Invited review: A quarter of a century-International genetic evaluation of dairy sires using MACE methodology.

For the past few decades, the international exchange of genetic materials has accelerated. This acceleration has been more substantial for dairy cattle compared with other species. The industry faced the need to put international genetic evaluation (IGE) systems in place. The Interbull Centre has been conducting IGE for various dairy cattle breeds and traits. This study reviews the past and the current status of IGE for dairy cattle, emphasizing the most prominent and well-established method of IGE, namely multiple across-country evaluation (MACE), and the challenges that should be addressed in the future of IGE. The first IGE methods were simple conversion equations. Only a limited number of common bulls between pairs of countries were considered. These bulls were a biased sample of highly selected animals, with their daughters under preferential treatment in the importing countries. Genetic relationships among animals were not considered either. The MACE method was the first IGE method based on mixed-model theory that could handle genotype by environment interaction (G × E) between countries. The G × E between countries is handled by treating the same trait in different countries as different traits, with genetic correlations less than unity between the traits. The G × E between countries is not solely due to different genetic expressions in different environments (countries), but is also attributable to different units or ways of measuring the trait, data editing, and statistical approaches and models used in different countries. The MACE method also considers different genetic means, genetic groups for unknown parents, heterogeneous genetic and residual variances among countries, and heterogeneous residual variances (precision weights for observations) within countries. Other IGE methods that came after MACE are rooted in MACE. The genomic revolution of the industry created new needs and opportunities. However, an unwanted aspect of it was genomic preselection bias. Genomic preselection causes directional information loss from pre-culled animals (bias) in statistical models for genetic and genomic evaluations, and preselected progeny of a mating are no longer a random sample of possible progeny from that mating. National genetic evaluations without genotypes are input to MACE, and biases in national evaluations are propagated internationally through MACE. Genomic preselection for the Holstein breed is a source of concern for introducing bias to MACE, especially when genomic preselection is practiced intensively in the population. However, MACE continues to be useful for other breeds, among other species, or for non-IGE purposes. Future methods will need to make optimum use of genomic information and be free of genomic preselection bias.

Estimates of genetic variance and variance of predicted genetic merits using pedigree or genomic relationship matrices in six Brown Swiss cattle populations for different traits.

The amount of variance captured in genetic estimations may depend on whether a pedigree-based or genomic relationship matrix is used. The purpose of this study was to investigate the genetic variance as well as the variance of predicted genetic merits (PGM) using pedigree-based or genomic relationship matrices in Brown Swiss cattle. We examined a range of traits in six populations amounting to 173 population-trait combinations. A main aim was to determine how using different relationship matrices affect variance estimation. We calculated ratios between different types of estimates and analysed the impact of trait heritability and population size. The genetic variances estimated by REML using a genomic relationship matrix were always smaller than the variances that were similarly estimated using a pedigree-based relationship matrix. The variances from the genomic relationship matrix became closer to estimates from a pedigree relationship matrix as heritability and population size increased. In contrast, variances of predicted genetic merits obtained using a genomic relationship matrix were mostly larger than variances of genetic merit predicted using pedigree-based relationship matrix. The ratio of the genomic to pedigree-based PGM variances decreased as heritability and population size rose. The increased variance among predicted genetic merits is important for animal breeding because this is one of the factors influencing genetic progress.

Multiple-breed genomic evaluation by principal component analysis in small size populations.

