A Multiple-SNP Approach for Genome-Wide Association Study of Milk Production Traits in Chinese Holstein Cattle

The multiple-SNP analysis has been studied by many researchers, in which the effects of multiple SNPs are simultaneously estimated and tested in a multiple linear regression. The multiple-SNP association analysis usually has higher power and lower false-positive rate for detecting causative SNP(s) than single marker analysis (SMA). Several methods have been proposed to simultaneously estimate and test multiple SNP effects. In this research, a fast method called MEML (Mixed model based Expectation-Maximization Lasso algorithm) was developed for simultaneously estimate of multiple SNP effects. An improved Lasso prior was assigned to SNP effects which were estimated by searching the maximum joint posterior mode. The residual polygenic effect was included in the model to absorb many tiny SNP effects, which is treated as missing data in our EM algorithm. A series of simulation experiments were conducted to validate the proposed method, and the results showed that compared with SMMA, the new method can dramatically decrease the false-positive rate. The new method was also applied to the 50k SNP-panel dataset for genome-wide association study of milk production traits in Chinese Holstein cattle. Totally, 39 significant SNPs and their nearby 25 genes were found. The number of significant SNPs is remarkably fewer than that by SMMA which found 105 significant SNPs. Among 39 significant SNPs, 8 were also found by SMMA and several well-known QTLs or genes were confirmed again; furthermore, we also got some positional candidate gene with potential function of effecting milk production traits. These novel findings in our research should be valuable for further investigation.     

Composite Interval Mapping Based on Lattice Design for Error Control May Increase Power of Quantitative Trait Locus Detection

Experimental error control is very important in quantitative trait locus (QTL) mapping. Although numerous statistical methods have been developed for QTL mapping, a QTL detection model based on an appropriate experimental design that emphasizes error control has not been developed. Lattice design is very suitable for experiments with large sample sizes, which is usually required for accurate mapping of quantitative traits. However, the lack of a QTL mapping method based on lattice design dictates that the arithmetic mean or adjusted mean of each line of observations in the lattice design had to be used as a response variable, resulting in low QTL detection power. As an improvement, we developed a QTL mapping method termed composite interval mapping based on lattice design (CIMLD). In the lattice design, experimental errors are decomposed into random errors and block-within-replication errors. Four levels of block-within-replication errors were simulated to show the power of QTL detection under different error controls. The simulation results showed that the arithmetic mean method, which is equivalent to a method under random complete block design (RCBD), was very sensitive to the size of the block variance and with the increase of block variance, the power of QTL detection decreased from 51.3% to 9.4%. In contrast to the RCBD method, the power of CIMLD and the adjusted mean method did not change for different block variances. The CIMLD method showed 1.2- to 7.6-fold higher power of QTL detection than the arithmetic or adjusted mean methods. Our proposed method was applied to real soybean (Glycine max) data as an example and 10 QTLs for biomass were identified that explained 65.87% of the phenotypic variation, while only three and two QTLs were identified by arithmetic and adjusted mean methods, respectively.     

Generalized Linear Model for Mapping Discrete Trait Loci Implemented with LASSO Algorithm

Generalized estimating equation (GEE) algorithm under a heterogeneous residual variance model is an extension of the iteratively reweighted least squares (IRLS) method for continuous traits to discrete traits. In contrast to mixture model-based expectation–maximization (EM) algorithm, the GEE algorithm can well detect quantitative trait locus (QTL), especially large effect QTLs located in large marker intervals in the manner of high computing speed. Based on a single QTL model, however, the GEE algorithm has very limited statistical power to detect multiple QTLs because of ignoring other linked QTLs. In this study, the fast least absolute shrinkage and selection operator (LASSO) is derived for generalized linear model (GLM) with all possible link functions. Under a heterogeneous residual variance model, the LASSO for GLM is used to iteratively estimate the non-zero genetic effects of those loci over entire genome. The iteratively reweighted LASSO is therefore extended to mapping QTL for discrete traits, such as ordinal, binary, and Poisson traits. The simulated and real data analyses are conducted to demonstrate the efficiency of the proposed method to simultaneously identify multiple QTLs for binary and Poisson traits as examples.     

