Empirical Threshold Values for Quantitative Trait Mapping

The detection of genes that control quantitative characters is a problem of great interest to the genetic mapping community. Methods for locating these quantitative trait loci (QTL) relative to maps of genetic markers are now widely used. This paper addresses an issue common to all QTL mapping methods, that of determining an appropriate threshold value for declaring significant QTL effects. An empirical method is described, based on the concept of a permutation test, for estimating threshold values that are tailored to the experimental data at hand. The method is demonstrated using two real data sets derived from F(2) and recombinant inbred plant populations. An example using simulated data from a backcross design illustrates the effect of marker density on threshold values.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. I. Prior knowledge

Summary Prior information on gene effects at individual quantitative trait loci (QTL) and on recombination rates between marker loci and QTL is derived. The prior distribution of QTL gene effects is assumed to be exponential with major effects less likely than minor ones. The prior probability of linkage between a marker and another single locus is a function of the number and length of chromosomes, and of the map function relating recombination rate to genetic distance among loci. The prior probability of linkage between a marker locus and a quantitative trait depends additionally on the number of detectable QTL, which may be determined from total additive genetic variance and minimum detectable QTL effect. The use of this prior information should improve linkage tests and estimates of QTL effects.     

Least squares interval mapping of quantitative trait loci under the infinitesimal genetic model in outbred populations.

Genetic marker and phenotypic data for a quantitative trait were simulated on 20 paternal half-sib families with 100 progeny to investigate properties of within-family-regression interval mapping of a postulated single quantitative trait locus (QTL) in a marker interval under the infinitesimal genetic model, which has been the basis of the application of quantitative genetics to genetic improvement programs, and to investigate use of the infinitesimal model as null hypothesis in testing for presence of a major QTL. Genetic effects on the marked chromosome were generated based on a major gene model, which simulated a central biallelic QTL, or based on 101 biallelic QTL of equal effect, which approximated the infinitesimal model. The marked chromosome contained 0, 3.3%, 13.3%, or 33.3% of genetic variance and heritability was 0.25 or 0.70. Under the polygenic model with 3.3% of genetic variance on the marked chromosome, which corresponds to the infinitesimal model for the bovine, significant QTL effects were found for individual families. Correlations between estimates of QTL effects and true chromosome substitution effects were 0.29 and 0.47 for heritabilities of 0.25 and 0.70 but up to 0.85 with 33.3% of polygenic variance on the marked chromosome. These results illustrate the potential of marker-assisted selection even under the infinitesimal genetic model. Power of tests for presence of QTL was substantially reduced when the polygenic model with 3.3% of genetic variance on the chromosome was used as a null hypothesis. The ability to determine whether genetic variance on a chromosome was contributed by a single QTL of major effect or a large number of QTL with minor effects, corresponding to the infinitesimal model, was limited.     

Gene-environment interactions in complex diseases: genetic models and methods for QTL mapping in multiple half-sib populations

An interval quantitative trait locus (QTL) mapping method for complex polygenic diseases (as binary traits) showing QTL by environment interactions (QEI) was developed for outbred populations on a within-family basis. The main objectives, within the above context, were to investigate selection of genetic models and to compare liability or generalized interval mapping (GIM) and linear regression interval mapping (RIM) methods. Two different genetic models were used: one with main QTL and QEI effects (QEI model) and the other with only a main QTL effect (QTL model). Over 30 types of binary disease data as well as six types of continuous data were simulated and analysed by RIM and GIM. Using table values for significance testing, results show that RIM had an increased false detection rate (FDR) for testing interactions which was attributable to scale effects on the binary scale. GIM did not suffer from a high FDR for testing interactions. The use of empirical thresholds, which effectively means higher thresholds for RIM for testing interactions, could repair this increased FDR for RIM, but such empirical thresholds would have to be derived for each case because the amount of FDR depends on the incidence on the binary scale. RIM still suffered from higher biases (15-100% over- or under-estimation of true values) and high standard errors in QTL variance and location estimates than GIM for QEI models. Hence GIM is recommended for disease QTL mapping with QEI. In the presence of QEI, the model including QEI has more power (20-80% increase) to detect the QTL when the average QTL effect is small (in a situation where the model with a main QTL only is not too powerful). Top-down model selection is proposed in which a full test for QEI is conducted first and then the model is subsequently simplified. Methods and results will be applicable to human, plant and animal QTL mapping experiments.     

