On the efficiency of composite interval mapping in an outbred population

Composite interval mapping (CIM) has been successfully applied to the detection of QTL in experimental animals and plants. However, practical analyses based on CIM have been reported mainly for populations derived from cross between inbred lines. There are few studies on QTL analyses with CIM in outbred populations. To evaluate the applicability of CIM to outbred populations is prerequisite for the fine mapping of QTL in industrial animals such as pig and chicken. Some markers are usually not fully informative in outbred populations. In application of CIM to outbred populations, the influence of inclusion of such uninformative markers used as covariates on the efficiency of CIM should be investigated. In this paper a least-squares method for CIM was formalized in an F(2) population derived by crossing two outbred lines. The efficiencies of CIM were evaluated for outbred populations in comparison with simple interval mapping (SIM) for several cases of marker informativeness using simulations. By incorporating markers linked to a tested position as well as those unlinked, CIM showed a higher efficiency to separate two linked QTL over SIM. The efficiency of dissection was enhanced as the marker informativeness was increased. The power of CIM to detect an isolated QTL was improved by excluding markers linked to a tested position from covariates and higher than SIM regardless of marker informativeness. In conclusion, CIM is a useful procedure for the analysis of QTL in outbred populations even under low marker informativeness.     

Statistical methods for dissecting triploid endosperm traits using molecular markers. An autogamous model

The endosperm, a result of double fertilization in flowering plants, is a triploid tissue whose genetic composition is more complex than diploid tissue. We present a new maximum-likelihood-based statistical method for mapping quantitative trait loci (QTL) underlying endosperm traits in an autogamous plant. Genetic mapping of quantitative endosperm traits is qualitatively different from traits for other plant organs because the endosperm displays complicated trisomic inheritance and represents a younger generation than its mother plant. Our endosperm mapping method is based on two different experimental designs: (1) a one-stage design in which marker information is derived from the maternal genome and (2) a two-stage hierarchical design in which marker information is derived from both the maternal and offspring genomes (embryos). Under the one-stage design, the position and additive effect of a putative QTL can be well estimated, but the estimates of the dominant and epistatic effects are upward biased and imprecise. The two-stage hierarchical design, which extracts more genetic information from the material, typically improves the accuracy and precision of the dominant and epistatic effects for an endosperm trait. We discuss the effects on the estimation of QTL parameters of different sampling strategies under the two-stage hierarchical design. Our method will be broadly useful in mapping endosperm traits for many agriculturally important crop plants and also make it possible to study the genetic significance of double fertilization in the evolution of higher plants.     

林木数量性状基因定位中的若干问题

随着ＤＮＡ分子标记技术的迅速发展,ＱＴＬ定位已成为当前生物学研究领域的前沿。迄今已对许多种动、植物定位了许多重要性状的ＱＴＬ。这些研究促进了遗传学的发展,并将作为育种的新策略应用。与作物相比,林木ＱＴＬ定位有其特性。本文详细讨论了林木的生物学特性对ＱＴＬ定位的影响、ＱＴＬ定位的系谱设计和统计分析方法。     

The role of pedigree information in combined linkage disequilibrium and linkage mapping of quantitative trait loci in a general complex pedigree

Combined linkage disequilibrium and linkage (LDL) mapping can exploit historical as well as recent and observed recombinations in a recorded pedigree. We investigated the role of pedigree information in LDL mapping and the performance of LDL mapping in general complex pedigrees. We compared using complete and incomplete genotypic data, spanning 5 or 10 generations of known pedigree, and we used bi- or multiallelic markers that were positioned at 1- or 5-cM intervals. Analyses carried out with or without pedigree information were compared. Results were compared with linkage mapping in some of the data sets. Linkage mapping or LDL mapping with sparse marker spacing ( approximately 5 cM) gave a poorer mapping resolution without considering pedigree information compared to that with considering pedigree information. The difference was bigger in a pedigree of more generations. However, LDL mapping with closely linked markers ( approximately 1 cM) gave a much higher mapping resolution regardless of using pedigree information. This study shows that when marker spacing is dense and there is considerable linkage disequilibrium generated from historical recombinations between flanking markers and QTL, the loss of power due to ignoring pedigree information is negligible and mapping resolution is very high.     

