Selective genotyping to detect quantitative trait loci affecting multiple traits: interval mapping analysis

 Segregating quantitative trait loci can be detected via linkage to genetic markers. By selectively genotyping individuals with extreme phenotypes for the quantitative trait, the power per individual genotyped is increased at the expense of the power per individual phenotyped, but linear-model estimates of the quantitative-locus effect will be biased. The properties of single- and multiple-trait maximum-likelihood estimates of quantitative-loci parameters derived from selectively genotyped samples were investigated using Monte-Carlo simulations of backcross populations. All individuals with trait records were included in the analyses. All quantitative-locus parameters and the residual correlation were unbiasedly estimated by multiple-trait maximum-likelihood methodology. With single-trait maximum-likelihood, unbiased estimates for quantitative-locus effect and location, and the residual variance, were obtained for the trait under selection, but biased estimates were derived for a correlated trait that was analyzed separately. When an effect of the QTL was simulated only on the trait under selection, a “ghost” effect was also found for the correlated trait. Furthermore, if an effect was simulated only for the correlated trait, then the statistical power was less than that obtained with a random sample of equal size. With multiple-trait analyses, the power of quantitative-trait locus detection was always greater with selective genotyping. Received: 23 February 1998 / Accepted: 15 May 1998     

Power of QTL mapping experiments in commercial Atlantic salmon populations, exploiting linkage and linkage disequilibrium and effect of limited recombination in males

Whereas detection and positioning of genes that affect quantitative traits (quantitative trait loci (QTL)) using linkage mapping uses only information from recombinants in the genotyped generations, linkage disequilibrium (LD) mapping uses historical recombinants. Thus, whereas linkage mapping requires large family sizes to detect and accurately position QTL, LD mapping is more dependent on the number of families sampled from the population. In commercial Atlantic salmon breeding programmes, only a small number of individuals per family are routinely phenotyped for traits such as disease resistance and meat colour. In this paper, we assess the power and accuracy of combined linkage disequilibrium linkage analysis (LDLA) to detect QTL in the commercial population using simulation. When 15 half-sib sire families (each sire mated to 30 dams, each dam with 10 progeny) were sampled from the population for genotyping, we were able to detect a QTL explaining 10% of the phenotypic variance in 85% of replicates and position this QTL within 3 cM of the true position in 70% of replicates. When recombination was absent in males, a feature of the salmon genome, power to detect QTL increased; however, the accuracy of positioning the QTL was decreased. By increasing the number of sire families sampled from the population to be genotyped to 30, we were able to increase both the proportion of QTL detected and correctly positioned (even with no recombination in males). QTL with much smaller effect could also be detected. The results suggest that even with the existing recording structure in commercial salmon breeding programmes, there is considerable power to detect and accurately position QTL using LDLA.     

Robust score statistics for QTL linkage analysis

The traditional variance components approach for quantitative trait locus (QTL) linkage analysis is sensitive to violations of normality and fails for selected sampling schemes. Recently, a number of new methods have been developed for QTL mapping in humans. Most of the new methods are based on score statistics or regression-based statistics and are expected to be relatively robust to non-normality of the trait distribution and also to selected sampling, at least in terms of type I error. Whereas the theoretical development of these statistics is more or less complete, some practical issues concerning their implementation still need to be addressed. Here we study some of these issues such as the choice of denominator variance estimates, weighting of pedigrees, effect of parameter misspecification, effect of non-normality of the trait distribution, and effect of incorporating dominance. We present a comprehensive discussion of the theoretical properties of various denominator variance estimates and of the weighting issue and then perform simulation studies for nuclear families to compare the methods in terms of power and robustness. Based on our analytical and simulation results, we provide general guidelines regarding the choice of appropriate QTL mapping statistics in practical situations.     

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/.     

Selective genotyping for determination of linkage between a marker locus and a quantitative trait locus

Summary Selective genotyping is the term used when the determination of linkage between marker loci and quantitative trait loci (QTL) affecting some particular trait is carried out by genotyping only individuals from the high and low phenotypic tails of the entire sample population. Selective genotyping can markedly decrease the number of individuals genotyped for a given power at the expense of an increase in the number of individuals phenotyped. The optimum proportion of individuals genotyped from the point of view of minimizing costs for a given experimental power depends strongly on the cost of completely genotyping an individual for all of the markers included in the experiment (including the costs of obtaining a DNA sample) relative to the cost of rearing and trait evaluation of an individual. However, in single trait studies, it will almost never be useful to genotype more than the upper and lower 25% of a population. It is shown that the observed difference in quantitative trait values associated with alternative marker genotypes in the selected population can be much greater than the actual gene effect at the quantitative trait locus when the entire population is considered. An expression and a figure is provided for converting observed differences under selective genotyping to actual gene effects.     

