Marker-assisted selection for commercial crossbred performance

Several studies have shown that selection of purebreds for increased performance of their crossbred descendants under field conditions is hampered by low genetic correlations between purebred and commercial crossbred (CC) performance. Although this can be addressed by including phenotypic data from CC relatives for selection of purebreds through combined crossbred and purebred selection (CCPS), this also increases rates of inbreeding and requires comprehensive systems for collection of phenotypic data and pedigrees at the CC level. This study shows that both these limitations can be overcome with marker-assisted selection (MAS) by using estimates of the effects of markers on CC performance. To evaluate the potential benefits of CC-MAS, a model to incorporate marker information in selection strategies was developed based on selection index theory, which allows prediction of responses and rates of inbreeding by using standard deterministic selection theory. Assuming a genetic correlation between purebred and CC performance of 0.7 for a breeding program representing a terminal sire line in pigs, CC-MAS was shown to substantially increase rates of response and reduce rates of inbreeding compared with purebred selection and CCPS, with 60 CC half sibs available for each purebred selection candidate. When the accuracy of marker-based EBV was 0.6, CC-MAS resulted in 34 and 10% greater responses in CC performance than purebred selection and CCPS. Corresponding rates of inbreeding were 1.4% per generation for CC-MAS, compared with 2.1% for purebred selection and 3.0% for CCPS. For marker-based EBV with an accuracy of 0.9, CC-MAS resulted in 75 and 43% greater responses than purebred selection and CCPS, and further reduced rates of inbreeding to 1.0% per generation. Selection on marker-based EBV derived from purebred phenotypes resulted in substantially less response in CC performance than in CC-MAS. In conclusion, effective use of MAS requires estimates of the effect on CC performance, and MAS based on such estimates enables more effective selection for CC performance without the need for extensive pedigree recording and while reducing rates of inbreeding.     

Theoretical efficiency of multiple-trait quantitative trait loci-assisted selection

The effectiveness of five selection methods for genetic improvement of net merit comprising trait 1 of low heritability (h² = 0.1) and trait 2 of high heritability (h² = 0.4) was examined: (i) two‐trait quantitative trait loci (QTL)‐assisted selection; (ii) partial QTL‐assisted selection based on trait 1; (iii) partial QTL‐assisted selection based on trait 2; (iv) QTL‐only selection; and (v) conventional selection index without QTL information. These selection methods were compared under 72 scenarios with different combinations of the relative economic weights, the genetic correlations between traits, the ratio of QTL variance to total genetic variance of the trait, and the ratio of genetic variances between traits. The results suggest that the detection of QTL for multiple‐trait QTL‐assisted selection is more important when the index traits are negatively correlated than when they are positively correlated. In contrast to literature reports that single‐trait marker‐assisted selection (MAS) is the most efficient for low heritability traits, this study found that the identified QTL of the low heritability trait contributed negligibly to total response in net merit. This is because multiple‐trait QTL‐assisted selection is designed to maximize total net merit rather than the genetic response of the individual index trait as in the case of single‐trait MAS. Therefore, it is not economical to identify the QTL of the low heritability traits for the improvement of total net merit. The efficient, cost‐effective selection strategy is to identify the QTL of the moderate or high heritability traits of the QTL‐assisted selection index to facilitate total economic returns. Detection of the QTL of the low h² traits for the QTL‐assisted index selection is justified when the low h² traits have high negative genetic correlation with the other index traits and/or when both economic weights and genetic variances of the low h² traits are larger as compared to the other index traits of higher h². This study deals with theoretical efficiency of QTL‐assisted selection, but the same principle applies to SNP‐based genomic selection when the proportion of the genetic variance ‘explained by the identified QTLs’ in this study is replaced by ‘explained by SNPs’.     

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.     

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.     

