Combined-cross analysis of genome-wide linkage scans for experimental autoimmune encephalomyelitis in rat

Unbiased genetic analysis of experimental autoimmune encephalomyelitis (EAE) can provide insights into the pathogenesis of multiple sclerosis. To date five genome-wide scans using F2 crosses between different inbred rats have been performed with the aim of defining EAE-regulating quantitative trait loci (QTLs) as the starting point for identification of the underlying genes. We here report the first combined-cross analysis of three F2 crosses previously performed in our group. The majority of QTLs was shared between the different strain combinations and was therefore reproduced by the combined-cross analysis. Consequently, combined-cross analysis improved the power to detect QTLs with modest effects and narrowed QTL confidence intervals. The findings also demonstrate a lack of power in previous F2 crosses and encourage future use of larger populations. Moreover, the allelic states of shared QTLs could be established, thus providing critical information for narrowing QTLs and identifying the key polymorphism by subsequent haplotype analysis.     

Linkage analysis of quantitative trait loci in multiple line crosses

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

Mouse inbred strain sequence information and yin-yang crosses for quantitative trait locus fine mapping

The shared ancestry of mouse inbred strains, together with the availability of sequence and phenotype information, is a resource that can be used to map quantitative trait loci (QTL). The difficulty in using only sequence information lies in the fact that in most instances the allelic state of the QTL cannot be unambiguously determined in a given strain. To overcome this difficulty, the performance of multiple crosses between various inbred strains has been proposed. Here we suggest and evaluate a general approach, which consists of crossing the two strains used initially to map the QTL and any new strain. We have termed these crosses "yin-yang," because they are complementary in nature as shown by the fact that the QTL will necessarily segregate in only one of the crosses. We used the publicly available SNP database of chromosome 16 to evaluate the mapping resolution achievable through this approach. Although on average the improvement of mapping resolution using only four inbred strains was relatively small (i.e., reduction of the QTL-containing interval by half at most), we found a great degree of variability among different regions of chromosome 16 with regard to mapping resolution. This suggests that with a large number of strains in hand, selecting a small number of strains may provide a significant contribution to the fine mapping of QTL.     

A general mixture model approach for mapping quantitative trait loci from diverse cross designs involving multiple inbred lines

Most current statistical methods developed for mapping quantitative trait loci (QTL) based on inbred line designs apply to crosses from two inbred lines. Analysis of QTL in these crosses is restricted by the parental genetic differences between lines. Crosses from multiple inbred lines or multiple families are common in plant and animal breeding programmes, and can be used to increase the efficiency of a QTL mapping study. A general statistical method using mixture model procedures and the EM algorithm is developed for mapping QTL from various cross designs of multiple inbred lines. The general procedure features three cross design matrices, W, that define the contribution of parental lines to a particular cross and a genetic design matrix, D, that specifies the genetic model used in multiple line crosses. By appropriately specifying W matrices, the statistical method can be applied to various cross designs, such as diallel, factorial, cyclic, parallel or arbitrary-pattern cross designs with two or multiple parental lines. Also, with appropriate specification for the D matrix, the method can be used to analyse different kinds of cross populations, such as F2 backcross, four-way cross and mixed crosses (e.g. combining backcross and F2). Simulation studies were conducted to explore the properties of the method, and confirmed its applicability to diverse experimental designs.     

A statistical framework for quantitative trait mapping

We describe a general statistical framework for the genetic analysis of quantitative trait data in inbred line crosses. Our main result is based on the observation that, by conditioning on the unobserved QTL genotypes, the problem can be split into two statistically independent and manageable parts. The first part involves only the relationship between the QTL and the phenotype. The second part involves only the location of the QTL in the genome. We developed a simple Monte Carlo algorithm to implement Bayesian QTL analysis. This algorithm simulates multiple versions of complete genotype information on a genomewide grid of locations using information in the marker genotype data. Weights are assigned to the simulated genotypes to capture information in the phenotype data. The weighted complete genotypes are used to approximate quantities needed for statistical inference of QTL locations and effect sizes. One advantage of this approach is that only the weights are recomputed as the analyst considers different candidate models. This device allows the analyst to focus on modeling and model comparisons. The proposed framework can accommodate multiple interacting QTL, nonnormal and multivariate phenotypes, covariates, missing genotype data, and genotyping errors in any type of inbred line cross. A software tool implementing this procedure is available. We demonstrate our approach to QTL analysis using data from a mouse backcross population that is segregating multiple interacting QTL associated with salt-induced hypertension.     

