Prediction of accuracy of estimated Mendelian sampling terms

This study describes a general framework for predicting the accuracy of Mendelian sampling terms when truncation selection is applied on best linear unbiased prediction (BLUP) estimated breeding values. A selection index approach is followed. The pseudo‐BLUP index is extended to include terms related to the Mendelian sampling term. Predicted accuracies are compared with those obtained through stochastic computer simulation. Good predictions for the accuracy of the Mendelian sampling term were obtained both at selection time and at convergence of long‐term contributions of selected candidates for a range of heritabilities and population structures. The prediction approach developed provides a key tool for obtaining predictions of genetic response from quadratic optimization that maximizes the rate of genetic progress while restricting the rate of inbreeding.     

Optimum contribution selection using traditional best linear unbiased prediction and genomic breeding values in aquaculture breeding schemes

The aim of this study was to compare genetic gain for a traditional aquaculture sib breeding scheme with breeding values based on phenotypic data (TBLUP) with a breeding scheme with genome-wide (GW) breeding values. Both breeding schemes were closed nuclei with discrete generations modeled by stochastic simulation. Optimum contribution selection was applied to restrict pedigree-based inbreeding to either 0.5 or 1% per generation. There were 1,000 selection candidates and a sib test group of either 4,000 or 8,000 fish. The number of selected dams and sires to create full sib families in each generation was determined from the optimum contribution selection method. True breeding values for a trait were simulated by summing the number of each QTL allele and the true effect of each of the 1,000 simulated QTL. Breeding values in TBLUP were predicted from phenotypic and pedigree information, whereas genomic breeding values were computed from genetic markers whose effects were estimated using a genomic BLUP model. In generation 5, genetic gain was 70 and 74% greater for the GW scheme than for the TBLUP scheme for inbreeding rates of 0.5 and 1%. The reduction in genetic variance was, however, greater for the GW scheme than for the TBLUP scheme due to fixation of some QTL. As expected, accuracy of selection increased with increasing heritability (e.g., from 0.77 with a heritability of 0.2 to 0.87 with a heritability of 0.6 for GW, and from 0.53 and 0.58 for TBLUP in generation 5 with sib information only). When the trait was measured on the selection candidate compared with only on sibs and the heritability was 0.4, accuracy increased from 0.55 to 0.69 for TBLUP and from 0.83 to 0.86 for GW. The number of selected sires to get the desired rate of inbreeding was in general less in GW than in TBLUP and was 33 for GW and 83 for TBLUP (rate of inbreeding 1% and heritability 0.4). With truncation selection, genetic gain for the scheme with GW breeding values was nearly twice as large as a scheme with traditional BLUP breeding values. The results indicate that the benefits of applying GW breeding values compared with TBLUP are reduced when contributions are optimized. In conclusion, genetic gain in aquaculture breeding schemes with optimized contributions can increase by as much as 81% by applying genome-wide breeding values compared with traditional BLUP breeding values.     

Impacts of genotyping strategies on long‐term genetic response in genomic selection

The present study investigated the effects of the choices of animals of reference populations on long‐term responses to genomic selection. Simulated populations comprised 300 individuals and 10 generations of selection practiced for a trait with heritability of 0.1, 0.3 or 0.5. Thirty individuals were randomly selected in the first five generations and selected by estimated breeding values from best linear unbiased prediction (BLUP) and genomic BLUP in the subsequent five generations. The reference populations comprise all animals for all generations (scenario 1), all animals for 6‐10 generations (scenario 2) and 2‐6 generations (scenario 3), and half of the animals for all generations (scenario 4). For all heritability levels, the genetic gains in generation 10 were similar in scenarios 1 and 2. Among scenarios 2 to 4, the highest genetic gains were obtained in scenario 2, with heritabilities of 0.1 and 0.3 as well as scenario 4 with heritability of 0.5. The inbreeding coefficients in scenarios 1, 2 and 4 were lower than those in BLUP, especially within cases with low heritability. These results indicate an appropriate choice of reference population can improve genetic gain and restrict inbreeding even when the reference population size is limited.     

