多个连锁数量性状位点的多性状最优化选择

一种扩展的方法能够在多个世代对具有多个数量性状位点的多性状选择进行最优化。这种方法的基础是在目标雨数中用综合遗传值替代单个性状遗传值,并在整个规划期内最大化所有世代选择反应的加权和。利用多阶段系统优化控制理论,整个最优化问题通过一个向前和向后的迭代循环解决。用一个实际育种猪群的育种参数来评价该方法的选择效果,并和标准QTL选择和常规BLUP选择进行比较。结果表明,优化选择要优于标准QTL选择和常规BLUP选择。经济权重对优化选择的影响较明显,随着达100kg日龄赋予的经济权重的增加,优化选择的优势越明显。优化选择通过两种方式增加总选择反应：1）选择早期减少一部分QTL选择反应;2）对达100kgH龄给予更大的权重。选择后期优化累积贴现选择比优化终端选择给予达100kgH龄更大的权重。     

不同QTL增效基因初始频率下标记辅助选择的效果

采用随机模拟方法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。在假定选择性状受一个位于常染色体上的QTL和多基因共同控制的情况下,采用动物模型标记辅助最佳线性无偏预测方法估计个体育种值并据此进行种畜的选留,并在此基础上系统地比较了QTL增效基因初始频率对标记辅助选择效果的影响。结果表明：当群体中QTL增效基因的初始频率较低时,选择所获得的QTL基因型值的进展会更大,标记辅助选择在单位时间内可获得较大的遗传进展;此时,尽管QTL增效基因在群体中固定所需的世代数会更长一些,但其频率上升的速度却更快。而QTL增效基因初始频率的高低对群体近交增量的影响不是很大。     

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。     

结合MOET技术的奶牛标记辅助选择方案比较

应用计算机模拟的方法比较利用遗传标记信息和/或超数排卵和胚胎移植(MOET)技术的一系列奶牛育种方案相对于传统育种方案的优越性. 模拟性状为产奶量, QTL作为已知遗传标记. 8个奶牛育种方案分别是：传统的后裔测定方案用STANPT表示; GASPT方案在青年公牛进入后裔测定前通过其自身QTL基因型进行预选择; MOETPT方案应用MOET技术产生青年公牛, 青年公牛预选择为家系内全同胞随机选择; GAMOPT方案结合了QTL预选择及MOET技术; COMBPT方案在GAMOPT方案基础上, 在个体育种值的评估中加入了QTL基因型效应; 另外对应后裔测定体系中MOETPT,GAMOPT,COMBPT方案设计了3个非后裔测定方案, 分别命名为MOET方案、GAMO方案及COMB方案. 动物个体通过相对应的动物模型进行育种值评估, 模拟针对产奶性状进行重叠世代连续17年的选择. 针对现役公牛、泌乳母牛、公牛母亲、公牛父亲和青年公牛5个不同群体, 对应用QTL信息和MOET技术对有利QTL基因频率、真实育种值、多基因值和累积遗传进展优势率产生的影响进行评估. 结果表明, 结合QTL信息和MOET技术的方案, 其真实育种值遗传进展显著高于其他方案, 仅应用QTL信息或MOET技术的单一改进方案间差异不显著, STANPT方案效率最低. 应用MOET技术的方案在第17年获得的多基因选择反应更大. 不同育种方案有利QTL基因频率增加速度在3个公畜群体中差异远大于泌乳母牛群体. GASPT,MOETPT,GAMOPT,COMBPT,MOET,GAMO 和COMB 方案相对STANPT方案, 累积遗传进展优势率在现役公牛群体中分别为8.42%, 3.59%, 14.58%, 18.54%, 4.12%, 14.12%和16.50%, 在泌乳母牛群体中分别为2.70%, 5.00%, 11.05%, 12.78%, 7.51%, 17.12%和25.38%.     

林木遗传图谱研究现状及发展趋势

林木具有世代长、高度杂合、遗传负荷大等遗传特性,使其遗传图谱研究不同于其他物种。高质量林木遗传图谱,可进行林木近缘树种比较图谱研究,了解林木的基因组结构和进化历程,进行有效QTL定位研究及开展林木复杂性状的标记辅助选择。目前林木作图存在着群体较小,构建的图谱和定位的QTL存在连锁平衡,以及作图策略未充分考虑林木的遗传学特性等问题。扩大作图群体、选择高度保守的标记系统以及研究适合林木作图的理论和方法将有助于林木基因组研究向纵深发展 。     

