Multiple-trait mapping of quantitative trait loci after selective genotyping using logistic regression

Robust regression based genome-wide multi-trait QTL analysis

In genome-wide quantitative trait locus (QTL) mapping studies, multiple quantitative traits are often measured along with the marker genotypes. Multi-trait QTL (MtQTL) analysis, which includes multiple quantitative traits together in a single model, is an efficient technique to increase the power of QTL identification. The two most widely used classical approaches for MtQTL mapping are Gaussian Mixture Model-based MtQTL (GMM-MtQTL) and Linear Regression Model-based MtQTL (LRM-MtQTL) analyses. There are two types of LRM-MtQTL approach known as least squares-based LRM-MtQTL (LS-LRM-MtQTL) and maximum likelihood-based LRM-MtQTL (ML-LRM-MtQTL). These three classical approaches are equivalent alternatives for QTL detection, but ML-LRM-MtQTL is computationally faster than GMM-MtQTL and LS-LRM-MtQTL. However, one major limitation common to all the above classical approaches is that they are very sensitive to outliers, which leads to misleading results. Therefore, in this study, we developed an LRM-based robust MtQTL approach, called LRM-RobMtQTL, for the backcross population based on the robust estimation of regression parameters by maximizing the β-likelihood function induced from the β-divergence with multivariate normal distribution. When β = 0, the proposed LRM-RobMtQTL method reduces to the classical ML-LRM-MtQTL approach. Simulation studies showed that both ML-LRM-MtQTL and LRM-RobMtQTL methods identified the same QTL positions in the absence of outliers. However, in the presence of outliers, only the proposed method was able to identify all the true QTL positions. Real data analysis results revealed that in the presence of outliers only our LRM-RobMtQTL approach can identify all the QTL positions as those identified in the absence of outliers by both methods. We conclude that our proposed LRM-RobMtQTL analysis approach outperforms the classical MtQTL analysis methods.

Allele substitution and dominance effects of CD166/ALCAM gene polymorphisms for endoparasite resistance and test-day traits in a small cattle population using logistic regression analyses

The study investigated the effects of four single-nucleotide polymorphisms (SNPs) in the activated leukocyte cell adhesion molecule (ALCAM) gene on liver fluke (Fasciola hepatica) infections (FH-INF), gastrointestinal nematode infections (GIN-INF) and disease indicator traits [e.g. somatic cell score (SCS), fat-to-protein ratio (FPR)] in German dual-purpose cattle (DSN). A genome-wide association study inferred the chip SNP ALCAMc.73+32791A>G as a candidate for F. hepatica resistance in DSN. Because of the crucial function of ALCAM in immune responses, SNPs in the gene might influence further resistance and performance traits. Causal mutations were identified in exon 9 (ALCAMc.1017T>C) and intron 9 (ALCAMc.1104+10T>A, ALCAMc.1104+85T>C) in a selective subset of 94 DSN cows. We applied logistic regression analyses for the association between SNP genotypes with residuals for endoparasite traits (rINF-FH, rGIN-INF) and estimated breeding values (EBVs) for test-day traits. The probability of the heterozygous genotype was estimated in dependency of the target trait. Allele substitution effects for rFH-INF were significant for all four loci. The T allele of the SNPs ALCAMc.1017T>C and ALCAMc.1104+85T>C was the favourable allele when improving resistance against FH-INF. Significant allele substitution for rGIN-INF was only found for the chip SNP ALCAMc.73+32791A>G. We identified significant associations between the SNPs with EBVs for milk fat%, protein% and FPR. Dominance effects for the EBVs of test-day traits ranged from 0.00 to 0.47 SD and were in the direction of improved resistance for rFH-INF. We estimated favourable dominance effects from same genotypes for rFH-INF and FPR, but dominance effects were antagonistic between rFH-INF and SCS.

Effect of selection and selective genotyping for creation of reference on bias and accuracy of genomic prediction