Optimization of selection and mating schemes in closed broiler lines

Minimum coancestry mating (MC) is a simple mating system to reduce inbreeding in populations, in which matings are allocated so as to minimize the average inbreeding coefficient of progeny. This system was compared with random mating (RM) in simulated broiler lines. The population structure and genetic parameters were determined on the basis of an existing broiler line. Comparison of mating systems was made under two selection methods. The first method (DIS) was based on selection index for achieving desired genetic gains. In the second method (LPS), a combination of the family index and linear programming technique was applied to obtain the desired genetic gains. The selected traits were body weight at 6 weeks of both sexes and age at sexual maturity of hen. Four schemes by all the possible combinations of selection and mating methods (DIS + RM, DIS + MC, LPS + RM and LPS + MC) were compared in terms of genetic gains and inbreeding during 15 generations of selection and mating. The results obtained are summarized as follows: (i) the four schemes produced similar genetic gains averaged over replicates; (ii) the variations of genetic gains under LPS + RM and LPS + MC schemes were much smaller than under DIS + RM and DIS + MC schemes; (iii) irrespective of the selection methods, MC reduced the average inbreeding coefficients to about 80% of RM and; (iv) the inbreeding coefficients of individuals in the schemes with RM were distributed in a wide range, while the inbreeding coefficients in the schemes with MC showed a high uniformity. From these results, the LPS + MC scheme was recommended as a selection and mating strategy in closed broiler lines.     

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.     

Developments in prediction theories of the effective size of populations under selection

The effective population size is a key parameter in the definition of selection programs, because the magnitude of this parameter determines both the rate of inbreeding and the amount of genetic drift in the population. Prediction of the effective size of selected populations is complicated by the fact that selection has a cumulative effect on the effective size. In the present article, two basic approaches to predict the effective size of populations under selection were summarized, and the interrelation among them was clarified. Several extensions to practical situations relevant to animal breeding, such as non‐random mating, index selection and marker‐assisted selection, were also reviewed.     

Linkage disequilibrium and selection response in two-stage marker-assisted selection of dairy cattle over several generations

A stochastic simulation was carried out to investigate the advantage of marker‐assisted selection (MAS) in comparison with traditional selection over several generations. The selection goal was a sex‐limited trait or a linear combination of traits with a polygenic component, two unlinked additive QTL and a non‐genetic component. The simulated QTL were moderate or large and the allele frequencies were varied. Two stages of selection among the male offspring were carried out. In the first stage marker information was used to select among full sibs (MAS) or one full sib was chosen at random. In the second stage young bulls were selected based on a progeny test. The response in total genetic gain was faster with MAS than with traditional selection and persisted over several generations. With a QTL of moderate size and initial allele frequencies of the favourable allele of 0.05 the response with MAS was 6% higher than with traditional selection in the sires selected after progeny test. MAS in a within‐family two‐stage selection scheme improved the genetic merit of selected bulls even when linkage disequilibrium between QTL and polygenes was initially increased.     

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.     

Genomic selection strategies to improve maternal traits in Norwegian White Sheep

This study tested and compared different implementation strategies for genomic selection for Norwegian White Sheep, aiming to increase genetic gain for maternal traits. These strategies were evaluated for their genetic gain ingrowth, carcass and maternal traits, total genetic gain, a weighted sum of the gain in each trait and rates of inbreeding through a full-scale stochastic simulation. Results showed genomic selection schemes to increase genetic gain for maternal traits but reduced genetic gain for other traits. This could also be obtained by selecting rams for artificial selection at a higher age. Implementation of genomic selection in the current breeding structure increased genetic gain for maternal traits up to 57%, outcompeted by reducing the generation interval for artificial insemination rams from current 3 to 2 years. Then, total genetic gain for maternal traits increased by 65%–77% and total genetic gain by18%–20%, but at increased rates of inbreeding.     

Comparison of selection methods at the same level of inbreeding.

