Impact of QTL properties on the accuracy of multi-breed genomic prediction

Background

Although simulation studies show that combining multiple breeds in one reference population increases accuracy of genomic prediction, this is not always confirmed in empirical studies. This discrepancy might be due to the assumptions on quantitative trait loci (QTL) properties applied in simulation studies, including number of QTL, spectrum of QTL allele frequencies across breeds, and distribution of allele substitution effects. We investigated the effects of QTL properties and of including a random across- and within-breed animal effect in a genomic best linear unbiased prediction (GBLUP) model on accuracy of multi-breed genomic prediction using genotypes of Holstein-Friesian and Jersey cows.

Methods

Genotypes of three classes of variants obtained from whole-genome sequence data, with moderately low, very low or extremely low average minor allele frequencies (MAF), were imputed in 3000 Holstein-Friesian and 3000 Jersey cows that had real high-density genotypes. Phenotypes of traits controlled by QTL with different properties were simulated by sampling 100 or 1000 QTL from one class of variants and their allele substitution effects either randomly from a gamma distribution, or computed such that each QTL explained the same variance, i.e. rare alleles had a large effect. Genomic breeding values for 1000 selection candidates per breed were estimated using GBLUP modelsincluding a random across- and a within-breed animal effect.

Results

For all three classes of QTL allele frequency spectra, accuracies of genomic prediction were not affected by the addition of 2000 individuals of the other breed to a reference population of the same breed as the selection candidates. Accuracies of both single- and multi-breed genomic prediction decreased as MAF of QTL decreased, especially when rare alleles had a large effect. Accuracies of genomic prediction were similar for the models with and without a random within-breed animal effect, probably because of insufficient power to separate across- and within-breed animal effects.

Conclusions

Accuracy of both single- and multi-breed genomic prediction depends on the properties of the QTL that underlie the trait. As QTL MAF decreased, accuracy decreased, especially when rare alleles had a large effect. This demonstrates that QTL properties are key parameters that determine the accuracy of genomic prediction.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0124-6) contains supplementary material, which is available to authorized users.     

Long-term response to genomic selection: effects of estimation method and reference population structure for different genetic architectures

Background

Genomic selection has become an important tool in the genetic improvement of animals and plants. The objective of this study was to investigate the impacts of breeding value estimation method, reference population structure, and trait genetic architecture, on long-term response to genomic selection without updating marker effects.

Methods

Three methods were used to estimate genomic breeding values: a BLUP method with relationships estimated from genome-wide markers (GBLUP), a Bayesian method, and a partial least squares regression method (PLSR). A shallow (individuals from one generation) or deep reference population (individuals from five generations) was used with each method. The effects of the different selection approaches were compared under four different genetic architectures for the trait under selection. Selection was based on one of the three genomic breeding values, on pedigree BLUP breeding values, or performed at random. Selection continued for ten generations.

Results

Differences in long-term selection response were small. For a genetic architecture with a very small number of three to four quantitative trait loci (QTL), the Bayesian method achieved a response that was 0.05 to 0.1 genetic standard deviation higher than other methods in generation 10. For genetic architectures with approximately 30 to 300 QTL, PLSR (shallow reference) or GBLUP (deep reference) had an average advantage of 0.2 genetic standard deviation over the Bayesian method in generation 10. GBLUP resulted in 0.6% and 0.9% less inbreeding than PLSR and BM and on average a one third smaller reduction of genetic variance. Responses in early generations were greater with the shallow reference population while long-term response was not affected by reference population structure.

Conclusions

The ranking of estimation methods was different with than without selection. Under selection, applying GBLUP led to lower inbreeding and a smaller reduction of genetic variance while a similar response to selection was achieved. The reference population structure had a limited effect on long-term accuracy and response. Use of a shallow reference population, most closely related to the selection candidates, gave early benefits while in later generations, when marker effects were not updated, the estimation of marker effects based on a deeper reference population did not pay off.     

