Sib mating designs for mapping quantitative trait loci

The power to separate the variance of a quantitative trait locus (QTL) from the polygenic variance is determined by the variability of genes identical by descent (IBD) at the QTL. This variability may increase with inbreeding. Selfing, the most extreme form of inbreeding, increases the variability of the IBD value shared by siblings, and thus has a higher efficiency for QTL mapping than random mating. In self-incompatible organisms, sib mating is the closest form of inbreeding. Similar to selfing, sib mating may also increase the power of QTL detection relative to random mating. In this study, we develop an IBD-based method under sib mating designs for QTL mapping. The efficiency of sib mating is then compared with random mating. Monte Carlo simulations show that sib mating designs notably increase the power for QTL detection. When power is intermediate, the power to detect a QTL using full-sib mating is, on average, 7% higher than under random mating. In addition, the IBD-based method proposed in this paper can be used to combine data from multiple families. As a result, the estimated QTL parameters can be applied to a wide statistical inference space relating to the entire reference population. This revised version was published online in July 2006 with corrections to the Cover Date.     

Power to detect higher-order epistatic interactions in a metabolic pathway using a new mapping strategy

Epistatic interactions among quantitative trait loci (QTL) contribute substantially to the variation in complex traits. The main objectives of this study were to (i) compare three- vs. four-step genome scans to identify three-way epistatic interactions among QTL belonging to a metabolic pathway, (ii) investigate by computer simulations the power and proportion of false positives (PFP) for detecting three-way interactions among QTL in recombinant inbred line (RIL) populations derived from a nested mating design, and (iii) compare these estimates to those obtained for detecting three-way interactions among QTL in RIL populations derived from diallel and different partial diallel mating designs. The single-nucleotide polymorphism haplotype data of B73 and 25 diverse maize inbreds were used to simulate the production of various RIL populations. Compared to the three-step genome scan, the power to detect three-way interactions was higher with the four-step genome scan. Higher power to detect three-way interactions was observed for RILs derived from optimally allocated distance-based designs than from nested designs or diallel designs. The power and PFP to detect three-way interactions using a nested design with 5000 RILs were for both the 4-QTL and the 12-QTL scenario of a magnitude that seems promising for their identification.     

Joint QTL linkage mapping for multiple-cross mating design sharing one common parent

Background

Nested association mapping (NAM) is a novel genetic mating design that combines the advantages of linkage analysis and association mapping. This design provides opportunities to study the inheritance of complex traits, but also requires more advanced statistical methods. In this paper, we present the detailed algorithm of a QTL linkage mapping method suitable for genetic populations derived from NAM designs. This method is called joint inclusive composite interval mapping (JICIM). Simulations were designed on the detected QTL in a maize NAM population and an Arabidopsis NAM population so as to evaluate the efficiency of the NAM design and the JICIM method.

Principal Findings

Fifty-two QTL were identified in the maize population, explaining 89% of the phenotypic variance of days to silking, and nine QTL were identified in the Arabidopsis population, explaining 83% of the phenotypic variance of flowering time. Simulations indicated that the detection power of these identified QTL was consistently high, especially for large-effect QTL. For rare QTL having significant effects in only one family, the power of correct detection within the 5 cM support interval was around 80% for 1-day effect QTL in the maize population, and for 3-day effect QTL in the Arabidopsis population. For smaller-effect QTL, the power diminished, e.g., it was around 50% for maize QTL with an effect of 0.5 day. When QTL were linked at a distance of 5 cM, the likelihood of mapping them as two distinct QTL was about 70% in the maize population. When the linkage distance was 1 cM, they were more likely mapped as one single QTL at an intermediary position.

Conclusions

Because it takes advantage of the large genetic variation among parental lines and the large population size, NAM is a powerful multiple-cross design for complex trait dissection. JICIM is an efficient and specialty method for the joint QTL linkage mapping of genetic populations derived from the NAM design.     