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。     

一个具选择、突变、迁移的群体的遗传差分模型

假设一个群体是由“单位点—双基因”的个体所组成的,在该群体内存在选择、突变、迁移、生死等效应的作用。本文给出了在上述假设下并满足:(1)世代重叠,选择、突变、迁移、生死等效应的作用均在世代遗传之间完成;(2)群体适当大,个体间交配随机,符合孟德尔式遗传;(3)没有任何意外的灾祸等约定的群体遗传的数学模型。通过模型分析,我们能够进一步用数学语言来解释一些生命现象。模型分析指出:虽然某些群体不满足Hardy-Weinberg定律所叙述的条件,但可能具有和Hardy-Weinberg定律的结论相似的结果。该文中还就几个主要参数的变化讨论了群体遗传和进化的某些性质,如平衡等。最后,我们给出了该模型的一个数值例子。     

染色体片段导入系在作物遗传育种中的应用

准确而有效的定位农作物数量性状基因座(Quantitative Trait Loci,QTLs)是植物分子育种的核心,传统的QTL定位群体遗传背景复杂,受群体大小和统计方法等多方面的限制,难以达到QTL精细定位。随着分子标记技术、计算机统计软件及分子辅助选择的飞速发展,一种新的QTL定位群体脱颖而出,这就是染色体片段导入系(Chromosome Segment Introgression Lines,CSILs)。它不但能有效消除"遗传背景噪音"对QTL定位的干扰,还能够在群体中挖掘出大量的有利隐蔽基因,对农作物遗传育种的进一步发展有巨大贡献。对染色体片段导入系的优越性,应用范围以及应用前景作以综述。     

远交群体动态性状基因定位的似然分析Ⅱ.模拟研究

以远交设计群体为例,在推导出动态性状基因定位的似然法分析过程的基础上,选择3阶Legendre多项式为子模型,采用Monte-Carlo方法模拟研究了不同个体数、测定日频数、标记密度和QTL遗传贡献率对两种分析方法检测QTL效率的影响。每个因素都取高、中和低3个水平,利用正交设计安排模拟因素试验组合。模拟试验结果表明：高QTL遗传贡献率要比低QTL遗传贡献率的QTL在检测时需要较少个体数和测定日抽样;但不论QTL遗传贡献率多大,300以上的群体大小和5％以上的测定日频数都可以保证足够高的检测效率。个体数和测定日频数对动态性状QTL的分析和检测具有几乎相同的作用,而且相同样本含量条件下两者呈现互补的关系。就某个动态点的QTL检测而言,模拟试验也同时证明：提出的这种以整个动态过程为定位目标的动态性状基因定位方法明显优于传统的逐个动态点的定位分析方法。     

畜禽遗传资源系统保存的理论与模拟实验研究──I．畜禽遗传资源系统保存的理论分析

本文提出了畜禽遗传资源系统保存的概念、基本思想及其群体遗传结构变化的数学模型。该理论是将一定时空内某一畜种所拥有的全部基因作为保存对象,既将活体保存作为基本方法,又将其有机地与高新生物技术结合在一起;既追求系统地保存控制畜种特性的基因资源,又可达到保存地方品种的目的。在假定无世代重叠,群体内存在选择、突变、迁移,且考虑漂变效应的情况下,本文所构建的两个数学模型可分别用来描述一个座位上多个主基因频率或数量性状群体均数的动态变化。     

Optimizing Selection on Multiple Identified Quantitative Trait Loci in Population with Overlapping Generations

A method was developed to model and optimize selection on multiple identified quantitative trait loci (QTLs) and polygenic estimated breeding value, in order to maximize a weighted sum of cumulative response to selection over multiple years in a population with overlapping generations. The model allows for a population with multiple sex-age classes, different number of age class between sires and dams, and varied genetic contribution of the age class. The optimization problem was formulated as a multiple-stage optimal control problem and solved by a forward and backward iteration loop. The practical utility of this method was illustrated in an example of pig breeding population with overlapping generations. The selection response of this method was compared with standard QTL selection and conventional best linear unbiased prediction (BLUP) selection. Simulation results show that optimal selection achieved greater selection response than either standard QTL or conventional BLUP selections. The influence of population structure on optimal selection was significant. Optimal QTL selection and standard QTL selection were more favorable in a population with overlapping generations than discrete generations, and obtained more benefits relative to conventional BLUP selection in a population with overlapping generations. Optimal QTL selection relative to conventional BLUP selection is also more favorable following increase of genetic contribution of two-year-old boars and sows in a population with overlapping generations.     

