BLUP Analysis Research Articles

Accuracy of genomic prediction using deregressed breeding values estimated from purebred and crossbred offspring phenotypes in pigs.

Genomic selection is applied to dairy cattle breeding to improve the genetic progress of purebred (PB) animals, whereas in pigs and poultry the target is a crossbred (CB) animal for which a different strategy appears to be needed. The source of information used to estimate the breeding values, i.e., using phenotypes of CB or PB animals, may affect the accuracy of prediction. The objective of our study was to assess the direct genomic value (DGV) accuracy of CB and PB pigs using different sources of phenotypic information. Data used were from 3 populations: 2,078 Dutch Landrace-based, 2,301 Large White-based, and 497 crossbreds from an F1 cross between the 2 lines. Two female reproduction traits were analyzed: gestation length (GLE) and total number of piglets born (TNB). Phenotypes used in the analyses originated from offspring of genotyped individuals. Phenotypes collected on CB and PB animals were analyzed as separate traits using a single-trait model. Breeding values were estimated separately for each trait in a pedigree BLUP analysis and subsequently deregressed. Deregressed EBV for each trait originating from different sources (CB or PB offspring) were used to study the accuracy of genomic prediction. Accuracy of prediction was computed as the correlation between DGV and the DEBV of the validation population. Accuracy of prediction within PB populations ranged from 0.43 to 0.62 across GLE and TNB. Accuracies to predict genetic merit of CB animals with one PB population in the training set ranged from 0.12 to 0.28, with the exception of using the CB offspring phenotype of the Dutch Landrace that resulted in an accuracy estimate around 0 for both traits. Accuracies to predict genetic merit of CB animals with both parental PB populations in the training set ranged from 0.17 to 0.30. We conclude that prediction within population and trait had good predictive ability regardless of the trait being the PB or CB performance, whereas using PB population(s) to predict genetic merit of CB animals had zero to moderate predictive ability. We observed that the DGV accuracy of CB animals when training on PB data was greater than or equal to training on CB data. However, when results are corrected for the different levels of reliabilities in the PB and CB training data, we showed that training on CB data does outperform PB data for the prediction of CB genetic merit, indicating that more CB animals should be phenotyped to increase the reliability and, consequently, accuracy of DGV for CB genetic merit.

Use of genomic recursions and algorithm for proven and young animals for single-step genomic BLUP analyses--a simulation study.

The purpose of this study was to examine accuracy of genomic selection via single-step genomic BLUP (ssGBLUP) when the direct inverse of the genomic relationship matrix (G) is replaced by an approximation of G(-1) based on recursions for young genotyped animals conditioned on a subset of proven animals, termed algorithm for proven and young animals (APY). With the efficient implementation, this algorithm has a cubic cost with proven animals and linear with young animals. Ten duplicate data sets mimicking a dairy cattle population were simulated. In a first scenario, genomic information for 20k genotyped bulls, divided in 7k proven and 13k young bulls, was generated for each replicate. In a second scenario, 5k genotyped cows with phenotypes were included in the analysis as young animals. Accuracies (average for the 10 replicates) in regular EBV were 0.72 and 0.34 for proven and young animals, respectively. When genomic information was included, they increased to 0.75 and 0.50. No differences between genomic EBV (GEBV) obtained with the regular G(-1) and the approximated G(-1) via the recursive method were observed. In the second scenario, accuracies in GEBV (0.76, 0.51 and 0.59 for proven bulls, young males and young females, respectively) were also higher than those in EBV (0.72, 0.35 and 0.49). Again, no differences between GEBV with regular G(-1) and with recursions were observed. With the recursive algorithm, the number of iterations to achieve convergence was reduced from 227 to 206 in the first scenario and from 232 to 209 in the second scenario. Cows can be treated as young animals in APY without reducing the accuracy. The proposed algorithm can be implemented to reduce computing costs and to overcome current limitations on the number of genotyped animals in the ssGBLUP method.

The effects of demography and long-term selection on the accuracy of genomic prediction with sequence data.

