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.     

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.     

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.     

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.     

世代重叠群体多个QTL最优化选择

一种扩展的方法能够在一个世代重叠的群体内对多个数量性状位点选择进行最优化,目的是为了在整个计划期内获得最大的累积反应加权和。该模型允许群体有多个性别年龄组、公母畜间有不同的年龄组数、各年龄组有不同的遗传贡献。整个最优化问题被描述成一个多阶段系统优化控制问题,通过一个向前和向后的迭代循环解决。用一个世代重叠的实际育种猪群的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。模拟结果表明,优化选择要优于标准QTL选择和常规BLUP选择。群体结构对优化选择的影响比较明显。优化QTL选择和标准QTL选择在世代重叠的群体内比在世代离散的群体内的选择优势更明显,相对于常规BLUP选择,能够获得更大的选择优势。在世代重叠群体内随着2岁公畜遗传贡献的增大,优化选择相对于常规BLUP选择的优势越明显。     

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。     

Long-term selection for 8-week body weight in chickens — direct and correlated responses

Summary A bidirectional selection experiment for 8-week body weight in chickens was conducted. In addition to 27 generations of selection, random samples were chosen from each selected line in generations 6, 13, 19 and 26 to initiate lines in which selection was relaxed. Genetic change was evident in the selected high-weight line through the first 75% of the study after which response in the direction opposing selection occurred. Selection for low body weight resulted in considerable reduction in body size, particularly in the last quarter of the study. Correlated responses evaluated were body weight at several ages, conformation, age at onset of lay, various reproductive and egg quality traits and ratio (female: male) of some traits. Data from lines where selection was relaxed indicated that natural selection opposed artificial selection with the effects greater in later generations.     

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.     

The genetic basis and evolution of acoustic mate recognition signals in a Ribautodelphax planthopper (Homoptera,Delphacidae) 1. The female call

Both sexes of the planthopper Ribautodelphax imitans produce species specific acoustic signals. Earlier experiments have shown that isolation between Ribautodelphax species in captivity is at least partly due to male preference for calls of conspecific females. The genetic basis of the female call is studied by bi-directional artificial selection for large and small interpulse intervals (IPI). This resulted in non-overlapping distributions of IPI after only five generations. The mean of eight realized heritability estimates over five generations was above 80%; estimates over ten generations were generally well above 50%. The character is shown to be of a polygenic nature, determined by at least 6 segregating genetic factors. The other features of the female call, strophe duration, and modulation of pulse repetition frequency within the strophe, showed significantly correlated responses. Sexual isolation tests after 10 generations of selection revealed significant symmetrical assortative mating, but coselected males did not exhibit a significant preference for playback calls of females from their own selection line. In view of the high heritability for the call character, and the considerable ecological isolation among Ribautodelphax species, it seems unlikely that the female call differentiated as an adaptation to prevent hybridization (reinforcement). More likely, call and call preference were shaped by sexual selection during allopatry, and may have (had) incidentally an effect in species isolation.     

An experimental comparison of selection alternatives to plateaued response

Three alternative selection methods for extending selection limits or breaking response plateaus were compared over ten generations in a replicated model experiment using two unrelated populations of Drosophila melanogaster that no longer responded to purebred selection for high egg number, a heterotic polygenic trait. The three methods were: (1) reciprocal recurrent selection (RRS) with selection within each of the plateaued populations based solely on crossbred performance, (2) a modification of reciprocal recurrent selection (MRRS) with selection within each population based on both purebred and crossbred performance, and (3) purebred selection within a new synthetic population formed by crossing the two plateaued populations.--Conflicting estimates were obtained for heritability of purebred egg number in each of the plateaued populations. The realized heritability values and estimates from diallel analyses indicated an absence of additive genetic variation for both populations; however, estimates from conventional intraclass correlation methods were positive. The diallel analyses revealed significant amounts of nonadditive gene effects for purebred egg number in each population, while the significant gene effects for crossbred egg numbers were additive. Estimates of the genetic correlation between purebred and crossbred egg number were negative (-0.85 +/- 0.68 and -0.32 +/- 0.25) for the two base populations.--All three alternatives to continued purebred selection gave significant responses, with the average gain per generation from MRRS being significantly superior to the other two methods. Observed purebred and crossbred responses under RRS were in agreement with quantitative genetic theory. Such was not the case for MRRS, which suggested the possibility of major gene segregation.--Evidence supporting a negative genetic correlation between purebred and crossbred performance and the possibility of overdominance is presented and discussed.     