Effects of the number of markers per haplotype and clustering of haplotypes on the accuracy of QTL mapping and prediction of genomic breeding values

The aim of this paper was to compare the effect of haplotype definition on the precision of QTL-mapping and on the accuracy of predicted genomic breeding values. In a multiple QTL model using identity-by-descent (IBD) probabilities between haplotypes, various haplotype definitions were tested i.e. including 2, 6, 12 or 20 marker alleles and clustering base haplotypes related with an IBD probability of > 0.55, 0.75 or 0.95. Simulated data contained 1100 animals with known genotypes and phenotypes and 1000 animals with known genotypes and unknown phenotypes. Genomes comprising 3 Morgan were simulated and contained 74 polymorphic QTL and 383 polymorphic SNP markers with an average r² value of 0.14 between adjacent markers. The total number of haplotypes decreased up to 50% when the window size was increased from two to 20 markers and decreased by at least 50% when haplotypes related with an IBD probability of > 0.55 instead of > 0.95 were clustered. An intermediate window size led to more precise QTL mapping. Window size and clustering had a limited effect on the accuracy of predicted total breeding values, ranging from 0.79 to 0.81. Our conclusion is that different optimal window sizes should be used in QTL-mapping versus genome-wide breeding value prediction.     

QTL mapping for teat number in an Iberian-by-Meishan pig intercross

The aim of this study was to investigate chromosomal regions affecting the number of teats in pigs and possible epistatic interactions between the identified quantitative trait loci (QTL). An experimental F2 cross between Iberian and Chinese Meishan lines was used for this purpose. A genomic scan was conducted with 117 markers covering the 18 porcine autosomes. Linkage analyses were performed by interval mapping using an animal model to estimate QTL and additive polygenic effects. Complementary analyses with models fitting two QTL were also carried out. The results showed three genomewide significant QTL mapping on chromosomes 5, 10 and 12, whose joint action control up to 30% of the phenotypic variance of the trait. Meishan alleles had a positive additive effect on teat number, and a positive-additive x additive-epistatic interaction was detected between QTL on chromosomes 10 and 12.     

孙女设计中标记密度对QTL定位精确性的影响

采用蒙特卡罗方法分析了在孙女设计中不同的嫩体结构、性状遗传力、ＱＴＬ效应大小和ＱＴＬ在染色体上的位置中个因素不同水平组合下４种标记密度（标记间隔５ｃＭ,１０ｃＭ,２０ｃＭ、５０ｃＭ对ＱＴＬ定位精确性（以均方误ＭＳＥ为衡量指标）的影响,并从经济学角度探讨了应用于标记辅助选（ＭＡＳ）的ＱＴＬ定位的最佳标记密度。结果表明,一般说来,在各因素水平都较低时,ＭＳＥ随标记密度加大而下降的相对幅度也较 小,反之     

影响动物模型MBLUP评定准确性的主要因素

标记辅助最佳线性无偏预测（marker-assisted best linear unbiased prediction,MBLUP）是对动物实施标记辅助选择（marker-assisted selection,MAS）的一种重要方法。通过计算机随机模拟研究了所选性状的遗传力、QTL方差和相邻两个标记间图距3个因素对动物模型MBLUP评定准确性的影响。结果表明,性状的遗传力越高、QTL方差和相邻两个标记间图距越小时,动物模型MBLUP评定的准确性越高;相反,当性状的遗传力较低、QTL方差和相邻两个标记间图距较大时,动物模型MBLUP评定的准确性则较低。     

A paternally imprinted QTL for mature body mass on mouse Chromosome 8

Body mass (BM) is a classic polygenic trait that has been extensively investigated to determine the underlying genetic architecture. Many previous studies looking at the genetic basis of variation in BM in murine animal models by quantitative trait loci (QTL) mapping have used crosses between two inbred lines. As a consequence it has not been possible to explore imprinting effects which have been shown to play an important role in the genetic basis of early growth with persistent effects throughout the growth curve. Here we use partially inbred mouse lines to identify QTL for mature BM by applying both Mendelian and Imprinting models. The analysis of an F₂ population (n ≈ 500) identified a number of QTL at 14, 16, and 18 weeks explaining in total 31.5%, 34.4%, and 30.5% of total phenotypic variation, respectively. On Chromosome 8 a QTL of large effect (14% of the total phenotypic variance at 14 weeks) was found to be explained by paternal imprinting. Although Chromosome 8 has not been previously associated with imprinting effects, features of candidate genes within the QTL confidence interval (CpG islands and direct clustered repeats) support the hypothesis that Insulin receptor substrate 2 may be associated with imprinting, but as yet is unidentified as being so.     