Animal geneticists predict higher genetic responses to selection by increasing the accuracy of selection using BLUP with information on relatives. Comparison of different selection methods is usually made with the same total number tested and with the same number of parents and mating structure so as to give some acceptable (low) level of inbreeding. Use of family information by BLUP results in the individuals selected being more closely related, and the levels of inbreeding are increased, thereby breaking the original restriction on inbreeding. An alternative is to compare methods at the same level of inbreeding. This would allow more intense selection (fewer males selected) with the less accurate methods. Stochastic simulation shows that, at the same level of inbreeding, differences between the methods are much smaller than if inbreeding is unrestricted. If low to moderate inbreeding levels are targeted, as in a closed line of limited size, then selection on phenotype can yield higher genetic responses than selection on BLUP. Extra responses by BLUP are at the expense of extra inbreeding. The results derived here show that selection on BLUP of breeding values may not be optimal in all cases. Thus, current theory and teaching on selection methods are queried. Revision of the methodology and a reappraisal of the optimization results of selection theory are required.     

Selection response in Tribolium to an index modified by introducing between-family or within-family or both restrictions in two steps

A fundamental strategy in selection programs is to combine maximum rate of response and minimum rate of inbreeding, these goals being in conflict with each other. Maximum selection response can be achieved at a cost of erosion in the effective number of breeding animals (a measure of the inbreeding level); reciprocally, the maximum effective number under selection can be preserved with a low response. The simultaneous consideration of both factors makes it difficult to decide on the use of individual (more effective in conserving effective number) or combined selection (maximizes response but yields low effective size). Q uinton et al. (1992) showed that comparing selection methods at the same level of inbreeding, rather than at the same selection intensity, changes the perspectives of current selection theory. If low to moderate inbreeding levels are considered, then phenotypic selection can yield higher response than selection on more accurate methods. Different methods have been proposed for maximizing selection response at the same level of inbreeding, i.e. to restrict the number of close relatives selected (N icholas and S mith 1983), to use false high heritability estimates in the genetic evaluation (G rundy and H ill 1993), to use assortative (S mith and H ammond 1986) or compensatory (G rundy et al. 1994) matings, to adjust estimated breeding values for the relationship with the already selected ones (G oddard and S mith 1990), to avoid matings of related individuals (T oro and P erez -E nciso 1990), or to use factorial rather than hierarchical matings (W oolliams 1989; L eitch et al. 1994). Q uinton and S mith (1995) compared the merits of these methods using stochastic simulation; they concluded that none of the methods was best over all conditions, and that the use of false high heritabilities, or adjusted estimated breeding values with the relationships, does not seem to be recommended; besides, mating together those individuals with the lowest relationship has little effect on the accumulated inbreeding. W ray and G oddard (1994), and B risbane and G ibson (1995) indicated that if G_n is the genetic mean after n generations of selection and F_n is the mean inbreeding coefficient, a reasonable selection objective is G_n ? DF_n, where D is the value of a unit of inbreeding relative to a unit of genetic gain. M euwissen (1997) showed that these methods do not guarantee maximum genetic gains at some level of inbreeding and presented a rule for maximizing the genetic response with a predefined rate of inbreeding. His algorithm can be used to put a constraint on the variance of the selection response by replacing the additive relationship matrix by the prediction error variance (W oolliams and M euwissen 1993). W ei (1995a) developed a restricted phenotypic selection by considering limits on the number of individuals that will be selected from a family or on the family number selected. This less sophisticated method balances response and inbreeding. A restriction on the family number may lead to an increased response (but a decreased effective size), whereas restricting the proportion of selected individuals from a family is an efficient way to control the inbreeding (decreased response). W ei (1995b) generalized the method by introducing both restrictions. In this study, rates of response were compared under between-family, within-family, or both restrictions for a two-trait selection index in a short-term experiment with Tribolium.     

