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

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

The empirical bias of estimates by restricted maximum likelihood, Bayesian method, and method R under selection for additive, maternal, and dominance models.

Bayesian analysis via Gibbs sampling, restricted maximum likelihood (REML), and Method R were used to estimate variance components for several models of simulated data. Four simulated data sets that included direct genetic effects and different combinations of maternal, permanent environmental, and dominance effects were used. Parents were selected randomly, on phenotype across or within contemporary groups, or on BLUP of genetic value. Estimates by Bayesian analysis and REML were always empirically unbiased in large data sets. Estimates by Method R were biased only with phenotypic selection across contemporary groups; estimates of the additive variance were biased upward, and all the other estimates were biased downward. No empirical bias was observed for Method R under selection within contemporary groups or in data without contemporary group effects. The bias of Method R estimates in small data sets was evaluated using a simple direct additive model. Method R gave biased estimates in small data sets in all types of selection except BLUP. In populations where the selection is based on BLUP of genetic value or where phenotypic selection is practiced mostly within contemporary groups, estimates by Method R are likely to be unbiased. In this case, Method R is an alternative to single-trait REML and Bayesian analysis for analyses of large data sets when the other methods are too expensive to apply.     

Choice of statistical model for estimating genetic parameters using restricted maximum likelihood in swine

Summary Restricted maximum likelihood (REML) was used to determine the choice of statistical model, additive genetic maternal and common litter effects and consequences of ignoring these effects on estimates of variance–covariance components under random and phenotypic selection in swine using computer simulation. Two closed herds of different size and two traits, (i) pre‐weaning average daily gain and (ii) litter size at birth, were considered. Three levels of additive direct and maternal genetic correlations (r_dm) were assumed to each trait. Four mixed models (denoted as GRM1 through GRM4) were used to generate data sets. Model GRM1 included only additive direct genetic effects, GRM2 included only additive direct genetic and common litter effects, GRM3 included only additive direct and maternal genetic effects and GRM4 included all the random effects. Four mixed animal models (defined as EPM1 through EPM4) were defined for estimating genetic parameters similar to GRM. Data from each GRM were fitted with EPM1 through EPM4. The largest biased estimates of additive genetic variance were obtained when EPM1 was fitted to data generated assuming the presence of either additive maternal genetic, common litter effects or a combination thereof. The bias of estimated additive direct genetic variance (VA_d) increased and those of recidual variance (VE) decreased with an increase in level of r_dm when GRM3 was used. EPM1, EPM2 and EPM3 resulted in biased estimation of the direct genetic variances. EPM4 was the most accurate in each GRM. Phenotypic selection substantially increased bias of estimated additive direct genetic effect and its mean square error in trait 1, but decreased those in trait 2 when ignored in the statistical model. For trait 2, estimates under phenotypic selection were more biased than those under random selection. It was concluded that statistical models for estimating variance components should include all random effects considered to avoid bias.     

Efficient Monte Carlo algorithm for restricted maximum likelihood estimation of genetic parameters

Monte Carlo (MC) methods have been found useful in estimation of variance parameters for large data and complex models with many variance components (VC), with respect to both computer memory and computing time. A disadvantage has been a fluctuation in round‐to‐round values of estimates that makes the estimation of convergence challenging. Furthermore, with Newton‐type algorithms, the approximate Hessian matrix might have sufficient accuracy, but the inaccuracy in the gradient vector exaggerates the round‐to‐round fluctuation to intolerable. In this study, the reuse of the same random numbers within each MC sample was used to remove the MC fluctuation. Simulated data with six VC parameters were analysed by four different MC REML methods: expectation‐maximization (EM), Newton–Raphson (NR), average information (AI) and Broyden's method (BM). In addition, field data with 96 VC parameters were analysed by MC EM REML. In all the analyses with reused samples, the MC fluctuations disappeared, but the final estimates by the MC REML methods differed from the analytically calculated values more than expected especially when the number of MC samples was small. The difference depended on the random numbers generated, and based on repeated MC AI REML analyses, the VC estimates were on average non‐biased. The advantage of reusing MC samples is more apparent in the NR‐type algorithms. Smooth convergence opens the possibility to use the fast converging Newton‐type algorithms. However, a disadvantage from reusing MC samples is a possible “bias” in the estimates. To attain acceptable accuracy, sufficient number of MC samples need to be generated.     

