Limitations of a two-step moment method for mapping linked multiple QTL

As an alternative to multiple-interval mapping a two-step moment method was recently proposed to map linked multiple quantitative trait loci (QTLs). The advantage of this moment method was supposed to be its simplicity and computational efficiency, especially in detecting closely linked QTLs within a marker bracket, but also in mapping QTLs in different marker intervals. Using simulations it is shown that the two-step moment method may give poor results compared with multiple-interval mapping, irrespective of whether the QTLs are in the same or in different marker intervals, especially if linked QTLs are in repulsion. The criteria of comparison are number of identified QTLs, likelihood ratio test statistics, means and empirical standard errors of the QTL position and QTL effects estimates, and the accuracy of the residual variance estimates. Further, the joint conditional probabilities of QTL genotypes for two putative QTLs within a marker interval were derived and compared with the unmodified approach ignoring the non-independence of the conditional probabilities.     

The Contribution of Quantitative Trait Loci and Neutral Marker Loci to the Genetic Variances and Covariances among Quantitative Traits in Random Mating Populations

Using Cockerham's approach of orthogonal scales, we develop genetic models for the effect of an arbitrary number of multiallelic quantitative trait loci (QTLs) or neutral marker loci (NMLs) upon any number of quantitative traits. These models allow the unbiased estimation of the contributions of a set of marker loci to the additive and dominance variances and covariances among traits in a random mating population. The method has been applied to an analysis of allozyme and quantitative data from the European oyster. The contribution of a set of marker loci may either be real, when the markers are actually QTLs, or apparent, when they are NMLs that are in linkage disequilibrium with hidden QTLs. Our results show that the additive and dominance variances contributed by a set of NMLs are always minimum estimates of the corresponding variances contributed by the associated QTLs. In contrast, the apparent contribution of the NMLs to the additive and dominance covariances between two traits may be larger than, equal to or lower than the actual contributions of the QTLs. We also derive an expression for the expected variance explained by the correlation between a quantitative trait and multilocus heterozygosity. This correlation explains only a part of the genetic variance contributed by the markers, i.e., in general, a combination of additive and dominance variances and, thus, provides only very limited information relative to the method supplied here.     

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.     

Identification and mode of action of quantitative trait loci affecting seedling height and leaf area in Eucalyptus nitens

 Regions of the genome influencing height and leaf area in seedlings of a three-generation outbred pedigree of Eucalyptus nitens have been identified. Three QTLs affecting height and two QTLs affecting leaf area were located using single-factor analysis of variance. The three QTLs affecting height each explained between 10.3 and 14.7% of the phenotypic variance, while the two QTLs for leaf area each explained between 9.8 and 11.6% of the phenotypic variation. Analysis of fully informative marker loci linked to the QTLs enabled the mode of action of the QTLs to be investigated. For three loci the QTL effect segregated from only one parent, while for two loci the QTL showed multiple alleles and the effect segregated from both parents in the pedigree. The two QTLs affecting leaf area were located in the same regions as two of the QTLs affecting height. Analysis of these regions with fully informative markers showed that both QTLs were linked to the same markers, but one had a similar size of effects and a similar mode of action for both height and leaf area, whilst the other showed a different mode of action for the two traits. These regions may contain two closely linked genes or may involve a single gene with a pleiotrophic effect on both height and leaf area. The QTL with the greatest effect showed multiple alleles and an intra-locus interaction that reduced the size of the effect. Assessment for two of the QTLs in a second related family did not show an effect associated with the marker loci; however, this was consistent with the mode of action of these QTLs and the pattern of inheritance in the second family. Received: 1 August 1996 / Accepted: 25 October 1996     

Quantitative genetic variance associated with chromosomal markers in segregating populations