In this study, the effects of breed composition and predictor dimensionality on the accuracy of direct genomic values (DGV) in a multiple breed (MB) cattle population were investigated. A total of 3559 bulls of three breeds were genotyped at 54 001 single nucleotide polymorphisms: 2093 Holstein (H), 749 Brown Swiss (B) and 717 Simmental (S). DGV were calculated using a principal component (PC) approach for either single (SB) or MB scenarios. Moreover, DGV were computed using all SNP genotypes simultaneously with SNPBLUP model as comparison. A total of seven data sets were used: three with a SB each, three with different pairs of breeds (HB, HS and BS), and one with all the three breeds together (HBS), respectively. Editing was performed separately for each scenario. Reference populations differed in breed composition, whereas the validation bulls were the same for all scenarios. The number of SNPs retained after data editing ranged from 36 521 to 41 360. PCs were extracted from actual genotypes. The total number of retained PCs ranged from 4029 to 7284 in Brown Swiss and HBS respectively, reducing the number of predictors by about 85% (from 82% to 89%). In all, three traits were considered: milk, fat and protein yield. Correlations between deregressed proofs and DGV were used to assess prediction accuracy in validation animals. In the SB scenarios, average DGV accuracy did not substantially change when either SNPBLUP or PC were used. Improvement of DGV accuracy were observed for some traits in Brown Swiss, only when MB reference populations and PC approach were used instead of SB-SNPBLUP (+10% HBS, +16%HB for milk yield and +3% HBS and +7% HB for protein yield, respectively). With the exclusion of the abovementioned cases, similar accuracies were observed using MB reference population, under the PC or SNPBLUP models. Random variation owing to sampling effect or size and composition of the reference population may explain the difficulty in finding a defined pattern in the results.

Multiple-trait multiple-country genetic evaluation of Holstein bulls for female fertility and milk production traits.

The aim of this study was to investigate the effect of including milk yield data in the international genetic evaluation of female fertility traits to reduce or eliminate a possible bias because of across-country selection for milk yield. Data included two female fertility traits from Great Britain, Italy and the Netherlands, together with milk yield data from the same countries and from the United States, because the genetic trends in other countries may be influenced by selection decisions on bulls in the United States. Potentially, female fertility data had been corrected nationally for within-country selection and management biases for milk yield. Using a multiple-trait multiple across-country evaluation (MT-MACE) for the analysis of female fertility traits with milk yield, across-country selection patterns both for female fertility and milk yield can be considered simultaneously. Four analyses were performed; one single-trait multiple across-country evaluation analysis including only milk yield data, one MT-MACE analysis including only female fertility traits, and one MT-MACE analysis including both female fertility and milk yield traits. An additional MT-MACE analysis was performed including both female fertility and milk yield traits, but excluding the United States. By including milk yield traits to the analysis, female fertility reliabilities increased, but not for all bulls in all the countries by trait combinations. The presence of milk yield traits in the analysis did not considerably change the genetic correlations, genetic trends or bull rankings of female fertility traits. Even though the predicted genetic merits of female fertility traits hardly changed by including milk yield traits to the analysis, the change was not equally distributed to the whole data. The number of bulls in common between the two sets of Top 100 bulls for each trait in the two analyses of female fertility traits, with and without the four milk yield traits and their rank correlations were low, not necessarily because of the absence of the US milk yield data. The joint international genetic evaluation of female fertility traits with milk yield is recommended to make use of information on several female fertility traits from different countries simultaneously, to consider selection decisions for milk yield in the genetic evaluation of female fertility traits for obtaining more accurate estimating breeding values (EBV) and to acquire female fertility EBV for bulls evaluated for milk yield, but not for female fertility.

Evaluation of genetic variation in the international Brown Swiss population.

The international Brown Swiss cattle population pedigree was studied to measure genetic variations and to identify the most influential animals. Twenty-two countries provided pedigree information on 71 497 Brown Swiss bulls used for artificial insemination (AI). The total number of animals with the pedigree is 181 094. The mean inbreeding coefficient for the pedigree population was 0.77%. There was, in most cases, an increase in the mean inbreeding coefficient, with the highest value at 2.89% during the last 5-year period (2000 to 2004). The mean average relatedness for the pedigree population was 1.1%. The effective population size in 2004 was 204. There was notable variation between average generation intervals for the four parental pathways. The longest average generation interval, at 8.73 years, was observed in the sire-son pathway. The average generation interval for the whole population was 6.53 years. Most genetically influential individuals were sires. The highest contributing founder was a sire with a 3.22% contribution, and the highest contributing founder dam made a contribution of 1.75%. The effective number of founders and the effective number of ancestors were 141 and 88, respectively. The study showed that genetic variation within the pedigree population has been decreasing over recent years. Increasing the number of AI bulls with a low individual coefficient of inbreeding could help to maintain a good level of genetic variation in the Brown Swiss population.

Short communication: Quantifying bias in a single-trait international model ignoring covariances from multiple-trait national models.