Confirmation and refinement of a QTL on BTA5 affecting milk production traits in the Fleckvieh dual purpose cattle breed

We analysed a QTL affecting milk yield (MY), milk protein yield (PY) and milk fat yield (FY) in the dual purpose cattle breed Fleckvieh on BTA5. Twenty-six microsatellite markers covering 135 cM were selected to analyse nine half-sib families containing 605 sons in a granddaughter design. We thereby assigned two new markers to the public linkage map using the CRI-MAP program. Phenotypic records were daughter yield deviations (DYD) originating from the routinely performed genetic evaluations of breeding animals. To determine the position of the QTL, three different approaches were applied: interval mapping (IM), linkage analysis by variance component analysis (LAVC), and combined linkage disequilibrium (LD) and linkage (LDL) analysis. All three methods mapped the QTL in the same marker interval ( BM2830-ETH152 ) with the greatest test-statistic value at 118, 119.33 and 119.33 cM respectively. The positive QTL allele simultaneously increases DYD in the first lactation by 272 kg milk, 7.1 kg milk protein and 7.0 kg milk fat. Although the mapping accuracy and the significance of a QTL effect increased from IM over LAVC to LDL, the confidence interval was large (13, 20 and 24 cM for FY, MY and PY respectively) for the positional cloning of the causal gene. The estimated averages of pair wise marker LD with a distance <5 cM were low (0.107) and reflect the large effective population size of the Fleckvieh subpopulation analysed. This low level of LD suggests a need for increase in marker density in following fine mapping steps.     

植物QTL分析的理论研究进展

数量性状的表型是由数量性状基因座 ( Quantitative trait locus,QTL)和环境效应共同作用的结果。传统的数量遗传学采用统计学的方法由一级统计量和二级统计量描述处理 QTL的复合作用 ,估计各种遗传参数 (例如遗传力、遗传相关、遗传进度、有效因子数等 ) ,用于指导遗传育种实践。然而 ,在传统的数量遗传学分析中 ,往往假设数量性状受微效多基因控制 ,这些基因具有相同的并且是较微小的效应 ,所估计的遗传参数反映的是数量性状多基因系统的整体特征 ,其理论方法不能用于追踪研究和描述单个数量性状基因的作用。近年来 ,由于分子生物学技…     

Maximum Likelihood Mapping of Quantitative Trait Loci Using Full-Sib Families

A maximum likelihood method is presented for the detection of quantitative trait loci (QTL) using flanking markers in full-sib families. This method incorporates a random component for common family effects due to additional QTL or the environment. Simulated data have been used to investigate this method. With a fixed total number of full sibs power of detection decreased substantially with decreasing family size. Increasing the number of alleles at the marker loci (i.e., polymorphism information content) and decreasing the interval size about the QTL increased power. Flanking markers were more powerful than single markers. In testing for a linked QTL the test must be made against a model which allows for between family variation (i.e., including an unlinked QTL or a between family variance component) or the test statistic may be grossly inflated. Mean parameter estimates were close to the simulated values in all situations when fitting the full model (including a linked QTL and common family effect). If the common family component was omitted the QTL effect was overestimated in data in which additional genetic variance was simulated and when compared with an unlinked QTL model there was reduced power. The test statistic curves, reflecting the likelihood of the QTL at each position along the chromosome, have discontinuities at the markers caused by adjacent pairs of markers providing different amounts of information. This must be accounted for when using flanking markers to search for a QTL in an outbred population.     