QTL detection with bidirectional and unidirectional selective genotyping: marker-based and trait-based analyses

Selective genotyping of one or both phenotypic extremes of a population can be used to detect linkage between markers and quantitative trait loci (QTL) in situations in which full-population genotyping is too costly or not feasible, or where the objective is to rapidly screen large numbers of potential donors for useful alleles with large effects. Data may be subjected to 'trait-based' analysis, in which marker allele frequencies are compared between classes of progeny defined based on trait values, or to 'marker-based' analysis, in which trait means are compared between progeny classes defined based on marker genotypes. Here, bidirectional and unidirectional selective genotyping were simulated, using population sizes and selection intensities relevant to cereal breeding. Control of Type I error was usually adequate with marker-based analysis of variance or trait-based testing using the normal approximation of the binomial distribution. Bidirectional selective genotyping was more powerful than unidirectional. Trait-based analysis and marker-based analysis of variance were about equally powerful. With genotyping of the best 30 out of 500 lines (6%), a QTL explaining 15% of the phenotypic variance could be detected with a power of 0.8 when tests were conducted at a marker 10 cM from the QTL. With bidirectional selective genotyping, QTL with smaller effects and (or) QTL farther from the nearest marker could be detected. Similar QTL detection approaches were applied to data from a population of 436 recombinant inbred rice lines segregating for a large-effect QTL affecting grain yield under drought stress. That QTL was reliably detected by genotyping as few as 20 selected lines (4.5%). In experimental populations, selective genotyping can reduce costs of QTL detection, allowing larger numbers of potential donors to be screened for useful alleles with effects across different backgrounds. In plant breeding programs, selective genotyping can make it possible to detect QTL using even a limited number of progeny that have been retained after selection.     

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

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

Power calculations for selective genotyping in QTL mapping in backcross mice

Selective genotyping concerns the genotyping of a portion of individuals chosen on the basis of their phenotypic values. Often individuals are selected for genotyping from the high and low extremes of the phenotypic distribution. This procedure yields savings in cost and time by decreasing the total number of individuals genotyped. Previous work by Darvasi et al. (1993) has shown that the power to detect a QTL by genotyping 40-50 % of a population is roughly equivalent to genotyping the entire sample. However, these power studies have not accounted for different strategies of analysing the data when phenotypes of individuals in the middle are excluded, nor have they investigated the genome-wide type I error rate under these different strategies or different selection percentages. Further, these simulation studies have not considered markers over the entire genome. In this paper, we present simulation studies of power for the maximum likelihood approach to QTL mapping by Lander & Botstein (1989) in the context of selective genotyping. We calculate the power of selectively genotyping the individuals from the middle of the phenotypic distribution when performing QTL mapping over the whole mouse genome.     

Linear and generalized linear models for the detection of QTL effects on within-subject variability

Quantitative trait loci (QTLs) may affect not only the mean of a trait but also its variability. A special aspect is the variability between multiple measured traits of genotyped animals, such as the within-litter variance of piglet birth weights. The sample variance of repeated measurements is assigned as an observation for every genotyped individual. It is shown that the conditional distribution of the non-normally distributed trait can be approximated by a gamma distribution. To detect QTL effects in the daughter design, a generalized linear model with the identity link function is applied. Suitable test statistics are constructed to test the null hypothesis H(0): No QTL with effect on the within-litter variance is segregating versus H(A): There is a QTL with effect on the variability of birth weight within litter. Furthermore, estimates of the QTL effect and the QTL position are introduced and discussed. The efficiency of the presented tests is compared with a test based on weighted regression. The error probability of the first type as well as the power of QTL detection are discussed and compared for the different tests.     