Summary Use of chromosomal markers can accelerate genetic progress for quantitative traits in pedigree selection programs by providing early information on Mendelian segregation effects for individual progeny. Potential effectiveness of selection using markers is determined by the amount of additive genetic variance traced from parents to progeny by the markers. Theoretical equations for the amount of additive genetic variance associated with a marker were derived at the individual level and for a segregating population in joint linkage equilibrium. Factors considered were the number of quantitative trait loci linked to the marker, their individual effects, and recombination rates with the marker. Subsequently, the expected amount of genetic variance associated with a marker in a segregating population was derived. In pedigree selection programs in segregating populations, a considerable fraction of the genetic variance on a chromosome is expected to be associated with a marker located on that chromosome. For an average chromosome in the bovine, this fraction is approximately 40% of the Mendelian segregation variance contributed by the chromosome. The effects of interference and position of the marker on this expectation are relative small. Length of the chromosome has a large effect on the expected variance. Effectiveness of MAS is, however, greatly reduced by lack of polymorphism at the marker and inaccuracy of estimation of chromosome substitution effects. The size of the expected amount of genetic variance associated with a chromosomal marker indicates that, even when the marker is not the active locus, large chromosome substitution effects are not uncommon in segregating populations.     

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.     

The effects of selective genotyping on estimates of proportion of recombination between linked quantitative trait loci

Selective genotyping is the marker assay of only the more extreme phenotypes for a quantitative trait and is intended to increase the efficiency of quantitative trait loci (QTL) mapping. We show that selective genotyping can bias estimates of the recombination frequency between linked QTLs — upwardly when QTLs are in repulsion phase, and downwardly when QTLs are in coupling phase. We examined these biases under simple models involving two QTLs segregating in a backcross or F₂ population, using both analytical models and computer simulations. We found that bias is a function of the proportion selected, the magnitude of QTL effects, distance between QTLs and the dominance of QTLs. Selective genotyping thus may decrease the power of mapping multiple linked QTLs and bias the construction of a marker map. We suggest a large proportion than previously suggested (50%) or the entire population be genotyped if linked QTLs of large effects (explain > 10% phenotypic variance) are evident. New models need to be developed to explicitly incorporate selection into QTL map construction.     

Detection of putative quantitative trait loci in line crosses under infinitesimal genetic models

Quantitative trait locus (QTL) mapping studies often employ segregating generations derived from a cross between genetically divergent inbred lines. In the analysis of such data it is customary to fit a single QTL and use a null hypothesis which assumes that the genomic region under study contributes no genetic variance. To explore the situation in which multiple linked genes contribute to the genetic variance, we simulated an F₂-mapping experiment in which the genetic difference between the two original inbred strains was caused by a large number of loci, each having equal effect on the quantitative trait. QTLs were either in coupling, dispersion or repulsion phase in the base population of inbred lines, with the expected F₂ genetic variance explained by the QTLs being equivalent in the three models. Where QTLs were in coupling phase, one inbred line was fixed for all plus alleles, and the other line was fixed for minus alleles. Where QTLs were in dispersion phase, they were assumed to be randomly fixed for one or other allele (as if the inbred lines had evolved from a common ancestor by random drift). Where QTLs were in repulsion phase alleles within an inbred line were alternating plus and minus at adjacent loci, and alternative alleles were fixed in the two inbred lines. In all these genetic models a standard interval mapping test statistic used to determine whether there is a QTL of large effect segregating in the population was inflated on average. Furthermore, the use of a threshold for QTL detection derived under the assumption that no QTLs were segregating would often lead to spurious conclusions regards the presence of genes of large effects (i.e. type I errors). The employment of an alternative model for the analysis, including linked markers as cofactors in the analysis of a single interval, reduced the problem of type I error rate, although test statistics were still inflated relative to the case of no QTLs. It is argued that in practice one should take into account the difference between the strains or the genetic variance in the F₂ population when setting significance thresholds. In addition, tests designed to probe the adequacy of a single-QTL model or of an alternative infinitesimal coupling model are described. Such tests should be applied in QTL mapping studies to help dissect the true nature of genetic variation.     

Association mapping and meta-analysis: two complementary approaches for the detection of reliable Septoria tritici blotch quantitative resistance in bread wheat (Triticum aestivum L.)