A simple method for calculating the statistical power for detecting a QTL located in a marker interval

We developed a simple method for calculating the statistical power for detecting a QTL located in an interval flanked by two markers. The statistical method for QTL detection is assumed to be the Haley and Knott's simple regression method of interval mapping. This method allows us to answer one of the fundamental questions in designing a QTL mapping experiment: What is the minimum marker density required to detect a QTL explaining a certain heritable proportion of the phenotypic variance (denoted by h(2)) with a power gamma under a Type I error alpha in an F(2) or other mating designs with a sample size n? Computing the statistical power only requires the ability to evaluate a non-central F-distribution function and the inverse function of this distribution.     

Novel linkage mapping approach using DNA pooling in human and animal genetics. II. Detection of quantitative traits loci in dairy cattle

Selective DNA pooling is an advanced methodology for linkage mapping of quantitative trait loci (QTL) in farm animals. The principle is based on densitometric estimates of marker allele frequency in pooled DNA samples of phenotypically extreme individuals from half-sib, backcross and F(2) experimental designs in farm animals. This methodology provides a rapid and efficient analysis of a large number of individuals with short tandem repeat markers that are essential to detect QTL through the genome - wide searching approach. Several strategies involving whole genome scanning with a high statistical power have been developed for systematic search to detect the quantitative traits loci and linked loci of complex traits. In recent studies, greater success has been achieved in mapping several QTLs in Israel-Holstein cattle using selective DNA pooling. This paper outlines the currently emerged novel strategies of linkage mapping to identify QTL based on selective DNA pooling with more emphasis on its theoretical pre-requisite to detect linked QTLs, applications, a general theory for experimental half-sib designs, the power of statistics and its feasibility to identify genetic markers linked QTL in dairy cattle. The study reveals that the application of selective DNA pooling in dairy cattle can be best exploited in the genome-wide detection of linked loci with small and large QTL effects and applied to a moderately sized half-sib family of about 500 animals.     

Strategies for genetic mapping of categorical traits

The search for efficient and powerful statistical methods and optimal mapping strategies for categorical traits under various experimental designs continues to be one of the main tasks in genetic mapping studies. Methodologies for genetic mapping of categorical traits can generally be classified into two groups, linear and non-linear models. We develop a method based on a threshold model, termed mixture threshold model to handle ordinal (or binary) data from multiple families. Monte Carlo simulations are done to compare its statistical efficiencies and properties of the proposed non-linear model with a linear model for genetic mapping of categorical traits using multiple families. The mixture threshold model has notably higher statistical power than linear models. There may be an optimal sampling strategy (family size vs number of families) in which genetic mapping reaches its maximal power and minimal estimation errors. A single large-sibship family does not necessarily produce the maximal power for detection of quantitative trait loci (QTL) due to genetic sampling of QTL alleles. The QTL allelic model has a marked impact on efficiency of genetic mapping of categorical traits in terms of statistical power and QTL parameter estimation. Compared with a fixed number of QTL alleles (two or four), the model with an infinite number of QTL alleles and normally distributed allelic effects results in loss of statistical power. The results imply that inbred designs (e.g. F₂ or four-way crosses) with a few QTL alleles segregating or reducing number of QTL alleles (e.g. by selection) in outbred populations are desirable in genetic mapping of categorical traits using data from multiple families. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the use of double haploids for detecting QTL in outbred populations

The power to detect quantitative trait loci (QTL) using the double haploid (DH), full-sib (FS) and hierarchical (HI) designs implemented in outbred fish populations was assessed for interval mapping using deterministic methods. The predictions were tested using simulation. The DH design was most efficient for the range of designs and parameters considered and was most beneficial when the FS design was not very powerful. The difference between the design was largest for a low amount of residual genetic variation. Accounting for an increase of the environmental variance due to the genetic constitution of the double haploid progeny changed the magnitude of the power, but the ranking of the designs remained the same. As large full sib family sizes can be obtained in fish, the practical value of HI designs as a strategy for increasing the power of QTL mapping experiments is limited when compared with the FS design. Overall, the results suggested that the DH design could be a very useful tool for QTL mapping in fish, and of particular importance when the effect of the QTL is low and the residual genetic variation from other chromosomes can be controlled by using multiple markers.     