Mapping interspecific genetic architecture in a host-parasite interaction system

Under a hypothesis that the host-parasite interaction system is governed by genome-for-genome interaction, we propose a genetic model that integrates genetic information from both the host and parasite genomes. The model can be used for mapping quantitative trait loci (QTL) conferring the interaction between host and parasite and detecting interactions among these QTL. A one-dimensional genome-scan strategy is used to map QTL in both the host and parasite genomes simultaneously conditioned on selected pairs of markers controlling the background genetic variation; a two-dimensional genome-scan procedure is conducted to search for epistasis within the host and parasite genomes and interspecific QTL-by-QTL interactions between the host and parasite genomes. A permutation test is adopted to calculate the empirical threshold to control the experimentwise false-positive rate of detected QTL and QTL interactions. Monte Carlo simulations were conducted to examine the reliability and the efficiency of the proposed models and methods. Simulation results illustrated that our methods could provide reasonable estimates of the parameters and adequate powers for detecting QTL and QTL-by-QTL interactions.     

水稻ＣＭＳ—ＷＡ育性恢复基因的定位

在由227个组合组成的珍汕97A×（珍汕97B×密阳46）F     

The effects of selected sampling on the transmission disequilibrium test of a quantitative trait locus

We investigate how sampling of parents or children based on their extreme phenotypic values selected from clinical databases would affect the power of identification of quantitative trait loci (QTL) by a transmission disequilibrium test (TDT). We consider three selective sampling schemes based on the selection of phenotypic values of parents or children in nuclear families: (1) two children, one of extreme value, the other random; (2) two children extremely discordant; (3) one parent of extreme value. Other family members not specified will be recruited randomly with regard to phenotypic values. Our study shows that the second sampling scheme can always enhance the power for QTL identification, sometimes dramatically so. The increase in the statistical power of the TDT is particularly dramatic when h2 at the QTL under test is small or intermediate (e.g. 0.05 or 0.10). For the other two sampling schemes, under dominant effects at the QTL, the power is always increased relative to random sampling; however, under recessive or additive genetic effects, the power gain is generally minor or even decreased a little sometimes. Allele frequencies at the QTL and the selection stringency are important for determining the effect of selective sampling on the power of QTL identification. Our study is useful as a practical guideline on how to perform the TDT efficiently in practice by taking advantage of the extensive databases accumulated that are enriched with people of extreme phenotypic values.     

Sequential elimination of major-effect contributors identifies additional quantitative trait loci conditioning high-temperature growth in yeast

Several quantitative trait loci (QTL) mapping strategies can successfully identify major-effect loci, but often have poor success detecting loci with minor effects, potentially due to the confounding effects of major loci, epistasis, and limited sample sizes. To overcome such difficulties, we used a targeted backcross mapping strategy that genetically eliminated the effect of a previously identified major QTL underlying high-temperature growth (Htg) in yeast. This strategy facilitated the mapping of three novel QTL contributing to Htg of a clinically derived yeast strain. One QTL, which is linked to the previously identified major-effect QTL, was dissected, and NCS2 was identified as the causative gene. The interaction of the NCS2 QTL with the first major-effect QTL was background dependent, revealing a complex QTL architecture spanning these two linked loci. Such complex architecture suggests that more genes than can be predicted are likely to contribute to quantitative traits. The targeted backcrossing approach overcomes the difficulties posed by sample size, genetic linkage, and epistatic effects and facilitates identification of additional alleles with smaller contributions to complex traits.     

