Quantitative trait loci (QTL) detection in multicross inbred designs: recovering QTL identical-by-descent status information from marker data

Mapping quantitative trait loci in plants is usually conducted using a population derived from a cross between two inbred lines. The power of such QTL detection and the parameter estimates depend largely on the choice of the two parental lines. Thus, the QTL detected in such populations represent only a small part of the genetic architecture of the trait. In addition, the effects of only two alleles are characterized, which is of limited interest to the breeder, while common pedigree breeding material remains unexploited for QTL mapping. In this study, we extend QTL mapping methodology to a generalized framework, based on a two-step IBD variance component approach, applicable to any type of breeding population obtained from inbred parents. We then investigate with simulated data mimicking conventional breeding programs the influence of different estimates of the IBD values on the power of QTL detection. The proposed method would provide an alternative to the development of specifically designed recombinant populations, by utilizing the genetic variation actually managed by plant breeders. The use of these detected QTL in assisting breeding would thus be facilitated.     

Genomic selection for marker-assisted improvement in line crosses

Efficiency of genomic selection with low-cost genotyping in a composite line from a cross between inbred lines was evaluated for a trait with heritability 0.10 or 0.25 using a low-density marker map. With genomic selection, selection was on the sum of estimates of effects of all marker intervals across the genome, fitted either as fixed (fixed GS) or random (random GS) effects. Reponses to selection over 10 generations, starting from the F₂, were compared with standard BLUP selection. Estimates of variance for each interval were assumed independent and equal. Both GS strategies outperformed BLUP selection, especially in initial generations. Random GS outperformed fixed GS in early generations and performed slightly better than fixed GS in later generations. Random GS gave higher genetic gain when the number of marker intervals was greater (180 or 10 cM intervals), whereas fixed GS gave higher genetic gain when the number of marker intervals was low (90 or 20 cM). Including interactions between generation and marker scores in the model resulted in lower genetic gains than models without interactions. When phenotypes were available only in the F₂ for GS, treating marker scores as fixed effects led to considerably lower genetic gain than random GS. Benefits of GS over standard BLUP were lower with high heritability. Genomic selection resulted in greater response than MAS based on only significant marker intervals (standard MAS) by increasing the frequency of QTL with both large and small effects. The efficiency of genomic selection over standard MAS depends on stringency of the threshold used for QTL detection. In conclusion, genomic selection can be effective in composite lines using a sparse marker map.     

Marker assisted selection for the improvement of two antagonistic traits under mixed inheritance

A Monte Carlo simulation was used to investigate the potential of Marker Assisted Selection (MAS) in a multiple-trait situation. Only additive effects were considered. The base population was assumed to be in linkage equilibrium and, next, the population was managed over 15 discrete generations, 10 males and 50 females were chosen out of the 100 candidates of each sex. Performance for two traits was simulated with an overall heritability of a given trait equal to 0.25 or 0.10 and the overall genetic correlation between traits was generally equal to -0.4 except in one case where it was equal to 0. The model involved one biallelic QTL, accounting for 10 or 20% of the genetic variance of a given trait, plus polygenes. Initial allelic frequencies at the QTL were generally equal to 0.5 but in one case were equal to 0.1 and 0.9. A marker with 120 different alleles in the 60 founder parents was simulated in the vicinity of the QTL. Two values of the recombination rate between these two loci were considered, 0.10 and 0.02. The genetic evaluation was based on a multiple-trait BLUP animal model, accounting (MAS) or not (conventional BLUP) for marker information. Two sets of simulations were run: (1) a "missing data"case, with males having no record for one of the traits, and (2) a "secondary trait"case, with one trait having a weight in the aggregate genotype 4 times less than the other trait and the QTL acting only on this secondary trait. In the first set, evaluation methods were found to mainly affect the accuracy of overall genetic values prediction for the trait with missing data. In comparison with BLUP, MAS led to an extra overall genetic response for the trait with missing data, which was strongly penalised under the conventional BLUP, and to a deficit in response for the other trait. This more balanced evolution of the two traits was obtained, however, at the expense of the long-term overall cumulated response for the aggregate genotype, which was 1 to 2.5% lower than the one obtained under the conventional BLUP. In the second set of simulation, in the case of low initial frequency (0.1) of the QTL allele favourable to the secondary trait, MAS was found to be substantially more efficient to avoid losing this allele than BLUP only when the QTL had a large effect and the marker was close. More benefits should be expected from MAS with more specific applications, such as early selection of animals, or by applying dynamic procedures i.e. letting the respective weights to QTL and polygenic values in the selection criterion vary across generation.     

