QTL linkage analysis of connected populations using ancestral marker and pedigree information

The common assumption in quantitative trait locus (QTL) linkage mapping studies that parents of multiple connected populations are unrelated is unrealistic for many plant breeding programs. We remove this assumption and propose a Bayesian approach that clusters the alleles of the parents of the current mapping populations from locus-specific identity by descent (IBD) matrices that capture ancestral marker and pedigree information. Moreover, we demonstrate how the parental IBD data can be incorporated into a QTL linkage analysis framework by using two approaches: a Threshold IBD model (TIBD) and a Latent Ancestral Allele Model (LAAM). The TIBD and LAAM models are empirically tested via numerical simulation based on the structure of a commercial maize breeding program. The simulations included a pilot dataset with closely linked QTL on a single linkage group and 100 replicated datasets with five linkage groups harboring four unlinked QTL. The simulation results show that including parental IBD data (similarly for TIBD and LAAM) significantly improves the power and particularly accuracy of QTL mapping, e.g., position, effect size and individuals’ genotype probability without significantly increasing computational demand.     

Multi-QTL mapping for quantitative traits using distorted markers

Marker segregation distortion is a common natural phenomenon. However, relatively little is known about utilizing distorted markers for detecting quantitative trait loci (QTL). Therefore, in this study we proposed a multi-QTL mapping approach that uses distorted markers. First, the information from all markers, including distorted markers, was used to detect segregation distortion loci (SDL). Second, the information from the detected SDL was used to correct the conditional probabilities of the QTL genotypes conditional on marker information, and these corrected probabilities were then incorporated into a multi-QTL mapping methodology. Finally, the proposed approach was validated by both Monte Carlo simulation studies and real data analysis. The results from the simulation studies show that as long as one or two SDL are placed around the simulated QTL, there are no differences between the new method and the ordinary interval mapping method in terms of the power of QTL detection or the estimates of the position and dominant effects of the QTL. However, the power of QTL detection is higher under the dominant genetic model of SDL than under the additive genetic model, and the estimate for the additive effect of QTL using the new method is significantly different from the estimate obtained using ordinary interval mapping. The above results were further confirmed by the detection of QTL for dried soymilk in 222 F_2:4 families in soybean.     

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.     

Optimum design of family structure and allocation of resources in association mapping with lines from multiple crosses

Family mapping is based on multiple segregating families and is becoming increasingly popular because of its advantages over population mapping. Athough much progress has been made recently, the optimum design and allocation of resources for family mapping remains unclear. Here, we addressed these issues using a simulation study, resample model averaging and cross-validation approaches. Our results show that in family mapping, the predictive power and the accuracy of quatitative trait loci (QTL) detection depend greatly on the population size and phenotyping intensity. With small population sizes or few test environments, QTL results become unreliable and are hampered by a large bias in the estimation of the proportion of genotypic variance explained by the detected QTL. In addition, we observed that even though good results can be achieved with low marker densities, no plateau is reached with our full marker complement. This suggests that higher quality results could be achieved with greater marker densities or sequence data, which will be available in the near future for many species.     

Mixed-model QTL mapping for kernel hardness and dough strength in bread wheat

Plant breeding data comprise unbalanced phenotypic data for inbreds with complex pedigrees. As traditional methods to map quantitative trait loci (QTL) cannot exploit plant breeding data, an alternative approach is QTL mapping via a mixed-model procedure. Our objective was to validate mixed-model QTL mapping for self-pollinated crops by detecting QTL for kernel hardness and dough strength from data in a bread wheat (Triticum aestivum L.) breeding program. We studied 80 parental and 373 experimental inbreds genotyped for 65 simple sequence repeat (SSR) markers and three candidate loci. The methodology involved three steps: variance component estimation, single-marker analyses, and a final multiple-marker analysis with marker effects treated as fixed effects. Two QTLs for kernel hardness were detected on chromosomes 1A (close to candidate locus GluA3) and 5D (close to candidate locus Ha). Four QTLs were detected for dough strength on chromosomes 1A, 1B, 1D, and 5B. Candidate gene GluA1, which was associated with dough strength, was the only candidate locus found significant. Results were consistent with previously reported markers and QTLs associated with kernel hardness and dough strength. Unlike previous studies that have assumed QTL effects as random, the assumption of fixed marker effects identified the favorable marker alleles to select for. We conclude that the detection of previously mapped QTL validates the usefulness of mixed-model QTL mapping in the context of a plant-breeding program.     