The use of dense SNPs to predict the genetic value of an individual for a complex trait is often referred to as "genomic selection" in livestock and crops, but is also relevant to human genetics to predict, for example, complex genetic disease risk. The accuracy of prediction depends on the strength of linkage disequilibrium (LD) between SNPs and causal mutations. If sequence data were used instead of dense SNPs, accuracy should increase because causal mutations are present, but demographic history and long-term negative selection also influence accuracy. We therefore evaluated genomic prediction, using simulated sequence in two contrasting populations: one reducing from an ancestrally large effective population size (Ne) to a small one, with high LD common in domestic livestock, while the second had a large constant-sized Ne with low LD similar to that in some human or outbred plant populations. There were two scenarios in each population; causal variants were either neutral or under long-term negative selection. For large Ne, sequence data led to a 22% increase in accuracy relative to ∼600K SNP chip data with a Bayesian analysis and a more modest advantage with a BLUP analysis. This advantage increased when causal variants were influenced by negative selection, and accuracy persisted when 10 generations separated reference and validation populations. However, in the reducing Ne population, there was little advantage for sequence even with negative selection. This study demonstrates the joint influence of demography and selection on accuracy of prediction and improves our understanding of how best to exploit sequence for genomic prediction.

Selection of sugar cane families by using BLUP and multi-diverse analyses for planting in the Brazilian savannah

This study evaluated different strategies to select sugar cane families and obtain clones adapted to the conditions of the Brazilian savannah. Specifically, 7 experiments were conducted, with 10 full sib families, and 2 witnesses in common to all experiments, in each experiment. The plants were grown in random blocks, with witnesses in common (incomplete blocks), and 6 repetitions of each experiment. The data were analyzed through the methodology of mixed patterns, in which the matrices of kinship between the families were identified by the method of restricted maximum likelihood. The characteristics that were evaluated included soluble solids content (BRIX), BRIX ton/ha, average mass of a culm, number of culms/m, and tons of culms/ha. A multi-diverse alternative based on the analysis of groupings by using the UPGMA method was used to identify the most viable families for selection, when considering the genotypic effects on all characteristics. This method appeared suitable for the selection of families, with 5 family groups being formed. The families that formed Group 2 appeared superior to all other families for all the evaluated characteristics. It is recommended that the families in Group 2 are preferentially used in sugar cane improvement programs to obtain varieties optimally adapted to the conditions of the Brazilian savannah.

Possibilities to improve the genetic evaluation of a rare breed using limited genomic information and multivariate BLUP

The use of molecular genetic information in the evaluation of livestock has become more common. This study looks at the efficacy of using such information to improve the genetic evaluation of a rare breed of dual-purpose cattle. Data were available in the form of pedigree information on the Gloucester cattle breed in the United Kingdom and recorded milk and beef performance on a small number of animals. In addition, molecular genetic information in the form of multi-marker, multiple regression results converted to a 1 to 10 score (Igenity scores) and 123 single nucleotide polymorphism (SNP) genotypes for 199 non-recorded animals were available. Appropriate mixed-animal models were explored for the recorded traits and these were used to calculate estimated breeding values (EBV), and their accuracies, for 6527 animals in the breed’s pedigree file. Various ways to improve the accuracy of these EBV were explored. This involved using multivariate BLUP analyses, genomic estimated breeding values (GEBV) and combining Igenity scores with recorded traits in a series of bivariate genetic analyses. Using the milk recording traits as an example, the accuracy of a number of traits could be improved using multivariate analyses by up to 14%, depending on the combination of traits used. The level of increase in accuracy largely corresponded to the absolute difference between the genetic and residual correlations between two traits, but this was not always symmetrical. The use of GEBV did not increase the accuracy of milk trait EBV owing to the low proportion of variance explained by the 101 SNPs used. Using Igenity scores in bivariate analyses with the recorded data was more successful in increasing EBV accuracy. The largest increases were found in genotyped animals with no recorded performance (e.g. a 58% increase in fat weight in milk); however, the size of the increase depended on the level of the genetic correlation between the recorded trait and the Igenity score for that trait. Lower levels of improvements in accuracy were seen in animals that were recoded but not genotyped, and ancestors which were neither genotyped nor recorded. This study demonstrated that it was possible to improve the accuracy of EBV estimation by including Igenity score information in genetic analyses but it also concluded that increasing the level of performance recording in the breed would be beneficial.

