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.     

Benefits from marker-assisted selection under an additive polygenic genetic model

This study investigated, through stochastic computer simulation, the extra gains expected from marker-assisted selection (MAS) in an infinitesimal model with linkage. The trait under selection was assumed to be controlled by 2,000 loci of additive small effect and evenly distributed in c chromosomes of one Morgan each (and c = 5, 10, 20, or 30). This approach differs from previous studies on the benefits of MAS that have considered mixed inheritance models. Marker information was used together with pedigree information to compute the relationship matrix used in BLUP genetic evaluations. The MAS schemes were compared with schemes where genetic evaluations were performed using standard BLUP (i.e., the relationship matrix is obtained using pedigree information only). When the number of markers was large enough (approximately one marker every 10 cM), there were increases in the accuracy of selection with MAS, and this led to extra gains compared with standard BLUP for all genome sizes considered. The benefit from MAS increased over generations. At the last generation of selection (Generation 10), the response from MAS was 11, 9, 7, and 5% greater than with standard BLUP for genomes with 5, 10, 20, and 30 chromosomes, respectively. Thus, although small, gains from MAS were nonetheless detectable for genome sizes typical of livestock populations.     

Optimal village breeding schemes under smallholder sheep farming systems

Despite challenges in the implementation of livestock genetic improvement programs in developing regions, including centralized nucleus breeding schemes, these programs can contribute to the improvement of the livelihood of smallholder farmers. In this paper, we present a community- or village-based breeding scheme in which breeding activities are carried out by communities of smallholder farmers. We evaluated genetic responses and the rate of inbreeding from alternative village sheep breeding schemes that were based on a survey of existing flock structure and breeding management in a sheep-barley system in Ethiopia. This survey showed that individual flock sizes were small, and that the majority of farmers practiced mixed grazing and uncontrolled mating of their flocks in communal grazing lands within villages. Here we evaluated within-village schemes (selection across flocks within a village) and across-village schemes (selection across villages) at different intensities of ram selection (i.e. proportions of rams selected, P). Our results showed that under within-village schemes, intensity of selection could not be increased (i.e. P could not be decreased below 0.149) when the rate of inbreeding was constrained to an acceptable level of 0.01, resulting in low genetic gain. The most optimal scheme was found to be across-village selection with at least three villages cooperating and P = 0.05. Our results also indicated that genetic gain from village breeding schemes with mass selection and BLUP selection is comparable. Village breeding schemes can make a significant contribution to the genetic improvement of livestock in Ethiopia and other developing countries.     

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.     

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.     

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.     

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。     

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。     

The joint regulation of genetic gain and inbreeding under mate selection

SUMMARY: Stochastic simulation was used to evaluate a range of selection strategies with respect to both additive genetic response and inbreeding. Strategies involving selection on BLUP ebvs or individual phenotype, followed by random mating, were compared with mate selection strategies which used portfolio analysis to give joint consideration to genetic merit and inbreeding. An adapted Mean Of Total Absolute Deviations (MOTAD) method was used in a mate selection model to define optimal matings with regard to aggregate genetic merit and inbreeding for a base population h(2) of 0.2. Compared with random mating following selection on BLUP ebvs, inbreeding levels after 10 years of selection were able to be reduced under BLUP plus mate selection from ～.23 to as little as .11. Additive genetic gain was either little compromised or increased. The results suggest that information linking expected levels of genetic merit and inbreeding can be used to find the preferred selection strategy. ZUSAMMENFASSUNG: Gemeinsame Kontrolle von Zuchtfortschritt und Inzucht bei Partnerselektion Es wurde stochastische Simulation zur Auswertung einer Reihe von Selektionsstrategien hinsichtlich Zuchtwertzuwachs und Inzucht verwendet. Strategien mit Selektion auf der Basis von BLUP ebvs oder individuellem Ph?notyp mit nachfolgender Zufallspaarung wurden mit Partnerselektionsstrategien verglichen, die Portfolioanalyse zur gemeinsamen Beachtung von Zuchtwert und Inzucht verwendeten. Eine Methode adaptierter MITTELWERTE TOTALER ABSOLUTER ABWEICHUNGEN (MOTAD) Methode wurde beim Partnerselektionsmodell zur Definition optimaler Paarungen in Hinblick auf Gesamtzuchtwert und Inzucht bei einer Populationsheritabilit?t von 0,2 verwendet. Verglichen mit Zufallspaarung nach Selektion auf BLUP ebvs waren die Inzuchtgrade nach 10 Selektionsjahren von 0,23 auf 0,11 reduziert und additiver Zuchtfortschritt war dabei wenig beeintr?chtigt oder nahm sogar zu. Die Ergebnisse weisen darauf hin, da? Information, die Zuchtwert und Inzucht verbindet, zur Identifikation erwünschter Selektionsstrategien führen kann.     