Detection and integration of quantitative trait loci for grain yield components and oil content in two connected recombinant inbred line populations of high-oil maize

Improvement in grain yield is an important objective in high-oil maize breeding. In this study, one high-oil maize inbred was crossed with two normal maize inbreds to produce two connected recombinant inbred line (RIL) populations with 282 and 263 F_7:8 families, respectively. The field experiments were conducted under four environments, and eight grain yield components and grain oil content were evaluated. Two genetic linkage maps were constructed using 216 and 208 polymorphic SSR markers. Quantitative trait loci (QTL) were detected for all traits under each environment and in combined analysis. Meta-analysis was used to integrate genetic maps and detected QTL in both populations. A total of 199 QTL were detected, 122 in population 1 and 87 in population 2. Seven, 11 and 19 QTL showed consistency across five environments, across two RIL populations and with respective F_2:3 generations, respectively. 183 QTL were integrated in 28 meta-QTL (mQTL). QTL with contributions over 15% were consistently detected in 3–4 cases and integrated in mQTL. Each mQTL included 3–19 QTL related to 1–4 traits, reflecting remarkable QTL co-location for grain yield components and oil content. Further research and marker-assisted selection (MAS) should be concentrated on 37 consistent QTL and four genetic regions of mQTL with more than 10 QTL at bins 3.04–3.05, 7.02, 8.04–8.05 and 9.04–9.05. Near-isogenic lines for 100-grain-weight QTL at bin 7.02–7.03, for ear-length QTL at bin 7.02–7.03 and for rows-per-ear QTL at bin 3.08 are now in construction using MAS. Co-located candidate genes could facilitate the identification of candidate genes for grain yield in maize.     

Usefulness of marker‐assisted selection to improve maize for increased resistance to Sesamia nonagrioides attack with no detrimental effect on yield

Two decades of investigations on maize resistance to Mediterranean corn borer (Sesamia nonagrioides Lefebvre; MCB) have shown that breeding for increased resistance to stem tunnelling by MCB often resulted in reduced yield because significant genetic correlation between both traits exists in some backgrounds. Unlike phenotypic selection, marker‐assisted selection (MAS) could differentiate markers linked only to one trait from those linked simultaneously to yield potential and susceptibility to the pest. In the current study, the suitability of MAS for improving resistance to stem tunnelling without adverse effects on yield has been tested. The unfavourable genetic relationship between yield potential and susceptibility could be overcome using MAS. Gains obtained using MAS were weak, because genetic variance explained by the quantitative trait loci (QTL) was low but results encourage us to persevere in using marker information for simultaneous improvement of resistance and yield especially if genome‐wide approaches are applied. Approaches to detect QTL are widely used, but studies on the suitability of markers linked to QTL for performing MAS have been mostly neglected.     

