Efficient selection against categorically scored hip dysplasia in dogs is possible using best linear unbiased prediction and optimum contribution selection: a simulation study

Breeding to reduce the prevalence of categorically scored hip dysplasia (HD), based on phenotypic assessment of radiographic hip status, has had limited success. The aim of this study was to evaluate two selection strategies for improved hip status: truncation selection based on phenotypic record versus best linear unbiased prediction (BLUP), using stochastic simulation and selection scenarios resembling those in real dog populations. In addition, optimum contribution selection (OCS) was evaluated. Two traits were considered: HD (as a categorical trait with five classes and a heritability of 0.45 on the liability scale) and a continuous trait (with a heritability of 0.25) intended to represent other characteristics in the breeding goal. A population structure mimicking that in real dog populations was modelled. The categorical nature of HD caused a considerably lower genetic gain compared to simulating HD as a continuous trait. Genetic gain was larger for BLUP selection than for phenotypic selection in all scenarios. However, BLUP selection resulted in higher rates of inbreeding. By applying OCS, the rate of inbreeding was lowered to about the same level as phenotypic selection but with increased genetic improvement. For efficient selection against HD, use of BLUP breeding values should be prioritized. In small populations, BLUP should be used together with OCS or similar strategy to maintain genetic variation.     

Assessing genetic gain, inbreeding, and bias attributable to different flock genetic means in alternative sheep sire referencing schemes

Flocks participating in sire referencing schemes can achieve greater genetic gains than those achievable by within-flock selection. However, requirements for joining these schemes can be prohibitive to some producers. The objectives of this study were to determine whether less restrictive schemes or schemes of shorter duration could achieve rates of gain and reduce inbreeding as efficiently as continuous sire referencing schemes (SRS) and to investigate whether bias from different genetic means could be reduced by these alternative schemes. Pedigree and performance data for a single trait with a within-flock heritability of 0.25 were simulated (50 replications) for 15 flocks with 40 to 140 ewes per flock. Founder genetic means for each flock were sampled from a normal distribution with mean 0 and SD equal to the trait's genetic SD. After 10 yr of random mating, flocks had the opportunity to join an SRS and begin selection for the simulated trait. Yearling rams were chosen as reference sires randomly from the top one-sixth of the population ranked on BLUP EBV. Every year, in each flock, 3 reference sires were mated to 10 ewes. Six sire referencing scenarios were considered, in which all flocks participated in a SRS for 1) 15 yr; 2) 5 yr before discontinuing the scheme; 3) 10 yr before discontinuing the scheme; 4) 2 out of every 3 yr; 5) 15 yr with reference sire mating by natural service; and 6) no years (no use of SRS). Ewes not mated to reference sires were mated either to their own home-bred sires exclusively or to a mixture of homebred and unrelated purchased rams of unknown merit. Genetic gain was equivalent whether the SRS used AI or natural service matings, although inbreeding was lower with natural service. Across all scenarios, genetic gain and inbreeding were greater when excess ewes were mated exclusively to homebred sires. Genetic gains without SRS were 80 to 82% lower than when the scheme operated for 15 yr, whereas inbreeding was considerably greater. Other scenarios were intermediate in both gain and inbreeding levels. In all SRS scenarios, bias in EBV attributable to differing flock genetic means rapidly decreased in the first 5 yr of sire referencing. Levels of bias did not substantially increase when flocks discontinued SRS after 5 or 10 yr, suggesting that further participation in an SRS may not be necessary to manage risk. Natural service and noncontinuous SRS are viable options to continuous AI SRS in terms of genetic gain, inbreeding, and bias reduction.     

Marker‐assisted selection reduces expected inbreeding but can result in large effects of hitchhiking

We used computer simulations to investigate to what extent true inbreeding, i.e. identity‐by‐descent, is affected by the use of marker‐assisted selection (MAS) relative to traditional best linear unbiased predictions (BLUP) selection. The effect was studied by varying the heritability (h² = 0.04 vs. 0.25), the marker distance (MAS vs. selection on the gene, GAS), the favourable QTL allele effect (α = 0.118 vs. 0.236) and the initial frequency of the favourable QTL allele (p = 0.01 vs. 0.1) in a population resembling the breeding nucleus of a dairy cattle population. The simulated genome consisted of two chromosomes of 100 cM each in addition to a polygenic component. On chromosome 1, a biallelic QTL as well as 4 markers were simulated in linkage disequilibrium. Chromosome 2 was selectively neutral. The results showed that, while reducing pedigree estimated inbreeding, MAS and GAS did not always reduce true inbreeding at the QTL relative to BLUP. MAS and GAS differs from BLUP by increasing the weight on Mendelian sampling terms and thereby lowering inbreeding, while increasing the fixation rate of the favourable QTL allele and thereby increasing inbreeding. The total outcome in terms of inbreeding at the QTL depends on the balance between these two effects. In addition, as a result of hitchhiking, MAS results in extra inbreeding in the region surrounding QTL, which could affect the overall genomic inbreeding.     