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).     

Detecting effective starting point of genomic selection by divergent trends from best linear unbiased prediction and single-step genomic best linear unbiased prediction in pigs,beef cattle,and broilers

Genomic selection has been adopted nationally and internationally in different livestock and plant species. However, understanding whether genomic selection has been effective or not is an essential question for both industry and academia. Once genomic evaluation started being used, estimation of breeding values with pedigree best linear unbiased prediction (BLUP) became biased because this method does not consider selection using genomic information. Hence, the effective starting point of genomic selection can be detected in two possible ways including the divergence of genetic trends and Realized Mendelian sampling (RMS) trends obtained with BLUP and single-step genomic BLUP (ssGBLUP). This study aimed to find the start date of genomic selection for a set of economically important traits in three livestock species by comparing trends obtained using BLUP and ssGBLUP. Three datasets were used for this purpose: 1) a pig dataset with 117k genotypes and 1.3M animals in pedigree, 2) an Angus cattle dataset consisted of ~842k genotypes and 11.5M animals in pedigree, and 3) a purebred broiler chicken dataset included ~154k genotypes and 1.3M birds in pedigree were used. The genetic trends for pigs diverged for the genotyped animals born in 2014 for average daily gain (ADG) and backfat (BF). In beef cattle, the trends started diverging in 2009 for weaning weight (WW) and in 2016 for postweaning gain (PWG), with little divergence for birth weight (BTW). In broiler chickens, the genetic trends estimated by ssGBLUP and BLUP diverged at breeding cycle 6 for two out of the three production traits. The RMS trends for the genotyped pigs diverged for animals born in 2014, more for ADG than for BF. In beef cattle, the RMS trends started diverging in 2009 for WW and in 2016 for PWG, with a trivial trend for BTW. In broiler chickens, the RMS trends from ssGBLUP and BLUP diverged strongly for two production traits at breeding cycle 6, with a slight divergence for another trait. Divergence of the genetic trends from ssGBLUP and BLUP indicates the onset of the genomic selection. The presence of trends for RMS indicates selective genotyping, with or without the genomic selection. The onset of genomic selection and genotyping strategies agrees with industry practices across the three species. In summary, the effective start of genomic selection can be detected by the divergence between genetic and RMS trends from BLUP and ssGBLUP.     

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.     

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.     

Effect of culling on selection response using phenotypic selection or best linear unbiased prediction of breeding values in small, closed herds of swine.