Septoria tritici blotch (STB), caused by the ascomycete Mycosphaerella graminicola, is one of the most ubiquitous and important diseases of bread wheat worldwide. The aim of this study was to identify markers linked to loci conferring resistance to STB from seven biparental populations. Linkage analysis, meta-analysis and association mapping were combined to identify robust quantitative trait loci (QTLs) for resistance. Linkage analysis led to the detection of 115 QTLs for resistance to STB and 66 QTLs linked to plant height and/or earliness. Meta-analysis clustered these 115 QTLs into 27 Meta-QTLs (MQTLs) of pathogen resistance, of which 14 were found to be linked to plant height and/or earliness. Both the relationship between dwarfing and susceptibility to STB and the significant negative correlation between earliness and STB symptoms were confirmed. Eleven loci were linked to STB resistance by association mapping using a general linear model and/or a mixed linear model, of which eight co-located with STB MQTLs and two co-located with individual QTLs. Associated markers located in MQTL regions enhanced the relevance of the results and validated the potential of an association mapping approach. With several biparental populations, meta-analysis is the most relevant form of genetic analysis study, but association mapping can be used as a validation method. Regions linked to resistance in both methods should be relevant for use in breeding programs for improving resistance to STB in wheat varieties. The main interest in comparing both approaches is to detect robust loci that will be functional in many genetic backgrounds rather than just in one or a few specific backgrounds.     

High-resolution joint linkage disequilibrium and linkage mapping of quantitative trait loci based on sibship data

This paper proposes variance component models for high resolution joint linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) based on sibship data; this can include population data if independent individuals are treated as single sibships. One application of these models is late onset complex disease gene mapping, when parental data are not available. The models simultaneously incorporate both LD and linkage information. The LD information is contained in mean coefficients of sibship data. The linkage information is contained in the variance-covariance matrices of trait values for sibships with at least two siblings. We derive formulas for calculating the probability of sharing two trait alleles identical by descent (IBD) for sibpairs in interval mapping of QTL; this is the coefficient of dominant variance of the trait covariance of sibpairs on major QTL. To investigate the performance of the formulas, we calculate the numerical values via the formulas and get satisfactory approximations. We compare the power and sample sizes for both LD and linkage mapping. By simulation and theoretical analysis, we compare the results with those of Fulker and Abecasis "AbAw" approach. It is well known that the resolution of linkage analysis can be low for complex disease gene mapping. LD mapping, on the other hand, can increase mapping precision and is useful in high resolution mapping. Linkage analysis is less sensitive to population subdivisions and admixtures. The level of LD is sensitive to population stratification which may easily lead to spurious association. Performing a joint analysis of LD and linkage mapping can help to overcome the limits of both approaches. Moreover, the advantages of the two complementary strategies can be utilized maximally. In practice, linkage analysis may be performed using pedigree data to identify suggestive linkage between markers and trait loci based on a sparse marker map. In the presence of linkage, joint LD and linkage mapping can be carried out to do fine gene mapping based on a dense genetic map using both pedigree and population data. Population and pedigree data of any type can be combined to perform a joint analysis of high resolution LD and linkage mapping of QTL by generalizing the method.     

A comparison of interval mapping procedures including the QTL-cluster mapping

Using the deterministic sampling, patterns of the log-likelihood surfaces expected in some interval mapping procedures for estimating the position of, and the effect for, QTL(s) were investigated for the situations where a single QTL or closely linked QTLs are contained in a chromosome segment bracketed with two markers. The mapping procedures compared were the conventional, likelihood-based interval mapping (IM), the regression interval mapping (RIM), and the QTL-cluster mapping (CM) in which the conditional probabilities of transmission of the whole segment marked by the flanking markers were taken into consideration. The half-sib design was used here, and several cases of the true genetic model were considered, differing in the number of QTLs contained in the marker interval, the linkage phase for the sire, and the magnitude of the QTL(s) effect. For the true genetic models where a single QTL or closely linked QTLs being in coupling phase are contained in the interval, with (R)IM, clear global maxima of the log-likelihood were observed within the range of the marker interval. It was shown that the estimates of the QTL(s) effect at the marked segment level are expected to be unbiased. On the other hand, in a setting where the linkage phase for the linked QTLs located in the interval was different from coupling and repulsion, there was found a ridge along the interval for the log-likelihood surface with (R)IM, indicating the dependency between the estimates of the position of, and the effect for, the putative QTL. For this case, it was found that the position of the putative QTL could be estimated as that of one of the flanking markers, and the estimate of the QTL effect be biased. In contrast, it was revealed that CM is expected to provide the unbiased estimate of the QTL(s)-effect at the segment level for any case of the true genetic models considered here. If the aim is for marker-assisted selection rather than mapping closely linked QTLs individually, then the CM approach is considered to be useful.     

