and in testcrosses and the predicted means of the lines were computed based on QTL effects and in all markers of the genome. Few QTL detected for GY and its components in the lines were coincident with the QTL for yield in testcrosses. The correlations between the predicted means of the lines and the phenotypic means of the testcrosses were not significant or low for most of the components. The coincidence of the selected lines and testcrosses was very low for all traits and the results were similar for both testcrosses and intensity. It is not possible to select testcrosses by using GY or its components information from the lines, even with the aid of molecular markers.

A penalized maximum likelihood method has been proposed as an important approach to the detection of epistatic quantitative trait loci (QTL). However, this approach is not optimal in two special situations: (1) closely linked QTL with effects in opposite directions and (2) small-effect QTL, because the method produces downwardly biased estimates of QTL effects. The present study aims to correct the bias by using correction coefficients and shifting from the use of a uniform prior on the variance parameter of a QTL effect to that of a scaled inverse chi-square prior. The results of Monte Carlo simulation experiments show that the improved method increases the power from 25 to 88% in the detection of two closely linked QTL of equal size in opposite directions and from 60 to 80% in the identification of QTL with small effects (0.5% of the total phenotypic variance). We used the improved method to detect QTL responsible for the barley kernel weight trait using 145 doubled haploid lines developed in the North American Barley Genome Mapping Project. Application of the proposed method to other shrinkage estimation of QTL effects is discussed.

Quantitative trait locus (QTL) models can provide useful insights into trait genetic architecture because of their straightforward interpretability but are less useful for genetic prediction because of the difficulty in including the effects of numerous small effect loci without overfitting. Tight linkage between markers introduces near collinearity among marker genotypes, complicating the detection of QTL and estimation of QTL effects in linkage mapping, and this problem is exacerbated by very high density linkage maps. Here we developed a thinning and aggregating (TAGGING) method as a new ensemble learning approach to QTL mapping. TAGGING reduces collinearity problems by thinning dense linkage maps, maintains aspects of marker selection that characterize standard QTL mapping, and by ensembling, incorporates information from many more markers-trait associations than traditional QTL mapping. The objective of TAGGING was to improve prediction power compared with QTL mapping while also providing more specific insights into genetic architecture than genome-wide prediction models. TAGGING was compared with standard QTL mapping using cross validation of empirical data from the maize (Zea mays L.) nested association mapping population. TAGGING-assisted QTL mapping substantially improved prediction ability for both biparental and multifamily populations by reducing both the variance and bias in prediction. Furthermore, an ensemble model combining predictions from TAGGING-assisted QTL and infinitesimal models improved prediction abilities over the component models, indicating some complementarity between model assumptions and suggesting that some trait genetic architectures involve a mixture of a few major QTL and polygenic effects.

BackgroundThe genetic architecture of egg production and egg quality traits, i.e. the quantitative trait loci (QTL) that influence these traits, is still poorly known. To date, 33 studies have focused on the detection of QTL for laying traits in chickens, but less than 10 genes have been identified. The availability of a high-density SNP (single nucleotide polymorphism) chicken array developed by Affymetrix, i.e. the 600K Affymetrix® Axiom® HD genotyping array offers the possibility to narrow down the localization of previously detected QTL and to detect new QTL. This high-density array is also anticipated to take research beyond the classical hypothesis of additivity of QTL effects or of QTL and environmental effects. The aim of our study was to search for QTL that influence laying traits using the 600K SNP chip and to investigate whether the effects of these QTL differed between diets and age at egg collection.ResultsOne hundred and thirty-one QTL were detected for 16 laying traits and were spread across all marked chromosomes, except chromosomes 16 and 25. The percentage of variance explained by a QTL varied from 2 to 10 % for the various traits, depending on diet and age at egg collection. Chromosomes 3, 9, 10 and Z were overrepresented, with more than eight QTL on each one. Among the 131 QTL, 60 had a significantly different effect, depending on diet or age at egg collection. For egg production traits, when the QTL × environment interaction was significant, numerous inversions of sign of the SNP effects were observed, whereas for egg quality traits, the QTL × environment interaction was mostly due to a difference of magnitude of the SNP effects.ConclusionsOur results show that numerous QTL influence egg production and egg quality traits and that the genomic regions, which are involved in shaping the ability of layer chickens to adapt to their environment for egg production, vary depending on the environmental conditions. The next question will be to address what the impact of these genotype × environment interactions is on selection.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-015-0160-2) contains supplementary material, which is available to authorized users.