Comparison of the power between microsatellite and single-nucleotide polymorphism markers for linkage and linkage disequilibrium mapping of an electrophysiological phenotype

We performed linkage and linkage disequilibrium (LD) mapping analyses to compare the power between microsatellite and single nucleotide polymorphism (SNP) markers. Chromosome-wide analyses were performed for a quantitative electrophysiological phenotype, ttth1, on chromosome 7. Multipoint analysis of microsatellite markers using the variance component (VC) method showed the highest LOD score of 4.20 at 162 cM, near D7S509 (163.7 cM). Two-point analysis of SNPs using the VC method yielded the highest LOD score of 3.98 in the Illumina SNP data and 3.45 in the Affymetrix SNP data around 152-153 cM. In family-based single SNP and SNP haplotype LD analysis, we identified seven SNPs associated with ttth1. We searched for any potential candidate genes in the location of the seven SNPs. The SNPs rs1476640 and rs768055 are located in the FLJ40852 gene (a hypothetical protein), and SNP rs1859646 is located in the TAS2R5 gene (a taste receptor). The other four SNPs are not located in any known or annotated genes. We found the high density SNP scan to be superior to microsatellites because it is effective in downstream fine mapping due to a better defined linkage region. Our study proves the utility of high density SNP in genome-wide mapping studies.     

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

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

Correcting the Bias in Estimation of Genetic Variances Contributed by Individual QTL

In addition to locating chromosomal positions of quantitative trait loci (QTL), estimating the sizes of identified QTL is also an important component in QTL mapping. The size of a QTL is usually measured by the proportion of the phenotypic variance contributed by the QTL. However, the genetic variance may be overestimated in a small line crossing experiment. In this study, we investigate this bias and develop a simple method to correct the bias. The bias correction, however, requires the error of the estimated genetic effect, which is not trivial if the genetic effect is estimated using the Expectation and Maximization (EM) algorithm. Therefore, we also develop a simple method to estimate the standard error of the estimated genetic effect, which is subsequently used to correct the bias in the variance estimate.     

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

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

QTL fine mapping by measuring and testing for Hardy-Weinberg and linkage disequilibrium at a series of linked marker loci in extreme samples of populations

It has recently been demonstrated that fine-scale mapping of a susceptibility locus for a complex disease can be accomplished on the basis of deviations from Hardy-Weinberg (HW) equilibrium at closely linked marker loci among affected individuals. We extend this theory to fine-scale localization of a quantitative-trait locus (QTL) from extreme individuals in populations, by means of HW and linkage-disequilibrium (LD) analyses. QTL mapping and/or linkage analyses can establish a large genomic region ( approximately 30 cM) that contains a QTL. The QTL can be fine mapped by examination of the degree of deviation from HW and LD at a series of closely linked marker loci. The tests can be performed for samples of individuals belonging to either high or low percentiles of the phenotype distribution or for combined samples of these extreme individuals. The statistical properties (the power and the size) of the tests of this fine-mapping approach are investigated and are compared extensively, under various genetic models and parameters for the QTL and marker loci. On the basis of the results, a two-stage procedure that uses extreme samples and different tests (for HW and LD) is suggested for QTL fine mapping. This two-step procedure is economic and powerful and can accurately narrow a genomic region containing a QTL from approximately 30-1 cM, a range that renders physical mapping feasible for identification of the QTL. In addition, the relationship between parameterizations of complex diseases, by means of penetrance, and those of complex quantitative traits, by means of genotypic values, is outlined. This means that many statistical genetic methods developed for searching for susceptibility loci of complex diseases can be directly adopted and/or extended to QTL mapping for quantitative traits.     

The Power of QTL Mapping with RILs

QTL (quantitative trait loci) mapping is commonly used to identify genetic regions responsible to important phenotype variation. A common strategy of QTL mapping is to use recombinant inbred lines (RILs), which are usually established by several generations of inbreeding of an F1 population (usually up to F6 or F7 populations). As this inbreeding process involves a large amount of labor, we are particularly interested in the effect of the number of inbreeding generations on the power of QTL mapping; a part of the labor could be saved if a smaller number of inbreeding provides sufficient power. By using simulations, we investigated the performance of QTL mapping with recombinant inbred lines (RILs). As expected, we found that the power of F4 population could be almost comparable to that of F6 and F7 populations. A potential problem in using F4 population is that a large proportion of RILs are heterozygotes. We here introduced a new method to partly relax this problem. The performance of this method was verified by simulations with a wide range of parameters including the size of the segregation population, recombination rate, genome size and the density of markers. We found our method works better than the commonly used standard method especially when there are a number of heterozygous markers. Our results imply that in most cases, QTL mapping does not necessarily require RILs at F6 or F7 generations; rather, F4 (or even F3) populations would be almost as useful as F6 or F7 populations. Because the cost to establish a number of RILs for many generations is enormous, this finding will cause a reduction in the cost of QTL mapping, thereby accelerating gene mapping in many species.     