An alternative derivation method of mixed model equations from best linear unbiased prediction (BLUP) and restricted BLUP of breeding values not using maximum likelihood

Two mixed model equations (MME) for best linear unbiased prediction (BLUP) of breeding values and for restricted BLUP of breeding values were derived by maximum likelihood from the joint normal probability distribution of the observations and breeding values. As a result, MME is actually more general than maximum likelihood because we can prove that each set of solutions of MME are identical to BLUP and restricted BLUP of breeding values and then it does not depend on normality. In the present study, the author shows deriving directly each MME from BLUP and restricted BLUP equations for breeding values without assuming the joint normal distribution of the data and random effects. However, if we cannot assume the multivariate normal density distribution of the estimated aggregate breeding value and each breeding value for selected traits, the response to selection by restricted BLUP may deviate from the expected values.     

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

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

Multiple-trait restricted maximum likelihood for simulated measures of ovulation rate with underlying multivariate normal distributions.

A data set that was used to estimate covariance components with REML for an animal model with eight measures of ovulation rate treated as separate traits was used as a template to simulate data sets of eight multivariate normal traits that were then truncated to binomial traits. The model for simulation included eight measures on 610 animals with 1,071 animals in the numerator relationship matrix. Heritabilities were equal for the eight measures, and both genetic and phenotypic correlations among the measures were equal. Ten replications for each combination of heritability (.15, .25, and .35) and genetic correlation (.50, .66, and .90) were simulated on the normal scale. For each replicate, estimates of the eight heritabilities and 28 genetic correlations were obtained by multiple-trait REML. The usual transformation of heritability estimated on the binomial scale overestimated heritability on the normal scale. Genetic correlations on the binomial scale seriously underestimated the correlations on the normal scale. Standard errors of the estimates obtained by replication were somewhat larger than the approximate SE from REMLPK (the multi-trait REML program of K. Meyer). A final set of 10 simulated replications with heritability of .25 and genetic correlation of 1.00 resulted in average estimates of .18 for heritability and of .66 for genetic correlation that agree closely with those from the analysis of measures of ovulation at eight estrous cycles used as a template; averages for heritability of .16 and for genetic correlation of .66 were obtained.     