Inbreeding in genome-wide selection

Traditional selection methods, such as sib and best linear unbiased prediction (BLUP) selection, which increased genetic gain by increasing accuracy of evaluation have also led to an increased rate of inbreeding per generation (DeltaFG). This is not necessarily the case with genome-wide selection, which also increases genetic gain by increasing accuracy. This paper explains why genome-wide selection reduces DeltaFG when compared with sib and BLUP selection. Genome-wide selection achieves high accuracies of estimated breeding values through better prediction of the Mendelian sampling term component of breeding values. This increases differentiation between sibs and reduces coselection of sibs and DeltaFG. The high accuracy of genome-wide selection is expected to reduce the between family variance and reweigh the emphasis of estimated breeding values of individuals towards the Mendelian sampling term. Moreover, estimation induced intraclass correlations of sibs are expected to be lower in genome-wide selection leading to a further decrease of coselection of sibs when compared with BLUP. Genome-wide prediction of breeding values, therefore, enables increased genetic gain while at the same time reducing DeltaFG when compared with sib and BLUP selection.     

The impact of using old germplasm on genetic merit and diversity—A cattle breed case study

Artificial selection and high genetic gains in livestock breeds led to a loss of genetic diversity. Current genetic diversity conservation actions focus on long‐term maintenance of breeds under selection. Gene banks play a role in such actions by storing genetic materials for future use and the recent development of genomic information is facilitating characterization of gene bank material for better use. Using the Meuse‐Rhine‐Issel Dutch cattle breed as a case study, we inferred the potential role of germplasm of old individuals for genetic diversity conservation of the current population. First, we described the evolution of genetic merit and diversity over time and then we applied the optimal contribution (OC) strategy to select individuals for maximizing genetic diversity, or maximizing genetic merit while constraining loss of genetic diversity. In the past decades, genetic merit increased while genetic diversity decreased. Genetic merit and diversity were both higher in an OC scenario restricting the rate of inbreeding when old individuals were considered for selection, compared to considering only animals from the current population. Thus, our study shows that gene bank material, in the form of old individuals, has the potential to support long‐term maintenance and selection of breeds.     

公母畜间有不同的年龄组数目条件下控制近交最大化选择反应

一种扩展的动态选择规则能够在公母畜间有不同的年龄组数目的世代重叠群体内约束年近交速率为一个预定义值，逐年最大化遗传反应。该规则考虑在世代重叠群体中按性别一年龄分组，通过限制父母亲群体性别一年龄组的平均加性遗传相关的增加，从而限制新生后代平均近交系数的增加。动态选择程序通过输入候选个体的BLUP估计育种值、所有个体的加性遗传相关矩阵和所有性别一年龄组的长期遗传贡献，给出最适宜的选留个体数及其每个选留个体最适宜的后代数。猪核心群随机模拟结果显示该动态选择规则能够获得预定义的近交速率。在相同的近交速率条件下，动态选择比截断选择获得高达10％的更多年遗传进展。     

Approaches to the management of inbreeding and relationship in the German Holstein dairy cattle population

The aim of this study was to estimate the current level of inbreeding in the German cow population and for bull dams born in Germany, to find out sires most related to different subsets of their breed and to demonstrate the negative effect of homozygosity in the case of complex vertebral malformation (CVM). Further on, the application of optimum genetic contribution (OGC) theory for the selection of bull dams and bull sires in different breeding scenarios was investigated. Levels of inbreeding for the cow population were in a low range from 0.97% to 1.70% evaluating birth years from 1996 to 1999 in a total dataset of 244,427 registered Holstein cows. The inbreeding coefficient of 8030 bull dams was much higher, i.e. 3.71%, for the birth year 1999. Increases in inbreeding of 0.19% per year indicated an effective population size of only 52 animals. Individual sires like R.O.R.A. Elevation and Hannoverhill Starbuck were highly related to potential bull dams with coefficients of relationship of 13.4% and 12.9%, respectively, whereas P.F. Arlinda Chief (16.3%) and Carlin-M Ivanhoe Bell (16.1%) were highest related to the best available AI sires. Coefficients of relationship were calculated by classes of estimated breeding values (EBV) for production traits showing highest values above 7% in the two highest EBV-classes. The optimum genetic contribution theory using official EBVs and approximative, for zero inbreeding corrected EBVs, was applied for elite matings in a breeding program embracing 30 young bulls per year to find the optimal allocations of bull sires and bull dams. Compared with the actual breeding program applied in practice, OGC-theory has the potential to increase genetic gain under the same constraint for the increase of average relationship by 13.1%. A more relaxed constraint on increase in inbreeding allowed even higher expected genetic gain whereas a more severe constraint resulted in more equal contributions of selected bull sires. Contributions from 21 selected bull sires and 30 selected bull dams for a scenario at 5% constrained relationship were used to develop a specific mating plan to minimise inbreeding in the short term in the following generation applying a simulated annealing algorithm. The expected coefficient of inbreeding of progeny was 66.3% less then the one resulting from random mating. Mating programs can address inbreeding concerns on the farm, at least in the short term, but long-term control of inbreeding in a dairy population requires consideration of relationships between young bulls entering AI progeny test programs. Significantly better EBVs of CVM-free bulls compared with CVM-carriers for the paternal fertility justify the application of OGC for elite matings.     