Genetic structure of susceptibility traits for hip dysplasia and microsatellite informativeness of an outcrossed canine pedigree

An outcrossed canine pedigree was developed for quantitative trait locus (QTL) mapping of hip dysplasia by breeding dysplastic Labrador retrievers to trait-free greyhounds. Measured susceptibility traits included age at onset of femoral capital chondroepiphyseal ossification (OSS), maximum hip distraction (laxity) index (DI), and the dorsolateral subluxation (DLS) score. The pedigrees consisted of 147 dogs representing four generations. For 59 dogs genotyped with 65 microsatellites, the median heterozygosity and polymorphic information content (PIC) values of the F(1) generation were 0.82 and 0.68, respectively. Seventy-seven percent of microsatellites had a PIC greater than 0.59 in the F(1)s. Ninety-six percent of alleles showed Mendelian inheritance. Based on marker informativeness, approximately 350 randomly selected markers would be required for genome-wide screening to obtain an average interval between informative markers of 10 cM. Heritability was estimated as 0.43, 0.5, and 0.61 for OSS, DI, and the DLS score, respectively. Biometric estimates of the mean (+/- variance) effective number of segregating QTLs was 1.2 (+/- 0.05), 0.8 (+/- 0.02), and 1.0 (+/- 0.03) for OSS, DI, and the DLS score, respectively. The distributions of simulated backcross trait data suggested that the loci controlling these traits acted additively and that the DI may be controlled by a major locus. When combined with previous power and quantitative genetic analyses, these estimates indicate that this pedigree is informative for QTL mapping of hip dysplasia traits.     

Methods for linkage disequilibrium mapping in crops

Linkage disequilibrium (LD) mapping in plants detects and locates quantitative trait loci (QTL) by the strength of the correlation between a trait and a marker. It offers greater precision in QTL location than family-based linkage analysis and should therefore lead to more efficient marker-assisted selection, facilitate gene discovery and help to meet the challenge of connecting sequence diversity with heritable phenotypic differences. Unlike family-based linkage analysis, LD mapping does not require family or pedigree information and can be applied to a range of experimental and non-experimental populations. However, care must be taken during analysis to control for the increased rate of false positive results arising from population structure and variety interrelationships. In this review, we discuss how suitable the recently developed alternative methods of LD mapping are for crops.     

A Generalization of the Mixture Model in the Mapping of Quantitative Trait Loci for Progeny from a Biparental Cross of Inbred Lines

The recent advent of molecular markers has created a great potential for the understanding of quantitative inheritance. In parallel to rapid developments and improvements in molecular marker technologies, biometrical models have been constructed, refined and generalized for the mapping of quantitative trait loci (QTL). However, current models present restricitions in terms of breeding designs to which they apply. In this paper, we develop an approach for the generalization of the mixture model for progeny from a single bi-parental cross of inbred lines. Detailed derivations are given for genetic designs involving populations developed by selfing, i.e., where marker genotypes are obtained from F(x) (x >=2) individuals and where phenotypes are measured on F(y) (y >=x) individuals or families. Extensions to designs involving doubled-haploids, backcross-derived individuals and random matings are outlined. The derivations presented here can easily be combined with current QTL mapping approaches.     

Empirical Threshold Values for Quantitative Trait Mapping

The detection of genes that control quantitative characters is a problem of great interest to the genetic mapping community. Methods for locating these quantitative trait loci (QTL) relative to maps of genetic markers are now widely used. This paper addresses an issue common to all QTL mapping methods, that of determining an appropriate threshold value for declaring significant QTL effects. An empirical method is described, based on the concept of a permutation test, for estimating threshold values that are tailored to the experimental data at hand. The method is demonstrated using two real data sets derived from F(2) and recombinant inbred plant populations. An example using simulated data from a backcross design illustrates the effect of marker density on threshold values.     

Mapping quantitative trait loci using the experimental designs of recombinant inbred populations

In the data collection of the QTL experiments using recombinant inbred (RI) populations, when individuals are genotyped for markers in a population, the trait values (phenotypes) can be obtained from the genotyped individuals (from the same population) or from some progeny of the genotyped individuals (from the different populations). Let Fu be the genotyped population and Fv (v>or=u) be the phenotyped population. The experimental designs that both marker genotypes and phenotypes are recorded on the same populations can be denoted as (Fu/Fv, u=v) designs and that genotypes and phenotypes are obtained from the different populations can be denoted as (Fu/Fv, v>u) designs. Although most of the QTL mapping experiments have been conducted on the backcross and F2(F2/F2) designs, the other (Fu/Fv, v>or=u) designs are also very popular. The great benefits of using the other (Fu/Fv, v>or=u) designs in QTL mapping include reducing cost and environmental variance by phenotyping several progeny for the genotyped individuals and taking advantages of the changes in population structures of other RI populations. Current QTL mapping methods including those for the (Fu/Fv, u=v) designs, mostly for the backcross or F2/F2 design, and for the F2/F3 design based on a one-QTL model are inadequate for the investigation of the mapping properties in the (Fu/Fv, uor=u) designs. In addition, the QTL mapping properties of the proposed and approximate methods in different designs are discussed. Simulations were performed to evaluate the performance of the proposed and approximate methods. The proposed method is proven to be able to correct the problems of the approximate and current methods for improving the resolution of genetic architecture of quantitative traits and can serve as an effective tool to explore the QTL mapping study in the system of RI populations.     