Partial and conditional maximum likelihood for variance-component estimation

SUMMARY: Patterson and Thompson's idea of 'error contrasts' (or restricted maximum likelihood) (1971) was extended to multiple sets of linear contrasts for variance component estimtion. The error contrasts were established in such a way that only errors are retained in the model. The error variance was then estimated by maximizing the likelihood function obtained from the error contrasts. More sets of linear contrasts were then progressively established such that each set of linear contrasts contains only one class of random effects and the errors. A likelihood function was constructed and maximized for each variance of random effects given the error variance held at its estimated value. The likelihood function for estimating the covariance component between two classes of random effects was established such that all other random effects are treated as fixed effects. The likelihood function was then maximized with respect to the covariance given the two variance components fixed at their estimated values. The multidimensional optimization problem in the traditional restricted maximum-likelihood problem was then turned into several one-dimensional optimization problems by using this technique. Inasmuch as the error variance was estimated using a partial likelihood function and the other variance components are estimated using likelihood functions conditional on the estimated error variance, the method is referred to as partial and conditional maximum likelihood (PCML). ZUSAMMENFASSUNG: Partielle und bedingte Maximum Likelihood zur Sch?tzung von Varianzkomponenten Die Patterson und Thompson Vorstellungen von 'Fehlerkontrasten' (1971) (oder beschr?nkte maximale Likelihood) wurde auf multiple Gruppen linearer Kontraste für Varianzkomponenten- sch?tzung ausgedehnt. Die Fehlerkontraste erfolgen in der Form, da? nur Fehler im Modell verbleiben. Die Fehlervarianz wurde dann durch Maximierung der Likelihood Funktion von Fehlerkontrasten gesch?tzt. Weitere Gruppen linearer Kontraste wurden nacheinander etabliert dergestalt, da? jede Gruppe linearer Kontraste nur eine Klasse zuf?lliger Wirkungen und die Fehler enth?lt. Eine Likelihood Funktion wurde konstruiert und für jede Varianz von Zufallsgr??en maximiert unter der Voraussetzung, da? die Fehlervarianz auf ihrem gesch?tzten Wert verbleibt. Die Likelihood Funktion zur Sch?tzung der Ko-Varianzkomponenten zwischen zwei Klassen zuf?lliger Wirkungen wurde in der Form aufgestellt, da? alle anderen Zufallswirkungen als fixe behandelt werden. Die Likelihood Funktion wurde maximiert im Hinblick auf Ko-Varianz bei gegebenen gesch?tzten Varianzkomponenten. Das multidimensionale Optimierungsproblem der traditionellen restringierten Maximum Likelihood wurde auf diese Weise in ein eindimensionales Optimierungsproblem verwandelt. Nachdem die Fehlervarianz aus der partiellen Likelihood Funktion und die anderen Varianzkomponenten unter Verwendung der bedingten Likelihood Funktionen gesch?tzt worden waren, wurde die Methode als partielle und bedingte Maximum Likelihood (pcml) bezeichnet.     

Employing a Monte Carlo algorithm in expectation maximization restricted maximum likelihood estimation of the linear mixed model

Multiple‐trait and random regression models have multiplied the number of equations needed for the estimation of variance components. To avoid inversion or decomposition of a large coefficient matrix, we propose estimation of variance components by Monte Carlo expectation maximization restricted maximum likelihood (MC EM REML) for multiple‐trait linear mixed models. Implementation is based on full‐model sampling for calculating the prediction error variances required for EM REML. Performance of the analytical and the MC EM REML algorithm was compared using a simulated and a field data set. For field data, results from both algorithms corresponded well even with one MC sample within an MC EM REML round. The magnitude of the standard errors of estimated prediction error variances depended on the formula used to calculate them and on the MC sample size within an MC EM REML round. Sampling variation in MC EM REML did not impair the convergence behaviour of the solutions compared with analytical EM REML analysis. A convergence criterion that takes into account the sampling variation was developed to monitor convergence for the MC EM REML algorithm. For the field data set, MC EM REML proved far superior to analytical EM REML both in computing time and in memory need.     

Comparison of (co)variance component estimates in control populations of red flour beetle (Tribolium castaneum) using restricted maximum likelihood and Gibbs sampling

Mixed model (co)variance component estimates by REML and Gibbs sampling for two traits were compared for base populations and control lines of Red Flour Beetle (Tribolium castaneum). Two base populations (1296 records in the first replication, 1292 in the second) were sampled from laboratory stock. Control lines were derived from corresponding base populations with random selection and mating for 16 generations. The REML estimate of each (co)variance component for both pupa weight and family size was compared with the mean and 95% central interval of the particular (co)variance estimated by Gibbs sampling with three different weights on the given priors: ‘flat’, smallest, and 3.7% degrees of belief. Results from Gibbs sampling showed that flat priors gave a wider and more skewed marginal posterior distribution than the other two weights on priors for all parameters. In contrast, the 3.7% degree of belief on priors provided reasonably narrow and symmetric marginal posterior distributions. Estimation by REML does not have the flexibility of changing the weight on prior information as does the Bayesian analysis implemented by Gibbs sampling. In general, the 95% central intervals from the three different weights on priors in the base populations were similar to those in control lines. Most REML estimates in base populations differed from REML estimates in control lines. Insufficient information from the data, and confounding of random effects contributed to the variability of REML estimates in base populations. Evidence is presented showing that some (co)variance components were estimated with less precision than others. Results also support the hypothesis that REML estimates were equivalent to the joint mode of posterior distribution obtained from a Bayesian analysis with flat priors, but only when there was sufficient information from data, and no confounding among random effects.     