PIT marker assisted family establishment in rainbow trout and rapid growth families screening

Cold-water fish culture first began in China in 1959 with a shipment of eyed eggs and fry of rainbow trout(Oncorhynchus mykiss) from the Democratic People's Republic of Korea.Since then,rainbow trout culture has expanded rapidly into more than 22 provinces.However,further advances depend on accelerating the process of selective breeding and preventing the genetic degeneration of this species.We evaluated the utility of PIT marker assisted selection using a generation one(G1) of a rainbow trout superior strain population which was be-ing selectively bred by the Heilongjiang River Fishery Research Institute(HRFRI) of the Chinese Academy of Fishery Sciences(CAFS).We developed 72 rainbow trout families using PIT marker assisted technology.All pedigreed fry were implanted with PIT markers and cultured in the same pond.Body weight and body length were measured for all the market size rainbow trout individuals 850 days after fertilization to screen for rapid growth families.The family effect was highly significantly for both body weight and body length(P0.01).We obtained 8 rapid-growth families in which the family effects for body weight and body length were both significant(P0.05).The family numbers were 682BABB,6717B7A,6828308,682A50A,6829C24,6829DC7,682A382,and 68284DA.Our results may be compared with our previous work based on BLUP analysis of individual estimated breeding values.Our study provides insight into methods for improving the accuracy of genetic selection for growth traits in rainbow trout,and for genetics and breeding research into quantitative traits in other aquatic ani-mals.

Predicted genetic gain and realised gain in stand volume of Eucalyptus globulus

Realised gains in stand volume of Eucalyptus globulus Labill. families at 7–9 years were compared with gains predicted at 3.5 years. Gain predictions were based on height, diameter at breast height (DBH), sectional area, and stem volume for 153 full-sib families and 18 commercial checks in five-tree line plots on three West Australian sites. Single-site narrow-sense heritability estimates were 0.12–0.24 for height, 0.08–0.12 for DBH, 0.09–0.13 for sectional area, and 0.14–0.19 for stem volume. Genetic dominance effects were significant (p < 0.05) in most cases, and the estimated dominance/additive genetic variance ratio was heterogeneous for height and DBH. Stand volume was measured for 93 of the same families and checks in 40-tree block plots on four sites. Heritability of stand volume was 0.25–0.76, with an across-sites estimate of 0.41. Dominance effects were statistically absent at two sites. Estimated region-wide additive genetic correlations between selection traits (in line plots) and stand volume (in block plots) ranged from 0.86 to 0.90. Estimated stand volume gain was 23 % of the mean for the best 12 % of families and 14 % of the mean for the best 24 % of families. Realised gain was under-estimated by predictions based on height, DBH, and sectional area, which had smaller coefficients of additive variation than did stem volume. It is concluded that although BLUP analysis of early-age height and DBH can provide for indirect selection on E. globulus stand volume, analysis of stem volume is required to predict genetic gain at an appropriate scale.

Applications of multi-trait selection in common bean using real and simulated experiments