Multiple QTL mapping in related plant populations via a pedigree-analysis approach

QTL mapping experiments in plant breeding may involve multiple populations or pedigrees that are related through their ancestors. These known relationships have often been ignored for the sake of statistical analysis, despite their potential increase in power of mapping. We describe here a Bayesian method for QTL mapping in complex plant populations and reported the results from its application to a (previously analysed) potato data set. This Bayesian method was originally developed for human genetics data, and we have proved that it is useful for complex plant populations as well, based on a sensitivity analysis that was performed here. The method accommodates robustness to complex structures in pedigree data, full flexibility in the estimation of the number of QTL across multiple chromosomes, thereby accounting for uncertainties in the transmission of QTL and marker alleles due to incomplete marker information, and the simultaneous inclusion of non-genetic factors affecting the quantitative trait.     

Analysis of allele fidelity, polymorphic information content, and density of microsatellites in a genome-wide screening for hip dysplasia in a crossbreed pedigree

Recent advances in genomics resources and tools are facilitating quantitative trait locus mapping. We developed a crossbreed pedigree for mapping quantitative trait loci for hip dysplasia in dogs by crossing dysplastic Labrador Retrievers and normal Greyhounds. We show that one advantage to using a crossbreed pedigree is the increased marker informativeness in the backcross/F2 population relative to the founder populations. We also discuss three factors that affect the detection power in the context of this crossbreed pedigree: being able to detect and correct genotyping errors, increasing marker density for chromosomes with a sparse coverage, and adding individuals to the mapping population as soon as they become available.     

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.     

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.     

Fine mapping of complex trait genes combining pedigree and linkage disequilibrium information: a Bayesian unified framework

We present a Bayesian method that combines linkage and linkage disequilibrium (LDL) information for quantitative trait locus (QTL) mapping. This method uses jointly all marker information (haplotypes) and all available pedigree information; i.e., it is not restricted to any specific experimental design and it is not required that phases are known. Infinitesimal genetic effects or environmental noise ("fixed") effects can equally be fitted. A diallelic QTL is assumed and both additive and dominant effects can be estimated. We have implemented a combined Gibbs/Metropolis-Hastings sampling to obtain the marginal posterior distributions of the parameters of interest. We have also implemented a Bayesian variant of usual disequilibrium measures like D' and r(2) between QTL and markers. We illustrate the method with simulated data in "simple" (two-generation full-sib families) and "complex" (four-generation) pedigrees. We compared the estimates with and without using linkage disequilibrium information. In general, using LDL resulted in estimates of QTL position that were much better than linkage-only estimates when there was complete disequilibrium between the mutant QTL allele and the marker. This advantage, however, decreased when the association was only partial. In all cases, additive and dominant effects were estimated accurately either with or without disequilibrium information.     

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.     

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.     

The efficiency of designs for fine-mapping of quantitative trait loci using combined linkage disequilibrium and linkage

In a simulation study, different designs were compared for efficiency of fine-mapping of QTL. The variance component method for fine-mapping of QTL was used to estimate QTL position and variance components. The design of many families with small size gave a higher mapping resolution than a design with few families of large size. However, the difference is small in half sib designs. The proportion of replicates with the QTL positioned within 3 cM of the true position is 0.71 in the best design, and 0.68 in the worst design applied to 128 animals with a phenotypic record and a QTL explaining 25% of the phenotypic variance. The design of two half sib families each of size 64 was further investigated for a hypothetical population with effective size of 1000 simulated for 6000 generations with a marker density of 0.25 cM and with marker mutation rate 4 × 10^-4 per generation. In mapping using bi-allelic markers, 42~55% of replicated simulations could position QTL within 0.75 cM of the true position whereas this was higher for multi allelic markers (48~76%). The accuracy was lowest (48%) when mutation age was 100 generations and increased to 68% and 76% for mutation ages of 200 and 500 generations, respectively, after which it was about 70% for mutation ages of 1000 generations and older. When effective size was linearly decreasing in the last 50 generations, the accuracy was decreased (56 to 70%). We show that half sib designs that have often been used for linkage mapping can have sufficient information for fine-mapping of QTL. It is suggested that the same design with the same animals for linkage mapping should be used for fine-mapping so gene mapping can be cost effective in livestock populations.     