Optimal selection on two quantitative trait loci with linkage

A mathematical approach to optimize selection on multiple quantitative trait loci (QTL) and an estimate of residual polygenic effects was applied to selection on two linked or unlinked additive QTL. Strategies to maximize total or cumulative discounted response over ten generations were compared to standard QTL selection on the sum of breeding values for the QTL and an estimated breeding value for polygenes, and to phenotypic selection. Optimal selection resulted in greater response to selection than standard QTL or phenotypic selection. Tight linkage between the QTL (recombination rate 0.05) resulted in a slightly lower response for standard QTL and phenotypic selection but in a greater response for optimal selection. Optimal selection capitalized on linkage by emphasizing selection on favorable haplotypes. When the objective was to maximize total response after ten generations and QTL were unlinked, optimal selection increased QTL frequencies to fixation in a near linear manner. When starting frequencies were equal for the two QTL, equal emphasis was given to each QTL, regardless of the difference in effects of the QTL and regardless of the linkage, but the emphasis given to each of the two QTL was not additive. These results demonstrate the ability of optimal selection to capitalize on information on the complex genetic basis of quantitative traits that is forthcoming.     

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.     

Factors Affecting Accuracy From Genomic Selection in Populations Derived From Multiple Inbred Lines: A Barley Case Study

We compared the accuracies of four genomic-selection prediction methods as affected by marker density, level of linkage disequilibrium (LD), quantitative trait locus (QTL) number, sample size, and level of replication in populations generated from multiple inbred lines. Marker data on 42 two-row spring barley inbred lines were used to simulate high and low LD populations from multiple inbred line crosses: the first included many small full-sib families and the second was derived from five generations of random mating. True breeding values (TBV) were simulated on the basis of 20 or 80 additive QTL. Methods used to derive genomic estimated breeding values (GEBV) were random regression best linear unbiased prediction (RR–BLUP), Bayes-B, a Bayesian shrinkage regression method, and BLUP from a mixed model analysis using a relationship matrix calculated from marker data. Using the best methods, accuracies of GEBV were comparable to accuracies from phenotype for predicting TBV without requiring the time and expense of field evaluation. We identified a trade-off between a method's ability to capture marker-QTL LD vs. marker-based relatedness of individuals. The Bayesian shrinkage regression method primarily captured LD, the BLUP methods captured relationships, while Bayes-B captured both. Under most of the study scenarios, mixed-model analysis using a marker-derived relationship matrix (BLUP) was more accurate than methods that directly estimated marker effects, suggesting that relationship information was more valuable than LD information. When markers were in strong LD with large-effect QTL, or when predictions were made on individuals several generations removed from the training data set, however, the ranking of method performance was reversed and BLUP had the lowest accuracy.     

A method to optimize selection on multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.     

Marker assisted selection for the improvement of two antagonistic traits under mixed inheritance

A Monte Carlo simulation was used to investigate the potential of Marker Assisted Selection (MAS) in a multiple-trait situation. Only additive effects were considered. The base population was assumed to be in linkage equilibrium and, next, the population was managed over 15 discrete generations, 10 males and 50 females were chosen out of the 100 candidates of each sex. Performance for two traits was simulated with an overall heritability of a given trait equal to 0.25 or 0.10 and the overall genetic correlation between traits was generally equal to -0.4 except in one case where it was equal to 0. The model involved one biallelic QTL, accounting for 10 or 20% of the genetic variance of a given trait, plus polygenes. Initial allelic frequencies at the QTL were generally equal to 0.5 but in one case were equal to 0.1 and 0.9. A marker with 120 different alleles in the 60 founder parents was simulated in the vicinity of the QTL. Two values of the recombination rate between these two loci were considered, 0.10 and 0.02. The genetic evaluation was based on a multiple-trait BLUP animal model, accounting (MAS) or not (conventional BLUP) for marker information. Two sets of simulations were run: (1) a "missing data"case, with males having no record for one of the traits, and (2) a "secondary trait"case, with one trait having a weight in the aggregate genotype 4 times less than the other trait and the QTL acting only on this secondary trait. In the first set, evaluation methods were found to mainly affect the accuracy of overall genetic values prediction for the trait with missing data. In comparison with BLUP, MAS led to an extra overall genetic response for the trait with missing data, which was strongly penalised under the conventional BLUP, and to a deficit in response for the other trait. This more balanced evolution of the two traits was obtained, however, at the expense of the long-term overall cumulated response for the aggregate genotype, which was 1 to 2.5% lower than the one obtained under the conventional BLUP. In the second set of simulation, in the case of low initial frequency (0.1) of the QTL allele favourable to the secondary trait, MAS was found to be substantially more efficient to avoid losing this allele than BLUP only when the QTL had a large effect and the marker was close. More benefits should be expected from MAS with more specific applications, such as early selection of animals, or by applying dynamic procedures i.e. letting the respective weights to QTL and polygenic values in the selection criterion vary across generation.     