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.     

Comparison of biometrical approaches for QTL detection in multiple segregating families

Detection of QTL in multiple segregating families possesses many advantages over the classical QTL mapping in biparental populations. It has thus become increasingly popular, and different biometrical approaches are available to analyze such data sets. We empirically compared an approach based on linkage mapping methodology with an association mapping approach. To this end, we used a large population of 788 elite maize lines derived from six biparental families genotyped with 857 SNP markers. In addition, we constructed genetic maps with reduced marker densities to assess the dependency of the performance of both mapping approaches on the marker density. We used cross-validation and resample model averaging and found that while association mapping performed better under high marker densities, this was reversed under low marker densities. In addition to main effect QTL, we also detected epistatic interactions. Our results suggest that both approaches will profit from a further increase in marker density and that a cross-validation should be applied irrespective of the biometrical approach.     

Efficiency of selective genotyping for genetic analysis of complex traits and potential applications in crop improvement

Selective genotyping of individuals from the two tails of the phenotypic distribution of a population provides a cost efficient alternative to analysis of the entire population for genetic mapping. Past applications of this approach have been confounded by the small size of entire and tail populations, and insufficient marker density, which result in a high probability of false positives in the detection of quantitative trait loci (QTL). We studied the effect of these factors on the power of QTL detection by simulation of mapping experiments using population sizes of up to 3,000 individuals and tail population sizes of various proportions, and marker densities up to one marker per centiMorgan using complex genetic models including QTL linkage and epistasis. The results indicate that QTL mapping based on selective genotyping is more powerful than simple interval mapping but less powerful than inclusive composite interval mapping. Selective genotyping can be used, along with pooled DNA analysis, to replace genotyping the entire population, for mapping QTL with relatively small effects, as well as linked and interacting QTL. Using diverse germplasm including all available genetics and breeding materials, it is theoretically possible to develop an “all-in-one plate” approach where one 384-well plate could be designed to map almost all agronomic traits of importance in a crop species. Selective genotyping can also be used for genomewide association mapping where it can be integrated with selective phenotyping approaches. We also propose a breeding-to-genetics approach, which starts with identification of extreme phenotypes from segregating populations generated from multiple parental lines and is followed by rapid discovery of individual genes and combinations of gene effects together with simultaneous manipulation in breeding programs.     

Mapping quantitative trait loci in noninbred mosquito crosses

The identification of genes that affect quantitative traits has been of great interest to geneticists for many decades, and many statistical methods have been developed to map quantitative trait loci (QTL). Most QTL mapping studies in experimental organisms use purely inbred lines, where the two homologous chromosomes in each individual are identical. As a result, many existing QTL mapping methods developed for experimental organisms are applicable only to genetic crosses between inbred lines. However, it may be difficult to obtain inbred lines for certain organisms, e.g., mosquitoes. Although statistical methods for QTL mapping in outbred populations, e.g., humans, can be applied for such crosses, these methods may not fully take advantage of the uniqueness of these crosses. For example, we can generally assume that the two grandparental lines are homozygous at the QTL of interest, but such information is not be utilized through methods developed for outbred populations. In addition, mating types and phases can be relatively easy to establish through the analysis of adjacent markers due to the large number of offspring that can be collected, substantially simplifying the computational need. In this article, motivated by a mosquito intercross experiment involving two selected lines that are not genetically homozygous across the genome, we develop statistical methods for QTL mapping for genetic crosses involving noninbred lines. In our procedure, we first infer parental mating types and use likelihood-based methods to infer phases in each parent on the basis of genotypes of offspring and one parent. A hidden Markov model is then employed to estimate the number of high-risk alleles at marker positions and putative QTL positions between markers in each offspring, and QTL mapping is finally conducted through the inferred QTL configuration across all offspring in all crosses. The performance of the proposed methods is assessed through simulation studies, and the usefulness of this method is demonstrated through its application to a mosquito data set.     