Comparison of Different Foreground and Background Selection Methods in Marker-Assisted Introgression

Three different methods for foreground selection and four different methods for background selection were compared in terms of the efficiency of marker-assisted introgression of a QTL allele from a donor line into a recipient line and also in terms of the recovery of the recipient genetic background. The results showed that for the introgression of a donor QTL allele, a direct selection on the QTL itself (when the QTL genotype can be directly identified) would ensure that the allele is successfully introgressed and rapidly fixed. However, when a direct selection on the QTL is not feasible, an indirect selection using two closely linked flanking markers can be used, which also shows similar results. For the recovery of the recipient genetic background, if the goal is to recover the whole genetic background of the recipient, genomic similarity selection or marker index selection would be the best choice: Only three generations of backcrosses were required to recover over 98% of the recipient genome. Whereas if the goal is to recover certain background traits of the recipient, MBLUP selection would give the best results, which achieved not only over 99% recovery of the recipient QTL alleles for the background traits after three generations of backcrosses, but also showed the best genetic improvement of these traits.     

标记辅助导入中不同前景和背景选择方法的比较

标记辅助导入是分子遗传信息应用于动物育种的一个重要方面,其目的是在标记信息的辅助下将一个品种（供体）中的一个或多个优良基因导入另一个品种（受体）,同时还要尽可能地保持受体群体原有的遗传背景。标记辅助导入的过程包括3个阶段,第一阶段是杂交,即供体与受体杂交产生F1代个体,第二阶段是回交,即F1个体以及后续各个世代的后代个体重复地与受体回交,以使受体的遗传背景得到恢复,第三阶段是横交,即重复回交后得到的个体彼此问交配,以便获得供体基因的纯合个体,使该基因在群体中固定。在回交和横交阶段,都要对参与交配的个体进行选择。在选择中,要分别进行前景选择和背景选择,前景选择是对供体基因的选择,选择携带有供体基因个体参加配种,从而使该基因在回交过程中不会丢失,并在横交过程中能尽快固定,背景选择是对受体遗传背景的选择,选择那些含有受体基因组比例较高的个体参加配种,从而加快恢复受体遗传背景的速度。本研究通过计算机模拟对不同的前景选择方法和不同的背景选择方法进行了比较。前景选择方法包括对受体基因的直接选择（假设该基冈可以直接测定）、利用单个连锁标记的间接选择和利用两侧标记的间接选择3种,背景选择方法包括随机选择、基因组相似性选择、指数选择和标记辅助BLUP（MBLUP）选择4种。研究结果表明,对于前景选择来说,对供体基因的直接选择能保证该基因在回交的各个世代中保持一个稳定的频率（0．25）并在横交阶段迅速固定（2个世代）,用两侧标记的间接选择也能得到类似的结果,但如果仅利用单个连锁标记进行选择,则会导致供体基因的频率在回交阶段中有所下降,并在横交阶段不能被固定。对于背景选择来说,如果最终的目的是要完全恢复受体的遗传背景,基因组相似性选择或标记指数选择是最好的选择方法,它们可使受体的遗传背景在回交3个世代后就恢复到98％以上,而随机选择或MBLUP选择需要至少5个世代的回交才能达到这个水平。但如果最终的目的只是要恢复受体的某些优良性状,则MBLUP选择是值得推荐的方法,它可使影响这些性状的受体基因频率在回交3个世代后就达到99％以上,而且还能在整个基因导入过程中给这些性状带来最大的遗传进展。虽然用标记指数选择也有相似的结果,但与之相比,MBLUP的成本要低得多,更具有实际可行性。     

长期人工选择对群体遗传结构的影响——一项计算机模拟研究 Ⅱ.长期选择对群体遗传方差的作用

本文给出了显性与超显性模型下加性方差的分剖公式,为研究选择作用下基因间关系的变化提供了有力的方法。并模拟研究了群体大小、连锁强度与遗传力水平对遗传方差变化的影响。小群体中遗传方差在世代间波动很大;大群体中则稳定下降、波动较小。选择作用下平衡加性方差下降很快,特别是高遗传力性状。紧密连锁在小群体中一方面降低选择反应,一方面维持了更多的加性方差,从而使得预测长期选择反应甚为困难。     

Genomic selection of purebreds for crossbred performance

Background

One of the main limitations of many livestock breeding programs is that selection is in pure breeds housed in high-health environments but the aim is to improve crossbred performance under field conditions. Genomic selection (GS) using high-density genotyping could be used to address this. However in crossbred populations, 1) effects of SNPs may be breed specific, and 2) linkage disequilibrium may not be restricted to markers that are tightly linked to the QTL. In this study we apply GS to select for commercial crossbred performance and compare a model with breed-specific effects of SNP alleles (BSAM) to a model where SNP effects are assumed the same across breeds (ASGM). The impact of breed relatedness (generations since separation), size of the population used for training, and marker density were evaluated. Trait phenotype was controlled by 30 QTL and had a heritability of 0.30 for crossbred individuals. A Bayesian method (Bayes-B) was used to estimate the SNP effects in the crossbred training population and the accuracy of resulting GS breeding values for commercial crossbred performance was validated in the purebred population.