A mating system to reduce inbreeding in selection programmes: Theoretical basis and modification of compensatory mating

Increased rate of inbreeding in selection programmes may have an important effect on mid- and long-term selection response and reproductive performance through reduction in genetic variance and inbreeding depression. Selection on an inherited trait inflates the rate of inbreeding and reduces the effective population size (R obertson 1961; S antiago and C aballero 1995). This can be particularly important in selection based on index with information from relatives (L ush 1947) or best liner unbiased prediction (BLUP) with an animal model (H enderson 1984). In recent years, various methods have been proposed to reduce the rates of inbreeding in selection programmes while keeping genetic gains at the same level. These methods assume various selection and mating strategies. G rundy et al. (1994) showed that the use of biased heritability estimates for BLUP evaluation is one of the simplest and most efficient methods. A direct reduction in the weight on family mean in index selection (T oro and P erez -E nciso 1990), selection for weighted ancestral Mendelian sampling estimates (W oolliams and T hompson 1994; G rundy et al. 1998) and limited use of selected parents (T oro and N ieto 1984; W ei 1995) have also been shown to be efficient methods. Other methods include nonrandom matings of selected parents, such as factorial mating designs (W oolliams 1989), minimum coancestry mating (T oro et al. 1988) and compensatory mating (S antiago and C aballero 1995). Simultaneous optimization of the selection of candidates and their mating allocations has been also considered through mate selection with linear programming techniques (T oro and P erez -E nciso 1990). Among these methods, compensatory mating is a very simple and efficient method (G rundy et al. 1994; S antiago and C aballero 1995; C aballero et al. 1996). This mating system was derived from the theoretical consideration on effective population size under selection (S antiago and C aballero 1995). Although S antiago and C aballero (1995) considered that implementation of this mating could counteract the cumulative effect of selection on the effective population size, the theoretical basis has been little studied. In this paper, the author gives the theoretical basis of compensatory mating. A modification to enhance the effect of compensatory mating is also proposed and the efficiency is examined by stochastic simulation.     

Use of marker haplotypes to refine covariances among relatives for breeding value estimation

Markers flanking DNA regions, where quantitative trait loci (QTL) have been previously spotted, can be used to trace the common inheritance of major genes for a better definition of covariances among animals. A practical approach to the use of marker data to refine the additive relationship matrix used in the traditional best linear unbiased prediction (BLUP) methodology is presented. The technique allows the number of the mixed model equations to be kept to an animal level, blending polygenic pedigree data with marker haplotype information. The advantage of this marker-assisted selection (MAS) approach over BLUP selection has been assessed through a stochastic simulation. A finite locus model with 32 independent biallelic loci was generated with normally distributed allelic effects. The heritability of the trait, measured on both sexes and on females only, was set to 0.2 and 0.5. Five-allelic markers 2, 10 and 20 cM apart, bracketed the QTL with the largest effect on the trait, accounting for 17% of the genetic variance. The bracketed QTL had two or eight alleles and its position was undefined within the bracket. Results show a moderate 2% advantage of MAS over BLUP in terms of higher genetic response when trait was recorded on both sexes and heritability was 0.2. The benefit is in the short term, but it lasts longer with polyallelic QTL. When the trait was recorded on females only, MAS produced only a small and insignificant genetic gain, but reduced the overall inbreeding in the population. MAS was also inefficient when heritability was 0.5.     

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.     

Genomic selection

Genomic selection is a form of marker-assisted selection in which genetic markers covering the whole genome are used so that all quantitative trait loci (QTL) are in linkage disequilibrium with at least one marker. This approach has become feasible thanks to the large number of single nucleotide polymorphisms (SNP) discovered by genome sequencing and new methods to efficiently genotype large number of SNP. Simulation results and limited experimental results suggest that breeding values can be predicted with high accuracy using genetic markers alone but more validation is required especially in samples of the population different from that in which the effect of the markers was estimated. The ideal method to estimate the breeding value from genomic data is to calculate the conditional mean of the breeding value given the genotype of the animal at each QTL. This conditional mean can only be calculated by using a prior distribution of QTL effects so this should be part of the research carried out to implement genomic selection. In practice, this method of estimating breeding values is approximated by using the marker genotypes instead of the QTL genotypes but the ideal method is likely to be approached more closely as more sequence and SNP data is obtained. Implementation of genomic selection is likely to have major implications for genetic evaluation systems and for genetic improvement programmes generally and these are discussed.     