不同作图群体对显隐性分子标记位点的作图效率

根据位点组合和位点的有效性,发展了一种对使用３种不同的作用图群体作图显隐性分子标记的作图效率评价方法,应用该方法所评价的结果是,双单倍体（ＤＨ）群体的作图效率最高,自交群体（Ｆ２群体）与回交群体的作图效率相同,因此使用双单倍体群体作图不仅所用费用低,而且作图速度快,但只有在极少数植物中能获得双单倍体群体,对于那些不能获得双单倍体的动植物物种而言,可使用自交群体或回交群体作图。如果作高密度的分子标记     

QTL detection power of multi-parental RIL populations in Arabidopsis thaliana

A major goal of today's biology is to understand the genetic basis of quantitative traits. This can be achieved by statistical methods that evaluate the association between molecular marker variation and phenotypic variation in different types of mapping populations. The objective of this work was to evaluate the statistical power of quantitative trait loci (QTL) detection of various multi-parental mating designs, as well as to assess the reasons for the observed differences. Our study was based on an empirical data of 20 Arabidopsis thaliana accessions, which have been selected to capture the maximum genetic diversity. The examined mating designs differed strongly with respect to the statistical power to detect QTL. We observed the highest power to detect QTL for the diallel cross with random mating design. The results of our study suggested that performing sibling mating within subpopulations of joint-linkage mapping populations has the potential to considerably increase the power for QTL detection. Our results, however, revealed that using designs in which more than two parental alleles segregate in each subpopulation increases the power even more.     

Quantitative trait loci mapping in F(2) crosses between outbred lines

We develop a mixed-model approach for QTL analysis in crosses between outbred lines that allows for QTL segregation within lines as well as for differences in mean QTL effects between lines. We also propose a method called "segment mapping" that is based in partitioning the genome in a series of segments. The expected change in mean according to percentage of breed origin, together with the genetic variance associated with each segment, is estimated using maximum likelihood. The method also allows the estimation of differences in additive variances between the parental lines. Completely fixed random and mixed models together with segment mapping are compared via simulation. The segment mapping and mixed-model behaviors are similar to those of classical methods, either the fixed or random models, under simple genetic models (a single QTL with alternative alleles fixed in each line), whereas they provide less biased estimates and have higher power than fixed or random models in more complex situations, i.e., when the QTL are segregating within the parental lines. The segment mapping approach is particularly useful to determining which chromosome regions are likely to contain QTL when these are linked.     

Mapping quantitative trait loci with dominant markers in four-way crosses

 A common problem in mapping quantitative trait loci (QTLs) is that marker data are often incomplete. This includes missing data, dominant markers, and partially informative markers, arising in outbred populations. Here we briefly present an iteratively re-weighted least square method (IRWLS) to incorporate dominant and missing markers for mapping QTLs in four-way crosses under a heterogeneous variance model. The algorithm uses information from all markers in a linkage group to infer the QTL genotype. Monte Carlo simulations indicate that with half dominant markers, QTL detection is almost as efficient as with all co-dominant markers. However, the precision of the estimated QTL parameters generally decreases as more markers become missing or dominant. Notable differences are observed on the standard deviation of the estimated QTL position for varying levels of marker information content. The method is relatively simple so that more complex models including multiple QTLs or fixed effects can be fitted. Finally, the method can be readily extended to QTL mapping in full-sib families. Received: 16 June 1998 / Accepted: 29 September 1998     

Mapping quantitative trait loci in complex pedigrees: a two-step variance component approach

There is a growing need for the development of statistical techniques capable of mapping quantitative trait loci (QTL) in general outbred animal populations. Presently used variance component methods, which correctly account for the complex relationships that may exist between individuals, are challenged by the difficulties incurred through unknown marker genotypes, inbred individuals, partially or unknown marker phases, and multigenerational data. In this article, a two-step variance component approach that enables practitioners to routinely map QTL in populations with the aforementioned difficulties is explored. The performance of the QTL mapping methodology is assessed via its application to simulated data. The capacity of the technique to accurately estimate parameters is examined for a range of scenarios.     