Selection of core animals in the Algorithm for Proven and Young using a simulation model

The Algorithm for Proven and Young (APY) enables the implementation of single‐step genomic BLUP (ssGBLUP) in large, genotyped populations by separating genotyped animals into core and non‐core subsets and creating a computationally efficient inverse for the genomic relationship matrix ( G ). As APY became the choice for large‐scale genomic evaluations in BLUP‐based methods, a common question is how to choose the animals in the core subset. We compared several core definitions to answer this question. Simulations comprised a moderately heritable trait for 95,010 animals and 50,000 genotypes for animals across five generations. Genotypes consisted of 25,500 SNP distributed across 15 chromosomes. Genotyping errors and missing pedigree were also mimicked. Core animals were defined based on individual generations, equal representation across generations, and at random. For a sufficiently large core size, core definitions had the same accuracies and biases, even if the core animals had imperfect genotypes. When genotyped animals had unknown parents, accuracy and bias were significantly better (p ≤ .05) for random and across generation core definitions.     

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     

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。     

Implications of SNP weighting on single‐step genomic predictions for different reference population sizes

We investigated the importance of SNP weighting in populations with 2,000 to 25,000 genotyped animals. Populations were simulated with two effective sizes (20 or 100) and three numbers of QTL (10, 50 or 500). Pedigree information was available for six generations; phenotypes were recorded for the four middle generations. Animals from the last three generations were genotyped for 45,000 SNP. Single‐step genomic BLUP (ssGBLUP) and weighted ssGBLUP (WssGBLUP) were used to estimate genomic EBV using a genomic relationship matrix ( G ). The WssGBLUP performed better in small genotyped populations; however, any advantage for WssGBLUP was reduced or eliminated when more animals were genotyped. WssGBLUP had greater resolution for genome‐wide association (GWA) as did increasing the number of genotyped animals. For few QTL, accuracy was greater for WssGBLUP than ssGBLUP; however, for many QTL, accuracy was the same for both methods. The largest genotyped set was used to assess the dimensionality of genomic information (number of effective SNP). The number of effective SNP was considerably less in weighted G than in unweighted G . Once the number of independent SNP is well represented in the genotyped population, the impact of SNP weighting becomes less important.     

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.     

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.     

Comparison of genomic and traditional BLUP-estimated breeding value accuracy and selection response under alternative trait and genomic parameters

Accuracy of prediction of estimated breeding values based on genome-wide markers (GEBV) and selection based on GEBV as compared with traditional Best Linear Unbiased Prediction (BLUP) was examined for a number of alternatives, including low heritability, number of generations of training, marker density, initial distributions, and effective population size (Ne). Results show that the more the generations of data in which both genotypes and phenotypes were collected, termed training generations (TG), the better the accuracy and persistency of accuracy based on GEBV. GEBV excelled for traits of low heritability regardless of initial equilibrium conditions, as opposed to traditional marker-assisted selection, which is not useful for traits of low heritability. Effective population size is critical for populations starting in Hardy-Weinberg equilibrium but not for populations started from mutation-drift equilibrium. In comparison with traditional BLUP, GEBV can exceed the accuracy of BLUP provided enough TG are included. Unfortunately selection rapidly reduces the accuracy of GEBV. In all cases examined, classic BLUP selection exceeds what was possible for GEBV selection. Even still, GEBV could have an advantage over traditional BLUP in cases such as sex-limited traits, traits that are expensive to measure, or can only be measured on relatives. A combined approach, utilizing a mixed model with a second random effect to account for quantitative trait loci in linkage equilibrium (the polygenic effect) was suggested as a way to capitalize on both methodologies.     