Combined line-cross and half-sib QTL analysis in Duroc–Pietrain population

A Duroc–Pietrain resource population was built to detect quantitative trait loci (QTL) that affect growth, carcass composition, and pork quality. The data were analyzed by applying three least-squares Mendelian models: a line-cross (LC) model, a half-sib (HS) model, and a combined LC and HS model (CB), which enabled the detection of QTL that had fixed, equal, and different allele frequencies for alternate breed alleles, respectively. Permutation tests were performed to determine 5% chromosome-wide and 5% genome-wide threshold values. A total of 40 (137) QTL were detected at the 5% genome-wide (chromosome-wide) level for the 35 traits analyzed. Of the 137 QTL detected, 62 were classified as the LC type (LC-QTL), 47 as the HS type (HS-QTL), and 28 as the CB type (CB-QTL). The results indicate that implementation of a series of model-based framework is not only beneficial to detect QTL, but also provides us with a new and more robust interpretation from which further methodology could be developed. G. Liu and J. J. Kim contributed equally to this work.     

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

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

Bayesian mapping of quantitative trait loci for complex binary traits

A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduced variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as multiple QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian statistics are particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitative genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to generate the value of a hypothetical underlying variable (called the liability) and a threshold, which in turn allow the use of existing Bayesian statistics. The reversible jump Markov chain Monte Carlo algorithm is used to simulate the posterior samples of all unknowns, including the number of QTL, the locations and effects of identified QTL, genotypes of each individual at both the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distribution of the number of QTL and the locations and effects of the identified QTL. Utilities of the method are demonstrated using a simulated outbred full-sib family. A computer program written in FORTRAN language is freely available on request.     

Confidence Intervals in Qtl Mapping by Bootstrapping

The determination of empirical confidence intervals for the location of quantitative trait loci (QTLs) was investigated using simulation. Empirical confidence intervals were calculated using a bootstrap resampling method for a backcross population derived from inbred lines. Sample sizes were either 200 or 500 individuals, and the QTL explained 1, 5, or 10% of the phenotypic variance. The method worked well in that the proportion of empirical confidence intervals that contained the simulated QTL was close to expectation. In general, the confidence intervals were slightly conservatively biased. Correlations between the test statistic and the width of the confidence interval were strongly negative, so that the stronger the evidence for a QTL segregating, the smaller the empirical confidence interval for its location. The size of the average confidence interval depended heavily on the population size and the effect of the QTL. Marker spacing had only a small effect on the average empirical confidence interval. The LOD drop-off method to calculate empirical support intervals gave confidence intervals that generally were too small, in particular if confidence intervals were calculated only for samples above a certain significance threshold. The bootstrap method is easy to implement and is useful in the analysis of experimental data.     

Tests of candidate genes in breed cross populations for QTL mapping in livestock

In recent years, several F₂ crosses between outbred lines of livestock have been developed to identify quantitative trait loci (QTL). These populations are valuable for further genetic analysis, including positional candidate gene loci (CGL). Analysis of CGL in F₂ populations is, however, hindered by extensive between-breed linkage disequilibrium (LD). The objectives here were to develop and evaluate three tests for CGL in simulated F₂ breed-cross populations. 1) A standard association test, based on the fixed effect of CGL genotype. This test was significant for CGL at considerable distances from the QTL. 2) A marker-assisted association test, based on a test at the CGL of the fixed effect of CGL genotype in a breed-cross QTL interval mapping model. This removed the impact of between-breed LD, but was not powerful in detecting CGL closely linked to the QTL, unless the CGL was the QTL. 3) An F-drop test, comparing F ratios for a QTL at the CGL with and without the CGL included as fixed effect. It had low power to distinguish close from distant CGL. Power to distinguish two CGL within 10 cM from the QTL was limited and little improved by including QTL effects associated with markers to remove between-breed LD, although the power was greater when one of the CGL was the causative mutation. Therefore, while we conclude that candidate gene tests in QTL mapping populations must be interpreted with caution, we now have a clearer picture of the value of candidate gene tests in these populations.     

Use of randomization testing to detect multiple epistatic QTLs

Here, we describe a randomization testing strategy for mapping interacting quantitative trait loci (QTLs). In a forward selection strategy, non-interacting QTLs and simultaneously mapped interacting QTL pairs are added to a total genetic model. Simultaneous mapping of epistatic QTLs increases the power of the mapping strategy by allowing detection of interacting QTL pairs where none of the QTL can be detected by their marginal additive and dominance effects. Randomization testing is used to derive empirical significance thresholds for every model selection step in the procedure. A simulation study was used to evaluate the statistical properties of the proposed randomization tests and for which types of epistasis simultaneous mapping of epistatic QTLs adds power. Least squares regression was used for QTL parameter estimation but any other QTL mapping method can be used. A genetic algorithm was used to search for interacting QTL pairs, which makes the proposed strategy feasible for single processor computers. We believe that this method will facilitate the evaluation of the importance at epistatic interaction among QTLs controlling multifactorial traits and disorders.     

