Optimum allocation of resources for QTL detection using a nested association mapping strategy in maize

In quantitative trait locus (QTL) mapping studies, it is mandatory that the available financial resources are spent in such a way that the power for detection of QTL is maximized. The objective of this study was to optimize for three different fixed budgets the power of QTL detection 1 − β* in recombinant inbred line (RIL) populations derived from a nested design by varying (1) the genetic complexity of the trait, (2) the costs for developing, genotyping, and phenotyping RILs, (3) the total number of RILs, and (4) the number of environments and replications per environment used for phenotyping. Our computer simulations were based on empirical data of 653 single nucleotide polymorphism markers of 26 diverse maize inbred lines which were selected on the basis of 100 simple sequence repeat markers out of a worldwide sample of 260 maize inbreds to capture the maximum genetic diversity. For the standard scenario of costs, the optimum number of test environments (E _opt) ranged across the examined total budgets from 7 to 19 in the scenarios with 25 QTL. In comparison, the E _opt values observed for the scenarios with 50 and 100 QTL were slightly higher. Our finding of differences in 1 − β* estimates between experiments with optimally and sub-optimally allocated resources illustrated the potential to improve the power for QTL detection without increasing the total resources necessary for a QTL mapping experiment. Furthermore, the results of our study indicated that also in studies using the latest genomics tools to dissect quantitative traits, it is required to evaluate the individuals of the mapping population in a high number of environments with a high number of replications per environment.     

QTL mapping under truncation selection in homozygous lines derived from biparental crosses

In plant breeding, a large number of progenies that will be discarded later in the breeding process must be phenotyped and marker genotyped for conducting QTL analysis. In many cases, phenotypic preselection of lines could be useful. However, in QTL analyses even moderate preselection can have a significant effect on the power of QTL detection and estimation of effects of the target traits. In this study, we provide exact formulas for quantifying the change of allele frequencies within marker classes, expectations of marker contrasts and the variance of the marker contrasts under truncation selection, for the general case of two QTL affecting the target trait and a correlated trait. We focused on homozygous lines derived at random from biparental crosses. The effects of linkage between the marker and the QTL under selection as well as the effect of selection on a correlated trait can be quantified with the given formulas. Theoretical results clearly show that depending on the magnitude of QTL effects, high selection intensities can lead to a dramatic reduction in power of QTL detection and that approximations based on the infinitesimal model deviate substantially from exact solutions. The presented formulas are valuable for choosing appropriate selection intensity when performing QTL mapping experiments on the data on phenotypically preselected traits and enable the calculation and bias correction of the effects of QTL under selection. Application of our theory to experimental data revealed that selection-induced bias of QTL effects can be successfully corrected.     

High-density linkage mapping of yield components and epistatic interactions in maize with doubled haploid lines from four crosses

Grain yield (GY) is a genetically complex and physiologically multiplicative trait which can be decomposed into the components kernel number (KN) and 100-kernel weight (HKW). Genetic analysis of these less complex yield component traits may give insights into the genetic architecture and predictive ability of complex traits. Here, we investigated how the incorporation of component traits and epistasis in quantitative trait locus (QTL) mapping approaches influences the accuracy of GY prediction. High-density genetic maps with 7,000–10,000 polymorphic single nucleotide polymorphisms were constructed for four biparental populations. The populations comprised between 99 and 227 doubled haploid maize lines which were phenotyped in field trials in two environments. Heritability was highest for HKW (88–89 %), intermediate for KN (72–80 %), and lowest for GY (64–83 %). Mapped QTL explained in total 21–55 %, 22–67 %, and 24–75 % of the genotypic variance for GY, KN, and HKW, respectively. Support intervals of QTL were short, indicating that QTL were located with high precision. Co-located QTLs with same parental origin of favorable alleles were detected within populations for different traits and between populations for the same traits. Using GY predictions based on the detected QTL, prediction accuracies (r) determined by cross validation ranged from 0.18 to 0.52. Epistatic models did not outperform the corresponding additive models. In conclusion, models based on QTL positions of component traits support the identification of favorable alleles for multiplicative traits and provide a basis to select superior inbred lines by marker-assisted breeding.     