Reference populations for genomic selection usually involve selected individuals, which may result in biased prediction of estimated genomic breeding values (GEBV). In a simulation study, bias and accuracy of GEBV were explored for various genetic models with individuals selectively genotyped in a typical nucleus breeding program. We compared the performance of three existing methods, that is, Best Linear Unbiased Prediction of breeding values using pedigree-based relationships (PBLUP), genomic relationships for genotyped animals only (GBLUP) and a Single-Step approach (SSGBLUP) using both. For a scenario with no-selection and random mating (RR), prediction was unbiased. However, lower accuracy and bias were observed for scenarios with selection and random mating (SR) or selection and positive assortative mating (SA). As expected, bias disappeared when all individuals were genotyped and used in GBLUP. SSGBLUP showed higher accuracy compared to GBLUP, and bias of prediction was negligible with SR. However, PBLUP and SSGBLUP still showed bias in SA due to high inbreeding. SSGBLUP and PBLUP were unbiased provided that inbreeding was accounted for in the relationship matrices. Selective genotyping based on extreme phenotypic contrasts increased the prediction accuracy, but prediction was biased when using GBLUP. SSGBLUP could correct the biasedness while gaining higher accuracy than GBLUP. In a typical animal breeding program, where it is too expensive to genotype all animals, it would be appropriate to genotype phenotypically contrasting selection candidates and use a Single-Step approach to obtain accurate and unbiased prediction of GEBV.

Dominance effects estimation of TLR4 and CACNA2D1 genes for health and production traits using logistic regression

Knowledge of nonadditive variance and genetic effects can be helpful in explaining the total genetic variation formost of the traits. The objective of this study was to estimate dominance effects of several single-nucleotide polymorphism (SNP) genotypes for the production traits and clinical mastitis residual (CMR), in Holstein dairy cattle in a case-control study. Records of 305 days lactation were obtained for production traits and CMR. Animals were selected based on extreme values for CMR from mixed model analyses. Samples were genotyped for four SNP-single genotypes and their associations with production traits (breeding values for protein and fat yield, and protein and fat percentage) were estimated by applying logistic regression analyses. Calculation of contrast between both homozygous and heterozygous genotypes permitted to estimate dominance effects, which ranged from -0.49 to 0.35 standard deviation units for the production traits and clinical mastitis (CM), respectively. Results showed that the dominance effects may be important in contribution of total genetic effects for production traits and CM. Therefore, evaluation of animals based on additive variance alone and disregarding nonadditive effects may lead to failure in selection programmes and exactly estimating the genetic variation. The method that we used would help breeders in accurately estimation of genotypic values in a new genomic selection scenario including dominance effects.

Novel Resampling Improves Statistical Power for Multiple-Trait QTL Mapping

Multiple-trait analysis typically employs models that associate a quantitative trait locus (QTL) with all of the traits. As a result, statistical power for QTL detection may not be optimal if the QTL contributes to the phenotypic variation in only a small proportion of the traits. Excluding QTL effects that contribute little to the test statistic can improve statistical power. In this article, we show that an optimal power can be achieved when the number of QTL effects is best estimated, and that a stringent criterion for QTL effect selection may improve power when the number of QTL effects is small but can reduce power otherwise. We investigate strategies for excluding trivial QTL effects, and propose a method that improves statistical power when the number of QTL effects is relatively small, and fairly maintains the power when the number of QTL effects is large. The proposed method first uses resampling techniques to determine the number of nontrivial QTL effects, and then selects QTL effects by the backward elimination procedure for significance test. We also propose a method for testing QTL-trait associations that are desired for biological interpretation in applications. We validate our methods using simulations and Arabidopsis thaliana transcript data.

From phenotyping towards breeding strategies: using in vivo indicator traits and genetic markers to improve meat quality in an endangered pig breed

In endangered and local pig breeds of small population sizes, production has to focus on alternative niche markets with an emphasis on specific product and meat quality traits to achieve economic competiveness. For designing breeding strategies on meat quality, an adequate performance testing scheme focussing on phenotyped selection candidates is required. For the endangered German pig breed 'Bunte Bentheimer' (BB), no breeding program has been designed until now, and no performance testing scheme has been implemented. For local breeds, mainly reared in small-scale production systems, a performance test based on in vivo indicator traits might be a promising alternative in order to increase genetic gain for meat quality traits. Hence, the main objective of this study was to design and evaluate breeding strategies for the improvement of meat quality within the BB breed using in vivo indicator traits and genetic markers. The in vivo indicator trait was backfat thickness measured by ultrasound (BFiv), and genetic markers were allele variants at the ryanodine receptor 1 (RYR1) locus. In total, 1116 records of production and meat quality traits were collected, including 613 in vivo ultrasound measurements and 713 carcass and meat quality records. Additionally, 700 pigs were genotyped at the RYR1 locus. Data were used (1) to estimate genetic (co)variance components for production and meat quality traits, (2) to estimate allele substitution effects at the RYR1 locus using a selective genotyping approach and (3) to evaluate breeding strategies on meat quality by combining results from quantitative-genetic and molecular-genetic approaches. Heritability for the production trait BFiv was 0.27, and 0.48 for backfat thickness measured on carcass. Estimated heritabilities for meat quality traits ranged from 0.14 for meat brightness to 0.78 for the intramuscular fat content (IMF). Genetic correlations between BFiv and IMF were higher than estimates based on carcass backfat measurements (0.39 v. 0.25). The presence of the unfavorable n allele was associated with increased electric conductivity, paler meat and higher drip loss. The allele substitution effect on IMF was unfavorable, indicating lower IMF when the n allele is present. A breeding strategy including the phenotype (BFiv) combined with genetic marker information at the RYR1 locus from the selection candidate, resulted in a 20% increase in accuracy and selection response when compared with a breeding strategy without genetic marker information.