Results

Results demonstrate that crossbred data can be used to evaluate purebreds for commercial crossbred performance. Accuracies based on crossbred data were generally not much lower than accuracies based on pure breed data and almost identical when the breeds crossed were closely related breeds. The accuracy of both models (ASGM and BSAM) increased with marker density and size of the training data. Accuracies of both models also tended to decrease with increasing distance between breeds. However the effect of marker density, training data size and distance between breeds differed between the two models. BSAM only performed better than AGSM when the number of markers was small (500), the number of records used for training was large (4000), and when breeds were distantly related or unrelated.

Conclusion

In conclusion, GS can be conducted in crossbred population and models that fit breed-specific effects of SNP alleles may not be necessary, especially with high marker density. This opens great opportunities for genetic improvement of purebreds for performance of their crossbred descendents in the field, without the need to track pedigrees through the system.     

Evaluation of marker-assisted selection through computer simulation

Computer simulation was used to evaluate responses to marker-assisted selection (MAS) and to compare MAS responses with those typical of phenotypic recurrent selection (PRS) in an allogamous annual crop species such as maize (Zea mays L.). Relative to PRS, MAS produced rapid responses early in the selection process; however, the rate of these responses diminished greatly within three to five cycles. The gains from MAS ranged from 44.7 to 99.5% of the maximum potential, depending on the genetic model considered. Linkage distance between markers and quantitative trait loci (QTLs) was the factor which most limited the responses from MAS. When averaged across all models considered, flanking QTLs within two marker loci produced 38% more gain than did selection based on single markers if markers were loosely-linked to a QTL (20% recombination). Flanking markers were much less advantageous when markers were closely-linked to a QTL (5% recombination), producing an advantage over single markers of only 11%. Markers were most effective in fully exploiting the genetic potential when fewer QTLs controlled the trait. Large QTL numbers exacerbated the problem of marker-QTL recombination by requiring more generations for fixation. In annual crop species, MAS may offer a primary advantage of enabling two selection cycles per year versus the 2 years per cycle required by most PRS schemes for the evaluation of testcross progeny. MAS thus appears to allow very rapid gains for the first 2–3 years of recurrent selection, after which time conventional methods might replace MAS to achieve further responses.Publication number 19, 330 of the Minnesota Agricultural Experiment Station     

RESPONSES OF FLORAL TRAITS TO SELECTION ON PRIMARY SEXUAL INVESTMENT IN SPERGULARIA MARINA: THE BATTLE BETWEEN THE SEXES

Two widespread assumptions underlie theoretical models of the evolution of sex allocation in hermaphroditic species: (1) resource allocations to male and female function are heritable; and (2) there is an intrinsic, genetically based negative correlation between male and female reproductive function. These assumptions have not been adequately tested in wild species, although a few studies have detected either genetic variation in pollen and ovule production per flower or evidence of trade-offs between male and female investment at the whole plant level. It may also be argued, however, that in highly autogamous, perfect-flowered plant taxa that exhibit genetic variation in gamete production, strong stabilizing selection for an efficient pollen:ovule ratio should result in a positive correlation among genotypes with respect to mean ovule and mean pollen production per flower. Here we report the results of a three-generation artificial selection experiment conducted on a greenhouse population of the autogamous annual plant Spergularia marina. Starting with a base population of 1200 individuals, we conducted intense mass selection for two generations, creating four selected lines (high and low ovule production per flower; high and low anther production per flower) and a control line. By examining the direct and correlated responses of several floral traits to selection on gamete production per flower, we evaluated the expectations that primary sexual investment would exhibit heritable variation and that resource-sharing, variation in resource-garnering ability, or developmental constraints mold the genetic correlations expressed among floral organs. The observed direct and correlated responses to selection on male and female gamete production revealed significant heritabilities of both ovule and anther production per flower and a significant negative genetic correlation between them. When plants were selected for increased ovules per flower over two generations, ovule production increased and anther production declined relative to the control line. Among plants selected for decreased anthers per flower, we observed a decline in anther production and an increase in ovule production relative to the control line. In contrast, the lines selected for low ovules per flower and for high anthers per flower exhibited no evidence for significant genetic correlations between male and female primary investment. Correlated responses to selection also indicate a genetically based negative correlation between the production of normal versus developmentally abnormal anthers (staminoid organs); a positive correlation between the production of ovules versus staminoid organs; and a positive correlation between the production of anthers and petals. The negative relationship between male versus female primary investment supports classical sex allocation theory, although the asymmetrical correlated responses to selection indicate that this relationship is not always expressed.     