北京迪卡猪核心群育种方案优化研究——群体规模及选择强度

应用确定性模型考察群体规模对北京迪卡猪核心群公猪系育种成本、育种产出、育种效益及近交系数的影响。猪规模为６０、８０、１００、１２０四个水平，公猪头猪为６、８、１０、１２四个水平。种畜的选择是基于多性状综合选择指数进行，应用基因流动法计算育种产出。结果表明，增加母猪规模，有利于提高公猪选择强度，从而加大育种产出，同时单位母猪育种成本下降，促进了育种效益的改善；公猪头数越少，公猪选择强度越大，育种进展     

Reducing inbreeding rates with a breeding circle: Theory and practice in Veluws Heideschaap

Breeding circles allow genetic management in closed populations without pedigrees. In a breeding circle, breeding is split over sub‐populations. Each sub‐population receives breeding males from a single sub‐population and supplies breeding males to one other sub‐population. Donor‐recipient combinations of sub‐populations remain the same over time. Here, we derive inbreeding levels both mathematically and by computer simulation and compare them to actual inbreeding rates derived from DNA information in a real sheep population. In Veluws Heideschaap, a breeding circle has been in operation for over 30 years. Mathematically, starting with inbreeding levels and kinships set to zero, inbreeding rates per generation (ΔF) initially were 0.29%–0.47% within flocks but later converged to 0.18% in all flocks. When, more realistically, inbreeding levels at the start were high and kinship between flocks low, inbreeding levels immediately dropped to the kinship levels between flocks and rates more gradually converged to 0.18%. In computer simulations with overlapping generations, inbreeding levels and rates followed the same pattern, but converged to a lower ΔF of 0.12%. ΔF was determined in the real population with a 12 K SNP chip in recent generations. ΔF in the real population was 0.29%, based on markers to 0.41% per generation based on heterozygosity levels. This is two to three times the theoretically derived values. These increased rates in the real population are probably due to selection and/or the presence of dominant rams siring a disproportionate number of offspring. When these were simulated, ΔF agreed better: 0.35% for selection, 0.38% for dominant rams and 0.67% for both together. The realized inbreeding rates are a warning that in a real population inbreeding rates in a breeding circle can be higher than theoretically expected due to selection and dominant rams. Without a breeding circle, however, inbreeding rates would have been even higher.     

Optimizing female allocation to reproductive technologies considering merit,inbreeding and cost in nucleus breeding programmes with genomic selection