Multiple trait multiple interval mapping of quantitative trait loci from inbred line crosses

ABSTRACT: BACKGROUND: Although many experiments have measurements on multiple traits, most studies performed the analysis of mapping of quantitative trait loci (QTL) for each trait separately using single trait analysis. Single trait analysis does not take advantage of possible genetic and environmental correlations between traits. In this paper, we propose a novel statistical method for multiple trait multiple interval mapping (MTMIM) of QTL for inbred line crosses. We also develop a novel score-based method for estimating genome-wide significance level of putative QTL effects suitable for the MTMIM model. The MTMIM method is implemented in the freely available and widely used Windows QTL Cartographer software. RESULTS: Throughout the paper, we provide compelling empirical evidences that: (1) the score-based threshold maintains proper type I error rate and tends to keep false discovery rate within an acceptable level; (2) the MTMIM method can deliver better parameter estimates and power than single trait multiple interval mapping method; (3) an analysis of Drosophila dataset illustrates how the MTMIM method can better extract information from datasets with measurements in multiple traits. CONCLUSIONS: The MTMIM method represents a convenient statistical framework to test hypotheses of pleiotropic QTL versus closely linked nonpleiotropic QTL, QTL by environment interaction, and to estimate the total genotypic variance-covariance matrix between traits and to decompose it in terms of QTL-specific variance-covariance matrices, therefore, providing more details on the genetic architecture of complex traits.     

Linkage disequilibrium pattern and genome‐wide association mapping for meat traits in multiple porcine F2 crosses

In the present study, data from four F2 crosses were analysed and used to study the linkage disequilibrium (LD) structure within and across the crosses. Genome‐wide association analyses (GWASes) for conductivity and dressing out meat traits were conducted using single‐marker and Bayesian multi‐marker models using the pooled data from all F2 crosses. Porcine F2 crosses generated from the distantly related founder breeds Wild Boar, Piétrain and Meishan, as well as from a porcine F2 cross from the closely related founder breed Piétrain and an F1 Large White × Landrace cross were pooled. A total of 2572 F2 animals were genotyped using a 62K SNP chip. The positions of the SNPs were based on genome assembly Sscrofa11.1. After post‐alignment and genotype filtering, approximately 50K SNPs were usable for LD studies and GWASes. The main findings of the present study are that the breakdown of LD was faster in crosses from closely related founder breeds compared to crosses from distantly related founders. The fastest breakdown of LD was observed by pooling the data. Based on the single‐marker results and LD structure, clusters and windows were built for 1‐Mb intervals. For conductivity and dressing out, 183 and 191 nominal significant associations respectively and six and five clusters respectively were found. Dominance was important for conductivity, and considering dominance in GWASes improved the mapping signals. Most clear signals were found for conductivity on SSC6, 8 and 15 and for dressing out on SSC2 and 7. Considering dominance might contribute to the accuracy of genomic selection and serve as a guide for choosing mating pairs with good combining abilities. However, further research is needed to investigate if dominance is also important in crossbreed pig breeding schemes.     

Advances in Bayesian multiple quantitative trait loci mapping in experimental crosses

Many complex human diseases and traits of biological and/or economic importance are determined by interacting networks of multiple quantitative trait loci (QTL) and environmental factors. Mapping QTL is critical for understanding the genetic basis of complex traits, and for ultimate identification of genes responsible. A variety of sophisticated statistical methods for QTL mapping have been developed. Among these developments, the evolution of Bayesian approaches for multiple QTL mapping over the past decade has been remarkable. Bayesian methods can jointly infer the number of QTL, their genomic positions and their genetic effects. Here, we review recently developed and still developing Bayesian methods and associated computer software for mapping multiple QTL in experimental crosses. We compare and contrast these methods to clearly describe the relationships among different Bayesian methods. We conclude this review by highlighting some areas of future research.     