Sexually antagonistic evolution caused by male–male competition in the pistil

Although sexual selection and sexual conflict are important evolutionary forces in animals, their significance in plants is uncertain. In hermaphroditic organisms, such as many plants, sexual conflict may occur both between mating partners (interlocus conflict) and between male and female sex roles within an individual (intralocus conflict). We performed experimental evolution, involving lines that were crossed with either one or two pollen donors (monogamous or polyandrous lines), in the hermaphroditic plant (Collinsia heterophylla) where early fertilizations are associated with female fitness costs (reduced seed set). Artificial polyandry for four generations resulted in enhanced pollen performance and increased female fitness costs compared to the monogamous and source (starting material) lines. Female fitness was also reduced in the monogamous line, indicating a possible trade‐off between sex roles, resulting from early pollination. We performed a second experiment to investigate a potential harming effect of pollen performance on seed set. We found that high siring success of early arriving pollen competing with later‐arriving pollen was associated with high female fitness costs, consistent with an interlocus sexual conflict. Our study provides evidence for the importance of sexual selection in shaping evolution of plant reproductive strategies, but also pinpoints the complexity of sexual conflict in hermaphroditic species.     

Genetic architecture of a selection response in Arabidopsis thaliana

Quantitative trait locus (QTL) mapping has become an established and effective method for studying the genetic architecture of complex traits. In this report, we use a QTL mapping approach in combination with data from a large selection experiment in Arabidopsis thaliana to explore a response to selection of experimental populations with differentiated genetic backgrounds. Experimental populations with genetic backgrounds derived from ecotypes Landsberg and Niederzenz were exposed to multiple generations of fertility and viability selection. This selection resulted in phenotypic shifts in a number of life-history and fitness-related characters including early development time, flowering time, dry biomass, longevity, and fruit production. Quantitative trait loci were mapped for these traits and their positions were compared to previously characterized allele frequency changes in the experimental populations (Ungerer et al. 2003). Quantitative trait locus positions largely colocalized with genomic regions under strong and consistent selection in populations with differentiated genetic backgrounds, suggesting that alleles for these traits were selected similarly in differentiated genetic backgrounds. However, one QTL region exhibited a more variable response; being positively selected on one genetic background but apparently neutral in another. This study demonstrates how QTL mapping approaches can be combined with map-based population genetic data to study how selection acts on standing genetic variation in populations.     

THE QUANTITATIVE GENETICS OF SEXUAL DIMORPHISM IN SILENE LATIFOLIA (CARYOPHYLLACEAE). II. RESPONSE TO SEX-SPECIFIC SELECTION

A well-established theoretical relationship exists between genetic correlations between the sexes and the dynamics of response to sex-specific selection. The present study investigates the response to sex-specific selection for two sexually dimorphic traits that have been documented to be genetically variable, calyx diameter and flower number, in Silene latifolia. Following the establishment of a base generation with a known genetic background, selection lines were established and two generations of sex-specific selection were imposed. Calyx diameter responded directly to sex-specific selection, and the positive genetic correlation between the sexes was reflected in correlated responses in the sex that was not the basis for selection within a particular line. Flower number showed a more erratic response to sex-specific selection in that selection in some lines was initially in the wrong direction, that is, selection for a decrease in flower number resulted in an increase. These erratic responses were attributable to genotype-environment interaction as reflected in significant heteroscedasticity in variance among families. Correlated responses to selection in the sex that was not the immediate basis for selection indicated the possible existence of a negative genetic correlation between the sexes for this trait. These results test for the first time the impact of genetic correlations between the sexes on the evolutionary dynamics of sexually dimorphic traits in a plant species.     

长期人工选择对群体遗传结构的影响——一项计算机模拟研究 Ⅰ.模拟模型与长期选择反应

运用数字计算机模拟研究了长期人工选择的反应。考虑了不同的基因作用模型(加性、显性与超显性)、群体含量(小群体N_f=Nm=10,Ne=20;大群体N_f=Nm=100,Ne=200)、遗传力水平以及位点间连锁强度等因素共54个组合,270个群体各49代的选择反应。结果表明,对于三种基因作用模型,只有强烈的连锁(相邻位点之间交换率为r=0.01)在小群体中对选择反应有显著影响,它可以阻碍有利基因的固定,加速它们的丢失,从而降低选择反应。中等强度的连锁(r=0.1)或大群体中的紧密连锁都没有显著的作用。大群体中的选择反应要明显地高于小群体中的,特别是遗传力低的性状。本文还讨论了不同选择系杂交以获致进一步进展的问题,讨论了长期选择理论研究结果与实际模拟的偏差。