Detection of quantitative trait Loci influencing recombination using recombinant inbred lines

The genetic basis of variation in recombination in higher plants is polygenic and poorly understood, despite its theoretical and practical importance. Here a method of detecting quantitative trait loci (QTL) influencing recombination in recombinant inbred lines (RILs) is proposed that relies upon the fact that genotype data within RILs carry the signature of past recombination. Behavior of the segregational genetic variance in numbers of chromosomal crossovers (recombination) over generations is described for self-, full-sib-, and half-sib-generated RILs with no dominance in true crossovers. This genetic variance, which as a fraction of the total phenotypic variance contributes to the statistical power of the method, was asymptotically greatest with half sibbing, less with sibbing, and least with selfing. The statistical power to detect a recombination QTL declined with diminishing QTL effect, genome target size, and marker density. For reasonably tight marker linkage power was greater with less intense inbreeding for later generations and vice versa for early generations. Generational optima for segregation variance and statistical power were found, whose onset and narrowness varied with marker density and mating design, being more pronounced for looser marker linkage. Application of this method to a maize RIL population derived from inbred lines Mo17 and B73 and developed by selfing suggested two putative QTL (LOD > 2.4) affecting certain chromosomes, and using a canonical transformation another putative QTL was detected. However, permutation tests failed to support their presence (experimentwise alpha = 0.05). Other populations with more statistical power and chosen specifically for recombination QTL segregation would be more effective.     

A new test for family-based association mapping with inbred lines from plant breeding programs

Association mapping holds great promise for the detection of quantitative trait loci (QTL) in plant breeding populations. The main objectives of this study were to (1) adapt the quantitative pedigree disequilibrium test to typical pedigrees of inbred lines produced in plant breeding programs, (2) compare the newly developed quantitative inbred pedigree disequilibrium test (QIPDT) with the commonly employed logistic regression ratio test (LRRT), with respect to the power and type I error rate of QTL detection, and (3) demonstrate the use of the QIPDT by applying it to flowering data of European elite maize inbreds. QIPDT and LRRT were compared based on computer simulations modeling 55 years of hybrid maize breeding in Central Europe. Furthermore, we applied QIPDT to a cross-section of 49 European elite maize inbred lines genotyped with 722 amplified fragment length polymorphism markers and phenotyped in four environments for days to anthesis. Compared to LRRT, the power to detect QTL was higher with QIPDT when using data collected routinely in plant breeding programs. Application of QIPDT to the 49 European maize inbreds resulted in a significant (P < 0.05) association located at a position for which a consensus QTL was detected in a previous study. The results of our study suggested that QIPDT is a promising QTL detection method for data collected routinely in plant breeding programs.     

A Random Model Approach to Interval Mapping of Quantitative Trait Loci

Mapping quantitative trait loci in outbred populations is important because many populations of organisms are noninbred. Unfortunately, information about the genetic architecture of the trait may not be available in outbred populations. Thus, the allelic effects of genes can not be estimated with ease. In addition, under linkage equilibrium, marker genotypes provide no information about the genotype of a QTL (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). To circumvent this problem, an interval mapping procedure based on a random model approach is described. Under a random model, instead of estimating the effects, segregating variances of QTLs are estimated by a maximum likelihood method. Estimation of the variance component of a QTL depends on the proportion of genes identical-by-descent (IBD) shared by relatives at the locus, which is predicted by the IBD of two markers flanking the QTL. The marker IBD shared by two relatives are inferred from the observed marker genotypes. The procedure offers an advantage over the regression interval mapping in terms of high power and small estimation errors and provides flexibility for large sibships, irregular pedigree relationships and incorporation of common environmental and fixed effects.     

Complex genetic effects in quantitative trait locus identification: a computationally tractable random model for use in F(2) populations

Methodology for mapping quantitative trait loci (QTL) has focused primarily on treating the QTL as a fixed effect. These methods differ from the usual models of genetic variation that treat genetic effects as random. Computationally expensive methods that allow QTL to be treated as random have been explicitly developed for additive genetic and dominance effects. By extending these methods with a variance component method (VCM), multiple QTL can be mapped. We focused on an F(2) crossbred population derived from inbred lines and estimated effects for each individual and their corresponding marker-derived genetic covariances. We present extensions to pairwise epistatic effects, which are computationally intensive because a great many individual effects must be estimated. But by replacing individual genetic effects with average genetic effects for each marker class, genetic covariances are approximated. This substantially reduces the computational burden by reducing the dimensions of covariance matrices of genetic effects, resulting in a remarkable gain in the speed of estimating the variance components and evaluating the residual log-likelihood. Preliminary results from simulations indicate competitiveness of the reduced model with multiple-interval mapping, regression interval mapping, and VCM with individual genetic effects in its estimated QTL positions and experimental power.     