Mapping quantitative trait loci by genotyping haploid tissues.

Mapping strategies based on a half- or full-sib family design have been developed to map quantitative trait loci (QTL) for outcrossing species. However, these strategies are dependent on controlled crosses where marker-allelic frequency and linkage disequilibrium between the marker and QTL may limit their application. In this article, a maximum-likelihood method is developed to map QTL segregating in an open-pollinated progeny population using dominant markers derived from haploid tissues from single meiotic events. Results from the haploid-based mapping strategy are not influenced by the allelic frequencies of markers and their linkage disequilibria with QTL, because the probabilities of QTL genotypes conditional on marker genotypes of haploid tissues are independent of these population parameters. Parameter estimation and hypothesis testing are implemented via expectation/conditional maximization algorithm. Parameters estimated include the additive effect, the dominant effect, the population mean, the chromosomal location of the QTL in the interval, and the residual variance within the QTL genotypes, plus two population parameters, outcrossing rate and QTL-allelic frequency. Simulation experiments show that the accuracy and power of parameter estimates are affected by the magnitude of QTL effects, heritability levels of a trait, and sample sizes used. The application and limitation of the method are discussed.     

A semiparametric approach for composite functional mapping of dynamic quantitative traits

Functional mapping has emerged as a powerful tool for mapping quantitative trait loci (QTL) that control developmental patterns of complex dynamic traits. Original functional mapping has been constructed within the context of simple interval mapping, without consideration of separate multiple linked QTL for a dynamic trait. In this article, we present a statistical framework for mapping QTL that affect dynamic traits by capitalizing on the strengths of functional mapping and composite interval mapping. Within this so-called composite functional-mapping framework, functional mapping models the time-dependent genetic effects of a QTL tested within a marker interval using a biologically meaningful parametric function, whereas composite interval mapping models the time-dependent genetic effects of the markers outside the test interval to control the genome background using a flexible nonparametric approach based on Legendre polynomials. Such a semiparametric framework was formulated by a maximum-likelihood model and implemented with the EM algorithm, allowing for the estimation and the test of the mathematical parameters that define the QTL effects and the regression coefficients of the Legendre polynomials that describe the marker effects. Simulation studies were performed to investigate the statistical behavior of composite functional mapping and compare its advantage in separating multiple linked QTL as compared to functional mapping. We used the new mapping approach to analyze a genetic mapping example in rice, leading to the identification of multiple QTL, some of which are linked on the same chromosome, that control the developmental trajectory of leaf age.     

A comparison of regression interval mapping and multiple interval mapping for linked QTL

Regression interval mapping and multiple interval mapping are compared with regard to mapping linked quantitative trait loci (QTL) in inbred-line cross experiments. For that purpose, a simulation study was performed using genetic models with two linked QTL. Data were simulated for F(2) populations of different sizes and with all QTL and marker alleles fixed for alternative alleles in the parental lines. The criteria for comparison are power of QTL identification and the accuracy of the QTL position and effect estimates. Further, the estimates of the relative QTL variance are assessed. There are distinct differences in the QTL position estimates between the two methods. Multiple interval mapping tends to be more powerful as compared to regression interval mapping. Multiple interval mapping further leads to more accurate QTL position and QTL effect estimates. The superiority increased with wider marker intervals and larger population sizes. If QTL are in repulsion, the differences between the two methods are very pronounced. For both methods, the reduction of the marker interval size from 10 to 5 cM increases power and greatly improves QTL parameter estimates. This contrasts with findings in the literature for single QTL scenarios, where a marker density of 10 cM is generally considered as sufficient. The use of standard (asymptotic) statistical theory for the computation of the standard errors of the QTL position and effect estimates proves to give much too optimistic standard errors for regression interval mapping as well as for multiple interval mapping.     