The analysis of multiples traits has been largely employed in animal and forestry crop breeding; however, in annual crops such as common bean this approach is practically lacking. This study examined the selective accuracy and estimates of genetic parameters in common bean using single- and multi-trait analyses in several designs of genetic correlations and heritabilities by means of simulated- and real-traits. We also compared the efficiency of the Bayesian and REML methods as regarding its selective accuracy and estimates of genetic parameters. In real data experiments, 100 endogamic families of common bean were assessed for grain yield (GY) and grain type (GT) in three environments using a 10 × 10 triple lattice design. Single- and multi-trait analyses were applied for these traits using REML-based BLUP analysis and Bayesian methods. In simulated experiments, traits corresponding to GY and yield components in common bean were simulated under several levels of genetic correlations and evaluated under different levels of heritability in order to verify in which genetic/experimental design it is advantageous to apply single- or multi-trait analyses. The results obtained in this study indicated that GY and GT present low genetic correlation and, therefore, multi-trait analysis may be unjustifiable for these traits. The Bayesian and REML multi-trait analyses were equivalent in point and interval estimates of genetic parameters and predictive accuracy, both for the field and simulated experiments. In addition, it was found that multi-trait analysis is justified in situations where the traits present low/moderate heritability and medium/high genetic correlations among them. It also was found that GY in common bean may be outstandingly favored in accuracy when evaluated jointly with its components. Thus, one can conclude that the simultaneous analysis of GY and yield components in common bean may provide superior gains accuracy and selection efficiency, being the response to selection better obtained by use of the multi-trait heritability.

Effect of BLUP prediction on genomic selection: practical considerations to achieve greater accuracy in genomic selection

Background Prediction of breeding values (BV) using only genotypic information is the final goal of Genomic Selection (GS) [1]. Commonly, BV prediction from traditional BLUP analysis is the input for constructing GS prediction models, and GS predicted BVs are correlated with traditional BLUP BVs to estimate the accuracy of GS models. The use of GS in plant breeding depends on the accuracy of the GS models to predict the BVs. Therefore, better accuracy and less bias in traditional BLUP BVs should improve the final accuracy of GS predictions. Such improvements in GS predictions are not due to GS modeling itself, but rather to the reduced noise in the BLUP BV used as input. Improvements in BLUP BV can be obtained simply by correcting errors in the pedigree [2] or using more complex approaches, such as applying a realized relationship matrix (RRM) in the BLUP prediction as an alternative to the relationship matrix (A) based on expected values derived from the pedigree [3]. Misspecification of effects in BLUP models tends to produce upward bias in the BV estimates, which also impact GS accuracy [4]. In addition, not correcting with the additive-genetic relationship information in the GS prediction model leads to overestimates in accuracies due to inadequate accounting for confounding genetic relationships found in the training population [5]. The inflated accuracy cannot be exploited in future generations and should be guarded against. Our objective was to use real data to study the effect on the GS accuracy from 1) pedigree errors, 2) incorporation of the RRM in the BLUP analysis, 3) misspecification of non-additive effects in the BLUP analysis and 4) the effect of ignoring the additive-genetic relationship in the GS prediction model.

Comparison of analyses of the QTLMAS XIV common dataset. I: genomic selection

BackgroundFor the XIV QTLMAS workshop, a dataset for traits with complex genetic architecture has been simulated and released for analyses by participants. One of the tasks was to estimate direct genomic values for individuals without phenotypes. The aim of this paper was to compare results of different approaches used by the participants to calculate direct genomic values for quantitative trait (QT) and binary trait (BT).ResultsParticipants applied 26 approaches for QT and 15 approaches for BT. Accuracy for QT was between 0.26 and 0.89 for males and between 0.31 and 0.89 for females, and for BT ranged from 0.27 to 0.85. For QT, percentage of lost response to selection varied from 8% to 83%, whereas for BT the loss was between 15% and 71%.ConclusionsBayesian model averaging methods predicted breeding values slightly better than GBLUP in a simulated data set. The methods utilizing genomic information performed better than traditional pedigree based BLUP analyses. Bivariate analyses was slightly advantageous over single trait for the same method. None of the methods estimated the non-additivity of QTL affecting the QT, which may be one of the constrains in accuracy observed in real data.