Records from 7,200 separate closed herds with either 12 or 25 sows that were mated to either four or eight boars per year were simulated by computer. Effects of selection method, herd size, and contemporary group variability on average genetic change, genetic variance, and inbreeding over 10 yr of selection were analyzed for traits with heritabilities of .1, .3, and .6. Selection of replacement animals was on individual phenotype or BLUP of breeding value using a reduced animal model. For both of these selection methods, two culling schemes were imposed: 1) based only on involuntary culling because of losses due to conception rate and age and 2) when an available replacement animal was projected to be superior to an existing breeding animal in the herd in addition to the involuntary culling. The contemporary group standard deviation was set at either .1 or .5 of a phenotypic standard deviation. Selection with BLUP gave 72, 36, and 12% more genetic improvement for heritabilities of .1, .3, and .6, respectively, than selection on individual phenotype after 10 yr. However, inbreeding increased 20 to 52% more rapidly and there was a decrease in genetic variance. Culling based on Scheme 2 increased genetic improvement over Scheme 1 by about 75% with coincident increases in inbreeding level and decreases in genetic variance. The largest changes in inbreeding and genetic variance were associated with culling on BLUP. Culling when a superior animal was available with individual phenotype had little effect on inbreeding and genetic variance. Use of four boars rather than eight boars and 25 rather than 12 sows per herd increased genetic response. Use of four boars also increased inbreeding and decreased genetic variance. Genetic variance was higher in herds with 25 sows, but the size of the sow herd had little effect on inbreeding. Contemporary group variation influenced only the genetic response of individual phenotypic selection with culling.     

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     

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.     

Effects of errors in pedigree on three methods of estimating breeding value for litter size, backfat and average daily gain in swine

Estimated breeding value (EBV) was calculated based on either individual phenotype (SP), an index of individual phenotype and full- and half-sib family averages (SI) or Best Linear Unbiased Prediction (BLUP). Calculations were done with correct data or data with 5, 10, 15 or 20% of the records per generation containing pedigree errors. Traits considered were litter size (LS), backfat (BF) and average daily gain (ADG). When data were correct, BLUP resulted in an advantage in expected genetic gain over SP of 22, 7.2 or 30.8% for LS, BF and ADG, respectively, and over SI of 9.6, 3.8 or 21.4%. When sire and dam pedigrees were incorrect for 20% of the pigs each generation, genetic gain using SI was reduced by 7, 2.5 or 6.5% and genetic gain using BLUP was reduced by 9.3, 3.2 or 12.4% for LS, BF and ADG, respectively. With 20% of the pedigrees in error, the advantages in genetic gain of using BLUP over SP, the method unaffected by errors in pedigree, were 10.5, 3.8 and 14.6% for LS, BF and ADG, respectively. These results suggest that, although BLUP is affected to a greater degree by pedigree errors than SP or SI, selection of swine using BLUP still would improve response to selection over the use of SP or SI.     

基于基因组和系谱信息的不同选配方案效果模拟研究

基因组选配（genomic mating,GM）是利用基因组信息进行优化的选种选配,可以有效控制群体近交水平的同时实现最大化的遗传进展。但基因组选配是对群体中所有个体进行选配,这与实际的育种工作有点相悖。本研究模拟了遗传力为0.5的9 000头个体的基础群数据,每个世代根据GEBV选择30头公畜、900头母畜作为种用个体,而后使用基因组选配、同质选配、异质选配、随机交配4种不同的选配方案。其中基因组选配中分别选取遗传进展最大的解、家系间方差最大的解、近交最小的解所对应的交配方案进行选育。每种方案选育5个世代,比较其后代群体的平均GEBV、每世代的遗传进展、近交系数、遗传方差,并重复5次取平均值。结果表明,3种基因组选配方案的ΔG均显著高于随机交配和异质选配（P<0.01）,而且,选取遗传进展最大的基因组选配方案的ΔG比同质选配还高出4.3%。3种基因组选配的方案的ΔF比同质选配低22.2%~94.1%,而且选取近交最小的基因组选配方案ΔF比异质选配低11.8%。同质选配的遗传方差迅速降低,在第5世代显著低于除基因组选配中选择遗传进展最大的方案以外的所有方案（P<0.05）,3种基因组选配方案的遗传方差比同质选配高10.8%~32.2%。这表明基因组选配不仅可以获得比同质选配更高的遗传进展,同时有效的降低了近交水平,并且减缓了遗传方差降低速度,保证了一定的遗传变异。基因组选配作为一种有效的可持续育种方法,在畜禽育种中开展十分有必要。     