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.     

Effects of missing marker and segregation distortion on QTL mapping in F2 populations

Missing marker and segregation distortion are commonly encountered in actual quantitative trait locus (QTL) mapping populations. Our objective in this study was to investigate the impact of the two factors on QTL mapping through computer simulations. Results indicate that detection power decreases with increasing levels of missing markers, and the false discovery rate increases. Missing markers have greater effects on smaller effect QTL and smaller size populations. The effect of missing markers can be quantified by a population with a reduced size similar to the marker missing rate. As for segregation distortion, if the distorted marker is not closely linked with any QTL, it will not have significant impact on QTL mapping; otherwise, the impact of the distortion will depend on the degree of dominance of QTL, frequencies of the three marker types, the linkage distance between the distorted marker and QTL, and the mapping population size. Sometimes, the distortion can result in a higher genetic variance than that of non-distortion, and therefore benefits the detection of linked QTL. A formula of the ratio of genetic variance explained by QTL under distortion and non-distortion was given in this study, so as to easily determine whether the segregation distortion marker (SDM) increases or decreases the QTL detection power. The effect of SDM decreases rapidly as its linkage relationship with QTL becomes looser. In general, distorted markers will not have a great effect on the position and effect estimations of QTL, and their effects can be ignored in large-size mapping populations.     

性状遗传力与QTL方差对标记辅助选择效果的影响

在采用动物模型标记辅助最佳线性无偏预测方法对个体育种值进行估计的基础上,模拟了在一个闭锁群体内连续对单个性状选择10个世代的情形,并系统地比较了性状遗传力和QTL方差对标记辅助选择所获得的遗传进展、QTL增效基因频率和群体近交系数变化的影响。结果表明：在对高遗传力和QTL方差较小的性状实施标记辅助选择时,可望获得更大的遗传进展;遗传力越高,QTL方差越大,则QTL增效基因频率的上升速度越快;遗传力较高时,群体近交系数上升的速度较为缓慢,而QTL方差对群体近交系数上升速度的影响则不甚明显。结合前人关于标记辅助选择相对效率的研究结果,可以认为：当选择性状的遗传力和QTL方差为中等水平时,标记辅助选择可望获得理想的效果。     

Haplotypic QTL mapping in an outbred pedigree

An offspring genome can be viewed as a mosaic of chromosomal segments or haplotypes contributed by multiple founders in any quantitative trait locus (QTL) detection study but tracing these is especially complex to achieve for outbred pedigrees. QTL haplotypes can be traced from offspring back to individual founders in outbred pedigrees by combining founder-origin probabilities with fully informative flanking markers. This haplotypic method was illustrated for QTL detection using a three-generation pedigree for a woody perennial plant, Pinus taeda L. Growth rate was estimated using height measurements from ages 2 to 10 years. Using simulated and actual datasets, power of the experimental design was shown to be efficient for detecting QTLs of large effect. Using interval mapping and fully informative markers, a large QTL accounting for 11.3% of the phenotypic variance in the growth rate was detected. This same QTL was expressed at all ages for height, accounting for 7.9-12.2% of the phenotypic variance. A mixed-model inheritance was more appropriate for describing genetic architecture of growth curves in P. taeda than a strictly polygenic model. The positive QTL haplotype was traced from the offspring to its contributing founder, GP3, then the haplotypic phase for GP3 was determined by assaying haploid megagametophytes. The positive QTL haplotype was a recombinant haplotype contributed by GP3. This study illustrates the combined power of fully informative flanking markers and founder origin probabilities for (1) estimating QTL haplotype magnitude, (2) tracing founder origin and (3) determining haplotypic transmission frequency.     