A wheat intervarietal genetic linkage map based on microsatellite and target region amplified polymorphism markers and its utility for detecting quantitative trait loci

Efficient user-friendly methods for mapping plant genomes are highly desirable for the identification of quantitative trait loci (QTLs), genotypic profiling, genomic studies, and marker-assisted selection. SSR (microsatellite) markers are user-friendly and efficient in detecting polymorphism, but they detect few loci. Target region amplification polymorphism (TRAP) is a relatively new PCR-based technique that detects a large number of loci from a single reaction without extensive pre-PCR processing of samples. In the investigation reported here, we used both SSRs and TRAPs to generate over 700 markers for the construction of a genetic linkage map in a hard red spring wheat intervarietal recombinant inbred population. A framework map consisting of 352 markers accounted for 3,045 cM with an average density of one marker per 8.7 cM. On average, SSRs detected 1.9 polymorphic loci per reaction, while TRAPs detected 24. Both marker systems were suitable for assigning linkage groups to chromosomes using wheat aneuploid stocks. We demonstrated the utility of the maps by identifying major QTLs for days to heading and reduced plant height on chromosomes 5A and 4B, respectively. Our results indicate that TRAPs are highly efficient for genetic mapping in wheat. The maps developed will be useful for the identification of quality and disease resistance QTLs that segregate in this population.     

A new approach for mapping quantitative trait loci using complete genetic marker linkage maps

A new approach based on nonlinear regression for the mapping of quantitative trait loci (QTLs) using complete genetic marker linkage maps is advanced in this paper. We call the approach joint mapping as it makes comprehensive use of the information from every marker locus on a chromosome. With this approach, both the detection of the existence of QTLs and the estimation of their positions, with corresponding confidence intervals, and effects can be realized simultaneously. This approach is widely applicable because only moments are used. It is simple and can save considerable computer time. It is especially useful when there are multiple QTLs and/or interactions between them on a chromosome.     

Identification of quantitative trait loci for agronomically important traits and their association with genic-microsatellite markers in sorghum

The identification of quantitative trait loci (QTLs) affecting agronomically important traits enable to understand their underlying genetic mechanisms and genetic basis of their complex interactions. The aim of the present study was to detect QTLs for 12 agronomic traits related to staygreen, plant early development, grain yield and its components, and some growth characters by analyzing replicated phenotypic datasets from three crop seasons, using the population of 168 F₇ RILs of the cross 296B × IS18551. In addition, we report mapping of a subset of genic-microsatellite markers. A linkage map was constructed with 152 marker loci comprising 149 microsatellites (100 genomic- and 49 genic-microsatellites) and three morphological markers. QTL analysis was performed by using MQM approach. Forty-nine QTLs were detected, across environments or in individual environments, with 1–9 QTLs for each trait. Individual QTL accounted for 5.2–50.4% of phenotypic variance. Several genomic regions affected multiple traits, suggesting the phenomenon of pleiotropy or tight linkage. Stable QTLs were identified for studied traits across different environments, and genetic backgrounds by comparing the QTLs in the study with previously reported QTLs in sorghum. Of the 49 mapped genic-markers, 18 were detected associating either closely or exactly as the QTL positions of agronomic traits. EST marker Dsenhsbm19, coding for a key regulator (EIL-1) of ethylene biosynthesis, was identified co-located with the QTLs for plant early development and staygreen trait, a probable candidate gene for these traits. Similarly, such exact co-locations between EST markers and QTLs were observed in four other instances. Collectively, the QTLs/markers identified in the study are likely candidates for improving the sorghum performance through MAS and map-based gene isolations.     