A new simple method for improving QTL mapping under selective genotyping

The selective genotyping approach, where only individuals from the high and low extremes of the trait distribution are selected for genotyping and the remaining individuals are not genotyped, has been known as a cost-saving strategy to reduce genotyping work and can still maintain nearly equivalent efficiency to complete genotyping in QTL mapping. We propose a novel and simple statistical method based on the normal mixture model for selective genotyping when both genotyped and ungenotyped individuals are fitted in the model for QTL analysis. Compared to the existing methods, the main feature of our model is that we first provide a simple way for obtaining the distribution of QTL genotypes for the ungenotyped individuals and then use it, rather than the population distribution of QTL genotypes as in the existing methods, to fit the ungenotyped individuals in model construction. Another feature is that the proposed method is developed on the basis of a multiple-QTL model and has a simple estimation procedure similar to that for complete genotyping. As a result, the proposed method has the ability to provide better QTL resolution, analyze QTL epistasis, and tackle multiple QTL problem under selective genotyping. In addition, a truncated normal mixture model based on a multiple-QTL model is developed when only the genotyped individuals are considered in the analysis, so that the two different types of models can be compared and investigated in selective genotyping. The issue in determining threshold values for selective genotyping in QTL mapping is also discussed. Simulation studies are performed to evaluate the proposed methods, compare the different models, and study the QTL mapping properties in selective genotyping. The results show that the proposed method can provide greater QTL detection power and facilitate QTL mapping for selective genotyping. Also, selective genotyping using larger genotyping proportions may provide roughly equivalent power to complete genotyping and that using smaller genotyping proportions has difficulties doing so. The R code of our proposed method is available on http://www.stat.sinica.edu.tw/chkao/.

Cumulative adversity sensitizes neural response to acute stress: association with health symptoms

Cumulative adversity (CA) increases stress sensitivity and risk of adverse health outcomes. However, neural mechanisms underlying these associations in humans remain unclear. To understand neural responses underlying the link between CA and adverse health symptoms, the current study assessed brain activity during stress and neutral-relaxing states in 75 demographically matched, healthy individuals with high, mid, and low CA (25 in each group), and their health symptoms using the Cornell Medical Index. CA was significantly associated with greater adverse health symptoms (P=0.01) in all participants. Functional magnetic resonance imaging results indicated significant associations between CA scores and increased stress-induced activity in the lateral prefrontal cortex, insula, striatum, right amygdala, hippocampus, and temporal regions in all 75 participants (p<0.05, whole-brain corrected). In addition to these regions, the high vs low CA group comparison revealed decreased stress-induced activity in the medial orbitofrontal cortex (OFC) in the high CA group (p<0.01, whole-brain corrected). Specifically, hypoactive medial OFC and hyperactive right hippocampus responses to stress were each significantly associated with greater adverse health symptoms (p<0.01). Furthermore, an inverse correlation was found between activity in the medial OFC and right hippocampus (p=0.01). These results indicate that high CA sensitizes limbic-striatal responses to acute stress and also identifies an important role for stress-related medial OFC and hippocampus responses in the effects of CA on increasing vulnerability to adverse health consequences.

Estimating the effect of SNP genotype on quantitative traits from pooled DNA samples

Background

Studies to detect associations between DNA markers and traits of interest in humans and livestock benefit from increasing the number of individuals genotyped. Performing association studies on pooled DNA samples can provide greater power for a given cost. For quantitative traits, the effect of an SNP is measured in the units of the trait and here we propose and demonstrate a method to estimate SNP effects on quantitative traits from pooled DNA data.

Methods

To obtain estimates of SNP effects from pooled DNA samples, we used logistic regression of estimated allele frequencies in pools on phenotype. The method was tested on a simulated dataset, and a beef cattle dataset using a model that included principal components from a genomic correlation matrix derived from the allele frequencies estimated from the pooled samples. The performance of the obtained estimates was evaluated by comparison with estimates obtained using regression of phenotype on genotype from individual samples of DNA.