Applying different genomic evaluation approaches on QTLMAS2010 dataset

BackgroundWith the availability of high throughput genotyping, genomic selection, the evaluation of animals based on dense SNP genotyping, is receiving more and more attention. Several statistical methods have been suggested for genomic selection. Compared to traditional selection, genomic selection can be more accurate which can lead to higher efficiency in terms of time and cost. Herein we applied different genomic evaluation methods on the 14th QTLMAS dataset.MethodsFour different approaches were used for the estimation of EBV of animals for the Quantitative and the Binary Trait (QT and BT respectively). It included two Bayes B types of approaches (BB): using only SNP information (GBB) or SNP and Pedigree information (GPBB); and two genomic BLUP, GBLUP and GPBLUP. Traditional BLUP was also used only for comparison. When using BB methodology, the probability of SNP having an effect on the traits (which include a quantitative and a binary trait) were also estimated. We also performed “standard” QTL mapping approaches including linkage and association analyses to compare them with BB results as a potential QTL mapping tools.ResultsFor QT, the best accuracy of EBV (correlation between EBVs and TBVs) for young animals, was obtained by BB methods (r = 0.68). Genomic BLUP estimations (GBLUP and GPBLUP) were less accurate (r = 0.60 and 0.61 respectively). Similar results were obtained for the BT: r were estimated at 0.82, 0.82, 0.71 and 0.70 for GPBB, GBB, GPBLUP and GBLUP respectively. Using traditional BLUP, r was at 0.39 and 0.47 for QT and BT respectively. The genetic correlation between the two traits (approximated by the correlation between EBVs for BT and QT using GBB method) was as high as 0.58.ConclusionsBetter accuracies were obtained using BB methods, compared to BLUP analyses. Compared to the traditional BLUP, the accuracy of the EBVs was improved about 70% and 50% using BB and GBLUP methods respectively. The benefit of genomic selection was the same for both the QT and BT. Models with and without polygenic effect led to similar accuracies in the estimation of breeding values. The BT and QT were genetically correlated (r=0.58) which suggested that bivariate analyses may be of advantages. Signal profile by GBB followed well the true QTL patterns, which was consistent with good estimation of EBVs by this method, suggesting its potential value for QTL mapping.

Genetic parameters and evaluation of the Tunisian dairy cattle population for milk yield by Bayesian and BLUP analyses

A Markov Chain Monte Carlo Bayesian method and BLUP analyses were used on Tunisian dairy cattle data. Data included 92,106 lactation records collected on 37,536 animals over 19 freshening years, from 1983 to 2001. Each record was partitioned into the fixed effects of herd-year, month of calving, and age-parity, a permanent environmental effect, an additive genetic effect, and a residual effect. Posterior conditional distributions were determined for variance components and model effects. Solutions (BLUE) and posterior means for levels of herd-year, month of calving, and age-parity showed similar patterns. Posterior means of heritability and repeatability were 0.17 ± 18 × 10 − 5 and 0.39 ± 8 × 10 − 5 , respectively. Posterior means of bull's breeding values were compared to bull's BLUP solutions. BLUP solutions were obtained using 0.17 and 0.39, estimated from the data, and 0.25 and 0.40 estimates for heritability and repeatability, respectively. Rank correlations between bull's posterior means and BLUP breeding values were 0.998 and 0.994 using genetic parameters estimated from the data and from the literature, respectively. This correlation coefficient was 0.995 between bull's BLUP solutions using either of the two sets of genetic parameters.

Selection against genetic defects in conservation schemes while controlling inbreeding

We studied different genetic models and evaluation systems to select against a genetic disease with additive, recessive or polygenic inheritance in genetic conservation schemes. When using optimum contribution selection with a restriction on the rate of inbreeding (ΔF) to select against a disease allele, selection directly on DNA-genotypes is, as expected, the most efficient strategy. Selection for BLUP or segregation analysis breeding value estimates both need 1–2 generations more to halve the frequency of the disease allele, while these methods do not require knowledge of the disease mutation at the DNA level. BLUP and segregation analysis methods were equally efficient when selecting against a disease with single gene or complex polygene inheritance, i.e. knowledge about the mode of inheritance of the disease was not needed for efficient selection against the disease. Smaller schemes or schemes with a more stringent restriction on ΔF needed more generations to halve the frequency of the disease alleles or the fraction of diseased animals. Optimum contribution selection maintained ΔF at its predefined level, even when selection of females was at random. It is argued that in the investigated small conservation schemes with selection against a genetic defect, control of ΔF is very important.

