Mapping quantitative trait loci using multiple families of line crosses.

To avoid a loss in statistical power as a result of homozygous individuals being selected as parents of a mapping population, one can use multiple families of line crosses for quantitative trait genetic linkage analysis. Two strategies of combining data are investigated: the fixed-model and the random-model strategies. The fixed-model approach estimates and tests the average effect of gene substitution for each parent, while the random-model approach treats each effect of gene substitution as a random variable and directly estimates and tests the variance of gene substitution. Extensive Monte Carlo simulations verify that the two strategies perform equally well, although the random model is preferable in combining data from a large number of families. Simulations also show that there may be an optimal sampling strategy (number of families vs. number of individuals per family) in which QTL mapping reaches its maximum power and minimum estimation error. Deviation from the optimal strategy reduces the efficiency of the method.     

Mapping quantitative trait loci using binned genotypes

Precise mapping of quantitative trait loci(QTLs)is critical for assessing genetic effects and identifying candidate genes for quantitative traits.Interval and composite interval mappings have been the methods of choice for several decades,which have provided tools for identifying genomic regions harboring causal genes for quantitative traits.Historically,the concept was developed on the basis of sparse marker maps where genotypes of loci within intervals could not be observed.Currently,genomes of many organisms have been saturated with markers due to the new sequencing technologies.Genotyping by sequencing usually generates hundreds of thousands of single nucleotide polymorphisms(SNPs),which often include the causal polymorphisms.The concept of interval no longer exists,prompting the necessity of a norm change in QTL mapping technology to make use of the high-volume genomic data.Here we developed a statistical method and a software package to map QTLs by binning markers into haplotype blocks,called bins.The new method detects associations of bins with quantitative traits.It borrows the mixed model methodology with a polygenic control from genome-wide association studies(GWAS)and can handle all kinds of experimental populations under the linear mixed model(LMM)framework.We tested the method using both simulated data and data from populations of rice.The results showed that this method has higher power than the current methods.An R package named binQTL is available from GitHub.     

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

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

A powerful and robust method for mapping quantitative trait loci in general pedigrees

The variance-components model is the method of choice for mapping quantitative trait loci in general human pedigrees. This model assumes normally distributed trait values and includes a major gene effect, random polygenic and environmental effects, and covariate effects. Violation of the normality assumption has detrimental effects on the type I error and power. One possible way of achieving normality is to transform trait values. The true transformation is unknown in practice, and different transformations may yield conflicting results. In addition, the commonly used transformations are ineffective in dealing with outlying trait values. We propose a novel extension of the variance-components model that allows the true transformation function to be completely unspecified. We present efficient likelihood-based procedures to estimate variance components and to test for genetic linkage. Simulation studies demonstrated that the new method is as powerful as the existing variance-components methods when the normality assumption holds; when the normality assumption fails, the new method still provides accurate control of type I error and is substantially more powerful than the existing methods. We performed a genomewide scan of monoamine oxidase B for the Collaborative Study on the Genetics of Alcoholism. In that study, the results that are based on the existing variance-components method changed dramatically when three outlying trait values were excluded from the analysis, whereas our method yielded essentially the same answers with or without those three outliers. The computer program that implements the new method is freely available.     

Analysis of quantitative trait loci using hybrid pedigrees: quantitative traits of animals

A method is proposed for analysis of quantitative traits in animal hybrid pedigrees formed by crosses between outbred lines differing in allele frequencies of the genes controlling the trait studied. The method is based on the decomposition of trait variances into components and uses maximization of the likelihood function for estimating model parameters, which allows the estimation of additive and dominance effects of the gene involved in trait determination and its allele frequencies, as well as determination of the chromosomal position of this gene relative to genotyped markers. To test the linkage of this gene with markers, a statistic with the noncentral chi(2) distribution has been chosen. Analytical expressions for the power of this method have been derived. The method has been tested on small model hybrid pedigrees. Phenotypic values of the trait and information on marker genotypes for each individual in hybrid pedigrees are original data for the analysis of a quantitative trait.     

Mapping of multiple quantitative trait loci affecting bovine spongiform encephalopathy

A whole-genome scan was conducted to map quantitative trait loci (QTL) for BSE resistance or susceptibility. Cows from four half-sib families were included and 173 microsatellite markers were used to construct a 2835-cM (Kosambi) linkage map covering 29 autosomes and the pseudoautosomal region of the sex chromosome. Interval mapping by linear regression was applied and extended to a multiple-QTL analysis approach that used identified QTL on other chromosomes as cofactors to increase mapping power. In the multiple-QTL analysis, two genome-wide significant QTL (BTA17 and X/Y(ps)) and four genome-wide suggestive QTL (BTA1, 6, 13, and 19) were revealed. The QTL identified here using linkage analysis do not overlap with regions previously identified using TDT analysis. One factor that may explain the disparity between the results is that a more extensive data set was used in the present study. Furthermore, methodological differences between TDT and linkage analyses may affect the power of these approaches.     