A Bayesian Nonparametric Approach for Mapping Dynamic Quantitative Traits

In biology, many quantitative traits are dynamic in nature. They can often be described by some smooth functions or curves. A joint analysis of all the repeated measurements of the dynamic traits by functional quantitative trait loci (QTL) mapping methods has the benefits to (1) understand the genetic control of the whole dynamic process of the quantitative traits and (2) improve the statistical power to detect QTL. One crucial issue in functional QTL mapping is how to correctly describe the smoothness of trajectories of functional valued traits. We develop an efficient Bayesian nonparametric multiple-loci procedure for mapping dynamic traits. The method uses the Bayesian P-splines with (nonparametric) B-spline bases to specify the functional form of a QTL trajectory and a random walk prior to automatically determine its degree of smoothness. An efficient deterministic variational Bayes algorithm is used to implement both (1) the search of an optimal subset of QTL among large marker panels and (2) estimation of the genetic effects of the selected QTL changing over time. Our method can be fast even on some large-scale data sets. The advantages of our method are illustrated on both simulated and real data sets.     

Linkage disequilibrium mapping via cladistic analysis of single-nucleotide polymorphism haplotypes

We present a novel approach to disease-gene mapping via cladistic analysis of single-nucleotide polymorphism (SNP) haplotypes obtained from large-scale, population-based association studies, applicable to whole-genome screens, candidate-gene studies, or fine-scale mapping. Clades of haplotypes are tested for association with disease, exploiting the expected similarity of chromosomes with recent shared ancestry in the region flanking the disease gene. The method is developed in a logistic-regression framework and can easily incorporate covariates such as environmental risk factors or additional unlinked loci to allow for population structure. To evaluate the power of this approach to detect disease-marker association, we have developed a simulation algorithm to generate high-density SNP data with short-range linkage disequilibrium based on empirical patterns of haplotype diversity. The results of the simulation study highlight substantial gains in power over single-locus tests for a wide range of disease models, despite overcorrection for multiple testing.     

Mapping quantitative trait loci in tetraploid populations

Knowledge of quantitative trait locus (QTL) mapping in polyploids is almost void, albeit many exquisite strategies of QTL mapping have been proposed and extensive investigations have been carried out in diploid animals and plants. In this paper we develop a simple algorithm which uses an iteratively reweighted least square method to map QTLs in tetraploid populations. The method uses information from all markers in a linkage group to infer the probability distribution of QTL genotype under the assumption of random chromosome segregation. Unlike QTL mapping in diploid species, here we estimate and test the compound 'gametic effect', which consists of the composite 'genic effect' of alleles and higher-order gene interactions. The validity and efficiency of the proposed method are investigated through simulation studies. Results show that the method can successfully locate QTLs and separates different sources (e.g. additive and dominance) of variance components contributed by the QTLs.     

Detection of closely linked multiple quantitative trait loci using a genetic algorithm

The existence of a quantitative trait locus (QTL) is usually tested using the likelihood of the quantitative trait on the basis of phenotypic character data plus the recombination fraction between QTL and flanking markers. When doing this, the likelihood is calculated for all possible locations on the linkage map. When multiple QTL are suspected close by, it is impractical to calculate the likelihood for all possible combinations of numbers and locations of QTL. Here, we propose a genetic algorithm (GA) for the heuristic solution of this problem. GA can globally search the optimum by improving the "genotype" with alterations called "recombination" and "mutation." The "genotype" of our GA is the number and location of QTL. The "fitness" is a function based on the likelihood plus Akaike's information criterion (AIC), which helps avoid false-positive QTL. A simulation study comparing the new method with existing QTL mapping packages shows the advantage of the new GA. The GA reliably distinguishes multiple QTL located in a single marker interval.     

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

Background

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

Principal Findings

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

Conclusions

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

A modified algorithm for the improvement of composite interval mapping

Composite interval mapping (CIM) is the most commonly used method for mapping quantitative trait loci (QTL) with populations derived from biparental crosses. However, the algorithm implemented in the popular QTL Cartographer software may not completely ensure all its advantageous properties. In addition, different background marker selection methods may give very different mapping results, and the nature of the preferred method is not clear. A modified algorithm called inclusive composite interval mapping (ICIM) is proposed in this article. In ICIM, marker selection is conducted only once through stepwise regression by considering all marker information simultaneously, and the phenotypic values are then adjusted by all markers retained in the regression equation except the two markers flanking the current mapping interval. The adjusted phenotypic values are finally used in interval mapping (IM). The modified algorithm has a simpler form than that used in CIM, but a faster convergence speed. ICIM retains all advantages of CIM over IM and avoids the possible increase of sampling variance and the complicated background marker selection process in CIM. Extensive simulations using two genomes and various genetic models indicated that ICIM has increased detection power, a reduced false detection rate, and less biased estimates of QTL effects.     