A simple regression method for mapping quantitative trait loci in line crosses using flanking markers

The use of flanking marker methods has proved to be a powerful tool for the mapping of quantitative trait loci (QTL) in the segregating generations derived from crosses between inbred lines. Methods to analyse these data, based on maximum-likelihood, have been developed and provide good estimates of QTL effects in some situations. Maximum-likelihood methods are, however, relatively complex and can be computationally slow. In this paper we develop methods for mapping QTL based on multiple regression which can be applied using any general statistical package. We use the example of mapping in an F(2) population and show that these regression methods produce very similar results to those obtained using maximum likelihood. The relative simplicity of the regression methods means that models with more than a single QTL can be explored and we give examples of two lined loci and of two interacting loci. Other models, for example with more than two QTL, with environmental fixed effects, with between family variance or for threshold traits, could be fitted in a similar way. The ease, speed of application and generality of regression methods for flanking marker analysis, and the good estimates they obtain, suggest that they should provide the method of choice for the analysis of QTL mapping data from inbred line crosses.     

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

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

Quantitative trait locus for starvation resistance in an intercontinental set of mapping populations of Drosophila melanogaster

Starvation resistance (SR) is an important trait for survival of insects in the wild. We used recombinant inbred lines (RIL) to search for quantitative trait loci (QTL) in crosses between intercontinental inbred lines that were originally selected for heat-knockdown resistance. SR was measured as the time of survival under repeated events of starvation. SR was consistently higher in females than in males. Composite interval mapping identified one QTL region (cytological range 64D - 66E2) on the left arm of chromosome 3 in males, and no QTL was found in females. Many candidate genes that were identified in previous studies of QTL for stress resistance are included within this QTL region. The QTL-allele that decreased SR was found in the line originating from the colder population (Denmark). We discuss our results with regard to multiple candidate genes, non-colocalization with thermotolerance QTL, and possible geographical variation.     

Mapping Quantitative Trait Loci onto a Phylogenetic Tree

Despite advances in genetic mapping of quantitative traits and in phylogenetic comparative approaches, these two perspectives are rarely combined. The joint consideration of multiple crosses among related taxa (whether species or strains) not only allows more precise mapping of the genetic loci (called quantitative trait loci, QTL) that contribute to important quantitative traits, but also offers the opportunity to identify the origin of a QTL allele on the phylogenetic tree that relates the taxa. We describe a formal method for combining multiple crosses to infer the location of a QTL on a tree. We further discuss experimental design issues for such endeavors, such as how many crosses are required and which sets of crosses are best. Finally, we explore the method's performance in computer simulations, and we illustrate its use through application to a set of four mouse intercrosses among five inbred strains, with data on HDL cholesterol.     

Mapping Quantitative Trait Loci in Crosses between Outbred Lines Using Least Squares

The use of genetic maps based upon molecular markers has allowed the dissection of some of the factors underlying quantitative variation in crosses between inbred lines. For many species crossing inbred lines is not a practical proposition, although crosses between genetically very different outbred lines are possible. Here we develop a least squares method for the analysis of crosses between outbred lines which simultaneously uses information from multiple linked markers. The method is suitable for crosses where the lines may be segregating at marker loci but can be assumed to be fixed for alternative alleles at the major quantitative trait loci (QTLs) affecting the traits under analysis (e.g., crosses between divergent selection lines or breeds with different selection histories). The simultaneous use of multiple markers from a linkage group increases the sensitivity of the test statistic, and thus the power for the detection of QTLs, compared to the use of single markers or markers flanking an interval. The gain is greater for more closely spaced markers and for markers of lower information content. Use of multiple markers can also remove the bias in the estimated position and effect of a QTL which may result when different markers in a linkage group vary in their heterozygosity in the F(1) (and thus in their information content) and are considered only singly or a pair at a time. The method is relatively simple to apply so that more complex models can be fitted than is currently possible by maximum likelihood. Thus fixed effects and effects of background genotype can be fitted simultaneously with the exploration of a single linkage group which will increase the power to detect QTLs by reducing the residual variance. More complex models with several QTLs in the same linkage group and two-locus interactions between QTLs can similarly be examined. Thus least squares provides a powerful tool to extend the range of crosses from which QTLs can be dissected whilst at the same time allowing flexible and realistic models to be explored.     