Female reproductive technologies such as multiple ovulation and embryo transfer (MOET) and juvenile in vitro fertilization and embryo transfer (JIVET) have been shown to accelerate genetic gain by increasing selection intensity and decreasing generation interval. Genomic selection (GS) increases the accuracy of selection of young candidates which can further accelerate genetic gain. Optimal contribution selection (OCS) is an effective method of keeping the rate of inbreeding at a sustainable level while increasing genetic merit. OCS could also be used to selectively and optimally allocate reproductive technologies in mate selection while accounting for their cost. This study uses stochastic simulation to simulate breeding programmes that use a combination of artificial insemination (AI) or natural mating (N), MOET and JIVET with GS. OCS was used to restrict inbreeding to 1.0% increase per generation and also to optimize use of reproductive technologies, considering their effect on genetic gain as well as their cost. Two Australian sheep breeding objectives were used as an example to illustrate the methodology—a terminal sire breeding objective (A) and a dual‐purpose self‐replacing breeding objective (B). The objective function used for optimization considered genetic merit, constrained inbreeding and cost of technologies where costs were offset by a premium paid to the seedstock breeder investing in female reproductive technologies. The premium was based on the cumulative discounted expression of genetic merit in the progeny of a commercial tier in the breeding programme multiplied by the proportion of that benefit received by the breeder. With breeding objective B, the highest premium of 64% paid to the breeder resulted in the highest allocation of reproductive technologies (4%–10% for MOET and 19%–54% for JIVET) and hence the highest annual genetic gain. Conversely, breeding objective A, which had a lower dollar value of the breeding objective and a maximum of 5% mating types for JIVET and zero for MOET were optimal, even when highest premiums were paid. This study highlights that the level of investment in breeding technologies to accelerate genetic gain depends on the investment of genetic improvement returned to the breeder per index point gain achieved. It also demonstrates that breeding programmes can be optimized including allocation of reproductive technologies at the individual animal level. Accounting for revenue to the breeder and cost of the technologies can facilitate more practical decision support for beef and sheep breeders.     

Effect of selection and selective genotyping for creation of reference on bias and accuracy of genomic prediction

Reference populations for genomic selection usually involve selected individuals, which may result in biased prediction of estimated genomic breeding values (GEBV). In a simulation study, bias and accuracy of GEBV were explored for various genetic models with individuals selectively genotyped in a typical nucleus breeding program. We compared the performance of three existing methods, that is, Best Linear Unbiased Prediction of breeding values using pedigree‐based relationships (PBLUP), genomic relationships for genotyped animals only (GBLUP) and a Single‐Step approach (SSGBLUP) using both. For a scenario with no‐selection and random mating (RR), prediction was unbiased. However, lower accuracy and bias were observed for scenarios with selection and random mating (SR) or selection and positive assortative mating (SA). As expected, bias disappeared when all individuals were genotyped and used in GBLUP. SSGBLUP showed higher accuracy compared to GBLUP, and bias of prediction was negligible with SR. However, PBLUP and SSGBLUP still showed bias in SA due to high inbreeding. SSGBLUP and PBLUP were unbiased provided that inbreeding was accounted for in the relationship matrices. Selective genotyping based on extreme phenotypic contrasts increased the prediction accuracy, but prediction was biased when using GBLUP. SSGBLUP could correct the biasedness while gaining higher accuracy than GBLUP. In a typical animal breeding program, where it is too expensive to genotype all animals, it would be appropriate to genotype phenotypically contrasting selection candidates and use a Single‐Step approach to obtain accurate and unbiased prediction of GEBV.     

动物模型BLUP选择效果的计算机模拟研究

在采用动物模型最佳线性无偏预测(BLUP) 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, 并系统地比较了群体规模、公母比例和性状遗传力对选择所获得的遗传进展和群体近交系数变化的影响。结果表明, 扩大育种群规模不仅可以获得更大的持续进展, 同时还可有效缓解近交系数的过快上升; 育种群中公畜比例过低时, 不仅会降低遗传进展, 群体近交系数的上升速度也会加快, 实际中应保证育种群具有一定的规模和适宜的公母比例。对高遗传力性状进行选择时, 可望获得更大的遗传进展, 同时近交系数的上升速度也会快一些。     

Implementation of Optimum Contributions Selection in endangered local breeds: the case of the Menorca Horse population

Limiting the inbreeding rate (?F) while maximizing genetic gain for any trait of economic interest is especially important in small populations of local breeds, like the Menorca Horse. In this breed, dressage performance is important for the profitability of the breed and should be accounted in the selection criterion. The aim of this study was to assess if a breeding programme aiming at improved dressage performance is feasible in such a small breed. To perform the analysis, animals that were currently available for breeding (between 3 and 20 years) were used. Selection was based on the estimated breeding values for dressage obtained by BLUP. The pedigree and molecular coancestry between potential breeding horses was used (separately or in combination) to account for the restriction on ?F. Results show that it is possible to avoid large increases in inbreeding while obtaining acceptable levels of genetic gain (i.e. a ?F of 1% would imply a maximum loss in genetic gain of 2%). Thus, the Menorca Horse population is suitable for a management procedure which jointly optimizes the response to selection and the levels of variability and inbreeding (Optimal Contribution selection). Regarding the source of information used to calculate the relationships, molecular information would provide a greater range of solutions to increase genetic gain than using pedigree coancestry (gain was 1–4% higher for the same levels of restriction on the increase in inbreeding).     