Analysis of Survival in Dairy Cows with Supplementary Data on Type Scores and Housing Systems from a Region of Northwest Germany

In survival analysis, type traits can be included as covariates to evaluate their use as predictors for survival. One problem in such an analysis is the availability of suitable data. Whereas data on the length of productive life (LPL) of individual cows can be retrieved from milk recording data, for type traits, all cows in the population must be scored for type at least once. In the present analysis, a dataset from the Osnabruck region in northwestern Germany, which fulfilled this requirement in recent years, was used. Data consisted of 169,733 cows with information on LPL for calving years 1980 to 1996 (dataset I) and of 39,233 cows with information on LPL and type for calving years 1990 to 1996 (dataset II). A further dataset (III) contained 43,116 cows from calving years 1987 to 1996 and included information on the housing system for each herd. The basic model included stage of lactation, relative production within herd, change of herd size, and year-season as time dependent effects; age at calving as a time-independent effect; and herd-year-season and sire as random effects. Other effects (information on type, housing system) were included additionally. For data-set II, the scores for 15 linear type traits were also included as corrected phenotypic values, estimated breeding values, and residuals from a previous BLUP analysis. The package Survival Kit 3.0 was used for all analyses. The results indicate a moderate heritability of 0.17 and 0.18 for true and functional LPL (dataset I). Almost all type traits analyzed (dataset II) exceeded a 0.001 level of significance in their effect on survival. The strongest relationships between survival and type were found for udder depth, fore udder attachment, and front teat placement. The main result from the comparison of housing systems (dataset III) was that bedding has a positive effect on survival.

Alternativas de análise de ensaios em látice no melhoramento vegetal

Compararam-se diferentes formas de análise de experimentos em blocos incompletos, abordadas como casos particulares de modelos mistos, quais sejam: (a) análise intrablocos, em que apenas o efeito do erro experimental é suposto aleatório; (b) análise interblocos (látice), com efeitos de blocos supostos aleatórios; (c) análise BLUP, com os efeitos de tratamentos supostos aleatórios, e (d) modelo aleatório. Além disso, montou-se a ANAVA, considerando duas alternativas: (e) usando o quadrado médio de tratamentos ajustados para blocos e o quadrado médio do erro efetivo do látice; (f) tomando as repetições como blocos completos. Um exemplo de análise de um teste de progênies de Eucalyptus grandis (Hill) Maiden ilustra as implicações da escolha dos modelos para fins de seleção e de caracterização genética de populações. Observou-se que em geral o ordenamento dos tratamentos sofreu maiores alterações ao se mudar a alternativa de análise do que as estimativas do progresso esperado pela seleção. Tendência que se reforça com a seleção mais intensa. As formas de análise que consideram a restrição da casualização (blocos incompletos) foram as mais precisas, e dentre estas, a análise BLUP de tratamentos é conceitualmente a melhor, pois os tratamentos eram progênies de polinização livre, sendo a que mais difere da análise usual do látice. Isto indica ser possível minorar os erros de seleção nas análises de blocos incompletos no melhoramento vegetal.

Genetic evaluation of Swedish standard‐bred trotters for racing performance traits and racing status