Further insights of the variance component method for detecting QTL in livestock and aquacultural species: relaxing the assumption of additive effects

Complex traits may show some degree of dominance at the gene level that may influence the statistical power of simple models, i.e. assuming only additive effects to detect quantitative trait loci (QTL) using the variance component method. Little has been published on this topic even in species where relatively large family sizes can be obtained, such as poultry, pigs, and aquacultural species. This is important, when the idea is to select regions likely to be harbouring dominant QTL or in marker assisted selection. In this work, we investigated the empirical power and accuracy to both detect and localise dominant QTL with or without incorporating dominance effects explicitly in the model of analysis. For this purpose, populations with variable family sizes and constant population size and different values for dominance variance were simulated. The results show that when using only additive effects there was little loss in power to detect QTL and estimates of position, using or not using dominance, were empirically unbiased. Further, there was little gain in accuracy of positioning the QTL with most scenarios except when simulating an overdominant QTL.     

Four rice QTL controlling number of spikelets per panicle expressed the characteristics of single Mendelian gene in near isogenic backgrounds

Development of quantitative trait loci (QTL) near isogenic lines is a crucial step to QTL isolation using the strategy of map-based cloning. In this study, a recombinant inbred line (RIL) population derived from two indica rice varieties, Zhenshan 97 and HR5, was employed to map QTL for spikelets per panicle (SPP). One major QTL (qSPP7) and three minor QTL (qSPP1, qSPP2 and qSPP3) were identified on chromosomes 7, 1, 2 and 3, respectively. Four sets of near isogenic lines (NILs) BC₄F₂ targeted for the four QTL were developed by following a standard procedure of consecutive backcross, respectively. These QTL were not only validated in corresponding NILs, but also explained amounts of phenotypic variation with much larger LOD scores compared with those identified in RILs. SPP in the four QTL-NILs expressed bimodal or discontinuous distributions and followed the expected segregation ratio of single Mendelian factor by progeny test. Finally, qSPP1, qSPP2, qSPP3 and qSPP7 were respectively mapped to a locus, 0.5 cM from MRG2746, 0.6 cM from MRG2762, 0.8 cM from RM49 and 0.7 cM from MRG4436, as co-dominant markers on the basis of progeny tests. These results indicate no matter how small effect minor QTL is, QTL may still express the characteristics of single Mendelian factor in NILs and isolation of minor QTL will be possible using high quality NILs. Pyramiding these QTL into a variety will largely enhance rice grain yield.     

Simultaneous fine mapping of multiple closely linked quantitative trait Loci using combined linkage disequilibrium and linkage with a general pedigree

Within a small region (e.g., <10 cM), there can be multiple quantitative trait loci (QTL) underlying phenotypes of a trait. Simultaneous fine mapping of closely linked QTL needs an efficient tool to remove confounded shade effects among QTL within such a small region. We propose a variance component method using combined linkage disequilibrium (LD) and linkage information and a reversible jump Markov chain Monte Carlo (MCMC) sampling for model selection. QTL identity-by-descent (IBD) coefficients between individuals are estimated by a hybrid MCMC combining the random walk and the meiosis Gibbs sampler. These coefficients are used in a mixed linear model and an empirical Bayesian procedure combines residual maximum likelihood (REML) to estimate QTL effects and a reversible jump MCMC that samples the number of QTL and the posterior QTL intensities across the tested region. Note that two MCMC processes are used, i.e., an (internal) MCMC for IBD estimation and an (external) MCMC for model selection. In a simulation study, the use of the multiple-QTL model clearly removes the shade effects between three closely linked QTL located at 1.125, 3.875, and 7.875 cM across the region of 10 cM, using 40 markers at 0.25-cM intervals. It is shown that the use of combined LD and linkage information gives much more useful information compared to using linkage information alone for both single- and multiple-QTL analyses. When using a lower marker density (11 markers at 1-cM intervals), the signal of the second QTL can disappear. Extreme values of past effective size (resulting in extreme levels of LD) decrease the mapping accuracy.     