The use of mathematical programming to control inbreeding in selection schemes

Selection on the best estimate of the breeding value of individuals should, in large populations, provide the maximal response in breeding value. However, many breeders deal with the selection of small numbers of animals from relatively small populations and therefore there is a trend for inbreeding to rise because of genetic drift. Moreover, as the evaluation of candidates is traditionally based on methodologies including information from relatives [selection indices, best linear unbiased predictor (BLUP)] more individuals are selected from the best families and so closely related individuals will generate most of the offspring. This effect is more important for traits with low heritability as phenotype gives little information on the breeding value of the individuals and more weight is given to relatives’ data. The need for controlling inbreeding refers not only to a better use of the genetic variability available and to a reduced inbreeding depression in the selected trait, but also to a reduced depression of fitness-related traits, which may be the most serious drawback at present due to the increase in inbreeding in domestic populations (M euwissen and W oolliams 1994). In recent years considerable work has been carried out on the design of strategies to maintain genetic diversity in selection programmes. These strategies are aimed at simultaneously optimizing genetic gain and inbreeding, either by reducing the rate of inbreeding (or variance of response) while keeping genetic gains at a predetermined level, or by increasing selection response under a restriction on inbreeding (or on variance of response). Following T oro and P& eacute ; rez -E nciso (1990) the different strategies can be classified according to the factor on which they act: (i) the selection criterion used; (ii) the mating system imposed; (iii) the number of selected individuals and their contribution to the next generation. The first group of strategies proposes the use of a suboptimal selection criterion that reduces the weight given to family information or the use of an upward-biased heritability in BLUP evaluation (T oro and P& eacute ; rez -E nciso 1990; see G rundy et al. 1998a for the latest development of this idea). The second group of strategies proposes action on the mating system including factorial mating designs, minimum co-ancestry mating (using linear programming) or compensatory mating (see review by C aballero et al. 1996). The third group of strategies includes the ones considered in the present work. The first possibility is to modify the contribution of the selected individuals of generation t to the selected individuals of generation t + 1, by practising some form of within-family selection with respect to BLUP values. Two strategies of this type were considered: modified within-family selection (MWFS) and restricted co-ancestry selection (RCS). The second possibility is to modify the contribution of the selected individuals of generation t to the evaluated individuals of generation t + 1 (instead of to the selected individuals) by a strategy called weighted selection (T oro and N ieto 1984). Three strategies were considered in this case: weighted selection (WS), restricted co-ancestry weighted selection (RCWS) and pair weighted selection (PWS). More specifically, the aim of the present paper is to show how these five strategies can be implemented using mathematical programming techniques. A small example comparing all of these strategies with standard truncation selection (TS) is also given for illustration.     

A comparison of restricted selection procedures to control genetic gains

Using Monte Carlo simulation, two schemes of restricted selection were compared under various combinations of genetic parameters and constraints on the genetic gains. The first selection scheme is the combination of best linear unbiased prediction (BLUP) evaluation and linear programming technique (BLUP + LP), and the second one is based on the restricted BLUP selection (RBLUP). Selection for two traits was supposed, in which animals were selected to maximize the genetic gain in trait 2 (Δg₂) under a proportional restriction on the genetic gain in trait 1 (Δg₁) to satisfy the intended ratio (Δg₁:Δg₂). Little differences were found between the two selection schemes with respect to the genetic gains averaged over replicates. However, in all the cases studied, the variance of genetic gains among replicates under BLUP + LP selection was smaller and less sensitive to the genetic parameters and the intended restriction than RBLUP selection. Under the situations of antagonistic selection, the difference tended to be larger. When the heritabilities of the two traits were different, RBLUP selection remarkably increased the variance of genetic gain in a trait with a higher heritability. These results suggest that BLUP + LP selection should always be preferable to RBLUP selection because of the smaller risk of selection. This choice is especially important for the situation where the genetic parameters act as limiting factors for the achievement of intended genetic gains.