The effects of selective genotyping on estimates of proportion of recombination between linked quantitative trait loci

Selective genotyping is the marker assay of only the more extreme phenotypes for a quantitative trait and is intended to increase the efficiency of quantitative trait loci (QTL) mapping. We show that selective genotyping can bias estimates of the recombination frequency between linked QTLs — upwardly when QTLs are in repulsion phase, and downwardly when QTLs are in coupling phase. We examined these biases under simple models involving two QTLs segregating in a backcross or F₂ population, using both analytical models and computer simulations. We found that bias is a function of the proportion selected, the magnitude of QTL effects, distance between QTLs and the dominance of QTLs. Selective genotyping thus may decrease the power of mapping multiple linked QTLs and bias the construction of a marker map. We suggest a large proportion than previously suggested (50%) or the entire population be genotyped if linked QTLs of large effects (explain > 10% phenotypic variance) are evident. New models need to be developed to explicitly incorporate selection into QTL map construction.     

Effectiveness of selective genotyping for detection of quantitative trait loci: an analysis of grain and malt quality traits in three barley populations.

Marker genotype data and grain and malt quality phenotype data from three barley (Hordeum vulgare L.) mapping populations were used to investigate the feasibility of selective genotyping for detection of quantitative trait loci (QTLs). With selective genotyping, only individuals with high and low phenotypic values for the trait of interest are genotyped. Here, genotyping of 10 to 70% of each population (i.e., 5 to 35% in each tail of the phenotypic distribution) was considered. Genomic positions detected by selective genotyping were compared to QTL position estimates from interval mapping analysis using marker genotype data from the entire population. Selective genotyping reliably detected almost all of the mapped QTLs, often with only 10% of the population genotyped. Selective genotyping also detected spurious QTLs in regions of the genome where no significant QTL had been mapped. Even with additional genotyping to verify putative QTLs, the total genotyping effort for detection of QTLs for a single trait by selective genotyping was usually less than 30% of that required for conventional interval mapping. Simultaneous investigation of two or more traits by selective genotyping would require additional genotyping effort, but could still be worthwhile.     

Significance thresholds for quantitative trait locus mapping under selective genotyping

In the case of selective genotyping, the usual permutation test to establish statistical significance for quantitative trait locus (QTL) mapping can give inappropriate significance thresholds, especially when the phenotype distribution is skewed. A stratified permutation test should be used, with phenotypes shuffled separately within the genotyped and ungenotyped individuals.     

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.     

Selective DNA Pooling for Determination of Linkage between a Molecular Marker and a Quantitative Trait Locus

Selective genotyping is a method to reduce costs in marker-quantitative trait locus (QTL) linkage determination by genotyping only those individuals with extreme, and hence most informative, quantitative trait values. The DNA pooling strategy (termed: ``selective DNA pooling') takes this one step further by pooling DNA from the selected individuals at each of the two phenotypic extremes, and basing the test for linkage on marker allele frequencies as estimated from the pooled samples only. This can reduce genotyping costs of marker-QTL linkage determination by up to two orders of magnitude. Theoretical analysis of selective DNA pooling shows that for experiments involving backcross, F(2) and half-sib designs, the power of selective DNA pooling for detecting genes with large effect, can be the same as that obtained by individual selective genotyping. Power for detecting genes with small effect, however, was found to decrease strongly with increase in the technical error of estimating allele frequencies in the pooled samples. The effect of technical error, however, can be markedly reduced by replication of technical procedures. It is also shown that a proportion selected of 0.1 at each tail will be appropriate for a wide range of experimental conditions.     

Improving QTL Mapping Resolution Based on Genotypic Sampling—a Case Using a RIL Population

The QTL mapping results were compared with the genotypically selected and random samples of the same size on the base of a RIL population. The results demonstrated that there were no obvious differences in the trait distribution and marker segregation distortion between the genotypically selected and random samples with the same population size. However, a significant increase in QTL detection power, sensitivity, specificity, and QTL resolution in the genotypically selected samples were observed. Moreover, the highly significant effect was detected in small size of genotypically selected samples. In QTL mapping, phenotyping is a more sensitive limiting factor than genotyping so that the selection of samples could be an attractive strategy for increasing genome-wide QTL mapping resolution. The efficient selection of samples should be more helpful for QTL maker assistant selection, fine mapping, and QTL cloning.     