Reducing the effect of parent averages from animal solutions in mixed model equations

Selection of animals based on their BLUP evaluations from an animal model results in animals that are closely related which leads to increased rates of inbreeding. The tendency for higher inbreeding rates is greater at low heritability values. Several attempts have been made to reduce the impact of parent average breeding values from animals evaluations in order to reduce inbreeding while not sacrificing genetic response. A method that modifies the rules for forming the inverse of the additive genetic relationship matrix for use in best linear unbiased estimation of breeding values via an animal model was developed. This method and several others were compared analytically and empirically, from the perspective of partitioning the animal solutions into contributions from the data, from progeny, and from the parent average. The ratio of genetic progress to average level of inbreeding showed that the modified relationship matrix method was superior to the other methods. Similar results could be obtained by using artificially high heritability in a usual BLUP analysis.     

Genome-wide marker-assisted selection combining all pedigree phenotypic information with genotypic data in one step: An example using broiler chickens

Data of broiler chickens for 2 pure lines across 3 generations were used for genomic evaluation. A complete population (full data set; FDS) consisted of 183,784 and 164,246 broilers for the 2 lines. The genotyped subsets (SUB) consisted of 3,284 and 3,098 broilers with 57,636 SNP. Genotyped animals were preselected based on more than 20 traits with different index applied to each line. Three traits were analyzed: BW at 6 wk (BW6), ultrasound measurement of breast meat (BM), and leg score (LS) coded 1 = no and 2 = yes for leg defect. Some phenotypes were missing for BM. The training population consisted of the first 2 generations including all animals in FDS or only genotyped animals in SUB. The validation data set contained only genotyped animals in the third generation. Genetic evaluations were performed using 3 approaches: 1) phenotypic BLUP, 2) extending BLUP methodologies to utilize pedigree and genomic information in a single step (ssGBLUP), and 3) Bayes A. Whereas BLUP and ssGBLUP utilized all phenotypic data, Bayes A could use only those of the genotyped subset. Heritabilities were 0.17 to 0.20 for BW6, 0.30 to 0.35 for BM, and 0.09 to 0.11 for LS. The average accuracies of the validation population with BLUP for BW6, BM, and LS were 0.46, 0.30, and <0 with SUB and 0.51, 0.34, and 0.28 with FDS. With ssGBLUP, those accuracies were 0.60, 0.34, and 0.06 with SUB and 0.61, 0.40, and 0.37 with FDS, respectively. With Bayes A, the accuracies were 0.60, 0.36, and 0.09 with SUB. With SUB, Bayes A and ssGBLUP had similar accuracies. For traits of high heritability, the accuracy of Bayes A/SUB and ssGBLUP/FDS were similar, and up to 50% better than BLUP/FDS. However, with low heritability, ssGBLUP/FDS was 4 to 6 times more accurate than Bayes A/SUB and 50% better than BLUP/FDS. An optimal genomic evaluation would be multi-trait and involve all traits and records on which selection is based.     

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.     

Bias in heritability estimates from genomic restricted maximum likelihood methods under different genotyping strategies

We investigated the effects of different strategies for genotyping populations on variance components and heritabilities estimated with an animal model under restricted maximum likelihood (REML), genomic REML (GREML), and single‐step GREML (ssGREML). A population with 10 generations was simulated. Animals from the last one, two or three generations were genotyped with 45,116 SNP evenly distributed on 27 chromosomes. Animals to be genotyped were chosen randomly or based on EBV. Each scenario was replicated five times. A single trait was simulated with three heritability levels (low, moderate, high). Phenotypes were simulated for only females to mimic dairy sheep and also for both sexes to mimic meat sheep. Variance component estimates from genomic data and phenotypes for one or two generations were more biased than from three generations. Estimates in the scenario without selection were the most accurate across heritability levels and methods. When selection was present in the simulations, the best option was to use genotypes of randomly selected animals. For selective genotyping, heritabilities from GREML were more biased compared to those estimated by ssGREML, because ssGREML was less affected by selective or limited genotyping.     

Performance of genomic selection under a single-step approach in autochthonous Spanish beef cattle populations

This study evaluated different strategies for implementing a single-step genomic selection programme in two autochthonous Spanish beef cattle populations (Pirenaica—Pi and Rubia Gallega—RG). The strategies were compared in terms of accuracy attained under different scenarios by simulating genomic data over the known genealogy. Several genotyping approaches were tested, as well as, other factors like marker density, effective population size, mutation rate and heritability of the trait. The results obtained showed gains in accuracy with respect to pedigree BLUP evaluation in all cases. The greatest benefit was obtained when the candidates to selection had their genotypes included in the evaluation. Moreover, genotyping the individuals with the most accurate predictions maximized the gains but other suboptimal strategies also yielded satisfactory results. Furthermore, the gains in accuracy increased with the marker density reaching a plateau at around 50,000 markers. Likewise, the effective population size and the mutation rate have also shown an effect, both increasing the accuracy with decreasing values of these population parameters. Finally, the results obtained for the RG population showed greater gains compared to the Pi population, probably attributed to the wider implantation of artificial insemination.     