Results

For the simulated data, the estimates of SNP effects from pooled DNA are similar but asymptotically different to those from individual DNA data. Error in estimating allele frequencies had a large effect on the accuracy of estimated SNP effects. For the beef cattle dataset, the principal components of the genomic correlation matrix from pooled DNA were consistent with known breed groups, and could be used to account for population stratification. Correctly modeling the contemporary group structure was essential to achieve estimates similar to those from individual DNA data, and pooling DNA from individuals within groups was superior to pooling DNA across groups. For a fixed number of assays, pooled DNA samples produced results that were more correlated with results from individual genotyping data than were results from one random individual assayed from each pool.

Conclusions

Use of logistic regression of allele frequency on phenotype makes it possible to estimate SNP effects on quantitative traits from pooled DNA samples. With pooled DNA samples, genotyping costs are reduced, and in cases where trait records are abundant this approach is promising to obtain SNP associations for marker-assisted selection.

Binary trait mapping in experimental crosses with selective genotyping

Selective genotyping is an efficient strategy for mapping quantitative trait loci. For binary traits, where there are only two distinct phenotypic values (e.g., affected/unaffected or present/absent), one may consider selective genotyping of affected individuals, while genotyping none or only some of the unaffected. If selective genotyping of this sort is employed, the usual method for binary trait mapping, which considers phenotypes conditional on genotypes, cannot be used. We present an alternative approach, instead considering genotypes conditional on phenotypes, and compare this to the more standard method of analysis, both analytically and by example. For studies of rare binary phenotypes, we recommend performing an initial genome scan with all affected individuals and an equal number of unaffected, followed by genotyping the full cross in genomic regions of interest to confirm results from the initial screen.

Genetic mapping of quantitative trait loci for resistance to Haemonchus contortus in sheep

This paper presents results from a mapping experiment to detect quantitative trait loci (QTL) for resistance to Haemonchus contortus infestation in merino sheep. The primary trait analysed was faecal worm egg count in response to artificial challenge at 6 months of age. In the first stage of the experiment, whole genome linkage analysis was used for broad-scale mapping. The animal resource used was a designed flock comprising 571 individuals from four half-sib families. The average marker spacing was about 20 cM. For the primary trait, 11 QTL (as chromosomal/family combinations) were significant at the 5% chromosome-wide level, with allelic substitution effects of between 0.19 and 0.38 phenotypic standard deviation units. In general, these QTL did not have a significant effect on faecal worm egg count recorded at 13 months of age. In the second stage of the experiment, three promising regions (located on chromosomes 1, 3 and 4) were fine-mapped. This involved typing more closely spaced markers on individuals from the designed flock as well as an additional 495 individuals selected from a related population with a deeper pedigree. Analysis was performed using a linkage disequilibrium-linkage approach, under additive, dominant and multiple QTL models. Of these, the multiple QTL model resulted in the most refined QTL positions, with resolutions of <10 cM achieved for two regions. Because of the moderate size of effect of the QTL, and the apparent age and/or immune status specificity of the QTL, it is suggested that a panel of QTL will be required for significant genetic gains to be achieved within industry via marker-assisted selection.

Microsatellite mapping of QTLs affecting resistance to coccidiosis (Eimeria tenella) in a Fayoumi x White Leghorn cross

Background

Avian coccidiosis is a major parasitic disease of poultry, causing severe economical loss to poultry production by affecting growth and feed efficiency of infected birds. Current control strategies using mainly drugs and more recently vaccination are showing drawbacks and alternative strategies are needed. Using genetic resistance that would limit the negative and very costly effects of the disease would be highly relevant. The purpose of this work was to detect for the first time QTL for disease resistance traits to Eimeria tenella in chicken by performing a genome scan in an F2 cross issued from a resistant Fayoumi line and a susceptible Leghorn line.

Results

The QTL analysis detected 21 chromosome-wide significant QTL for the different traits related to disease resistance (body weight growth, plasma coloration, hematocrit, rectal temperature and lesion) on 6 chromosomes. Out of these, a genome-wide very significant QTL for body weight growth was found on GGA1, five genome-wide significant QTL for body weight growth, plasma coloration and hematocrit and one for plasma coloration were found on GGA1 and GGA6, respectively. Two genome-wide suggestive QTL for plasma coloration and rectal temperature were found on GGA1 and GGA2, respectively. Other chromosme-wide significant QTL were identified on GGA2, GGA3, GGA6, GGA15 and GGA23. Parent-of-origin effects were found for QTL for body weight growth and plasma coloration on GGA1 and GGA3. Several QTL for different resistance phenotypes were identified as co-localized on the same location.