Power analysis for quantitative trait locus mapping in populations derived by multiple backcrosses

 Populations derived by multiple backcrosses are potentially useful for quantitative trait locus (QTL) mapping studies. Comparisons of relative power to detect QTL using populations derived by multiple back-crosses are needed to make decisions when mapping projects are initiated. The objective of this study was to theoretically compare the power to detect QTL in populations derived by multiple backcrosses relative to mapping in a recombinant inbred population of equal size. Backcrossing results in a reduction in genetic variance with each generation and also results in an increasing frequency of the recurrent parent marker genotype. The relevant outcome for QTL mapping is a reduction in genetic variance to partition between marker genotype classes and increasing unbalance of the number of individuals contributing to the mean of the marker genotypes. Both of these factors lead to a decrease in the power to detect a QTL as the number of backcross generations increases. Experimental error was held constant with the populations compared. From a theoretical standpoint, backcross-derived populations offer few advantages for QTL detection. If, however, a backcrossing approach is the most efficient method to achieve a desired breeding objective and if QTL detection is an objective of equal or less importance, backcross-derived populations are a reasonable approach to QTL detection. Received: 4 August 1996 / Accepted: 4 April 1997     

The Statistical Power of Inclusive Composite Interval Mapping in Detecting Digenic Epistasis Showing Common F2 Segregation Ratios

Epistasis is a commonly observed genetic phenomenon and an important source of variation of complex traits,which could maintain additive variance and therefore assure the long-term genetic gain in breeding.Inclusive composite interval mapping（ICIM） is able to identify epistatic quantitative trait loci（QTLs） no matter whether the two interacting QTLs have any additive effects.In this article,we conducted a simulation study to evaluate detection power and false discovery rate（FDR） of ICIM epistatic mapping,by considering F₂ and doubled haploid（DH） populations,different F₂ segregation ratios and population sizes.Results indicated that estimations of QTL locations and effects were unbiased,and the detection power of epistatic mapping was largely affected by population size,heritability of epistasis,and the amount and distribution of genetic effects.When the same likelihood of odd（LOD） threshold was used,detection power of QTL was higher in F₂ population than power in DH population;meanwhile FDR in F₂ was also higher than that in DH.The increase of marker density from 10 cM to 5 cM led to similar detection power but higher FDR.In simulated populations,ICIM achieved better mapping results than multiple interval mapping（MIM） in estimation of QTL positions and effect.At the end,we gave epistatic mapping results of ICIM in one actual population in rice（Oryza sativa L.）.     

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

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

Quantitative 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.     

Evaluation of multi-locus models for genome-wide association studies: a case study in sugar beet

Association mapping has become a widely applied genomic approach to dissect the genetic architecture of complex traits. A major issue for association mapping is the need to control for the confounding effects of population structure, which is commonly done by mixed models incorporating kinship information. In this case study, we employed experimental data from a large sugar beet population to evaluate multi-locus models for association mapping. As in linkage mapping, markers are selected as cofactors to control for population structure and genetic background variation. We compared different biometric models with regard to important quantitative trait locus (QTL) mapping parameters like the false-positive rate, the QTL detection power and the predictive power for the proportion of explained genotypic variance. Employing different approaches we show that the multi-locus model, that is, incorporating cofactors, outperforms the other models, including the mixed model used as a reference model. Thus, multi-locus models are an attractive alternative for association mapping to efficiently detect QTL for knowledge-based breeding.     