Genomic selection for maternal traits in pigs

The aim of this study was to compare alternative designs for implementation of genomic selection to improve maternal traits in pigs, with a conventional breeding scheme and a progeny testing scheme. The comparison was done through stochastic simulation of a pig population. It was assumed that selection was performed based on a trait that could be measured on females after the first litter, with a heritability of 0.1. Genomic selection increased genetic gain and reduced the rate of inbreeding, compared with conventional selection without progeny testing. Progeny testing could also increase genetic gain and decrease the rate of inbreeding, but because of the increased generation interval, the increase in annual genetic gain was only 7%. When genomic selection was applied, genetic gain was increased by 23 to 91%, depending on which and how many animals were genotyped. Genotyping dams in addition to the male selection candidates gave increased accuracy of the genomic breeding values, increased genetic gain, and decreased rate of inbreeding. To genotype 2 or 3 males from each litter, in order to perform within-litter selection, increased genetic gain 8 to 12%, compared with schemes with the same number of genotyped females but only 1 male candidate per litter. Comparing schemes with the same total number of genotyped animals revealed that genotyping more females caused a greater increase in genetic gain than genotyping more males because greater accuracy of selection was more advantageous than increasing the number of male selection candidates. When more than 1 male per litter was genotyped, and thereby included as selection candidates, rate of inbreeding increased because of coselection of full sibs. The conclusion is that genomic selection can increase genetic gain for traits that are measured on females, which includes several traits with economic importance in maternal pig breeds. Genotyping females is essential to obtain a high accuracy of selection.     

There is room for selection in a small local pig breed when using optimum contribution selection: a simulation study

Selection progress must be carefully balanced against the conservation of genetic variation in small populations of local breeds. Well-defined breeding programs?with specified selection traits are rare in local pig breeds. Given the small population size,?the focus is often on the management of genetic diversity. However, in local breeds, optimum contribution selection can be applied to control the rate of inbreeding and to avoid reduced performance in traits with high market value. The aim of this study was to assess the extent to which a breeding program aiming for improved product quality in a small local breed would be feasible. We used stochastic simulations to compare 25 scenarios. The scenarios differed in?size of population, selection intensity of boars, type of selection (random selection, truncation selection based on BLUP breeding values, or optimum contribution selection based on BLUP breeding values), and heritability of?the selection trait. It was assumed that the local breed is used in an extensive system for a high-meat-quality market.?The?simulations showed that in the smallest population (300 female reproducers), inbreeding increased by 0.8% when selection was performed at random. With optimum contribution selection, genetic progress can be achieved that is almost as great as that with truncation selection based on BLUP breeding values (0.2 to 0.5 vs. 0.3 to 0.5 genetic SD, P < 0.05), but at a considerably decreased rate of inbreeding (0.7 to 1.2 vs. 2.3 to 5.7%, P < 0.01). This confirmation of the potential utilization of OCS even in small populations is important in the context of sustainable management and the use of animal genetic resources.     

Persistency of accuracy of genomic breeding values for different simulated pig breeding programs in developing countries

Genetic improvement of pigs in tropical developing countries has focused on imported exotic populations which have been subjected to intensive selection with attendant high population‐wide linkage disequilibrium (LD). Presently, indigenous pig population with limited selection and low LD are being considered for improvement. Given that the infrastructure for genetic improvement using the conventional BLUP selection methods are lacking, a genome‐wide selection (GS) program was proposed for developing countries. A simulation study was conducted to evaluate the option of using 60 K SNP panel and observed amount of LD in the exotic and indigenous pig populations. Several scenarios were evaluated including different size and structure of training and validation populations, different selection methods and long‐term accuracy of GS in different population/breeding structures and traits. The training set included previously selected exotic population, unselected indigenous population and their crossbreds. Traits studied included number born alive (NBA), average daily gain (ADG) and back fat thickness (BFT). The ridge regression method was used to train the prediction model. The results showed that accuracies of genomic breeding values (GBVs) in the range of 0.30 (NBA) to 0.86 (BFT) in the validation population are expected if high density marker panels are utilized. The GS method improved accuracy of breeding values better than pedigree‐based approach for traits with low heritability and in young animals with no performance data. Crossbred training population performed better than purebreds when validation was in populations with similar or a different structure as in the training set. Genome‐wide selection holds promise for genetic improvement of pigs in the tropics.     