Parameter estimation for carcass traits including growth information of Simmental beef cattle using restricted maximum likelihood with a multiple-trait model.

(Co)variance component estimates were computed for retail cuts per day of age (kilograms per day), cutability (percentage of carcass weight), and marbling score (1 through 11) using a multiple-trait sire model. Restricted maximum likelihood estimates of (co)variance components were obtained via an expectation-maximization algorithm. Carcass data consisted of 8,265 progeny records collected by U.S. Simmental producers. Growth trait information (birth weight, weaning weight, and[or] postweaning gain) for those progeny with carcass data and an additional 5,405 contemporaries formed the complete data set for analysis. A total of 420 sires were represented. Three models differing in number of traits were investigated: 1) carcass traits with growth traits, 2) carcass traits only, and 3) single trait. The final models did not include postweaning gain because of convergence problems. Parameter estimates for all three models were essentially the same. Heritability estimates were .30, .18, and .23 for retail cuts per day, cutability, and marbling score, respectively. Correlations between growth and carcass traits were low except for those with retail cuts per day, which were moderate and positive. The additional information gained by adding growth traits to the carcass-traits-only evaluation lowered prediction error variances most for retail cuts per day. Little change in prediction error variances was found for cutability and marbling score. Inclusion of growth traits in future sire evaluations for carcass traits will benefit the evaluation of retail cuts per day but have considerably less effect on cutability and marbling score.     

Estimation of genetic correlations between racing times recorded at different racing distances by restricted maximum likelihood in Thoroughbred racehorses

SUMMARY: Genetic correlations between racing times on track type (turf and dirt), and at racing distances on turf (1200 m, 1400 m, 1600 m, 1800 m, and/or 2000 m) and dirt (1000 m, 1200 m, 1400 m, 1600 m, 1700 m, and/or 1800 m) tracks, were estimated in Thoroughbred horses. (Co)variance components were estimated using multiple-trait derivative-free restricted maximum likelihood (MTDFREML). The data used were collected by the Japan Racing Association from 1992 to 1993. The generation 2 pedigree information was preferable for (co)variance estimates. The genetic correlations between racing times on turf and dirt tracks ranged from 0.69 to 0.31 (average 0.51). The genetic correlations between racing distances ranged from 0.68 to 1.00 (average 0.85) and from 0.53 to 1.00 (average 0.88) on turf and dirt tracks, respectively. These results suggest that the racing time per 100 m can be used for horse genetic evaluation within one track type. ZUSAMMENFASSUNG: Sch?tzung genetischer Korrelationen zwischen Rennzeiten von Vollblüternüber verschiednen Distanzen mittels restringierter Genetische Korrelationen zwischen Rennzeiten auf Rasen- und Erdbahnen, Renndistanzen auf Rasen- (1200, 1400, 1600, 1800 und 2000 m) und Erdbahnen (1000, 1200, 1400, 1600, 1700 und 2000 m) wurden für Vollblüter gesch?tzt. (Co)Varianzkomponenten wurden mittels Mehr-Merkmal Ableitungsfreier Restringierter Maximum Likelihood (MTDFREML) gesch?tzt. Die Unterlagen wurden von der Japanischen Renn Vereinigung 1992 und 1993 gesammelt. Generation 2 Abstammungsinformation war für die Co-Varianzsch?tzung günstig. Genetische Korrelationen zwischen Rennzeiten auf Rasen und auf Erdbahnen waren zwischen 0.69 und 0.31 (Durchschnitt 0.51), jene zwischen Distanzen zwischen 0.68 und 1.00 (Durchschnitt 0.85) und zwischen 0.53 und 1.00 (Durchschnitt 0.88) auf Rasen und Erdbahnen. Die Ergebnisse zeigen, da? Rennzeit per 100 m zur Bewertung der Pferde geeignet ist.     