Detection of seed dormancy QTL in multiple mapping populations derived from crosses involving novel barley germplasm

Seed dormancy is one of the most important traits in germination process to control malting and pre-harvest sprouting in barley (Hordeum vulgare L.). EST based linkage maps were constructed on seven recombinant inbred (RI) and one doubled haploid (DH) populations derived from crosses including eleven cultivated and one wild barley strains showing the wide range of seed dormancy levels. Seed dormancy of each RI and DH line was estimated from the germination percentage at 5 and 10 weeks post-harvest after-ripening periods in 2003 and 2005. Quantitative trait loci (QTLs) controlling seed dormancy were detected by the composite interval mapping procedure on the RI and DH populations. A total of 38 QTLs clustered around 11 regions were identified on the barley chromosomes except 2H among the eight populations. Several QTL regions detected in the present study were reported on similar positions in the previous QTL studies. The QTL on at the centromeric region of long arm of chromosome 5H was identified in all the RI and DH populations with the different degrees of dormancy depth and period. The responsible gene of the QTL might possess a large allelic variation among the cross combinations, or can be multiple genes located on the same region. The various loci and their different effects in dormancy found in the barley germplasm in the present study enable us to control the practical level of seed dormancy in barley breeding programs. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Quantitative trait Loci association mapping by imputation of strain origins in multifounder crosses

Although mapping quantitative traits in inbred strains is simpler than mapping the analogous traits in humans, classical inbred crosses suffer from reduced genetic diversity compared to experimental designs involving outbred animal populations. Multiple crosses, for example the Complex Trait Consortium's eight-way cross, circumvent these difficulties. However, complex mating schemes and systematic inbreeding raise substantial computational difficulties. Here we present a method for locally imputing the strain origins of each genotyped animal along its genome. Imputed origins then serve as mean effects in a multivariate Gaussian model for testing association between trait levels and local genomic variation. Imputation is a combinatorial process that assigns the maternal and paternal strain origin of each animal on the basis of observed genotypes and prior pedigree information. Without smoothing, imputation is likely to be ill-defined or jump erratically from one strain to another as an animal's genome is traversed. In practice, one expects to see long stretches where strain origins are invariant. Smoothing can be achieved by penalizing strain changes from one marker to the next. A dynamic programming algorithm then solves the strain imputation process in one quick pass through the genome of an animal. Imputation accuracy exceeds 99% in practical examples and leads to high-resolution mapping in simulated and real data. The previous fastest quantitative trait loci (QTL) mapping software for dense genome scans reduced compute times to hours. Our implementation further reduces compute times from hours to minutes with no loss in statistical power. Indeed, power is enhanced for full pedigree data.     

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.     

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.     

Combining data from multiple inbred line crosses improves the power and resolution of quantitative trait loci mapping

Rodent inbred line crosses are widely used to map genetic loci associated with complex traits. This approach has proven to be powerful for detecting quantitative trait loci (QTL); however, the resolution of QTL locations, typically approximately 20 cM, means that hundreds of genes are implicated as potential candidates. We describe analytical methods based on linear models to combine information available in two or more inbred line crosses. Our strategy is motivated by the hypothesis that common inbred strains of the laboratory mouse are derived from a limited ancestral gene pool and thus QTL detected in multiple crosses are likely to represent shared ancestral polymorphisms. We demonstrate that the combined-cross analysis can improve the power to detect weak QTL, can narrow support intervals for QTL regions, and can be used to separate multiple QTL that colocalize by chance. Moreover, combined-cross analysis can establish the allelic states of a QTL among a set of parental lines, thus providing critical information for narrowing QTL regions by haplotype analysis.     

Optimum prediction of three-way crosses from single crosses in forage maize (Zea mays L.)