Mapping quantitative trait loci using molecular marker linkage maps

Summary High-density restriction fragment length polymorphism (RFLP) and allozyme linkage maps have been developed in several plant species. These maps make it technically feasible to map quantitative trait loci (QTL) using methods based on flanking marker genetic models. In this paper, we describe flanking marker models for doubled haploid (DH), recombinant inbred (RI), backcross (BC), F₁ testcross (F₁TC), DH testcross (DHTC), recombinant inbred testcross (RITC), F₂, and F₃ progeny. These models are functions of the means of quantitative trait locus genotypes and recombination frequencies between marker and quantitative trait loci. In addition to the genetic models, we describe maximum likelihood methods for estimating these parameters using linear, nonlinear, and univariate or multivariate normal distribution mixture models. We defined recombination frequency estimators for backcross and F₂ progeny group genetic models using the parameters of linear models. In addition, we found a genetically unbiased estimator of the QTL heterozygote mean using a linear function of marker means. In nonlinear models, recombination frequencies are estimated less efficiently than the means of quantitative trait locus genotypes. Recombination frequency estimation efficiency decreases as the distance between markers decreases, because the number of progeny in recombinant marker classes decreases. Mean estimation efficiency is nearly equal for these methods.     

Mapping quantitative trait loci in F2 incorporating phenotypes of F3 progeny

In plants and laboratory animals, QTL mapping is commonly performed using F(2) or BC individuals derived from the cross of two inbred lines. Typical QTL mapping statistics assume that each F(2) individual is genotyped for the markers and phenotyped for the trait. For plant traits with low heritability, it has been suggested to use the average phenotypic values of F(3) progeny derived from selfing F(2) plants in place of the F(2) phenotype itself. All F(3) progeny derived from the same F(2) plant belong to the same F(2:3) family, denoted by F(2:3). If the size of each F(2:3) family (the number of F(3) progeny) is sufficiently large, the average value of the family will represent the genotypic value of the F(2) plant, and thus the power of QTL mapping may be significantly increased. The strategy of using F(2) marker genotypes and F(3) average phenotypes for QTL mapping in plants is quite similar to the daughter design of QTL mapping in dairy cattle. We study the fundamental principle of the plant version of the daughter design and develop a new statistical method to map QTL under this F(2:3) strategy. We also propose to combine both the F(2) phenotypes and the F(2:3) average phenotypes to further increase the power of QTL mapping. The statistical method developed in this study differs from published ones in that the new method fully takes advantage of the mixture distribution for F(2:3) families of heterozygous F(2) plants. Incorporation of this new information has significantly increased the statistical power of QTL detection relative to the classical F(2) design, even if only a single F(3) progeny is collected from each F(2:3) family. The mixture model is developed on the basis of a single-QTL model and implemented via the EM algorithm. Substantial computer simulation was conducted to demonstrate the improved efficiency of the mixture model. Extension of the mixture model to multiple QTL analysis is developed using a Bayesian approach. The computer program performing the Bayesian analysis of the simulated data is available to users for real data analysis.     

Mapping loci influencing blood pressure in the Framingham pedigrees using model-free LOD score analysis of a quantitative trait

This paper presents a method of performing model-free LOD-score based linkage analysis on quantitative traits. It is implemented in the QMFLINK program. The method is used to perform a genome screen on the Framingham Heart Study data. A number of markers that show some support for linkage in our study coincide substantially with those implicated in other linkage studies of hypertension. Although the new method needs further testing on additional real and simulated data sets we can already say that it is straightforward to apply and may offer a useful complementary approach to previously available methods for the linkage analysis of quantitative traits.     

Mapping quantitative trait loci using the MCMC procedure in SAS

The MCMC procedure in SAS (called PROC MCMC) is particularly designed for Bayesian analysis using the Markov chain Monte Carlo (MCMC) algorithm. The program is sufficiently general to handle very complicated statistical models and arbitrary prior distributions. This study introduces the SAS/MCMC procedure and demonstrates the application of the program to quantitative trait locus (QTL) mapping. A real life QTL mapping experiment in wheat female fertility trait was used as an example for the demonstration. The fertility trait phenotypes were described under three different models: (1) the Poisson model, (2) the Bernoulli model and (3) the zero-truncated Poisson model. One QTL was identified on the second chromosome. This QTL appears to control the switch of seed-producing ability of female plants but does not affect the number of seeds produced once the switch is turned on.     