基于基因型选择提高QTL作图的精度——以一个RIL群体为例

以PCR为基础的分子标记以及其他检测技术的发展,使得大规模的标记分析成为现实。这也为通过大群体标记分析,然后基于基因型选择挑选合适的小群体,从而提高QTL定位准确性和精度提供了可能。以一个包含294个家系的重组自交系（RIL）群体为例,通过基因型选择和随机选择的办法产生了一系列大小不等的亚群体,比较了两类群体QTL定位的结果。分析表明：相同大小的基因型选择群体与随机群体相比性状的表型分布都符合正态分布;标记的偏分离情况也没有明显的差别,都随着群体大小的增大,偏分离的比例也逐渐增大。但同等大小的基因型选择群体比随机群体的交换富集率（CE）要大,且随着选择强度的增大不断增大,如群体大小为270时,CE=1．04,群体大小为30时,CE=1．45。总体上,随着群体大小的增加,不管是随机群体还是选择群体,其QTL检测能力、灵敏性和特异性也随之增加,但选择群体的检测能力、灵敏性和特异性总体上要好于随机群体。当群体大于或等于240时,其QTL检测能力基本没有差别;群体大小大于或等于210时,其QTL检测的灵敏性和特异性也没有什么差别。这也说明：选择强度越大,效果越明显。以QTLI—LOD区间作为衡量QTL精度的一个指标,结果显示所有基因型选择群体都比相同大小随机群体的QTL定位精度高。目前QTL定位研究中,基因型数据较表型数据而言更容易准确获得,因此通过基因型选择可以更好的优化群体结构,减少田间实验的工作量,提高全基因组水平QTL作图的精度,为随后的QTL辅助选择和精细定位以及克隆提供帮助。     

Sib mating designs for mapping quantitative trait loci

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

Power analysis for quantitative trait locus mapping in populations derived by multiple backcrosses

 Populations derived by multiple backcrosses are potentially useful for quantitative trait locus (QTL) mapping studies. Comparisons of relative power to detect QTL using populations derived by multiple back-crosses are needed to make decisions when mapping projects are initiated. The objective of this study was to theoretically compare the power to detect QTL in populations derived by multiple backcrosses relative to mapping in a recombinant inbred population of equal size. Backcrossing results in a reduction in genetic variance with each generation and also results in an increasing frequency of the recurrent parent marker genotype. The relevant outcome for QTL mapping is a reduction in genetic variance to partition between marker genotype classes and increasing unbalance of the number of individuals contributing to the mean of the marker genotypes. Both of these factors lead to a decrease in the power to detect a QTL as the number of backcross generations increases. Experimental error was held constant with the populations compared. From a theoretical standpoint, backcross-derived populations offer few advantages for QTL detection. If, however, a backcrossing approach is the most efficient method to achieve a desired breeding objective and if QTL detection is an objective of equal or less importance, backcross-derived populations are a reasonable approach to QTL detection. Received: 4 August 1996 / Accepted: 4 April 1997     

Prediction of the power of detection of marker-quantitative trait locus linkages using analysis of variance

Analysis of variance can be used to detect the linkage of segregating quantitative trait loci (QTLs) to molecular markers in outbred populations. Using independent full-sib families and assuming linkage equilibrium, equations to predict the power of detection of a QTL are described. These equations are based on an hierarchical analysis of variance assuming either a completely random model or a mixed model, in which the QTL effect is fixed. A simple prediction of power from the mean squares is used that assumes a random model so that in the mixed-model situation this is an approximation. Simulation is used to illustrate the failure of the random model to predict mean squares and, hence, the power. The mixed model is shown to provide accurate prediction of the mean squares and, using the approximation, of power.     

Optimal designs for linkage disequilibrium mapping and candidate gene association tests in livestock populations

Simulation was used to evaluate the performance of different selective genotyping strategies when using linkage disequilibrium across large half-sib families to position a QTL within a previously defined genomic region. Strategies examined included standard selective genotyping and different approaches of discordant and concordant sib selection applied to arbitrary or selected families. Strategies were compared as a function of effect and frequency of QTL alleles, heritability, and phenotypic expression of the trait. Large half-sib families were simulated for 100 generations and 2% of the population was genotyped in the final generation. Simple ANOVA was applied and the marker with the greatest F-value was considered the most likely QTL position. For traits with continuous phenotypes, genotyping the most divergent pairs of half-sibs from all families was the best strategy in general, but standard selective genotyping was somewhat more precise when heritability was low. When the phenotype was distributed in ordered categories, discordant sib selection was the optimal approach for positioning QTL for traits with high heritability and concordant sib selection was the best approach when genetic effects were small. Genotyping of a few selected sibs from many families was generally more efficient than genotyping many individuals from a few highly selected sires.