The current method in use for international genetic evaluations, called single-trait multiple across-country evaluation (ST-MACE), does not consider residual covariances among traits, making possible only the inclusion of one trait per country in an analysis. The aim of this study was to quantify the effect of bias resulting from treating traits from the same country as nationally independent in an international genetic evaluation. Data from the September 2007 Interbull test evaluation for Holstein female fertility traits were used. Data included were 1 trait from Belgium, Switzerland, Spain, and the United States of America, and 2 traits from Canada, Germany-Austria, and Denmark-Finland-Sweden. The biased results were obtained from a 10-variate ST-MACE analysis including all country traits. The unbiased results were obtained from 8 different 7-variate ST-MACE analyses, each including only 1 trait per country. Average absolute bias in the genetic correlations among 2-trait countries (0.11) was higher than for between 1-trait countries and 2-trait countries (0.07) and for among 1-trait countries (0.03). The results of the biased and the unbiased analyses were different, not only due to bias, but also because of different number of traits involved in the analyses. Differences were considerable (on average, 0.08 to 6.91) for reliabilities, which were higher for traits with lower heritability. Average differences were minor (-0.04 to 0.03 standard deviations) for predicted genetic merits. However, for the top 100 bulls in each country trait, these differences were important (on average, -0.26 to 0.11 standard deviation of predicted genetic merit), which caused considerable changes in bull rankings. The results of this study showed that the effect of bias, caused by ignoring covariances from multiple-trait national models in an ST-MACE analysis, is of such a magnitude that necessitates the use of another method such as multiple-trait multiple across-country evaluation.

Application of a multiple-trait, multiple-country genetic evaluation model for female fertility traits.

The need to implement a method that can handle multiple traits per country in international genetic evaluations is evident. Today, many countries have implemented multiple-trait national genetic evaluations and they may expect to have their traits simultaneously analyzed in international genetic evaluations. Traits from the same country are residually correlated and the method currently in use, single-trait multiple across-country evaluation (ST-MACE), cannot handle nonzero residual correlations. Therefore, multiple-trait, multiple across-country evaluation (MT-MACE) was proposed to handle several traits from the same country simultaneously. To test the robustness of MT-MACE on real data, female fertility was chosen as a complex trait with low heritability. Data from 7 Holstein populations, 3 with 2 traits and 4 with 1 trait, were used. The differences in the estimated genetic correlations by MT-MACE and the single ST-MACE analysis (average absolute deviation of 0.064) were due to the bias of considering several traits from the same country in the ST-MACE analysis. However, the differences between the estimated genetic correlations by MT-MACE and multiple ST-MACE analyses avoiding more than one trait per country in each analysis (average absolute deviation of 0.066) were due to the lack of analysis of the correlated traits from the same country together and using the reported within-country genetic correlations. Applying MT-MACE resulted in reliability gain in international genetic evaluations, which was different from trait to trait and from bull to bull. The average reliability gain by MT-MACE over ST-MACE was 3.0 points for domestic bulls and 6.3 points for foreign bulls. Even countries with 1 trait benefited from the joint analysis of traits from the 2-trait countries. Another superiority of MT-MACE over ST-MACE is that the bulls that do not have national genetic evaluation for some traits from multiple trait countries will receive international genetic evaluations for those traits. Rank correlations were high between ST-MACE and MT-MACE when considering all bulls. However, the situation was different for the top 100 bulls. Simultaneous analysis of traits from the same country affected bull ranks, especially for top 100 bulls. Multi-trait MACE is a recommendable and robust method for international genetic evaluations and is appropriate for handling multiple traits per country, which can increase the reliability of international genetic evaluations.

Data subsetting strategies for estimation of across-country genetic correlations.