Comparison of whole-genome prediction models for traits with contrasting genetic architecture in a diversity panel of maize inbred lines

ABSTRACT: BACKGROUND: There is increasing empirical evidence that whole-genome prediction (WGP) is a powerful tool for predicting line and hybrid performance in maize. However, there is a lack of knowledge about the sensitivity of WGP models towards the genetic architecture of the trait. Whereas previous studies exclusively focused on highly polygenic traits, important agronomic traits such as disease resistances, nutrifunctional or climate adaptational traits have a genetic architecture which is either much less complex or unknown. For such cases, information about model robustness and guidelines for model selection are lacking. Here, we compared five WGP models with different assumptions about the distribution of the underlying genetic effects. As contrasting model traits, we chose three highly polygenic agronomic traits and three metabolites each with a major QTL explaining 22 to 30 % of the genetic variance in a panel of 289 diverse maize inbred lines genotyped with 56,110 SNPs. RESULTS: We found the five WGP models to be remarkable robust towards trait architecture with the largest differences in prediction accuracies ranging between 0.05 and 0.14 for the same trait, most likely as the result of the high level of linkage disequilibrium prevailing in elite maize germplasm. Whereas RR-BLUP performed best for the agronomic traits, it was inferior to LASSO or elastic net for the three metabolites. We found the approach of genome partitioning of genetic variance, first applied in human genetics, as useful in guiding the breeder which model to choose, if prior knowledge of the trait architecture is lacking. CONCLUSIONS: Our results suggest that in diverse germplasm of elite maize inbred lines with a high level of LD, WGP models differ only slightly in their accuracies, irrespective of the number and effects of QTL found in previous linkage or association mapping studies. However, small gains in prediction accuracies can be achieved if the WGP model is selected according to the genetic architecture of the trait. If the trait architecture is unknown e.g. for novel traits which only recently received attention in breeding, we suggest to inspect the distribution of the genetic variance explained by each chromosome for guiding model selection in WGP.     

Factors Affecting Accuracy From Genomic Selection in Populations Derived From Multiple Inbred Lines: A Barley Case Study

We compared the accuracies of four genomic-selection prediction methods as affected by marker density, level of linkage disequilibrium (LD), quantitative trait locus (QTL) number, sample size, and level of replication in populations generated from multiple inbred lines. Marker data on 42 two-row spring barley inbred lines were used to simulate high and low LD populations from multiple inbred line crosses: the first included many small full-sib families and the second was derived from five generations of random mating. True breeding values (TBV) were simulated on the basis of 20 or 80 additive QTL. Methods used to derive genomic estimated breeding values (GEBV) were random regression best linear unbiased prediction (RR–BLUP), Bayes-B, a Bayesian shrinkage regression method, and BLUP from a mixed model analysis using a relationship matrix calculated from marker data. Using the best methods, accuracies of GEBV were comparable to accuracies from phenotype for predicting TBV without requiring the time and expense of field evaluation. We identified a trade-off between a method's ability to capture marker-QTL LD vs. marker-based relatedness of individuals. The Bayesian shrinkage regression method primarily captured LD, the BLUP methods captured relationships, while Bayes-B captured both. Under most of the study scenarios, mixed-model analysis using a marker-derived relationship matrix (BLUP) was more accurate than methods that directly estimated marker effects, suggesting that relationship information was more valuable than LD information. When markers were in strong LD with large-effect QTL, or when predictions were made on individuals several generations removed from the training data set, however, the ranking of method performance was reversed and BLUP had the lowest accuracy.     