Properties and power of the Drosophila Synthetic Population Resource for the routine dissection of complex traits

The Drosophila Synthetic Population Resource (DSPR) is a newly developed multifounder advanced intercross panel consisting of >1600 recombinant inbred lines (RILs) designed for the genetic dissection of complex traits. Here, we describe the inference of the underlying mosaic founder structure for the full set of RILs from a dense set of semicodominant restriction-site-associated DNA (RAD) markers and use simulations to explore how variation in marker density and sequencing coverage affects inference. For a given sequencing effort, marker density is more important than sequence coverage per marker in terms of the amount of genetic information we can infer. We also assessed the power of the DSPR by assigning genotypes at a hidden QTL to each RIL on the basis of the inferred founder state and simulating phenotypes for different experimental designs, different genetic architectures, different sample sizes, and QTL of varying effect sizes. We found the DSPR has both high power (e.g., 84% power to detect a 5% QTL) and high mapping resolution (e.g., ～1.5 cM for a 5% QTL).     

Power and precision of alternate methods for linkage disequilibrium mapping of quantitative trait loci

Linkage disequilibrium (LD) analysis in outbred populations uses historical recombinations to detect and fine map quantitative trait loci (QTL). Our objective was to evaluate the effect of various factors on power and precision of QTL detection and to compare LD mapping methods on the basis of regression and identity by descent (IBD) in populations of limited effective population size (N(e)). An 11-cM region with 6-38 segregating single-nucleotide polymorphisms (SNPs) and a central QTL was simulated. After 100 generations of random mating with N(e) of 50, 100, or 200, SNP genotypes and phenotypes were generated on 200, 500, or 1000 individuals with the QTL explaining 2 or 5% of phenotypic variance. To detect and map the QTL, phenotypes were regressed on genotypes or (assumed known) haplotypes, in comparison with the IBD method. Power and precision to detect QTL increased with sample size, marker density, and QTL effect. Power decreased with N(e), but precision was affected little by N(e). Single-marker regression had similar or greater power and precision than other regression models, and was comparable to the IBD method. Thus, for rapid initial screening of samples of adequate size in populations in which drift is the primary force that has created LD, QTL can be detected and mapped by regression on SNP genotypes without recovering haplotypes.     

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.     

On the use of mathematically-derived traits in QTL mapping

Mathematically-derived traits from two or more component traits, either by addition, subtraction, multiplication, or division, have been frequently used in genetics and breeding. When used in quantitative trait locus (QTL) mapping, derived traits sometimes show discrepancy with QTL identified for the component traits. We used three QTL distributions and three genetic effects models, and an actual maize mapping population, to investigate the efficiency of using derived traits in QTL mapping, and to understand the genetic and biological basis of derived-only QTL, i.e., QTL identified for a derived trait but not for any component trait. Results indicated that the detection power of the four putative QTL was consistently greater than 90% for component traits in simulated populations, each consisting of 200 recombinant inbred lines. Lower detection power and higher false discovery rate (FDR) were observed when derived traits were used. In an actual maize population, simulations were designed based on the observed QTL distributions and effects. When derived traits were used, QTL detected for both component and derived traits had comparable power, but those detected for component traits but not for derived traits had low detection power. The FDR from subtraction and division in the maize population were higher than the FDR from addition and multiplication. The use of derived traits increased the gene number, caused higher-order gene interactions than observed in component traits, and possibly complicated the linkage relationship between QTL as well. The increased complexity of the genetic architecture with derived traits may be responsible for the reduced detection power and the increased FDR. Derived-only QTL identified in practical genetic populations can be explained either as minor QTL that are not significant in QTL mapping of component traits, or as false positives.     