Summary Three-way cross means were predicted with formulae involving linear functions of general (GCA) and specific combining ability (SCA) effects estimated from single-cross factorials between genetically divergent populations. Data from an experiment with 66 single-cross and 66 three-way cross forage maize (Zea mays L.) hybrids was used for comparing the prediction formulae. The genotypic correlation (r) between observed and predicted three-way crosses increased with increasing , the weighting factor of SCA effects, for plant height and ear dry matter (DM) content. It displayed slightly convex curves for total and stover DM yield, ear percentage, and metabolizable energy content of stover. For Jenkins' method B, r was considerably less than 1.0 for all traits, indicating the presence of epistasis. The square root of heritability (h) of the predicted means decreased with increasing , the reduction being small with a greater number of test environments. Using the product r·h as a criterion of efficiency, none of the prediction methods was consistently superior and the differences among them were rather small (< 7.5%) for all traits, irrespective of the number of test environments. We recommend evaluating the GCA of a greater number of lines from each parent population in testcrosses with a small number of elite lines from the opposite population. All possible three-way or double crosses between both sets of lines should be predicted by Jenkins's method C. This procedure allows one to select with a higher intensity among the predicted hybrids and thus should increase the genetic gain.Extended version of a paper (Geiger et al. 1986) read at the sixth meeting of the EUCARPIA Section Biometrics in Plant Breeding held at Birmingham, UK, July 28–August 1, 1986     

Inbred lines of mice derived from long-term growth selected lines: unique resources for mapping growth genes

Lines of mice selected for many generations for high or low growth in several laboratories around the world have been collected, and from these, inbred lines are being developed by recurrent full-sib mating in Edinburgh. There are seven high selected lines and four low lines (each low line is from the same base population as one of the high lines), and the histories of each are summarized. Mean body weight of males at 70 days of age in the Edinburgh laboratory in the heaviest inbred line (77 g) is 4.8-fold higher than in the lightest line (16 g), and 1.9-fold higher than in the least extreme high line (41 g). Litter size, food intake, and fat content also differ substantially. These inbred extreme selected lines are a uniquely valuable resource for QTL or gene mapping, candidate gene identification, and elucidation of epistatic effects. Received: 19 February 2001 / Accepted: 3 May 2001     

Optimum allocation of test resources and comparison of breeding strategies for hybrid wheat

Key message

The use of a breeding strategy combining the evaluation of line per se with testcross performance maximizes annual selection gain for hybrid wheat breeding.

Abstract

Recent experimental studies confirmed a high commercial potential for hybrid wheat requiring the design of optimum breeding strategies. Our objectives were to (1) determine the optimum allocation of the type and number of testers, the number of test locations and the number of doubled haploid lines for different breeding strategies, (2) identify the best breeding strategy and (3) elaborate key parameters for an efficient hybrid wheat breeding program. We performed model calculations using the selection gain for grain yield as target variable to optimize the number of lines, testers and test locations in four different breeding strategies. A breeding strategy (BS2) combining the evaluation of line per se performance and general combining ability (GCA) had a far larger annual selection gain across all considered scenarios than a breeding strategy (BS1) focusing only on GCA. In the combined strategy, the production of testcross seed conducted in parallel with the first yield trial for line per se performance (BS2_rapid) resulted in a further increase of the annual selection gain. For the current situation in hybrid wheat, this relative superiority of the strategy BS2_rapid amounted to 67 % in annual selection gain compared to BS1. Varying a large number of parameters, we identified the high costs for hybrid seed production and the low variance of GCA in hybrid wheat breeding as key parameters limiting selection gain in BS2_rapid.     

Mixture generalized linear models for multiple interval mapping of quantitative trait Loci in experimental crosses

Summary .  Quantitative trait loci mapping in experimental organisms is of great scientific and economic importance. There has been a rapid advancement in statistical methods for quantitative trait loci mapping. Various methods for normally distributed traits have been well established. Some of them have also been adapted for other types of traits such as binary, count, and categorical traits. In this article, we consider a unified mixture generalized linear model (GLIM) for multiple interval mapping in experimental crosses. The multiple interval mapping approach was proposed by Kao, Zeng, and Teasdale (1999, Genetics 152, 1203–1216) for normally distributed traits. However, its application to nonnormally distributed traits has been hindered largely by the lack of an efficient computation algorithm and an appropriate mapping procedure. In this article, an effective expectation–maximization algorithm for the computation of the mixture GLIM and an epistasis-effect-adjusted multiple interval mapping procedure is developed. A real data set, Radiata Pine data, is analyzed and the data structure is used in simulation studies to demonstrate the desirable features of the developed method.     