Optimization of a crossing system using mate selection

A simple model based on one single identified quantitative trait locus (QTL) in a two-way crossing system was used to demonstrate the power of mate selection algorithms as a natural means of opportunistic line development for optimization of crossbreeding programs over multiple generations. Mate selection automatically invokes divergent selection in two parental lines for an over-dominant QTL and increased frequency of the favorable allele toward fixation in the sire-line for a fully-dominant QTL. It was concluded that an optimal strategy of line development could be found by mate selection algorithms for a given set of parameters such as genetic model of QTL, breeding objective and initial frequency of the favorable allele in the base populations, etc. The same framework could be used in other scenarios, such as programs involving crossing to exploit breed effects and heterosis. In contrast to classical index selection, this approach to mate selection can optimize long-term responses.     

Genomic selection for marker-assisted improvement in line crosses

Efficiency of genomic selection with low-cost genotyping in a composite line from a cross between inbred lines was evaluated for a trait with heritability 0.10 or 0.25 using a low-density marker map. With genomic selection, selection was on the sum of estimates of effects of all marker intervals across the genome, fitted either as fixed (fixed GS) or random (random GS) effects. Reponses to selection over 10 generations, starting from the F₂, were compared with standard BLUP selection. Estimates of variance for each interval were assumed independent and equal. Both GS strategies outperformed BLUP selection, especially in initial generations. Random GS outperformed fixed GS in early generations and performed slightly better than fixed GS in later generations. Random GS gave higher genetic gain when the number of marker intervals was greater (180 or 10 cM intervals), whereas fixed GS gave higher genetic gain when the number of marker intervals was low (90 or 20 cM). Including interactions between generation and marker scores in the model resulted in lower genetic gains than models without interactions. When phenotypes were available only in the F₂ for GS, treating marker scores as fixed effects led to considerably lower genetic gain than random GS. Benefits of GS over standard BLUP were lower with high heritability. Genomic selection resulted in greater response than MAS based on only significant marker intervals (standard MAS) by increasing the frequency of QTL with both large and small effects. The efficiency of genomic selection over standard MAS depends on stringency of the threshold used for QTL detection. In conclusion, genomic selection can be effective in composite lines using a sparse marker map.     

Allele frequency changes due to hitch-hiking in genomic selection programs

Background

Genomic selection makes it possible to reduce pedigree-based inbreeding over best linear unbiased prediction (BLUP) by increasing emphasis on own rather than family information. However, pedigree inbreeding might not accurately reflect loss of genetic variation and the true level of inbreeding due to changes in allele frequencies and hitch-hiking. This study aimed at understanding the impact of using long-term genomic selection on changes in allele frequencies, genetic variation and level of inbreeding.

Methods

Selection was performed in simulated scenarios with a population of 400 animals for 25 consecutive generations. Six genetic models were considered with different heritabilities and numbers of QTL (quantitative trait loci) affecting the trait. Four selection criteria were used, including selection on own phenotype and on estimated breeding values (EBV) derived using phenotype-BLUP, genomic BLUP and Bayesian Lasso. Changes in allele frequencies at QTL, markers and linked neutral loci were investigated for the different selection criteria and different scenarios, along with the loss of favourable alleles and the rate of inbreeding measured by pedigree and runs of homozygosity.

Results

For each selection criterion, hitch-hiking in the vicinity of the QTL appeared more extensive when accuracy of selection was higher and the number of QTL was lower. When inbreeding was measured by pedigree information, selection on genomic BLUP EBV resulted in lower levels of inbreeding than selection on phenotype BLUP EBV, but this did not always apply when inbreeding was measured by runs of homozygosity. Compared to genomic BLUP, selection on EBV from Bayesian Lasso led to less genetic drift, reduced loss of favourable alleles and more effectively controlled the rate of both pedigree and genomic inbreeding in all simulated scenarios. In addition, selection on EBV from Bayesian Lasso showed a higher selection differential for mendelian sampling terms than selection on genomic BLUP EBV.

Conclusions

Neutral variation can be shaped to a great extent by the hitch-hiking effects associated with selection, rather than just by genetic drift. When implementing long-term genomic selection, strategies for genomic control of inbreeding are essential, due to a considerable hitch-hiking effect, regardless of the method that is used for prediction of EBV.