Strategies for mapping and cloning quantitative trait genes in rodents

Over the past 15 years, more than 2,000 quantitative trait loci (QTLs) have been identified in crosses between inbred strains of mice and rats, but less than 1% have been characterized at a molecular level. However, new resources, such as chromosome substitution strains and the proposed Collaborative Cross, together with new analytical tools, including probabilistic ancestral haplotype reconstruction in outbred mice, Yin-Yang crosses and in silico analysis of sequence variants in many inbred strains, could make QTL cloning tractable. We review the potential of these strategies to identify genes that underlie QTLs in rodents.     

Quantitative trait loci affecting life span in replicated populations of Drosophila melanogaster. I. Composite interval mapping

Composite interval mapping was used to identify life-span QTL in F2 progeny of three crosses between different pairs of inbred lines. Each inbred line was derived from a different outbred population that had undergone long-term selection for either long or short life span. Microsatellite loci were used as genetic markers, and confidence intervals for QTL location were estimated by bootstrapping. A minimum of 10 QTL were detected, nine of which were located on the two major autosomes. Five QTL were present in at least two crosses and five were present in both sexes. Observation of the same QTL in more than one cross was consistent with the hypothesis that genetic variation for life span is maintained by balancing selection. For all QTL except one, allelic effects were in the direction predicted on the basis of outbred source population. Alleles that conferred longer life were always at least partially dominant.     

Mapping quantitative trait loci using naturally occurring genetic variance among commercial inbred lines of maize (Zea mays L.)

Many commercial inbred lines are available in crops. A large amount of genetic variation is preserved among these lines. The genealogical history of the inbred lines is usually well documented. However, quantitative trait loci (QTL) responsible for the genetic variances among the lines are largely unexplored due to lack of statistical methods. In this study, we show that the pedigree information of the lines along with the trait values and marker information can be used to map QTL without the need of further crossing experiments. We develop a Monte Carlo method to estimate locus-specific identity-by-descent (IBD) matrices. These IBD matrices are further incorporated into a mixed-model equation for variance component analysis. QTL variance is estimated and tested at every putative position of the genome. The actual QTL are detected by scanning the entire genome. Applying this new method to a well-documented pedigree of maize (Zea mays L.) that consists of 404 inbred lines, we mapped eight QTL for the maize male flowering trait, growing degree day heat units to pollen shedding (GDUSHD). These detected QTL contributed >80% of the variance observed among the inbred lines. The QTL were then used to evaluate all the inbred lines using the best linear unbiased prediction (BLUP) technique. Superior lines were selected according to the estimated QTL allelic values, a technique called marker-assisted selection (MAS). The MAS procedure implemented via BLUP may be routinely used by breeders to select superior lines and line combinations for development of new cultivars.     

A General Modeling Framework for Genome Ancestral Origins in Multiparental Populations

The next generation of QTL (quantitative trait loci) mapping populations have been designed with multiple founders, where one to a number of generations of intercrossing are introduced prior to the inbreeding phase to increase accumulated recombinations and thus mapping resolution. Examples of such populations are Collaborative Cross (CC) in mice and Multiparent Advanced Generation Inter-Cross (MAGIC) lines in Arabidopsis. The genomes of the produced inbred lines are fine-grained random mosaics of the founder genomes. In this article, we present a novel framework for modeling ancestral origin processes along two homologous autosomal chromosomes from mapping populations, which is a major component in the reconstruction of the ancestral origins of each line for QTL mapping. We construct a general continuous time Markov model for ancestral origin processes, where the rate matrix is deduced from the expected densities of various types of junctions (recombination breakpoints). The model can be applied to monoecious populations with or without self-fertilizations and to dioecious populations with two separate sexes. The analytic expressions for map expansions and expected junction densities are obtained for mapping populations that have stage-wise constant mating schemes, such as CC and MAGIC. Our studies on the breeding design of MAGIC populations show that the intercross mating schemes do not matter much for large population size and that the overall expected junction density, and thus map resolution, are approximately proportional to the inverse of the number of founders.     