Conclusion

Using an F2 cross from resistant and susceptible chicken lines proved to be a successful strategy to identify QTL for different resistance traits to Eimeria tenella, opening the way for further gene identification and underlying mechanisms and hopefully possibilities for new breeding strategies for resistance to coccidiosis in the chicken. From the QTL regions identified, several candidate genes and relevant pathways linked to innate immune and inflammatory responses were suggested. These results will be combined with functional genomics approaches on the same lines to provide positional candidate genes for resistance loci for coccidiosis. Results suggested also for further analysis, models tackling the complexity of the genetic architecture of these correlated disease resistance traits including potential epistatic effects.

Detection and characterization of amplified fragment length polymorphism markers for clinical mastitis in Canadian Holsteins

Mastitis is the most frequent, complex, and costly disease in dairy cattle. Genetic improvement of milk production traits has accompanied an increased susceptibility to mastitis. To determine genome-wide quantitative trait locus-linked markers for mastitis resistance, a total of 200 cows, comprising 100 top clinical mastitis- (CM) resistant and 100 top CM-susceptible cows, were screened by selective DNA pooling and amplified fragment length polymorphism (AFLP) technique. The AFLP analysis on resistant and susceptible pools using 89 selective primer combinations revealed 27 significant AFLP markers at a false discovery rate (FDR) of < 5%. The most promising AFLP marker was then selected for further characterization. Individual AFLP genotyping of the marker on all selected animals confirmed a significant difference. Sequence analysis detected a single nucleotide polymorphism (A<-->G) responsible for the AFLP polymorphism, which was named CGIL4. The PCR-RFLP analysis indicated that the frequency of allele A was significantly higher in the resistant group. The logistic regression analysis demonstrated that the marker was significantly associated with somatic cell score, CM residual values, and production traits. Radiation hybrid mapping assigned the marker to Bos taurus autosome 22. The present study provides promising markers for marker-assisted selection for CM resistance. Our results also demonstrated the capability of AFLP on selective DNA pools as a method for detection of genome regions containing quantitative trait loci.

Mapping quantitative trait loci from a single-tail sample of the phenotype distribution including survival data

A new effective Bayesian quantitative trait locus (QTL) mapping approach for the analysis of single-tail selected samples of the phenotype distribution is presented. The approach extends the affected-only tests to single-tail sampling with quantitative traits such as the log-normal survival time or censored/selected traits. A great benefit of the approach is that it enables the utilization of multiple-QTL models, is easy to incorporate into different data designs (experimental and outbred populations), and can potentially be extended to epistatic models. In inbred lines, the method exploits the fact that the parental mating type and the linkage phases (haplotypes) are known by definition. In outbred populations, two-generation data are needed, for example, selected offspring and one of the parents (the sires) in breeding material. The idea is to statistically (computationally) generate a fully complementary, maximally dissimilar, observation for each offspring in the sample. Bayesian data augmentation is then used to sample the space of possible trait values for the pseudoobservations. The benefits of the approach are illustrated using simulated data sets and a real data set on the survival of F(2) mice following infection with Listeria monocytogenes.

Bayesian mapping of quantitative trait loci for multiple complex traits with the use of variance components

Complex traits important for humans are often correlated phenotypically and genetically. Joint mapping of quantitative-trait loci (QTLs) for multiple correlated traits plays an important role in unraveling the genetic architecture of complex traits. Compared with single-trait analysis, joint mapping addresses more questions and has advantages for power of QTL detection and precision of parameter estimation. Some statistical methods have been developed to map QTLs underlying multiple traits, most of which are based on maximum-likelihood methods. We develop here a multivariate version of the Bayes methodology for joint mapping of QTLs, using the Markov chain-Monte Carlo (MCMC) algorithm. We adopt a variance-components method to model complex traits in outbred populations (e.g., humans). The method is robust, can deal with an arbitrary number of alleles with arbitrary patterns of gene actions (such as additive and dominant), and allows for multiple phenotype data of various types in the joint analysis (e.g., multiple continuous traits and mixtures of continuous traits and discrete traits). Under a Bayesian framework, parameters--including the number of QTLs--are estimated on the basis of their marginal posterior samples, which are generated through two samplers, the Gibbs sampler and the reversible-jump MCMC. In addition, we calculate the Bayes factor related to each identified QTL, to test coincident linkage versus pleiotropy. The performance of our method is evaluated in simulations with full-sib families. The results show that our proposed Bayesian joint-mapping method performs well for mapping multiple QTLs in situations of either bivariate continuous traits or mixed data types. Compared with the analysis for each trait separately, Bayesian joint mapping improves statistical power, provides stronger evidence of QTL detection, and increases precision in estimation of parameter and QTL position. We also applied the proposed method to a set of real data and detected a coincident linkage responsible for determining bone mineral density and areal bone size of wrist in humans.