International genetic evaluation of dairy cattle requires estimation of genetic correlations among populations to account for genotype-environment interaction. Simultaneous estimation of across-country genetic correlations among all populations of a widespread breed, such as the Holstein breed is, however, hampered by connectedness problems and computational challenges. The purpose of this study was to examine the effects of using bulls with across-country, balanced distribution of daughters on estimates of genetic correlations. For this purpose, dairy cattle populations undergoing selection in 6 countries were simulated. Two population-size settings were used. In the small population-size setting (S-populations), the 6 simulated countries had 2000 cows and 20 young progeny testing bulls per generation. In the larger population-size setting (L-populations), the 6 simulated countries had between 2000 and 64,000 cows and 20 to 640 young progeny testing bulls per generation. The simulated (true) across-country genetic correlations, depending on the country combination, varied between 0.5 and 0.9. Simulations comprised a base population and 10 generations and were replicated 16 times. Results for the S-populations were not conclusive. For the L-populations, results indicated that by use of data from a relatively small subset of bulls with distribution of daughters balanced across countries, genetic correlations could be estimated with very small bias (overall average of absolute value of bias across replicates was 0.03 for the L-populations). The suggested bull subsetting strategy would allow simultaneous estimation of across-country genetic correlations to be computed for a larger number of countries and in a shorter window of time than was possible previously.

A simple method for weighted bending of genetic (co)variance matrices.

Due to computational demand, elements of genetic correlation matrices may have been estimated separately and then combined together into a single correlation matrix at a later stage. Because these matrices should be positive definite (PD) a statistical method commonly known as "bending" is used to make them positive definite. The conventional bending method ignores the reliability of different correlations and may subject any of them to change in order to make a positive definite correlation matrix. A simple method to obtain a weighted bended matrix to be used in animal breeding applications is proposed, and the implementation of the method is demonstrated by an example.

Bayesian analysis of birth weight and litter size in Baluchi sheep using Gibbs sampling.

Variance and covariance components for birth weight (BWT), as a lamb trait, and litter size measured on ewes in the first, second, and third parities (LS1 through LS3) were estimated using a Bayesian application of the Gibbs sampler. Data came from Baluchi sheep born between 1966 and 1989 at the Abbasabad sheep breeding station, located northeast of Mashhad, Iran. There were 10,406 records of BWT recorded for all ewe lambs and for ram lambs that later became sires or maternal grandsires. All lambs that later became dams had records of LS1 through LS3. Separate bivariate analyses were done for each combination of BWT and one of the three variables LS1 through LS3. The Gibbs sampler with data augmentation was used to draw samples from the marginal posterior distribution for sire, maternal grandsire, and residual variances and the covariance between the sire and maternal grandsire for BWT, variances for the sire and residual variances for the litter size traits, and the covariances between sire effects for different trait combinations, sire and maternal grandsire effects for different combinations of BWT and LS1 through LS3, and the residual covariations between traits. Although most of the densities of estimates were slightly skewed, they seemed to fit the normal distribution well, because the mean, mode, and median were similar. Direct and maternal heritabilities for BWT were relatively high with marginal posterior modes of .14 and .13, respectively. The average of the three direct-maternal genetic correlation estimates for BWT was low, .10, but had a high standard deviation. Heritability increased from LS1 to LS3 and was relatively high, .29 to .37. Direct genetic correlations between BWT and LS1 and between BWT and LS3 were negative, -.32 and -.43, respectively. Otherwise, the same correlation between BWT and LS2 was positive and low, .06. Genetic correlations between maternal effects for BWT and direct effects for LS1 through LS3 were all highly negative and consistent for all parities, circa -.75. Environmental correlations between BWT and LS1 through LS3 were relatively low and ranged from .18 to .29 and had high standard errors.

Population parameters for birth and ewe fleece weight at different parities in Baluchi sheep.