Optimal sampling of a population to determine QTL location, variance, and allelic number

In a population intended for breeding and selection, questions of interest relative to a specific segregating QTL are the variance it generates in the population, and the number and effects of its alleles. One approach to address these questions is to extract several inbreds from the population and use them to generate multiple mapping families. Given random sampling of parents, sampling strategy may be an important factor determining the power of the analysis and its accuracy in estimating QTL variance and allelic number. We describe appropriate multiple-family QTL mapping methodology and apply it to simulated data sets to determine optimal sampling strategies in terms of family number versus family size. Genomes were simulated with seven chromosomes, on which 107 markers and six QTL were distributed. The total heritability was 0.60. Two to ten alleles were segregating at each QTL. Sampling strategies ranged from sampling two inbreds and generating a single family of 600 progeny to sampling 40 inbreds and generating 40 families of 15 progeny each. Strategies involving only one to five families were subject to variation due to the sampling of inbred parents. For QTL where more than two alleles were segregating, these strategies did not sample QTL alleles representative of the original population. Conversely, strategies involving 30 or more parents were subject to variation due to sampling of QTL genotypes within the small families obtained. Given these constraints, greatest QTL detection power was obtained for strategies involving five to ten mapping families. The most accurate estimation of the variance generated by the QTL, however, was obtained with strategies involving 20 or more families. Finally, strategies with an intermediate number of families best estimated the number of QTL alleles. We conclude that no overall optimal sampling strategy exists but that the strategy adopted must depend on the objective.Communicated by P. Langridge     

大豆遗传图谱的构建和若干农艺性状的QTL定位分析

大豆许多重要农艺性状都是由微效多基因控制的数量性状,对这些数量性状进行QTL定位是大豆数量性状遗传研究领域的一个重要内容.本研究利用栽培大豆科新3号为父本、中黄20为母本杂交得到含192个单株的F2分离群体,构建了含122 个SSR标记、覆盖1719.6cM、由33个连锁群组成的连锁遗传图谱.利用复合区间作图法,对该群体的株高、主茎节数、单株粒重和蛋白质含量等农艺性状的调查数据进行QTL分析,共找到两个株高QTL,贡献率分别为9.15%和6.08%;两个主茎节数QTL,贡献率分别为10. 1%和8.6%;一个蛋白质含量QTL,贡献率为9.8%;一个单株粒重QTL,贡献率为11.4% .通过遗传作图共找到与所定位的4个农艺性状QTL连锁的6个SSR标记,这些标记可以应用于大豆种质资源的分子标记辅助选择,从而为大豆分子标记辅助育种提供理论依据.     

Interval mapping methods for detecting QTL affecting survival and time-to-event phenotypes

Quantitative trait loci (QTL) are usually searched for using classical interval mapping methods which assume that the trait of interest follows a normal distribution. However, these methods cannot take into account features of most survival data such as a non-normal distribution and the presence of censored data. We propose two new QTL detection approaches which allow the consideration of censored data. One interval mapping method uses a Weibull model (W), which is popular in parametrical modelling of survival traits, and the other uses a Cox model (C), which avoids making any assumption on the trait distribution. Data were simulated following the structure of a published experiment. Using simulated data, we compare W, C and a classical interval mapping method using a Gaussian model on uncensored data (G) or on all data (G'=censored data analysed as though records were uncensored). An adequate mathematical transformation was used for all parametric methods (G, G' and W). When data were not censored, the four methods gave similar results. However, when some data were censored, the power of QTL detection and accuracy of QTL location and of estimation of QTL effects for G decreased considerably with censoring, particularly when censoring was at a fixed date. This decrease with censoring was observed also with G', but it was less severe. Censoring had a negligible effect on results obtained with the W and C methods.     