Bayesian reanalysis of a quantitative trait locus accounting for multiple environments by scaling in broilers1

A Bayesian method was developed to handle QTL analyses of multiple experimental data of outbred populations with heterogeneity of variance between sexes for all random effects. The method employed a scaled reduced animal model with random polygenic and QTL allelic effects. A parsimonious model specification was applied by choosing assumptions regarding the covariance structure to limit the number of parameters to estimate. Markov chain Monte Carlo algorithms were applied to obtain marginal posterior densities. Simulation demonstrated that joint analysis of multiple environments is more powerful than separate single trait analyses of each environment. Measurements on broiler BW obtained from 2 experiments concerning growth efficiency and carcass traits were used to illustrate the method. The population consisted of 10 full-sib families from a cross between 2 broiler lines. Microsatellite genotypes were determined on generations 1 and 2, and phenotypes were collected on groups of generation 3 animals. The model included a polygenic correlation, which had a posterior mean of 0.70 in the analyses. The reanalysis agreed on the presence of a QTL in marker bracket MCW0058-LEI0071 accounting for 34% of the genetic variation in males and 24% in females in the growth efficiency experiment. In the carcass experiment, this QTL accounted for 19% of the genetic variation in males and 6% in females.

Regression-based quantitative trait loci mapping: robust, efficient and effective

Regression has always been an important tool for quantitative geneticists. The use of maximum likelihood (ML) has been advocated for the detection of quantitative trait loci (QTL) through linkage with molecular markers, and this approach can be very effective. However, linear regression models have also been proposed which perform similarly to ML, while retaining the many beneficial features of regression and, hence, can be more tractable and versatile than ML in some circumstances. Here, the use of linear regression to detect QTL in structured outbred populations is reviewed and its perceived shortfalls are revisited. It is argued that the approach is valuable now and will remain so in the future.

Estimation of breeding values using selected pedigree records

Fish bred in tanks or ponds cannot be easily tagged individually. The parentage of any individual may be determined by DNA fingerprinting, but is sufficiently expensive that large numbers cannot be so finger-printed. The measurement of the objective trait can be made on a much larger sample relatively cheaply. This article deals with experimental designs for selecting individuals to be finger-printed and for the estimation of the individual and family breeding values. The general setup provides estimates for both genetic effects regarded as fixed or random and for fixed effects due to known regressors. The family effects can be well estimated when even very small numbers are finger-printed, provided that they are the individuals with the most extreme phenotypes.

New joint covariance- and marginal-based tests for association and linkage for quantitative traits for random and non-random sampling

We develop novel statistical tests for transmission disequilibrium testing (tests of linkage in the presence of association) for quantitative traits using parents and offspring. These joint tests utilize information in both the covariance (or more generally, dependency) between genotype and phenotype and the marginal distribution of genotype. Using computer simulation we test the validity (Type I error rate control) and power of the proposed methods, for additive, dominant, and recessive modes of inheritance, locus-specific heritability of the trait 0.05, 0.1, 0.2 with allele frequencies of P=0.2 and 0.4, and sample sizes of 500, 200, and 100 trios. Both random sampling and extreme sampling schemes were investigated. A multinomial logistic joint test provides the highest overall power irrespective of sample size, allele frequency, heritability, and modes of inheritance.

Use of the Extreme Groups Approach: A Critical Reexamination and New Recommendations

Analysis of continuous variables sometimes proceeds by selecting individuals on the basis of extreme scores of a sample distribution and submitting only those extreme scores to further analysis. This sampling method is known as the extreme groups approach (EGA). EGA is often used to achieve greater statistical power in subsequent hypothesis tests. However, there are several largely unrecognized costs associated with EGA that must be considered. The authors illustrate the effects EGA can have on power, standardized effect size, reliability, model specification, and the interpretability of results. Finally, the authors discuss alternative procedures, as well as possible legitimate uses of EGA. The authors urge researchers, editors, reviewers, and consumers to carefully assess the extent to which EGA is an appropriate tool in their own research and in that of others.