Fine mapping of quantitative trait loci affecting female fertility in dairy cattle on BTA03 using a dense single-nucleotide polymorphism map

Fertility quantitative trait loci (QTL) are of high interest in dairy cattle since insemination failure has dramatically increased in some breeds such as Holstein. High-throughput SNP analysis and SNP microarrays give the opportunity to genotype many animals for hundreds SNPs per chromosome. In this study, due to these techniques a dense SNP marker map was used to fine map a QTL underlying nonreturn rate measured 90 days after artificial insemination previously detected with a low-density microsatellite marker map. A granddaughter design with 17 Holstein half-sib families (926 offspring) was genotyped for a set of 437 SNPs mapping to BTA3. Linkage analysis was performed by both regression and variance components analysis. An additional analysis combining both linkage analysis and linkage-disequilibrium information was applied. This method first estimated identity-by-descent probabilities among base haplotypes. These probabilities were then used to group the base haplotypes in different clusters. A QTL explaining 14% of the genetic variance was found with high significance (P < 0.001) at position 19 cM with the linkage analysis and four sires were estimated to be heterozygous (P < 0.05). Addition of linkage-disequilibrium information refined the QTL position to a set of narrow peaks. The use of the haplotypes of heterozygous sires offered the possibility to give confidence in some peaks while others could be discarded. Two peaks with high likelihood-ratio test values in the region of which heterozygous sires shared a common haplotype appeared particularly interesting. Despite the fact that the analysis did not fine map the QTL in a unique narrow region, the method proved to be able to handle efficiently and automatically a large amount of information and to refine the QTL position to a small set of narrow intervals. In addition, the QTL identified was confirmed to have a large effect (explaining 13.8% of the genetic variance) on dairy cow fertility as estimated by nonreturn rate at 90 days.     

An efficient variance component approach implementing an average information REML suitable for combined LD and linkage mapping with a general complex pedigree

Variance component (VC) approaches based on restricted maximum likelihood (REML) have been used as an attractive method for positioning of quantitative trait loci (QTL). Linkage disequilibrium (LD) information can be easily implemented in the covariance structure among QTL effects (e.g. genotype relationship matrix) and mapping resolution appears to be high. Because of the use of LD information, the covariance structure becomes much richer and denser compared to the use of linkage information alone. This makes an average information (AI) REML algorithm based on mixed model equations and sparse matrix techniques less useful. In addition, (near-) singularity problems often occur with high marker densities, which is common in fine-mapping, causing numerical problems in AIREML based on mixed model equations. The present study investigates the direct use of the variance covariance matrix of all observations in AIREML for LD mapping with a general complex pedigree. The method presented is more efficient than the usual approach based on mixed model equations and robust to numerical problems caused by near-singularity due to closely linked markers. It is also feasible to fit multiple QTL simultaneously in the proposed method whereas this would drastically increase computing time when using mixed model equation-based methods.     

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

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

Fine mapping of a quantitative trait locus for twinning rate using combined linkage and linkage disequilibrium mapping

A novel and robust method for the fine-scale mapping of genes affecting complex traits, which combines linkage and linkage-disequilibrium information, is proposed. Linkage information refers to recombinations within the marker-genotyped generations and linkage disequilibrium to historical recombinations before genotyping started. The identity-by-descent (IBD) probabilities at the quantitative trait locus (QTL) between first generation haplotypes were obtained from the similarity of the marker alleles surrounding the QTL, whereas IBD probabilities at the QTL between later generation haplotypes were obtained by using the markers to trace the inheritance of the QTL. The variance explained by the QTL is estimated by residual maximum likelihood using the correlation structure defined by the IBD probabilities. Unlinked background genes were accounted for by fitting a polygenic variance component. The method was used to fine map a QTL for twinning rate in cattle, previously mapped on chromosome 5 by linkage analysis. The data consisted of large half-sib families, but the method could also handle more complex pedigrees. The likelihood of the putative QTL was very small along most of the chromosome, except for a sharp likelihood peak in the ninth marker bracket, which positioned the QTL within a region <1 cM in the middle part of bovine chromosome 5. The method was expected to be robust against multiple genes affecting the trait, multiple mutations at the QTL, and relatively low marker density.     

Sib mating designs for mapping quantitative trait loci

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