Further studies on using multiple-cross mapping (MCM) to map quantitative trait loci

We have completed whole-genome scans for quantitative trait loci (QTLs) associated with acute ethanol-induced activation in the six F₂ intercrosses that can be formed from the C57BL/6J (B6), DBA/2J (D2) , BALB/cJ (C), and LP/J (LP) inbred strains. The goal was to test the hypothesis that given the relatively simple structure of the laboratory mouse genome, the same QTLs will be detected in multiple crosses which in turn will provide support for the strategy of multiple-cross mapping (MCM). QTLs with LOD scores greater than 4 were detected on Chrs 1, 2, 3, 8, 9, 13, 14, and 16. Only for the QTL on distal Chr 1 was there convincing evidence that the same or at least a very similar QTL was detected in multiple crosses. We also mapped the Chr 2 QTL directly in heterogeneous stock (HS) animals derived from the four inbred strains. At G₁₉ the QTL was mapped to an approximately 3-Mbp interval and this interval was associated with a haplotype block with a largely biallelic structure: B6-L:C-D2. We conclude that mapping in HS animals not only provides significantly greater QTL resolution, at least in some cases it provides significantly more information about the QTL haplotype structure.     

Mapping epistatic quantitative trait loci with one-dimensional genome searches

The discovery of epistatically interacting QTL is hampered by the intractability and low power to detect QTL in multidimensional genome searches. We describe a new method that maps epistatic QTL by identifying loci of high QTL by genetic background interaction. This approach allows detection of QTL involved not only in pairwise but also higher-order interaction, and does so with one-dimensional genome searches. The approach requires large populations derived from multiple related inbred-line crosses as is more typically available for plants. Using maximum likelihood, the method contrasts models in which QTL allelic values are either nested within, or fixed over, populations. We apply the method to simulated doubled-haploid populations derived from a diallel among three inbred parents and illustrate the power of the method to detect QTL of different effect size and different levels of QTL by genetic background interaction. Further, we show how the method can be used in conjunction with standard two-locus QTL detection models that use two-dimensional genome searches and find that the method may double the power to detect first-order epistasis.     

High-Resolution Genetic Mapping of Complex Traits from a Combined Analysis of F2 and Advanced Intercross Mice

Genetic influences on anxiety disorders are well documented; however, the specific genes underlying these disorders remain largely unknown. To identify quantitative trait loci (QTL) for conditioned fear and open field behavior, we used an F₂ intercross (n = 490) and a 34th-generation advanced intercross line (AIL) (n = 687) from the LG/J and SM/J inbred mouse strains. The F₂ provided strong support for several QTL, but within wide chromosomal regions. The AIL yielded much narrower QTL, but the results were less statistically significant, despite the larger number of mice. Simultaneous analysis of the F₂ and AIL provided strong support for QTL and within much narrower regions. We used a linear mixed-model approach, implemented in the program QTLRel, to correct for possible confounding due to familial relatedness. Because we recorded the full pedigree, we were able to empirically compare two ways of accounting for relatedness: using the pedigree to estimate kinship coefficients and using genetic marker estimates of “realized relatedness.” QTL mapping using the marker-based estimates yielded more support for QTL, but only when we excluded the chromosome being scanned from the marker-based relatedness estimates. We used a forward model selection procedure to assess evidence for multiple QTL on the same chromosome. Overall, we identified 12 significant loci for behaviors in the open field and 12 significant loci for conditioned fear behaviors. Our approach implements multiple advances to integrated analysis of F₂ and AILs that provide both power and precision, while maintaining the advantages of using only two inbred strains to map QTL.     

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.     

Interval Mapping of Multiple Quantitative Trait Loci

The interval mapping method is widely used for the mapping of quantitative trait loci (QTLs) in segregating generations derived from crosses between inbred lines. The efficiency of detecting and the accuracy of mapping multiple QTLs by using genetic markers are much increased by employing multiple QTL models instead of the single QTL models (and no QTL models) used in interval mapping. However, the computational work involved with multiple QTL models is considerable when the number of QTLs is large. In this paper it is proposed to combine multiple linear regression methods with conventional interval mapping. This is achieved by fitting one QTL at a time in a given interval and simultaneously using (part of) the markers as cofactors to eliminate the effects of additional QTLs. It is shown that the proposed method combines the easy computation of the single QTL interval mapping method with much of the efficiency and accuracy of multiple QTL models.