大尾寒羊体尺性状的遗传参数估计

利用动物模型BLUP法对大尾寒羊体尺性状进行了遗传力估计。结果表明,体重、体高、体长和胸围的遗传力分别为0.14、0.11、0.11和0.15,它们属于中等遗传力(0.1相似文献   

基于元共祖的基因组联合育种模拟研究

旨在将整合元共祖的一步法(single-step genomic best linear unbiased prediction with metafounders,MF-SSGBLUP)应用到基因组联合育种中,并与其他经典基因组选择方法进行比较分析。本研究使用QMSim软件模拟3个系谱相互独立的奶牛群体;分别使用广义最小二乘法(generalized least squares,GLS)和原始方法(naïve,NAI)估计不同群体间的祖先关系矩阵Γ;将MF-SSGBLUP、SSGBLUP和BLUP用于3个模拟群体的联合育种,评估各方法在遗传参数和育种值估计方面的差异。在不同遗传力下,GLS所得的Γ矩阵在对角线元素上略低于NAI法,在非对角线元素上没有明显差异,且基因组关系矩阵与基于元共祖构建的亲缘关系矩阵对角线元素相关系数(0.750~0.775)高于基因组关系矩阵与传统的亲缘关系矩阵相关系数(0.508~0.572)。MF-SSGBLUP遗传力估计值(0.138、0.140、0.297和0.298)与当代群体遗传力(0.107和0.296)的偏差小于其余两种方法(0.145、0.173、0.273和0.340),且MF-SSGBLUP估计育种值准确性(0.888~0.908)高于SSGBLUP法(0.863~0.876)和BLUP法(0.854~0.871)。表明,MF-SSGBLUP的遗传参数估计值无偏性更好,估计育种值准确性更高。根据上述模拟数据结果表明,在联合育种中,整合元共祖的基因组选择方法优于其他经典基因组选择方法。     

Accuracy of breeding values when using and ignoring the polygenic effect in genomic breeding value estimation with a marker density of one SNP per cM

Genomic selection is based on breeding values that are estimated using genome-wide dense marker maps. The objective of this paper was to investigate the effect of including or ignoring the polygenic effect on the accuracy of total genomic breeding values, when there is coverage of the genome with approximately one SNP per cM. The importance of the polygenic effect might differ for high and low heritability traits, and might depend on the design of the reference dataset. Hence, different scenarios were evaluated using stochastic simulation. Accuracies of the total breeding value of juvenile selection candidates depended on the number of animals included in the reference data. When excluding polygenic effects, those accuracies ranged from 0.38 to 0.55 and from 0.73 to 0.79 for traits with heritabilities of 10 and 50%, respectively. Accuracies were improved by including a polygenic effect in the model for the low heritability trait, when the LD-measure r2 between adjacent markers became smaller than approximately 0.10, while for the high heritability trait there was already a small improvement at r2 between adjacent markers of 0.14. In all situations, the estimated total genetic variance was underestimated, particularly when the polygenic effect was excluded from the model. The haplotype variance was less underestimated when more animals were added in the reference dataset.     

Estimation of additive genetic variance when base populations are selected

A population of size 40 was simulated 1,000 times for 10 generations. Five out of twenty males were selected each generation, and each male was mated to four females to have two progeny. The additive genetic variance (sigma 2a) before selection was 10, and the initial heritability was .5. Due to covariances among animals, inbreeding and gametic disequilibrium, the genetic variance was reduced to 6.72 after 10 generations of selection. Reduction of variance was lower in another population simulated with size 400 and 10% of the males selected. Restricted Maximum Likelihood was used to estimate sigma 2a using an animal model. The estimate of sigma 2a was empirically unbiased when all data and all relationships were used. Omitting data from selected ancestors caused biased estimates of sigma 2a due to not accounting for all gametic disequilibrium. Including additional relationships between assumed base animals adjusted for inbreeding and for covariances. Bias from gametic disequilibrium decreased slightly with the use of more relationship information, and it was smaller in the small population and(or) when selection had been practiced for just a few generations.     

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。