Animal model estimation of non-additive genetic parameters in dairy cattle, and their effect on heritability estimation and breeding value prediction

SUMMARY: First lactation production records of pedigree Holstein-Friesian cows in the UK were analysed by an animal model, in order to estimate effects of heterosis and recombination loss between North American Holstein and European Friesian cattle and the influence of these effects on breeding value prediction. Coefficients of heterosis and recombination loss were fitted in the animal model as covariables and unknown parents were assigned to a varying number of genetic groups. The estimates of heterosis effects were 104 kg, 4.3 kg and 2.9 kg for milk, fat and protein yield, respectively, while the corresponding coefficients for recombination loss were -135 kg, -2.6 kg and -3.7 kg respectively. Neither the sire component of variance nor the heritability estimates were appreciably affected by the inclusion of heterosis and recombination loss in the model. Including both these effects in the breeding value estimation increased the predicted sire proof for fat plus protein of a typical F1 Holstein × Friesian sire by 3 kg. ZUSAMMENFASSUNG: Tiermodellsch?tzungen nicht-additiv genetischer Parameter bei Milchrindern und ihre Auswirkung auf Heritabilit?tssch?tzung und Zuchtwertvoraussage Laktationsleistungen von Herdbuch Holstein-Friesen Kühen im UK wurden mittels eines Tiermodells analysiert zur Sch?tzung der Wirkungen von Heterosis und Rekombinationsverlust zwischen nordamerikanischen Holstein und europ?ischen Schwarzbunten und Einflu? dieser Wirkungen auf Zuchtwahlvorhersagen. Koeffizienten für Heterosis und für Rekombinationsverlust wurden im Tiermodell als Co-Variable berücksichtigt und unbekannte Eltern einer unterschiedlichen Zahl genetischer Gruppen zugeordnet. Sch?tzungen der Heterosiswirkungen waren 104 kg, 4,3 kg und 2,1 kg für Milch-, Fett- Proteinmengen, w?hrend die diesbezüglichen Koeffizienten für Rekombinationsverlust -135, -2,6 und -3,7 kg waren. Weder die Vatervarianzkomponente noch Heritabilit?tswerte wurden durch Berücksichtigung von Heterosis und Rekombinationsverluste im Modell tangiert. Berücksichtigung beider Wirkungen in der Zuchtwertsch?tzung erh?hte den gesch?tzten Vaterzuchtwert für Fett + Protein eines typischen F1 Holstein-Friesen-Stieres um 3kg.     

A method of computing restricted best linear unbiased prediction of breeding values for some animals in a population

Restricted BLUP (R-BLUP) is derived by imposing restrictions directly within a multiple-trait mixed model. As a result, the R-BLUP procedure requires the solution of high-order simultaneous equations. If restrictions are imposed on breeding values for only some animals in a population, calculations become more complex. A new procedure for computing the R-BLUP of breeding values was derived when constraints were imposed on the additive genetic values of only some animals in a population. Rules for including records when proportional constraints are imposed were developed based on the traits that are recorded for an animal. The technique was better than the previous method in both memory requirement and central processing unit time.     