Optimal genetic contribution selection in Danish Holstein depends on pedigree quality

The aim of this study was to assess the importance of pedigree depth when performing optimal contribution selection as implemented in the software program EVA. This was done by applying optimal genetic contribution in the breeding program of the major Danish Dairy breed Danish Holstein. In the analyses earlier breeding decisions were considered by including all AI waiting- and young bulls and contract matings. Twenty potential sires, 2169 potential dams, 1421 AI-bulls and 754 contract matings plus pedigree animals were included. Results showed that the outcome was very dependent on quality of pedigree, also for information going more than 25 years (5–7 generations) back. The analyses showed that EVA works satisfactorily as a management tool for planning of breeding schemes with respect to contributions of sires of sons at population level in maximising the genetic gain, while controlling the increase in future inbreeding. The more weight put on the average additive genetic relationship in next generation relative to genetic merit, the lower the average merit of the matings, and the lower average additive genetic relationship among the chosen matings and the present breeding animals. Furthermore more weight on average additive genetic relationship gives a more diverse use of sires of sons. Given the potential sires and dams the average additive genetic relationship among the selected matings and the present breeding animals can be reduced from 0.1621 to 0.1495 at the cost of 0.7 genetic S.D. units at the total merit index. This reduction was obtained when selection was only on reduction of average relationship compared to selection only on genetic merit. Optimal genetic contribution selection is a promising tool for managing breeding schemes for populations facing inbreeding problems, such as Danish Holstein and other dairy breeds. However sufficient pedigree information is a necessity.     

Restricting inbreeding while maintaining selection response for weight gain in Mus musculus

An experiment with mice was designed to test the relative efficiency of three selection methods that help to minimize the rate of inbreeding during selection. A common house mice (Mus musculus) population was selected for 17 generations to increase the weight gain between 21 and 42 days. The population was split at random into three lines A, B and C where three selection methods were applied: individual selection and random mating, weighted selection with random mating and individual selection with minimum coancestry mating, respectively. There were three replicates for each line. Cumulated selection response was similar in the three lines, but there were differences in the level of inbreeding attained (in percentage): 31.24 (method A), 24.72 (method B) and 27.88 (method C). As consequence, lines B and C (weighted selection and minimum coancestry) showed a lower value of deterioration of fitness traits (the intrauterine mortality and the mortality at birth) than line A (random mating).     

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.     

标记辅助选择在猪育种中应用效果的研究

本研究针对猪育种中重点考虑的窝产活仔猪数（NBA）、达100 kg体重日增重（ADG）、饲料利用率（FCR）、达100 kg体重的背膘厚（BF）、肌内脂肪含量（IMF） 5个性状,利用连锁平衡（linkage equilibrium,LE）、连锁不平衡（linkage disequilibrium,LD）标记和直接标记（direct marker,DR）3种类型的分子遗传标记,设计了3个规模不同的基础群,母猪数分别为100、200、300头,公猪数都为10头,基础群个体间无亲缘关系,育种群实施闭锁繁育。用Monte Carlo方法模拟了MAS的5个世代选择试验。育种值估计采用标准BLUP（Standard BLUP,SBLUP）模型（此育种值作为对照）、QBLUP模型（使用DR标记）、MBLUP模型（使用LD和LE标记）。结果表明,利用DR标记在各种情况下都比利用LD和LE标记获得的选择效率高;5个性状中,MAS对低遗传力、限性性状NBA的选择效率最高;当性状的QTL方差占遗传方差基本相同时,中等遗传力性状FCR的选择效率比高遗传力性状BF的更高;当性状的遗传力差异不大时,QTL方差占遗传方差比例大的性状FCR的选择效率比QTL方差占遗传方差比例小的性状ADG的更高。当利用QBLUP模型时,MAS对NBA的选择效率最高,ADG的选择效率最低。