Consequences of recombination rate variation on quantitative trait locus mapping studies. Simulations based on the Drosophila melanogaster genome

We examine the effect of variation in gene density per centimorgan on quantitative trait locus (QTL) mapping studies using data from the Drosophila melanogaster genome project and documented regional rates of recombination. There is tremendous variation in gene density per centimorgan across this genome, and we observe that this variation can cause systematic biases in QTL mapping studies. Specifically, in our simulated mapping experiments of 50 equal-effect QTL distributed randomly across the physical genome, very strong QTL are consistently detected near the centromeres of the two major autosomes, and few or no QTL are often detected on the X chromosome. This pattern persisted with varying heritability, marker density, QTL effect sizes, and transgressive segregation. Our results are consistent with empirical data collected from QTL mapping studies of this species and its close relatives, and they explain the "small X-effect" that has been documented in genetic studies of sexual isolation in the D. melanogaster group. Because of the biases resulting from recombination rate variation, results of QTL mapping studies should be taken as hypotheses to be tested by additional genetic methods, particularly in species for which detailed genetic and physical genome maps are not available.     

Fine mapping of quantitative trait loci using linkage disequilibria with closely linked marker loci

A multimarker linkage disequilibrium mapping method was developed for the fine mapping of quantitative trait loci (QTL) using a dense marker map. The method compares the expected covariances between haplotype effects given a postulated QTL position to the covariances that are found in the data. The expected covariances between the haplotype effects are proportional to the probability that the QTL position is identical by descent (IBD) given the marker haplotype information, which is calculated using the genedropping method. Simulation results showed that a QTL was correctly positioned within a region of 3, 1.5, or 0.75 cM in 70, 62, and 68%, respectively, of the replicates using markers spaced at intervals of 1, 0.5, and 0.25 cM, respectively. These results were rather insensitive to the number of generations since the QTL occurred and to the effective population size, except that 10 generations yielded rather poor estimates of the QTL position. The position estimates of this multimarker disequilibrium mapping method were more accurate than those from a single marker transmission disequilibrium test. A general approach for identifying QTL is suggested, where several stages of disequilibrium mapping are used with increasingly dense marker spacing.     

Combined linkage and linkage disequilibrium QTL mapping in multiple families of maize (Zea mays L.) line crosses highlights complementarities between models based on parental haplotype and single locus polymorphism

Advancements in genotyping are rapidly decreasing marker costs and increasing marker density. This opens new possibilities for mapping quantitative trait loci (QTL), in particular by combining linkage disequilibrium information and linkage analysis (LDLA). In this study, we compared different approaches to detect QTL for four traits of agronomical importance in two large multi-parental datasets of maize (Zea mays L.) of 895 and 928 testcross progenies composed of 7 and 21 biparental families, respectively, and genotyped with 491 markers. We compared to traditional linkage-based methods two LDLA models relying on the dense genotyping of parental lines with 17,728 SNP: one based on a clustering approach of parental line segments into ancestral alleles and one based on single marker information. The two LDLA models generally identified more QTL (60 and 52 QTL in total) than classical linkage models (49 and 44 QTL in total). However, they performed inconsistently over datasets and traits suggesting that a compromise must be found between the reduction of allele number for increasing statistical power and the adequacy of the model to potentially complex allelic variation. For some QTL, the model exclusively based on linkage analysis, which assumed that each parental line carried a different QTL allele, was able to capture remaining variation not explained by LDLA models. These complementarities between models clearly suggest that the different QTL mapping approaches must be considered to capture the different levels of allelic variation at QTL involved in complex traits.