Multiple-marker mapping of wood density loci in an outbred pedigree of radiata pine

The objective of this study was to determine the genetic location and effects of genomic regions controlling wood density at three stages, i.e., rings corresponding to ages 1–5 (WD1_5), rings corresponding to ages 6–10 (WD6_10), and outer wood density (WD14) in a full-sib pedigree (850.055×850.096) of Pinus radiata. The number of offspring measured at these three stages were 80, 93 and 93, respectively. Only a single linkage group of the parent 850.55 was considered for mapping quantitative trait loci (QTLs). A multiple-marker least-squares approach was employed for mapping QTLs for each of the three traits, using a single-QTL model. Logistic regression was used for multiple-trait QTL mapping. Critical values for test-statistic were calculated empirically by ’shuffling’ the data. A putative QTL with large effect on WD1_5 appears to be segregating at the 73 cM position (experimentwise P<0.01). The width of the 95% bootstrap confidence interval for this putative QTL was 40 cM (i.e. 56–96 cM). The effect of this QTL on the expression of wood density at later stages was diminished. From multiple-trait analysis, two marker locations (at 66 cM and 91 cM) were found to be significantly associated (experimentwise P <0.05) with the expression of wood density at different ages. These results are encouraging for the application of marker information to early selection in order to increase juvenile wood density, although the putative QTLs detected in this study need to be verified in an independent population. Received: 23 July 1999 / Accepted: 27 August 1999     

Quantitative resistance against Bemisia tabaci in Solanum pennellii: Genetics and metabolomics

The whitefly Bemisia tabaci is a serious threat in tomato cultivation worldwide as all varieties grown today are highly susceptible to this devastating herbivorous insect.Many accessions of the tomato wild relative Solanum pennellii show a high resistance towards B. tabaci. A mapping approach was used to elucidate the genetic background of whiteflyresistance related traits and associated biochemical traits in this species. Minor quantitative trait loci(QTLs) for whitefly adult survival(AS) and oviposition rate(OR) were identified and some were confirmed in an F2BC1 population, where they showed increased percentages of explained variance(more than 30%). Bulked segregant analyses on pools of whiteflyresistant and-susceptible F2 plants enabled the identification of metabolites that correlate either with resistance or susceptibility. Genetic mapping of these metabolites showed that a large number of them co-localize with whiteflyresistance QTLs. Some of these whitefly-resistance QTLs are hotspots for metabolite QTLs. Although a large number of metabolite QTLs correlated to whitefly resistance or susceptibility, most of them are yet unknown compounds and further studies are needed to identify the metabolic pathways and genes involved. The results indicate a direct genetic correlation between biochemical-based resistance characteristics and reduced whitefly incidence in S. pennellii.     

Identification of QTLs influencing wood property traits in loblolly pine ( Pinus taeda L.). II. Chemical wood properties

Chemical wood property traits were analyzed for the presence of quantitative trait loci (QTLs) in a three-generation outbred pedigree of loblolly pine (Pinus taeda L.). These traits were assayed using pyrolysis molecular beam mass spectrometry and include mass spectrum peak intensities associated with carbohydrates, α-cellulose and hemicellulose sugars, and lignin. Models for projection to latent structures (PLS) were used to also estimate the chemical composition of cell walls (i.e., α-cellulose, galactan and lignin) from mass spectrum data using multivariate regression. Both earlywood and latewood fractions from the fifth annual ring were analyzed for each trait. An interval mapping approach designed for an outbred pedigree was used to estimate the number of QTLs, the magnitude of QTL effects, and their genomic position. Eight unique QTLs influencing cell wall chemistry were detected from multiple peak intensities and/or PLS estimates using the one- and two-QTL models. Significant differences in chemical contents were observed among the populations from North Carolina vs Oklahoma, and results from QTL×environment analyses suggest that QTLs interact with environmental location. QTLs should be verified in larger experiments and in different genetic and environmental backgrounds. QTL mapping will help towards eventually identifying genes having a major effect on chemical wood properties. Received: 19 January 2001 / Accepted: 31 May 2001     

Comparative genomics and association mapping approaches for opaque2 modifier genes in finger millet accessions using genic,genomic and candidate gene-based simple sequence repeat markers