Mapping quantitative trait loci in oligogenic models

We discuss strategies for mapping quantitative trait loci with emphasis on certain issues of study design that have recently received attention: e.g. genotyping only selected pedigrees and the comparative value of large pedigrees versus sib pairs. We use a standard variance components model and a parametrization of the genetic effects in which the 'segregation' parameters are locally orthogonal to the 'linkage' parameters. This permits simple explicit expressions for the expectation of the score statistic, which we use to compare the power of different strategies. We also discuss robustness of the score statistic.     

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.     

Mapping quantitative trait loci for seedling vigor in rice using RFLPs

Improving seedling vigor is an important objective of modern rice (Oryza saliva L.) breeding programs. The purpose of this study was to identify and map quantitative trait loci (QTL) underlying seedling vigor-related traits using restriction fragment length polymorphisms (RFLPs). An F₂ population of 204 plants was developed from a cross between a low-vigor japonica cultivar Labelle (LBL) and a high-vigor indica cultivar Black Gora (BG). A linkage map was constructed of 117 markers spanning 1496 Haldane cM and encompassing the 12 rice chromosomes with an average marker spacing of 14 cM. The length of the shoots, roots, coleoptile and mesocotyl were measured on F₃ families in slantboard tests conducted at two temperatures (18° and 25°C). By means of interval analysis, 13 QTLs, each accounting for 7% to 38% of the phenotypic variance, were identified and mapped in the two temperature regimes at a log-likelihood (LOD) threshold of 2.5. Four QTLs controlled shoot length, 2 each controlled root and coleoptile lengths and 5 influenced mesocotyl length. Single-point analysis confirmed the presence of these QTLs and detected additional loci for shoot, root and coleoptile lengths, these latter usually accounting for less than 5% of the phenotypic variation. Only 3 QTLs detected both by interval and singlepoint analyses were expressed under both temperature regimes. Additive, dominant and overdominant modes of gene action were observed. Contrary to what was predicted from parental phenotype, the low-vigor LBL contributed 46% of the positive alleles for shoot, root and coleoptile lengths. Positive alleles from the high-vigor parent BG were identified for increased root, coleoptile and mesocotyl lengths. However, BG contributed alleles with only minor effects for shoot length, the most important determinant of seedling vigor in water-seeded rice, suggesting that it would not be an ideal donor parent for introducing faster shoot growth alleles into temperate japonica cultivars.     

Analysis of quantitative trait loci using hybrid pedigrees: Quantitative traits of animals

A method is proposed for analysis of quantitative traits in animal hybrid pedigrees formed by crosses between outbred lines differing in allele frequencies of the genes controlling the trait studied. The method is based on the decomposition of trait variances into components and uses maximization of the likelihood function for estimating model parameters, which allows the estimation of additive and dominance effects of the gene involved in trait determination and its allele frequencies, as well as determination of the chromosomal position of this gene relative to genotyped markers. To test the linkage of this gene with markers, a statistic with the noncentral x ² distribution has been chosen. Analytical expressions for the power of this method have been derived. The method has been tested on small model hybrid pedigrees. Phenotypic values of the trait and information on marker genotypes for each individual in hybrid pedigrees are initial data for the analysis of a quantitative trait.     

Mapping quantitative trait loci with censored observations

The existing statistical methods for mapping quantitative trait loci (QTL) assume that the phenotype follows a normal distribution and is fully observed. These assumptions may not be satisfied when the phenotype pertains to the survival time or failure time, which has a skewed distribution and is usually subject to censoring due to random loss of follow-up or limited duration of the experiment. In this article, we propose an interval-mapping approach for censored failure time phenotypes. We formulate the effects of QTL on the failure time through parametric proportional hazards models and develop efficient likelihood-based inference procedures. In addition, we show how to assess genome-wide statistical significance. The performance of the proposed methods is evaluated through extensive simulation studies. An application to a mouse cross is provided.     