性状遗传力与QTL方差对标记辅助选择效果的影响

在采用动物模型标记辅助最佳线性无偏预测方法对个体育种值进行估计的基础上,模拟了在一个闭锁群体内连续对单个性状选择10个世代的情形,并系统地比较了性状遗传力和QTL方差对标记辅助选择所获得的遗传进展、QTL增效基因频率和群体近交系数变化的影响。结果表明：在对高遗传力和QTL方差较小的性状实施标记辅助选择时,可望获得更大的遗传进展;遗传力越高,QTL方差越大,则QTL增效基因频率的上升速度越快;遗传力较高时,群体近交系数上升的速度较为缓慢,而QTL方差对群体近交系数上升速度的影响则不甚明显。结合前人关于标记辅助选择相对效率的研究结果,可以认为：当选择性状的遗传力和QTL方差为中等水平时,标记辅助选择可望获得理想的效果。     

Allele frequency changes due to hitch-hiking in genomic selection programs

Background

Genomic selection makes it possible to reduce pedigree-based inbreeding over best linear unbiased prediction (BLUP) by increasing emphasis on own rather than family information. However, pedigree inbreeding might not accurately reflect loss of genetic variation and the true level of inbreeding due to changes in allele frequencies and hitch-hiking. This study aimed at understanding the impact of using long-term genomic selection on changes in allele frequencies, genetic variation and level of inbreeding.

Methods

Selection was performed in simulated scenarios with a population of 400 animals for 25 consecutive generations. Six genetic models were considered with different heritabilities and numbers of QTL (quantitative trait loci) affecting the trait. Four selection criteria were used, including selection on own phenotype and on estimated breeding values (EBV) derived using phenotype-BLUP, genomic BLUP and Bayesian Lasso. Changes in allele frequencies at QTL, markers and linked neutral loci were investigated for the different selection criteria and different scenarios, along with the loss of favourable alleles and the rate of inbreeding measured by pedigree and runs of homozygosity.

Results

For each selection criterion, hitch-hiking in the vicinity of the QTL appeared more extensive when accuracy of selection was higher and the number of QTL was lower. When inbreeding was measured by pedigree information, selection on genomic BLUP EBV resulted in lower levels of inbreeding than selection on phenotype BLUP EBV, but this did not always apply when inbreeding was measured by runs of homozygosity. Compared to genomic BLUP, selection on EBV from Bayesian Lasso led to less genetic drift, reduced loss of favourable alleles and more effectively controlled the rate of both pedigree and genomic inbreeding in all simulated scenarios. In addition, selection on EBV from Bayesian Lasso showed a higher selection differential for mendelian sampling terms than selection on genomic BLUP EBV.

Conclusions

Neutral variation can be shaped to a great extent by the hitch-hiking effects associated with selection, rather than just by genetic drift. When implementing long-term genomic selection, strategies for genomic control of inbreeding are essential, due to a considerable hitch-hiking effect, regardless of the method that is used for prediction of EBV.     

Quantitative trait loci affecting a courtship signal in Drosophila melanogaster

Courtship plays a major role in the sexual isolation of species, yet the genetics underlying courtship behaviour are poorly understood. Here we analyse quantitative trait loci (QTL) for a major component of courtship song in recombinant inbred lines derived from two laboratory strains of Drosophila melanogaster. The total variance among lines exceeds that between parental strains, and is broadly similar to that seen among geographic strains of the Cosmopolitan form of this species. Previous studies of the quantitative genetics of fly song have implied a polygenic additive inheritance with numerous genes spread throughout the genome. We find evidence for only three significant QTLs explaining 54% of the genetic variance in total. Thus there is evidence for a few large effect genes contributing to the genetic variance among lines. Interestingly, almost all of the candidate song genes previously described for D. melanogaster do not coincide with our QTLs.     