Estimation of genetic parameters and prediction of breeding values for multivariate threshold and continuous data in a simulated horse population using Gibbs sampling and residual maximum likelihood

Simulated horse data were used to compare multivariate estimation of genetic parameters and prediction of breeding values (BV) for categorical, continuous and molecular genetic data using linear animal models via residual maximum likelihood (REML) and best linear unbiased prediction (BLUP) and mixed linear-threshold animal models via Gibbs sampling (GS). Simulation included additive genetic values, residuals and fixed effects for one continuous trait, liabilities of four binary traits, and quantitative trait locus (QTL) effects and genetic markers with different recombination rates and polymorphism information content for one of the liabilities. Analysed data sets differed in the number of animals with trait records and availability of genetic marker information. Consideration of genetic marker information in the model resulted in marked overestimation of the heritability of the QTL trait. If information on 10,000 or 5,000 animals was used, bias of heritabilities and additive genetic correlations was mostly smaller, correlation between true and predicted BV was always higher and identification of genetically superior and inferior animals was - with regard to the moderately heritable traits, in many cases - more reliable with GS than with REML/BLUP. If information on only 1,000 animals was used, neither GS nor REML/BLUP produced genetic parameter estimates with relative bias 50% for all traits. Selection decisions for binary traits should rather be based on GS than on REML/BLUP breeding values.     

Two generations of selection on restricted best linear unbiased prediction breeding values for income minus feed cost in laying hens.

Two generations of selection on restricted BLUP breeding values were applied in an experiment with laying hens. Selection had been on phenotype of income minus feed cost (IFC) between 21 and 40 wk of age in the previous five generations. The restriction of no genetic change in egg weight was included in the EBV for power-transformed IFC (i.e., IFCt, with t-values of 3.7 and 3.6 in the two generations, respectively). The experiment consisted of two selection lines plus a randomly bred control of 20 male and 80 female breeders each. Observations on 8,844 survivors to 40 wk were available. Relative to the base population average, the restriction reduced genetic gain in IFC from 4.1 and 3.9% to 2.0 and 2.2% per generation in the two selection lines, respectively. Average EBV for egg weight remained nearly constant after a strong increase in the previous five generations. Rates of genetic gain for egg number, body weight, and feed conversion (feed/egg mass) were not affected significantly. In the seventh generation, a genetic gain in feed conversion of 10.3% relative to the phenotypic mean of the base population was obtained.     

用BLUP方法估计辽宁绒山羊种公羊育种值的研究

由于羊的最优线性无偏估计法(BLUP法)评定育种工作开展得较晚,特别在绒山羊的育种工作中应用更少.本研究试图利用辽宁绒山羊原种场的生产资料对BLUP法用于种公羊的育种值评估方面进行初步尝试,以推进BLUP法在绒山羊育种中的应用.     

Evaluation of breeding objectives for purebred and crossbred selection schemes for adoption in indigenous chicken breeding programmes

1. The aim of the study was to evaluate the genetic and economic breeding objectives for an indigenous chicken (IC) breeding programme in Kenya.

2. A closed three-tier nucleus breeding programme with three breeding objectives and two selection schemes was simulated. The breeding objectives included IC dual-purpose (ICD) for both eggs and meat, IC layer (ICL) for eggs and IC broiler (ICB) for meat production.

3. Pure line selection scheme (PLS) for development of IC pure breeds and crossbreeding scheme (CBS) for the production of hybrids were considered. Two-and three-way crossbreeding strategies were evaluated under CBS and the impact of nucleus size on genetic gains and profitability of the breeding programme were investigated.

4. Males were the main contributors to genetic gains. The highest genetic gains for egg number (2·71 eggs) and growth traits (1·74?g average daily gain and 57·96?g live weight at 16 weeks) were realised under PLS in ICL and ICB, respectively.

5. The genetic response for age at first egg was desirable in all the breeding objectives, while that for fertility and hatchability were only favourable under ICL and PLS in ICD. Faecal egg count and immune antibody response had low, but positive gains except under PLS where the later was unfavourable. ICB was the most profitable breeding objective, followed by ICD and ICL under all the selection schemes.

6. Although PLS was superior in genetic gains and profitability and recommended in breeding programmes targeting ICL and ICB, a three line CBS should be considered in development of a dual-purpose breed.

7. Increasing the nucleus size beyond 5% of the IC population was not attractive as it resulted in declining profitability of the breeding programme.     

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.