UNLABELLED: ZUSAMMENFASSUNG: Populationsparameter für Geburts- und Vließgewicht von Baluchi Schafen Das Datenmarterial stammt von zwei Herden einer Schafzuchtstation in NO Iran aus den Jahren 1966-1989. Die Tiere waren unselektiert und stammten aus zufällig verteilten Paarungen. Es wurden Geburtsgewicht und Vließgewicht bei verschiedenen Altersstufen erhoben und Varianzkomponenten mittels Restringierter Maximaler Likelihood mit einem bivariaten Tiermodell mit fixen Wirkungen von Jahr, Geschlecht, Geburtstyp und Parität sowie Zufallswirkungen für additiven Genotyp des Lammes (direkt) und des Mutterschafes (maternal), gemeinsamer Umwelt (ausgenommen Vließgewicht) und Resteinfluß geschätzt. Direkte und maternale genetische Korrelationen zwischen Leistungen verschiedener Paritäten wurden berechnet. In Herde 1 scheinen Varianzen und Heritabilitätswerte für Lammgewicht bis Parität 5 zuzunehmen, kaum aber in Herde 2. Die durchschnittlichen Heritabilitätswerte, direkt, maternal und gesamt waren 0.12, 0.11 und 0.26, die genetische Korrelation zwischen direkten und maternalen Wirkungen 0.42. Bei Vließgewicht waren in Herde 1 keine Veränderungen der Varianzen und Heritabilitätswerte mit Alter zu erkennen, aber bei Herde 2 nahmen phänotypische und Umweltvarianz mit Alter leicht zu. Durchschnittliche direkte, maternale und Gesamtheritabilität waren 0.19, 0.04 und 0.22, die genetische Korrelation zwischen direkten und maternalen Wirkungen geringgradig positiv in Herde 1, aber mit Alter zunehmend negativ in Herde 2. Die genetischen Korrelationen für direkte Wirkungen auf Geburtsgewicht waren hoch zwischen Paritäten 1 bis 5, aber niedriger bei Parität 6 und jene zwischen maternal bedingten Wirkungen zeigten ähnliche Trends. In Herde 2 waren Werte mit Parität 6 ähnlich wie die zwischen den übrigen Paritäten. Die die Vließgewichte betreffenden direkt genetischen Korrelationen zwischen Paritäten waren in beiden Herden ähnlich (0.73-0.92), jene, die maternale Wirkungen betreffen, deutlich geringer, besonders soweit sie Paritäten 5 und 6 betroffen haben und zeigten besonders bei Herde 2 starke Schwankungen (-0.54 bis 0.74). SUMMARY: Direct and maternal performance of ewes at different parities were examined in Baluchi sheep. The data set was collected during the period 1966-1989 from two flocks at a sheep breeding station in the north-east of Iran. The animals included in the data set were unselected and randomly mated. The traits analysed were birth weight of lamb and fleece weight at different parities of the ewe. Variance components were estimated using Restricted Maximum Likelihood with a bivariate animal model including fixed effects of year, sex, type of birth and parity, and random effects of additive genotype of lamb (direct genetic effect), additive genotype of ewe (maternal genetic effect) and common environment (excluded for ewe fleece weight), and random residual effect. Direct and maternal genetic correlations between different parities were estimated. There was evidence of increasing phenotypic and genetic variances and heritabilities from parity 5 for birth weight of lamb in flock 1, but only evidence of a slightly increasing age trend for the environmental and phenotypic variance in flock 2. The average heritabilities over flocks and parities were 0.12, 0.11 and 0.26 for the direct, maternal and total heritability, respectively, while the average genetic correlation between direct and maternal effects for this trait was 0.42. There were no indications of any age changes in variances or heritabilities for ewe fleece weight in flock 1, but indications of slightly increasing age trends for the environmental and phenotypic variance. The average heritabilities over flocks and parities were 0.19, 0.04 and 0.22 for the direct, maternal and total heritability, respectively, while the average genetic correlation between direct and maternal effects was slightly positive in flock 1 but increasingly negative with age of the ewe in flock 2. Direct genetic correlations between parities 1-5 were very high for birth weight of lambs (on average 0.96) in contrast to the markedly lower correlations of parities 1-5 with parity 6 (on average 0.67) in flock 1 with a similar pattern for the maternal genetic correlations. In flock 2, these correlations were also high but without the marked decrease between parities 1-5 with parity 6 that was found in flock 1. Direct genetic correlations between the various parities for ewe fleece weight were similar for the two flocks, ranging from 0.73 to 0.92 and without any obvious differences between the various combinations of parities. However, the maternal were markedly lower than the direct genetic correlations, especially for the combinations of parity 5 and 6 with the earlier parities, and most pronounced in flock 2 fluctuating from -0.54 to 0.79. To obtain reliable estimates of breeding values for birth weight of lamb, it is recommended that the prediction should include not only earlier but also later parities (ages) of the ewe.