Quantitative genetic dissection of complex traits in a QTL-mapping pedigree

This paper summarizes and modifies quantitative genetic analyses on a pedigree used to map genetic factors (i.e., QTLs) underlying a complex trait. The total genetic variance can be exactly estimated based on the F₂ family derived from two homozygous parents for alternative alleles at all QTLs of interest. The parents, F₁ hybrids, and two backcrosses are combined to each parent, and the total number of QTLs and the number of dominant QTLs are estimated under the assumptions of gene association with the two parents, equal gene effect, no linkage, and no epistasis among QTLs. Further relaxation for each of the assumptions are made in detail. The biometric estimator for the QTL number and action mode averaged over the entire genome could provide some basic and complementary information to QTL mapping designed to detect the effect and location of specific genetic factors.     

Genetic mapping and quantitative trait locus analysis of fiber quality traits using a three-parent composite population in upland cotton (Gossypium hirsutum L.)

Composite cross populations (CP) developed from three or more cultivars/lines are frequently used to improve agronomic and economic traits in crop cultivar development programs. Employing CP in linkage map construction and quantitative trait locus (QTL) mapping may increase the marker density of upland cotton (Gossypium hirsutum L.) genetic maps, exploit more adequate gene resources and facilitate marker-assisted selection (MAS). To construct a relatively high-density map and identify QTL associated with fiber quality traits in upland cotton, three elite upland cultivars/lines, Yumian 1, CRI 35 and 7,235, were used to obtain the segregating population, Yumian 1/CRI 35//Yumian 1/7,235. A genetic map containing 978 simple sequence repeat (SSR) loci and 69 linkage groups was constructed; the map spanned 4,184.4 cM, covering approximately 94.1% of the entire tetraploid cotton genome. A total of 63 QTL were detected, explaining 8.1–55.8% of the total phenotypic variance: 11 QTL for fiber elongation, 16 QTL for fiber length, 9 QTL for fiber micronaire reading, 10 QTL for fiber strength and 17 QTL for fiber length uniformity. The genetic map and QTL detected for fiber quality traits are promising for further breeding programs of upland cotton with improved fiber quality.     

Using Molecular Markers to Estimate Quantitative Trait Locus Parameters: Power and Genetic Variances for Unreplicated and Replicated Progeny

Many of the progeny types used to estimate quantitative trait locus (QTL) parameters can be replicated, e.g., recombinant inbred, doubled haploid, and F3 lines. These parameters are estimated using molecular markers or QTL genotypes estimated from molecular markers as independent variables. Experiment designs for replicated progeny are functions of the number of replications per line (r) and the number of replications per QTL genotype (n). The value of n is determined by the size of the progeny population (N), the progeny type, and the number of simultaneously estimated QTL parameters (q - 1). Power for testing hypotheses about means of QTL genotypes is increased by increasing r and n, but the effects of these factors have not been quantified. In this paper, we describe how power is affected by r, n, and other factors. The genetic variance between lines nested in QTL genotypes (sigma 2n:q) is the fraction of the genetic variance between lines (sigma 2n) which is not explained by simultaneously estimated intralocus and interlocus QTL parameters (phi 2Q); thus, sigma 2n:q = sigma 2n - phi 2Q. If sigma 2n:q not equal to 0, then power is not efficiently increased by increasing r and is maximized by maximizing n and using r = 1; however, if sigma 2n:q = 0, then r and n affect power equally and power is efficiently increased by increasing r and is maximized by maximizing N.r. Increasing n efficiently increases power for a wide range of values of sigma 2n:q.sigma 2n:q = 0 when the genetic variance between lines is fully explained by QTL parameters (sigma 2n = phi 2Q).(ABSTRACT TRUNCATED AT 250 WORDS)     

The effect of using approximate gametic variance covariance matrices on marker assisted selection by BLUP