Linkage analysis of quantitative trait loci in multiple line crosses

Simple line crosses, for example, backcross and F₂, are commonly used in mapping quantitative trait loci (QTL). However, these simple crosses are rarely used alone in commercial plant breeding; rather, crosses involving multiple inbred lines or several simple crosses but connected by shared inbred lines may be common in plant breeding. Mapping QTL using crosses of multiple lines is more relevant to plant breeding. Unfortunately, current statistical methods and computer programs of QTL mapping are all designed for simple line crosses or multiple line crosses but under a regular mating system. It is not straightforward to extend the existing methods to handle multiple line crosses under irregular and complicated mating designs. The major hurdle comes from irregular inbreeding, multiple generations, and multiple alleles. In this study, we develop a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm for mapping QTL using complicated multiple line crosses. With the MCMC algorithm, we are able to draw a complete path of the gene flow from founder alleles to their descendents via a recursive process. This has greatly simplified the problem caused by irregular mating and inbreeding in the mapping population. Adopting the reversible jump MCMC algorithm, we are able to simultaneously search for multiple QTL along the genome. We can even infer the posterior distribution of the number of QTL, one of the most important parameters in QTL study. Application of the new MCMC based QTL mapping procedure is demonstrated using two different mating designs. Design I involves two inbred lines and their derived F₁, F₂, and BC populations. Design II is a half-diallel cross involving three inbred lines. The two designs appear different, but can be handled with the same robust computer program.     

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.     

Effects of missing marker and segregation distortion on QTL mapping in F2 populations

Missing marker and segregation distortion are commonly encountered in actual quantitative trait locus (QTL) mapping populations. Our objective in this study was to investigate the impact of the two factors on QTL mapping through computer simulations. Results indicate that detection power decreases with increasing levels of missing markers, and the false discovery rate increases. Missing markers have greater effects on smaller effect QTL and smaller size populations. The effect of missing markers can be quantified by a population with a reduced size similar to the marker missing rate. As for segregation distortion, if the distorted marker is not closely linked with any QTL, it will not have significant impact on QTL mapping; otherwise, the impact of the distortion will depend on the degree of dominance of QTL, frequencies of the three marker types, the linkage distance between the distorted marker and QTL, and the mapping population size. Sometimes, the distortion can result in a higher genetic variance than that of non-distortion, and therefore benefits the detection of linked QTL. A formula of the ratio of genetic variance explained by QTL under distortion and non-distortion was given in this study, so as to easily determine whether the segregation distortion marker (SDM) increases or decreases the QTL detection power. The effect of SDM decreases rapidly as its linkage relationship with QTL becomes looser. In general, distorted markers will not have a great effect on the position and effect estimations of QTL, and their effects can be ignored in large-size mapping populations.     

Family-based mapping of quantitative trait loci in plant breeding populations with resistance to Fusarium head blight in wheat as an illustration

Traditional quantitative trait loci (QTL) mapping approaches are typically based on early or advanced generation analysis of bi-parental populations. A limitation associated with this methodology is the fact that mapping populations rarely give rise to new cultivars. Additionally, markers linked to the QTL of interest are often not immediately available for use in breeding and they may not be useful within diverse genetic backgrounds. Use of breeding populations for simultaneous QTL mapping, marker validation, marker assisted selection (MAS), and cultivar release has recently caught the attention of plant breeders to circumvent the weaknesses of conventional QTL mapping. The first objective of this study was to test the feasibility of using family-pedigree based QTL mapping techniques generally used with humans and animals within plant breeding populations (PBPs). The second objective was to evaluate two methods (linkage and association) to detect marker-QTL associations. The techniques described in this study were applied to map the well characterized QTL, Fhb1 for Fusarium head blight resistance in wheat (Triticum aestivum L.). The experimental populations consisted of 82 families and 793 individuals. The QTL was mapped using both linkage (variance component and pedigree-wide regression) and association (using quantitative transmission disequilibrium test, QTDT) approaches developed for extended family-pedigrees. Each approach successfully identified the known QTL location with a high probability value. Markers linked to the QTL explained 40–50% of the phenotypic variation. These results show the usefulness of a human genetics approach to detect QTL in PBPs and subsequent use in MAS.