Identification of alleles responsible for opaque2 modifiers (Opm) influencing tryptophan content in finger millet is a major aim for further improvement of the quality of the locally adapted finger millet germplasm. Since there is little genome sequence information available, comparative genomics plays a very important role in identification of genes/quantitative trait loci (QTLs) linked to the Opm genes using simple sequence repeat (SSR) markers. In the present study, a total of 74 genic SSRs were developed and then used for genetic diversity and population structure analysis of a global collection of 190 finger millet genotypes. The 74 SSRs yielded 133 scorable alleles and the polymorphism information content values varied from 0.186 to 0.707, with an average of 0.408. The gene diversity was in the range of 0.208–0.752, with an average of 0.501. The SSRs developed from the aspartate kinase2 gene of the lysine pathway showed more polymorphism than the other candidate genes. The 74 genic SSR loci grouped the 190 finger millet genotypes into three major clusters based on their tryptophan content, using both phylogenetic clustering and population structure analysis by STRUCTURE software. Association mapping for Opm was done using 120 (74 genic and 46 genomic) SSR loci for identification of QTLs linked to Opm influencing tryptophan content, and found two QTLs for tryptophan and one QTL for protein content. The QTLs for tryptophan content were associated with the genic marker OM5 at a P value of 0.009 and explained 11 % of phenotypic variance (R ²). The OM5 marker was designed from the 27-kDa γ-zein gene of Opm, which influences the tryptophan content to a large extent, whereas the genomic marker FM8 was linked at a P value of 0.004 and explained 9 % of R ². The QTLs for protein content were associated with the genic SSR marker FMO2EST1, which was designed from the RISBZ1 gene of rice and was linked at a P value of 0.002 and explained 9 % of R ². The 220-bp allele of SSR locus OM5 was found to be present mostly in the high tryptophan-containing genotypes such as exotic genotypes, and among the Indian genotypes it was present in NW Himalayan genotypes. The markers linked to the QTLs for Opm found in the present study can be further used for cloning of the full-length gene, for fine mapping and in the marker-assisted breeding programmes for introgression of alleles into locally well-adapted germplasm.     

Bayesian association mapping of multiple quantitative trait loci and its application to the analysis of genetic variation among <Emphasis Type="Italic">Oryza sativa</Emphasis> L. germplasms

One way to use a crop germplasm collection directly to map QTLs without using line-crossing experiments is the whole genome association mapping. A major problem with association mapping is the presence of population structure, which can lead to both false positives and failure to detect genuine associations (i.e., false negatives). Particularly in highly selfing species such as Asian cultivated rice, high levels of population structure are expected and therefore the efficiency of association mapping remains almost unknown. Here, we propose an approach that combines a Bayesian method for mapping multiple QTLs with a regression method that directly incorporates estimates of population structure. That is, the effects due to both multiple QTLs and population structure were included in our statistical model. We evaluated the efficiency of our approach in simulated- and real-trait analyses of a rice germplasm collection. Simulation analyses based on real marker data showed that our model could suppress both false-positive and false-negative rates and the error of estimation of genetic effects over single QTL models, indicating that our model has statistically desirable attributes over single QTL models. As real traits, we analyzed the size and shape of milled rice grains and found significant markers that may be linked to QTLs reported previously. Association mapping should have good prospects in highly selfing species such as rice if proper methods are adopted. Our approach will be useful for the whole genome association mapping of various selfing crop species.     

Multipoint quantitative-trait linkage analysis in general pedigrees.

Multipoint linkage analysis of quantitative-trait loci (QTLs) has previously been restricted to sibships and small pedigrees. In this article, we show how variance-component linkage methods can be used in pedigrees of arbitrary size and complexity, and we develop a general framework for multipoint identity-by-descent (IBD) probability calculations. We extend the sib-pair multipoint mapping approach of Fulker et al. to general relative pairs. This multipoint IBD method uses the proportion of alleles shared identical by descent at genotyped loci to estimate IBD sharing at arbitrary points along a chromosome for each relative pair. We have derived correlations in IBD sharing as a function of chromosomal distance for relative pairs in general pedigrees and provide a simple framework whereby these correlations can be easily obtained for any relative pair related by a single line of descent or by multiple independent lines of descent. Once calculated, the multipoint relative-pair IBDs can be utilized in variance-component linkage analysis, which considers the likelihood of the entire pedigree jointly. Examples are given that use simulated data, demonstrating both the accuracy of QTL localization and the increase in power provided by multipoint analysis with 5-, 10-, and 20-cM marker maps. The general pedigree variance component and IBD estimation methods have been implemented in the SOLAR (Sequential Oligogenic Linkage Analysis Routines) computer package.