Mapping quantitative trait loci with epistatic effects

Epistatic variance can be an important source of variation for complex traits. However, detecting epistatic effects is difficult primarily due to insufficient sample sizes and lack of robust statistical methods. In this paper, we develop a Bayesian method to map multiple quantitative trait loci (QTLs) with epistatic effects. The method can map QTLs in complicated mating designs derived from the cross of two inbred lines. In addition to mapping QTLs for quantitative traits, the proposed method can even map genes underlying binary traits such as disease susceptibility using the threshold model. The parameters of interest are various QTL effects, including additive, dominance and epistatic effects of QTLs, the locations of identified QTLs and even the number of QTLs. When the number of QTLs is treated as an unknown parameter, the dimension of the model becomes a variable. This requires the reversible jump Markov chain Monte Carlo algorithm. The utility of the proposed method is demonstrated through analysis of simulation data.     

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.     

Mapping quantitative trait loci for bovine ovulation rate

An elite, three-generation family from the USDA Meat Animal Research Center twinning population was examined for evidence of ovulation rate quantitative trait loci (QTL). This work was both a continuation of previously reported results suggesting evidence for ovulation rate QTL on bovine Chromosome (Chr) 7 and an extension of a genome-wide search for QTL. Additional markers were typed on Chr 7 to facilitate interval mapping and testing of the hypothesis of one versus two QTL on that chromosome. In addition, 14 other informative markers were added to a selective genotyping genome screening of this family, and markers exhibiting nominal significance were used to identify chromosomal regions that were then subjected to more exhaustive analysis. For Chr 7, a total of 12 markers were typed over a region spanning the proximal two-thirds of the chromosome. Results from interval mapping analyses indicated evidence suggestive of the presence of QTL (nominal P < 0.00077) within this region. Subsequent analysis with a model postulating two QTL provided evidence (P < 0.05) for two rather than one QTL on this chromosome. Preliminary analysis with additional markers indicated nominal significance (P < 0.05) for regions of Chrs 5, 10, and 19. Each of these regions was then typed with additional markers for the entire three-generation pedigree. Significant evidence (P < 0.000026) of ovulation rate QTL was found for Chrs 5 and 19, while support on Chr 10 failed to exceed a suggestive linkage threshold (P > 0.00077). Received: 14 May 1999 / Accepted: 14 October 1999     

Mapping quantitative trait loci mediating sensitivity to etomidate

Long- and Short-Sleep (LS and SS) mice were selectively bred for differences in ethanol-induced loss of the righting reflex (LORR) and have been found to differ in LORR induced by various anesthetic agents. We used a two-stage mapping strategy to identify quantitative trait loci (QTLs) affecting duration of LORR caused by the general anesthetic etomidate and brain levels of etomidate (BEL) following regain of the righting reflex. Analysis of recombinant-inbred strains derived from a cross between LS and SS mice (LSXSS) yielded a heritability estimate of 0.23 for etomidate-induced LORR and identified one marker that showed suggestive linkage for a QTL, on mouse Chromosome (chr) 12. Mapping in an F(2) population derived from a cross between inbred LS and SS (ILS and ISS) revealed a significant QTL for etomidate-induced LORR on Chr 12, and two significant QTLs mediating BEL on Chrs 6 and 12. Several QTLs showing suggestive linkage for etomidate-induced LORR and BEL were also identified in the F(2) population. Brain levels of etomidate in the RI and F(2) mice suggested that differences in LORR were due to differential central nervous system sensitivity, rather than differential etomidate metabolism. Interestingly, the region on Chr 7 has also been identified as a region influencing ethanol-induced LORR, suggesting the possibility of a common genetic mechanism mediating etomidate and ethanol sensitivity. These QTL regions need to be further narrowed before the testing of candidate genes is feasible.     

Theoretical and empirical power of regression and maximum-likelihood methods to map quantitative trait loci in general pedigrees

Both theoretical calculations and simulation studies have been used to compare and contrast the statistical power of methods for mapping quantitative trait loci (QTLs) in simple and complex pedigrees. A widely used approach in such studies is to derive or simulate the expected mean test statistic under the alternative hypothesis of a segregating QTL and to equate a larger mean test statistic with larger power. In the present study, we show that, even when the test statistic under the null hypothesis of no linkage follows a known asymptotic distribution (the standard being chi(2)), it cannot be assumed that the distribution under the alternative hypothesis is noncentral chi(2). Hence, mean test statistics cannot be used to indicate power differences, and a comparison between methods that are based on simulated average test statistics may lead to the wrong conclusion. We illustrate this important finding, through simulations and analytical derivations, for a recently proposed new regression method for the analysis of general pedigrees to map quantitative trait loci. We show that this regression method is not necessarily more powerful nor computationally more efficient than a maximum-likelihood variance-component approach. We advocate the use of empirical power to compare trait-mapping methods.