Linkage analysis of molecular markers and quantitative trait loci in populations of inbred backcross lines of Brassica napus L.

Backcross populations are often used to study quantitative trait loci (QTL) after they are initially discovered in balanced populations, such as F(2), BC(1), or recombinant inbreds. While the latter are more powerful for mapping marker loci, the former have the reduced background genetic variation necessary for more precise estimation of QTL effects. Many populations of inbred backcross lines (IBLs) have been developed in plant and animal systems to permit simultaneous study and dissection of quantitative genetic variation introgressed from one source to another. Such populations have a genetic structure that can be used for linkage estimation and discovery of QTL. In this study, four populations of IBLs of oilseed Brassica napus were developed and analyzed to map genomic regions from the donor parent (a winter-type cultivar) that affect agronomic traits in spring-type inbreds and hybrids. Restriction fragment length polymorphisms (RFLPs) identified among the IBLs were used to calculate two-point recombination fractions and LOD scores through grid searches. This information allowed the enrichment of a composite genetic map of B. napus with 72 new RFLP loci. The selfed and hybrid progenies of the IBLs were evaluated during two growing seasons for several agronomic traits. Both pedigree structure and map information were incorporated into the QTL analysis by using a regression approach. The number of QTL detected for each trait and the number of effective factors calculated by using biometrical methods were of similar magnitude. Populations of IBLs were shown to be valuable for both marker mapping and QTL analysis.     

Multiple-interval mapping for quantitative trait loci controlling endosperm traits

Endosperm traits are trisomic inheritant and are of great economic importance because they are usually directly related to grain quality. Mapping for quantitative trait loci (QTL) underlying endosperm traits can provide an efficient way to genetically improve grain quality. As the traditional QTL mapping methods (diploid methods) are usually designed for traits under diploid control, they are not the ideal approaches to map endosperm traits because they ignore the triploid nature of endosperm. In this article, a statistical method considering the triploid nature of endosperm (triploid method) is developed on the basis of multiple-interval mapping (MIM) to map for the underlying QTL. The proposed triploid MIM method is derived to broadly use the marker information either from only the maternal plants or from both the maternal plants and their embryos in the backcross and F2 populations for mapping endosperm traits. Due to the use of multiple intervals simultaneously to take multiple QTL into account, the triploid MIM method can provide better detection power and estimation precision, and as shown in this article it is capable of analyzing and searching for epistatic QTL directly as compared to the traditional diploid methods and current triploid methods using only one (or two) interval(s). Several important issues in endosperm trait mapping, such as the relation and differences between the diploid and triploid methods, variance components of genetic variation, and the problems if effects are present and ignored, are also addressed. Simulations are performed to further explore these issues, to investigate the relative efficiency of different experimental designs, and to evaluate the performance of the proposed and current methods in mapping endosperm traits. The MIM-based triploid method can provide a powerful tool to estimate the genetic architecture of endosperm traits and to assist the marker-assisted selection for the improvement of grain quality in crop science. The triploid MIM FORTRAN program for mapping endosperm traits is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data

A general fine-scale Bayesian quantitative trait locus (QTL) mapping method for outcrossing species is presented. It is suitable for an analysis of complete and incomplete data from experimental designs of F2 families or backcrosses. The amount of genotyping of parents and grandparents is optional, as well as the assumption that the QTL alleles in the crossed lines are fixed. Grandparental origin indicators are used, but without forgetting the original genotype or allelic origin information. The method treats the number of QTL in the analyzed chromosome as a random variable and allows some QTL effects from other chromosomes to be taken into account in a composite interval mapping manner. A block-update of ordered genotypes (haplotypes) of the whole family is sampled once in each marker locus during every round of the Markov Chain Monte Carlo algorithm used in the numerical estimation. As a byproduct, the method gives the posterior distributions for linkage phases in the family and therefore it can also be used as a haplotyping algorithm. The Bayesian method is tested and compared with two frequentist methods using simulated data sets, considering two different parental crosses and three different levels of available parental information. The method is implemented as a software package and is freely available under the name Multimapper/outbred at URL http://www.rni.helsinki.fi/mjs/.