Joint mapping of quantitative trait Loci for multiple binary characters

Joint mapping for multiple quantitative traits has shed new light on genetic mapping by pinpointing pleiotropic effects and close linkage. Joint mapping also can improve statistical power of QTL detection. However, such a joint mapping procedure has not been available for discrete traits. Most disease resistance traits are measured as one or more discrete characters. These discrete characters are often correlated. Joint mapping for multiple binary disease traits may provide an opportunity to explore pleiotropic effects and increase the statistical power of detecting disease loci. We develop a maximum-likelihood method for mapping multiple binary traits. We postulate a set of multivariate normal disease liabilities, each contributing to the phenotypic variance of one disease trait. The underlying liabilities are linked to the binary phenotypes through some underlying thresholds. The new method actually maps loci for the variation of multivariate normal liabilities. As a result, we are able to take advantage of existing methods of joint mapping for quantitative traits. We treat the multivariate liabilities as missing values so that an expectation-maximization (EM) algorithm can be applied here. We also extend the method to joint mapping for both discrete and continuous traits. Efficiency of the method is demonstrated using simulated data. We also apply the new method to a set of real data and detect several loci responsible for blast resistance in rice.

A General Likelihood Approach to Trait-Based Multipoint Linkage Analysis in Large Groups of Half-Sibs and Super Sisters

The idea of trait-based linkage analysis in half-sibs is extended by comparing the frequency of parental marker haplotypes in animals with different phenotypes. This article first presents the likelihood of observing different classes of paternal haplotypes in a half-sib family, where only family members of a certain phenotype (e.g., affected) are genotyped and are fully informative. The likelihood function is then generalized to multiple phenotypic categories. A linear predictor allows for discontinuous as well as for continuous phenotypes and other explanatory variables. Finally, how to incorporate not fully informative offspring and how to analyze super sister families are shown. Maximum-likelihood estimates of all parameters can be found by a Newton-Raphson algorithm, which mimics an iteratively weighted least-squares procedure. The method allows for any multilocus feasible mapping function and, among others, for situations with selective or nonselective genotyping, single or multiple traits, and continuous or categorical traits. No parameters are required to describe the mode of inheritance and the method copes with virtually any family size. Fields of applications are therefore mapping experiments in species with a high reproductive capacity, such as cattle, pigs, horses, honey bees, trees, and fish.

Powerful regression-based quantitative-trait linkage analysis of general pedigrees

We present a new method of quantitative-trait linkage analysis that combines the simplicity and robustness of regression-based methods and the generality and greater power of variance-components models. The new method is based on a regression of estimated identity-by-descent (IBD) sharing between relative pairs on the squared sums and squared differences of trait values of the relative pairs. The method is applicable to pedigrees of arbitrary structure and to pedigrees selected on the basis of trait value, provided that population parameters of the trait distribution can be correctly specified. Ambiguous IBD sharing (due to incomplete marker information) can be accommodated in the method by appropriate specification of the variance-covariance matrix of IBD sharing between relative pairs. We have implemented this regression-based method and have performed simulation studies to assess, under a range of conditions, estimation accuracy, type I error rate, and power. For normally distributed traits and in large samples, the method is found to give the correct type I error rate and an unbiased estimate of the proportion of trait variance accounted for by the additive effects of the locus-although, in cases where asymptotic theory is doubtful, significance levels should be checked by simulations. In large sibships, the new method is slightly more powerful than variance-components models. The proposed method provides a practical and powerful tool for the linkage analysis of quantitative traits.

Mathematics-assisted mapping in analysis of medical disease

Genetic mapping in analysis of medical disease is performed under several assumptions and (experimental) conditions, which are made about the data in general and the disease in particular. Here we discuss these conditions, what they mean, and what kind of deleterious effects they might have on the analysis. We also illustrate how to proceed and what kind of possibilities the statistical analysis may provide to medical scientists.

Mapping quantitative trait Loci using generalized estimating equations

A number of statistical methods are now available to map quantitative trait loci (QTL) relative to markers. However, no existing methodology can simultaneously map QTL for multiple nonnormal traits. In this article we rectify this deficiency by developing a QTL-mapping approach based on generalized estimating equations (GEE). Simulation experiments are used to illustrate the application of the GEE-based approach.