Under additive inheritance, the Henderson mixed model equations (HMME) provide an efficient approach to obtaining genetic evaluations by marker assisted best linear unbiased prediction (MABLUP) given pedigree relationships, trait and marker data. For large pedigrees with many missing markers, however, it is not feasible to calculate the exact gametic variance covariance matrix required to construct HMME. The objective of this study was to investigate the consequences of using approximate gametic variance covariance matrices on response to selection by MABLUP. Two methods were used to generate approximate variance covariance matrices. The first method (Method A) completely discards the marker information for individuals with an unknown linkage phase between two flanking markers. The second method (Method B) makes use of the marker information at only the most polymorphic marker locus for individuals with an unknown linkage phase. Data sets were simulated with and without missing marker data for flanking markers with 2, 4, 6, 8 or 12 alleles. Several missing marker data patterns were considered. The genetic variability explained by marked quantitative trait loci (MQTL) was modeled with one or two MQTL of equal effect. Response to selection by MABLUP using Method A or Method B were compared with that obtained by MABLUP using the exact genetic variance covariance matrix, which was estimated using 15 000 samples from the conditional distribution of genotypic values given the observed marker data. For the simulated conditions, the superiority of MABLUP over BLUP based only on pedigree relationships and trait data varied between 0.1% and 13.5% for Method A, between 1.7% and 23.8% for Method B, and between 7.6% and 28.9% for the exact method. The relative performance of the methods under investigation was not affected by the number of MQTL in the model.     

QTL analysis of shading sensitive related traits in maize under two shading treatments

During maize development and reproduction, shading stress is an important abiotic factor influencing grain yield. To elucidate the genetic basis of shading stress in maize, an F(2:3) population derived from two inbred lines, Zhong72 and 502, was used to evaluate the performance of six traits under shading treatment and full-light treatment at two locations. The results showed that shading treatment significantly decreased plant height and ear height, reduced stem diameter, delayed day-to-tassel (DTT) and day-to-silk (DTS), and increased anthesis-silking interval (ASI). Forty-three different QTLs were identified for the six measured traits under shading and full light treatment at two locations, including seven QTL for plant height, nine QTL for ear height, six QTL for stem diameter, seven QTL for day-to-tassel, six QTL for day-to-silk, and eight QTL for ASI. Interestingly, three QTLs, qPH4, qEH4a, and qDTT1b were detected under full sunlight and shading treatment at two locations simultaneously, these QTL could be used for selecting elite hybrids with high tolerance to shading and high plant density. And the two QTL, qPH10 and qDTS1a, were only detected under shading treatment at two locations, should be quit for selecting insensitive inbred line in maize breeding procedure by using MAS method.     

A general mixture model approach for mapping quantitative trait loci from diverse cross designs involving multiple inbred lines

Most current statistical methods developed for mapping quantitative trait loci (QTL) based on inbred line designs apply to crosses from two inbred lines. Analysis of QTL in these crosses is restricted by the parental genetic differences between lines. Crosses from multiple inbred lines or multiple families are common in plant and animal breeding programmes, and can be used to increase the efficiency of a QTL mapping study. A general statistical method using mixture model procedures and the EM algorithm is developed for mapping QTL from various cross designs of multiple inbred lines. The general procedure features three cross design matrices, W, that define the contribution of parental lines to a particular cross and a genetic design matrix, D, that specifies the genetic model used in multiple line crosses. By appropriately specifying W matrices, the statistical method can be applied to various cross designs, such as diallel, factorial, cyclic, parallel or arbitrary-pattern cross designs with two or multiple parental lines. Also, with appropriate specification for the D matrix, the method can be used to analyse different kinds of cross populations, such as F2 backcross, four-way cross and mixed crosses (e.g. combining backcross and F2). Simulation studies were conducted to explore the properties of the method, and confirmed its applicability to diverse experimental designs.