A test for selection employing quantitative trait locus and mutation accumulation data

Evolutionary biologists attribute much of the phenotypic diversity observed in nature to the action of natural selection. However, for many phenotypic traits, especially quantitative phenotypic traits, it has been challenging to test for the historical action of selection. An important challenge for biologists studying quantitative traits, therefore, is to distinguish between traits that have evolved under the influence of strong selection and those that have evolved neutrally. Most existing tests for selection employ molecular data, but selection also leaves a mark on the genetic architecture underlying a trait. In particular, the distribution of quantitative trait locus (QTL) effect sizes and the distribution of mutational effects together provide information regarding the history of selection. Despite the increasing availability of QTL and mutation accumulation data, such data have not yet been effectively exploited for this purpose. We present a model of the evolution of QTL and employ it to formulate a test for historical selection. To provide a baseline for neutral evolution of the trait, we estimate the distribution of mutational effects from mutation accumulation experiments. We then apply a maximum-likelihood-based method of inference to estimate the range of selection strengths under which such a distribution of mutations could generate the observed QTL. Our test thus represents the first integration of population genetic theory and QTL data to measure the historical influence of selection.     

大白×梅山杂交组合肉质性状的数量性状位点定位分析

为寻找影响猪肉质数量性状基因位点的染色体区域 ,以 3头英系大白公猪和 7头梅山母猪建立F2 资源家系。随机选留 14 7头F2 代个体 (1998年 81头 ,2 0 0 0年 66头 ) ,经检测均获得肉质性状表型数据。对资源家系内的所有个体位于染色体 1、2、3、4、6和 7上的 48个微卫星位点进行扩增。利用线性模型最小二乘法分别对各年度及两年综合后的肉质性状进行数量性状位点 (QTL)区间定位 ,利用置换法确定显著性阈值。研究结果表明 :在 2 0 0 0年群体中 ,猪 4号染色体 (SSC4)上定位了肌内脂肪QTL ,达到染色体极显著水平 (P <0 0 1)和基因组显著水平 (P <0 0 5) ,解释表型变异为 5 2 4% ,梅山猪具有增加肌内脂肪QTL ;两年度群体综合后 ,在上述 4号染色体同一区间 ,肌内脂肪QTL接近染色体显著水平 ;股二头肌pH值和半棘肌pH值QTL分别定位在SSC1和 3上 ;在 1998年和 2 0 0 0年群体中分别发现 1个和 3个达染色体显著水平 (P <0 0 5)的系水力QTL ;在 1998年群体中 ,肌肉含水量QTL位于SSC6;两年综合群体中 ,SSC2、6和 7上定位了肌肉含水量QTL ,达到染色体显著水平 ,含水量QTL均有印迹效应 ,梅山和大白猪各有增效基因     

QTL mapping of grain length in rice (Oryza sativa L.) using chromosome segment substitution lines

Chromosome segment substitution (CSS) lines have the potential for use in QTL fine mapping and map-based cloning. The standard t-test used in the idealized case that each CSS line has a single segment from the donor parent is not suitable for non-idealized CSS lines carrying several substituted segments from the donor parent. In this study, we present a likelihood ratio test based on stepwise regression (RSTEP-LRT) that can be used for QTL mapping in a population consisting of non-idealized CSS lines. Stepwise regression is used to select the most important segments for the trait of interest, and the likelihood ratio test is used to calculate the LOD score of each chromosome segment. This method is statistically equivalent to the standard t-test with idealized CSS lines. To further improve the power of QTL mapping, a method is proposed to decrease multicollinearity among markers (or chromosome segments). QTL mapping with an example CSS population in rice consisting of 65 non-idealized CSS lines and 82 chromosome segments indicated that a total of 18 segments on eight of the 12 rice chromosomes harboured QTLs affecting grain length under the LOD threshold of 2.5. Three major stable QTLs were detected in all eight environments. Some minor QTLs were not detected in all environments, but they could increase or decrease the grain length constantly. These minor genes are also useful in marker-assisted gene pyramiding.