Enhanced efficiency of quantitative trait loci mapping analysis based on multivariate complexes of quantitative traits

An approach to increase the efficiency of mapping quantitative trait loci (QTL) was proposed earlier by the authors on the basis of bivariate analysis of correlated traits. The power of QTL detection using the log-likelihood ratio (LOD scores) grows proportionally to the broad sense heritability. We found that this relationship holds also for correlated traits, so that an increased bivariate heritability implicates a higher LOD score, higher detection power, and better mapping resolution. However, the increased number of parameters to be estimated complicates the application of this approach when a large number of traits are considered simultaneously. Here we present a multivariate generalization of our previous two-trait QTL analysis. The proposed multivariate analogue of QTL contribution to the broad-sense heritability based on interval-specific calculation of eigenvalues and eigenvectors of the residual covariance matrix allows prediction of the expected QTL detection power and mapping resolution for any subset of the initial multivariate trait complex. Permutation technique allows chromosome-wise testing of significance for the whole trait complex and the significance of the contribution of individual traits owing to: (a) their correlation with other traits, (b) dependence on the chromosome in question, and (c) both a and b. An example of application of the proposed method on a real data set of 11 traits from an experiment performed on an F(2)/F(3) mapping population of tetraploid wheat (Triticum durum x T. dicoccoides) is provided.

Multitrait least squares for quantitative trait loci detection

A multiple-trait QTL mapping method using least squares is described. It is presented as an extension of a single-trait method for use with three-generation, outbred pedigrees. The multiple-trait framework allows formal testing of whether the same QTL affects more than one trait (i.e., a pleiotropic QTL) or whether more than one linked QTL are segregating. Several approaches to the testing procedure are presented and their suitability discussed. The performance of the method is investigated by simulation. As previously found, multitrait analyses increase the power to detect a pleiotropic QTL and the precision of its location estimate. With enough information, discrimination between alternative genetic models is possible.

On the differences between maximum likelihood and regression interval mapping in the analysis of quantitative trait loci

The differences between maximum-likelihood (ML) and regression (REG) interval mapping in the analysis of quantitative trait loci (QTL) are investigated analytically and numerically by simulation. The analytical investigation is based on the comparison of the solution sets of the ML and REG methods in the estimation of QTL parameters. Their differences are found to relate to the similarity between the conditional posterior and conditional probabilities of QTL genotypes and depend on several factors, such as the proportion of variance explained by QTL, relative QTL position in an interval, interval size, difference between the sizes of QTL, epistasis, and linkage between QTL. The differences in mean squared error (MSE) of the estimates, likelihood-ratio test (LRT) statistics in testing parameters, and power of QTL detection between the two methods become larger as (1) the proportion of variance explained by QTL becomes higher, (2) the QTL locations are positioned toward the middle of intervals, (3) the QTL are located in wider marker intervals, (4) epistasis between QTL is stronger, (5) the difference between QTL effects becomes larger, and (6) the positions of QTL get closer in QTL mapping. The REG method is biased in the estimation of the proportion of variance explained by QTL, and it may have a serious problem in detecting closely linked QTL when compared to the ML method. In general, the differences between the two methods may be minor, but can be significant when QTL interact or are closely linked. The ML method tends to be more powerful and to give estimates with smaller MSEs and larger LRT statistics. This implies that ML interval mapping can be more accurate, precise, and powerful than REG interval mapping. The REG method is faster in computation, especially when the number of QTL considered in the model is large. Recognizing the factors affecting the differences between REG and ML interval mapping can help an efficient strategy, using both methods in QTL mapping to be outlined.

Maximum likelihood analysis of quantitative trait loci under selective genotyping

Selective genotyping is a cost-saving strategy in mapping quantitative trait loci (QTLs). When the proportion of individuals selected for genotyping is low, the majority of the individuals are not genotyped, but their phenotypic values, if available, are still included in the data analysis to correct the bias in parameter estimation. These ungenotyped individuals do not contribute much information about linkage analysis and their inclusion can substantially increase the computational burden. For multiple trait analysis, ungenotyped individuals may not have a full array of phenotypic measurements. In this case, unbiased estimation of QTL effects using current methods seems to be impossible. In this study, we develop a maximum likelihood method of QTL mapping under selective genotyping using only the phenotypic values of genotyped individuals. Compared with the full data analysis (using all phenotypic values), the proposed method performs well. We derive an expectation-maximization (EM) algorithm that appears to be a simple modification of the existing EM algorithm for standard interval mapping. The new method can be readily incorporated into a standard QTL mapping software, e.g. MAPMAKER. A general recommendation is that whenever full data analysis is possible, the full maximum likelihood analysis should be performed. If it is impossible to analyse the full data, e.g. sample sizes are too large, phenotypic values of ungenotyped individuals are missing or composite interval mapping is to be performed, the proposed method can be applied.