Mapping multiple QTL of different effects: comparison of a simple sequential testing strategy and multiple QTL mapping

The aim of this study was to explore, by computer simulation, the mapping of QTLs in a realistic but complex situation of many (linked) QTLs with different effects, and to compare two QTL mapping methods. A novel method to dissect genetic variation on multiple chromosomes using molecular markers in backcross and F₂ populations derived from inbred lines was suggested, and its properties tested using simulations. The rationale for this sequential testing method was to explicitly test for alternative genetic models. The method consists of a series of four basic statistical tests to decide whether variance was due to a single QTL, two QTLs, multiple QTLs, or polygenes, starting with a test to detect genetic variance associated with a particular chromosome. The method was able to distinguish between different QTL configurations, in that the probability to `detect' the correct model was high, varying from 0.75 to 1. For example, for a backcross population of 200 and an overall heritability of 50%, in 78% of replicates a polygenic model was detected when that was the underlying true model. To test the method for multiple chromosomes, QTLs were simulated on 10 chromosomes, following a geometric series of allele effects, assuming positive alleles were in coupling in the founder lines For these simulations, the sequential testing method was compared to the established Multiple QTL Mapping (MQM) method. For a backcross population of 400 individuals, power to detect genetic variance was low with both methods when the heritability was 0.40. For example, the power to detect genetic variation on a chromosome on which 6 QTLs explained 12.6% of the genetic variance, was less than 60% for both methods. For a large heritability (0.90), the power of MQM to detect genetic variance and to dissect QTL configurations was generally better, due to the simultaneous fitting of markers on all chromosomes. It is concluded that when testing different QTL configurations on a single chromosome using the sequential testing procedure, regions of other chromosomes which explain a significant amount of variation should be fitted in the model of analysis. This study reinforces the need for large experiments in plants and other species if the aim of a genome scan is to dissect quantitative genetic variation.     

QTL analysis: unreliability and bias in estimation procedures

Several statistical methods which employ multiple marker data are currently available for the analysis of quantitative trait loci (QTL) in experimental populations. Although comparable estimates of QTL location and effects have been obtained by these methods, using simulated and real data sets, their accuracy and reliability have not been extensively investigated. The present study specifically examines the merit of using F₂ and doubled haploid populations for locating QTL and estimating their effects. Factors which may affect accuracy and reliability of QTL mapping, such as the number and position of the markers available, the accuracy of the marker locations and the size of the experimental population used, are considered. These aspects are evaluated for QTL of differing heritabilities and locations along the chromosome.A population of 300 F₂ individuals and 150 doubled haploid lines gave estimates of QTL position and effect which were comparable, albeit extremely unreliable. Even for a QTL of high heritability (10%), the confidence interval was 35 cM. There was little increase in reliability to be obtained from using 300, rather than 200, F₂ individuals and 100 doubled haploid lines gave similar results to 150. QTL estimates were not significantly improved either by using the expected, rather than the observed, marker positions or by using a dense map of markers rather than a sparse map. A QTL which was asymmetrically located in the linkage group resulted in inaccurate estimates of QTL position which were seriously biassed at low heritability of the QTL. In a population of 300 F₂ individuals the bias increased from 4 cM to 20 cM, for a QTL with 10% and 2% heritability respectively.     

Estimates of marker-associated QTL effects in Monte Carlo backcross generations using multiple regression

Summary The decision of whether or not to use QTLassociated markers in breeding programs needs further information about the magnitude of the additive and dominance effects that can be estimated. The objectives of this paper are (1) to apply some of the Moreno-Gonzalez (1993) genetic models to backcross simulation data generated by the Monte Carlo method, and (2) to get simulation information about the number of testing progenies and mapping density in relation to the magnitude of gene effect estimates. Results of the Monte Carlo study show that the stepwise regression analysis was able to detect relatively small additive and dominance effects when the QTL are independently segregating. When testing selfed families derived from backcross individuals, dominance effects had a larger error standard deviation and were estimated at a lower frequency. Linked QTL require a higher marker mapping density on the genome and a larger number of progenies to detect small genetic effects. Reduction of the environmental error variance by evaluating selfed backcross families in replicate experiments increased the power of the test. Expressions of the number of progenies for detecting significant additive effects were developed for some genetic situations. The ratio of the within-backcross genetic variance to the square of a gene effect estimate is a function of the number of progenies, the heritability of the trait, the marker map density and the portion of the genetic variance explained by the model. Different values (from 0 to 1) assigned to (relative position of the QTL in the marker segment) did not cause a large shift in the residual mean square of the model.