Anna-Maria Tyrisevä

Principal component approach in variance component estimation for international sire evaluation

BackgroundThe dairy cattle breeding industry is a highly globalized business, which needs internationally comparable and reliable breeding values of sires. The international Bull Evaluation Service, Interbull, was established in 1983 to respond to this need. Currently, Interbull performs multiple-trait across country evaluations (MACE) for several traits and breeds in dairy cattle and provides international breeding values to its member countries. Estimating parameters for MACE is challenging since the structure of datasets and conventional use of multiple-trait models easily result in over-parameterized genetic covariance matrices. The number of parameters to be estimated can be reduced by taking into account only the leading principal components of the traits considered. For MACE, this is readily implemented in a random regression model.MethodsThis article compares two principal component approaches to estimate variance components for MACE using real datasets. The methods tested were a REML approach that directly estimates the genetic principal components (direct PC) and the so-called bottom-up REML approach (bottom-up PC), in which traits are sequentially added to the analysis and the statistically significant genetic principal components are retained. Furthermore, this article evaluates the utility of the bottom-up PC approach to determine the appropriate rank of the (co)variance matrix.ResultsOur study demonstrates the usefulness of both approaches and shows that they can be applied to large multi-country models considering all concerned countries simultaneously. These strategies can thus replace the current practice of estimating the covariance components required through a series of analyses involving selected subsets of traits. Our results support the importance of using the appropriate rank in the genetic (co)variance matrix. Using too low a rank resulted in biased parameter estimates, whereas too high a rank did not result in bias, but increased standard errors of the estimates and notably the computing time.ConclusionsIn terms of estimations accuracy, both principal component approaches performed equally well and permitted the use of more parsimonious models through random regression MACE. The advantage of the bottom-up PC approach is that it does not need any previous knowledge on the rank. However, with a predetermined rank, the direct PC approach needs less computing time than the bottom-up PC.

Principal component and factor analytic models in international sire evaluation

BackgroundInterbull is a non-profit organization that provides internationally comparable breeding values for globalized dairy cattle breeding programmes. Due to different trait definitions and models for genetic evaluation between countries, each biological trait is treated as a different trait in each of the participating countries. This yields a genetic covariance matrix of dimension equal to the number of countries which typically involves high genetic correlations between countries. This gives rise to several problems such as over-parameterized models and increased sampling variances, if genetic (co)variance matrices are considered to be unstructured.MethodsPrincipal component (PC) and factor analytic (FA) models allow highly parsimonious representations of the (co)variance matrix compared to the standard multi-trait model and have, therefore, attracted considerable interest for their potential to ease the burden of the estimation process for multiple-trait across country evaluation (MACE). This study evaluated the utility of PC and FA models to estimate variance components and to predict breeding values for MACE for protein yield. This was tested using a dataset comprising Holstein bull evaluations obtained in 2007 from 25 countries.ResultsIn total, 19 principal components or nine factors were needed to explain the genetic variation in the test dataset. Estimates of the genetic parameters under the optimal fit were almost identical for the two approaches. Furthermore, the results were in a good agreement with those obtained from the full rank model and with those provided by Interbull. The estimation time was shortest for models fitting the optimal number of parameters and prolonged when under- or over-parameterized models were applied. Correlations between estimated breeding values (EBV) from the PC19 and PC25 were unity. With few exceptions, correlations between EBV obtained using FA and PC approaches under the optimal fit were ≥ 0.99. For both approaches, EBV correlations decreased when the optimal model and models fitting too few parameters were compared.ConclusionsGenetic parameters from the PC and FA approaches were very similar when the optimal number of principal components or factors was fitted. Over-fitting increased estimation time and standard errors of the estimates but did not affect the estimates of genetic correlations or the predictions of breeding values, whereas fitting too few parameters affected bull rankings in different countries.

Detection of evaluation bias caused by genomic preselection

The aim of this simulation study was to investigate whether it is possible to detect the effect of genomic preselection on Mendelian sampling (MS) means or variances obtained by the MS validation test. Genomic preselection of bull calves is 1 additional potential source of bias in international evaluations unless adequately accounted for in national evaluations. Selection creates no bias in traditional breeding value evaluation if the data of all animals are included. However, this is not the case with genomic preselection, as it excludes culled bulls. Genomic breeding values become biased if calculated using a multistep procedure instead of, for example, a single-step method. Currently, about 60% of the countries participating in international bull evaluations have already adopted genomic selection in their breeding schemes. The data sent for multiple across-country evaluation can, therefore, be very heterogeneous, and a proper validation method is needed to ensure a fair comparison of the bulls included in international genetic evaluations. To study the effect of genomic preselection, we generated a total of 50 replicates under control and genomic preselection schemes using the structures of the real data and pedigree from a medium-size cow population. A genetic trend of 15% of the genetic standard deviation was created for both schemes. In carrying out the analyses, we used 2 different heritabilities: 0.25 and 0.10. From the start of genomic preselection, all bulls were genomically preselected. Their MS deviations were inflated with a value corresponding to selection of the best 10% of genomically tested bull calves. For cows, the MS deviations were unaltered. The results revealed a clear underestimation of bulls breeding values (BV) after genomic preselection started, as well as a notable deviation from zero both in true and estimated MS means. The software developed recently for the MS validation test already produces yearly MS means, and they can be used to devise an appropriate test. Mean squared true MS of genomically preselected bulls was clearly inflated. After correcting for the simulated preselection bias, the true genetic variance was smaller than the parametric value used to simulate BV, and also below the variance based on the estimated BV. Based on this study, the lower the traits heritability, the stronger the bias in estimated BV and MS means and variances. Daughters of genomically preselected bulls had higher true and estimated BV compared with the control scheme and only slightly elevated MS means, but no effect on genetic variances was observed.

Validation of consistency of Mendelian sampling variance

Experiences from international sire evaluation indicate that the multiple-trait across-country evaluation method is sensitive to changes in genetic variance over time. Top bulls from birth year classes with inflated genetic variance will benefit, hampering reliable ranking of bulls. However, none of the methods available today enable countries to validate their national evaluation models for heterogeneity of genetic variance. We describe a new validation method to fill this gap comprising the following steps: estimating within-year genetic variances using Mendelian sampling and its prediction error variance, fitting a weighted linear regression between the estimates and the years under study, identifying possible outliers, and defining a 95% empirical confidence interval for a possible trend in the estimates. We tested the specificity and sensitivity of the proposed validation method with simulated data using a real data structure. Moderate (M) and small (S) size populations were simulated under 3 scenarios: a control with homogeneous variance and 2 scenarios with yearly increases in phenotypic variance of 2 and 10%, respectively. Results showed that the new method was able to estimate genetic variance accurately enough to detect bias in genetic variance. Under the control scenario, the trend in genetic variance was practically zero in setting M. Testing cows with an average birth year class size of more than 43,000 in setting M showed that tolerance values are needed for both the trend and the outlier tests to detect only cases with a practical effect in larger data sets. Regardless of the magnitude (yearly increases in phenotypic variance of 2 or 10%) of the generated trend, it deviated statistically significantly from zero in all data replicates for both cows and bulls in setting M. In setting S with a mean of 27 bulls in a year class, the sampling error and thus the probability of a false-positive result clearly increased. Still, overall estimated genetic variance was close to the parametric value. Only rather strong trends in genetic variance deviated statistically significantly from zero in setting S. Results also showed that the new method was sensitive to the quality of the approximated reliabilities of breeding values used in calculating the prediction error variance. Thus, we recommend that only animals with a reliability of Mendelian sampling higher than 0.1 be included in the test and that low heritability traits be analyzed using bull data sets only.