IntroductionThe BLUP methodology has been applied to the genetic evaluation of Swedish standard‐bred trotters for well over a decade. Initially a BLUP sire model was applied for evaluating breeding values of stallions on the basis of the racing performance of their offspring (Árnason et al. 1989). In 1992 an animal model (AM‐) BLUP was introduced and official publication of index values were offered as an aid for effective selection of stallions and brood mares (Árnason 1992; Árnason and S vendsen 1991). The implementation of the BLUP animal model index has apparently caused profound enhancement in the selection intensity for both stallions and mares (Árnason 1997). The AM‐BLUP evaluation has involved the following traits, which were all based on accumulated racing results as 3‐ to 5‐year‐olds: Number of races (starts); % of races ranked first to third at the finish (i.e. placed first to third); earnings per race; total earnings; best racing time per km; and racing (or start) status, which is denoted as one if the horse did race at least once as a 3‐ to 5‐year‐old and zero otherwise. The two traits: number of races and racing status were initially treated as single traits, in the AM‐BLUP analyses, uncorrelated with the other racing performance traits. Those other traits are direct measures of racing performance for horses that have actually competed on the race track. They are highly intercorrelated and have been treated as a multivariate complex in the analyses. The computational load of general multivariate analyses has been considerably reduced by transformation of the records into uncorrelated canonical variates (e.g. Árnason 1982).In Sweden, about 40% of standard‐bred trotters do not enter a race course and their racing performance variables have previously been treated as missing. Early analysis on the population of standard‐bred trotters in Sweden did not show any correlation between racing status of brood mares and the racing performance of their offspring (M. B endroth, unpublished results). That gave justification for assuming that racing status had mainly environmental causes, and to be practically genetically uncorrelated with performance. The exclusion of nonracers (nonstarters) was therefore not expected to bias genetic evaluations for the performance traits. The expansion of the population during the 1980s and the early 1990s, and increase in the level of prize money, has probably invalidated the implication of these results and partly changed the racing status into a preselection criterion for racing performance. K lemetsdal (1992) has clearly illustrated that such a culling process can result in substantial bias in estimated breeding values. In 1995 a new enhanced procedure replaced the older version used for routine genetic evaluation of Swedish standard‐bred trotters, with the aim of eliminating, or at least reducing, the selection bias and increasing the accuracy in the genetic evaluations.The main objective of this paper was to describe the enhanced procedure for genetic evaluation of Swedish standard‐bred trotters where racing status and racing performance traits were treated in a complete multiple trait framework. The task was made computationally feasible by the application of a procedure which allows solution of multiple trait AM‐BLUP with missing data on some traits using multiple step canonical transformation of records and solutions during the iterative solution phase (D ucrocq and B esbes 1993). The pertinence of the method for establishing a sound selection criterion was verified by stochastic simulations on simplified data structures. The second objective of this study was to evaluate the model and assess the set of genetic parameters used in the BLUP analysis, by linear regressions of the genetic predictions based on the most recent data on genetic predictions obtained in subsamples of the whole data set (method R, R everter et al. 1994a, b).

A Comparison of Breeding Value Predictors for Longevity Using a Linear Model and Survival Analysis

A comparison was made among breeding values of sires for longevity that were obtained by different methods: phenotypic averages of daughters using only uncensored records, BLUP using only uncensored records, survival analysis using only uncensored records, and survival analysis using both censored and uncensored records. Two data files were used: one contained data from small herds, and the other contained data from large herds. The results from both data files were similar. Different methods of predicting breeding values resulted in different rankings of sires. The results obtained using phenotypic averages were weakly correlated (≤0.46) with those results obtained using the other methods of prediction. The REML BLUP had strong correlations (≤−0.91) with the survival analysis predictor if the same data were used, and correlations weakened (≤−0.60) when censored records were included in the survival analysis. The correlations are negative because the linear method analyzed longevity, and survival analysis measured the risk of being culled, which has an antagonistic relationship with longevity. The results from REML BLUP and survival analysis methods differed mainly because of the different data that were used (uncensored only versus both censored and uncensored).

Effects of multiple-sire matings on genetic evaluations, selection response and rates of inbreeding

Multiple-sire mating is evaluated for a range of conditions, for its impact on regular genetic evaluation analyses in performance recording, and on selection response and inbreeding in breeding programs as a whole. Substitution of the average for the complete numerator relationship matrix (NRM) in the mixed model equations produced little bias in genetic trend estimates but substantial bias of inbreeding estimates. By recording sire group membership and dam identification under multiple-sire mating and using these and the average NRM in genetic evaluation analyses, it is shown that: 26–63% more genetic gain is achievable compared with selection on individual performance alone (no genetic analysis); and realised genetic gain is reduced by less than 6–24% compared with single-sire mating and use of complete BLUP analysis.