Genetic design and statistical power of nested association mapping in maize

We investigated the genetic and statistical properties of the nested association mapping (NAM) design currently being implemented in maize (26 diverse founders and 5000 distinct immortal genotypes) to dissect the genetic basis of complex quantitative traits. The NAM design simultaneously exploits the advantages of both linkage analysis and association mapping. We demonstrated the power of NAM for high-power cost-effective genome scans through computer simulations based on empirical marker data and simulated traits with different complexities. With common-parent-specific (CPS) markers genotyped for the founders and the progenies, the inheritance of chromosome segments nested within two adjacent CPS markers was inferred through linkage. Genotyping the founders with additional high-density markers enabled the projection of genetic information, capturing linkage disequilibrium information, from founders to progenies. With 5000 genotypes, 30-79% of the simulated quantitative trait loci (QTL) were precisely identified. By integrating genetic design, natural diversity, and genomics technologies, this new complex trait dissection strategy should greatly facilitate endeavors to link molecular variation with phenotypic variation for various complex traits.     

QTL mapping of combining ability and heterosis of agronomic traits in rice backcross recombinant inbred lines and hybrid crosses

Background

Combining ability effects are very effective genetic parameters in deciding the next phase of breeding programs. Although some breeding strategies on the basis of evaluating combining ability have been utilized extensively in hybrid breeding, little is known about the genetic basis of combining ability. Combining ability is a complex trait that is controlled by polygenes. With the advent and development of molecular markers, it is feasible to evaluate the genetic bases of combining ability and heterosis of elite rice hybrids through QTL analysis.

Methodology/Principal Findings

In the present study, we first developed a QTL-mapping method for dissecting combining ability and heterosis of agronomic traits. With three testcross populations and a BCRIL population in rice, biometric and QTL analyses were conducted for ten agronomic traits. The significance of general combining ability and special combining ability for most of the traits indicated the importance of both additive and non-additive effects on expression levels. A large number of additive effect QTLs associated with performance per se of BCRIL and general combining ability, and dominant effect QTLs associated with special combining ability and heterosis were identified for the ten traits.

Conclusions/Significance

The combining ability of agronomic traits could be analyzed by the QTL mapping method. The characteristics revealed by the QTLs for combining ability of agronomic traits were similar with those by multitudinous QTLs for agronomic traits with performance per se of BCRIL. Several QTLs (1–6 in this study) were identified for each trait for combining ability. It demonstrated that some of the QTLs were pleiotropic or linked tightly with each other. The identification of QTLs responsible for combining ability and heterosis in the present study provides valuable information for dissecting genetic basis of combining ability.     

Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines

Dominant phenotype of a genetic marker provides incomplete information about the marker genotype of an individual. A consequence of using this incomplete information for mapping quantitative trait loci (QTL) is that the inference of the genotype of a putative QTL flanked by a marker with dominant phenotype will depend on the genotype or phenotype of the next marker. This dependence can be extended further until a marker genotype is fully observed. A general algorithm is derived to calculate the probability distribution of the genotype of a putative QTL at a given genomic position, conditional on all observed marker phenotypes in the region with dominant and missing marker information for an individual. The algorithm is implemented for various populations stemming from two inbred lines in the context of mapping QTL. Simulation results show that if only a proportion of markers contain missing or dominant phenotypes, QTL mapping can be almost as efficient as if there were no missing information in the data. The efficiency of the analysis, however, may decrease substantially when a very large proportion of markers contain missing or dominant phenotypes and a genetic map has to be reconstructed first on the same data as well. So it is important to combine dominant markers with codominant markers in a QTL mapping study. This revised version was published online in July 2006 with corrections to the Cover Date.