Predicting rates of inbreeding for livestock improvement schemes

This article presents a deterministic method to predict rates of inbreeding (deltaF) for typical livestock improvement schemes. The method is based on a recently developed general theory to predict rates of inbreeding, which uses the concept of long-term genetic contributions. A typical livestock breeding population was modeled, with overlapping generations, BLUP selection, and progeny testing of male selection candidates. Two types of selection were practiced: animals were either selected by truncation on estimated breeding values (EBV) across age classes, or the number of parents selected from each age class was set to a fixed value and truncation selection was practiced within age classes. Bulmer's equilibrium genetic parameters were obtained by iterating on a pseudo-BLUP selection index and deltaF was predicted for the equilibrium situation. Predictions were substantially more accurate than predictions from other available methods, which ignore the effect of selection on deltaF. Predictions were accurate for schemes with up to 20 sires. Predicted deltaF was somewhat too low for schemes with more than 20 sires, which was due to the use of simple linear models to predict genetic contributions. The present method provides a computationally feasible (i.e., deterministic) tool to consider both the rate of inbreeding and the rate of genetic gain when optimizing livestock improvement schemes.     

闭锁群体BLUP选择下遗传方差和近交系数的变化

采用计算机随机模拟方法模拟了在一个闭锁群体内连续对单个性状进行 1 5个世代选择的情况。选择过程中世代不重叠 ,每个世代的种畜根据动物模型最佳线性无偏预测 (BLUP)法估计的育种值进行选留 ,并在此基础上系统地比较了不同群体规模、公母比例和性状遗传力对群体遗传方差和近交系数变化的影响。结果表明 ,扩大育种群规模、增加公畜比例以及对低遗传力性状进行选择时 ,群体遗传方差降低的速度和近交系数上升的速度会更慢 ,在长期选择时可望获得更大的持续进展和适宜的近交增量     

Genetic diversity in an indigenous horse breed: implications for mating strategies and the control of future inbreeding

The Franches-Montagnes is an indigenous Swiss horse breed, with approximately 2500 foalings per year. The stud book is closed, and no introgression from other horse breeds was conducted since 1998. Since 2006, breeding values for 43 different traits (conformation, performance and coat colour) are estimated with a best linear unbiased prediction (BLUP) multiple trait animal model. In this study, we evaluated the genetic diversity for the breeding population, considering the years from 2003 to 2008. Only horses with at least one progeny during that time span were included. Results were obtained based on pedigree information as well as from molecular markers. A series of software packages were screened to combine best the best linear unbiased prediction (BLUP) methodology with optimal genetic contribution theory. We looked for stallions with highest breeding values and lowest average relationship to the dam population. Breeding with such stallions is expected to lead to a selection gain, while lowering the future increase in inbreeding within the breed.     

Breeding programme for Piétrain pigs in Bavaria with an estimation of genetic trends and effective population size

Population structure, performance testing and breeding scheme of the sire breed Piétrain in Bavaria were analyzed as a basis for further optimization studies of the breeding programme. To evaluate the current breeding programme, genetic trends and effective population size were estimated. Four data sets were used which contained breeding animals born between 1981 and 2005, estimated breeding values of traits in the breeding goal, records from young boars in field test and records from purebred and crossbred progeny on test stations. The population is subdivided in many small herds. That has disadvantages with respect to a uniform breeding goal used across herds and with respect to selection intensity and the avoidance of inbreeding. The idealized selection practice consists of three selection stages. On the first two stages information from half and full sibs on test stations is most important so that the risk of co-selecting related animals is increased. The breeding scheme is a mixture of a half sib design and a progeny testing design, but both have disadvantages. Nevertheless, genetic trends are in the desired directions. To improve accuracy and intensity of selection, only AI-boars should be used instead of natural service sires. Though the effective population size is high, the recent trend of inbreeding shows that the extensive use of popular AI-boars can lead to a rapid increase of inbreeding.