Heterogeneity of variances across regions of northern Germany and adjustment in genetic evaluation

Evaluation of extent and amount of heterogeneous variance for milk yield in Uruguayan Holsteins

The extent and amount of heterogeneous phenotypic variance for milk yield in the Uruguayan Holstein population were evaluated and a simple method of accounting for heterogeneity was developed. Lactation records (159 169) collected between 1989 and 1998 by two recording schemes were used to form 8955 herd-year-season-parity-lactation length contemporary groups. A log-linear model was used to identify factors affecting heterogeneity of phenotypic variance. The model included effects of production level, contemporary group size, recording scheme, herd, season of calving, parity number, calving year period and length of lactation and accounted for 50% of the variation in log variances. Estimates from this model were used in a Bayesian manner, to obtain posterior mean estimates of within-contemporary-group variances, which were then used to standardize records to a baseline variance. Effects of the adjustment were assessed by comparing coefficients of variation before and after correction, by correlation and regression between mean and standard deviations, and by using Gini coefficients and Lorenz curves. The adjustment procedure reduced heteroscedasticity primarily by decreasing the frequency of low-variance contemporary groups. Lorenz curves and Gini coefficients indicated that the largest impact of the standardization procedure was related to the size of the contemporary group. Some differences in the effect of the correction were found between recording schemes. The method for adjusting records is simple and easy to adapt to current genetic evaluation procedures.

Ability of sire breeding values to predict progeny bodyweight, fat and muscle using various transformations across environments in terminal sire sheep breeds

Data used for the genetic evaluation of the terminal sire sheep breeds in Australia originate from a large range of genotypes and environments. This means there are large differences in the level of production and therefore contemporary group means and variances within the data. This study examined four transformations to account for the heterogeneity of variance in the observed data and their effect on the ability of estimated breeding values of sires (sire EBV) to predict progeny performance. This predictive ability was described by regressing offspring performance on sire EBV. The expected value of this regression is 0.5, which indicates that half of the sire EBV differences can be expected in the progeny. The transformations of observed data were investigated in low, medium and high production environments for weight and ultrasound scan traits (fat and muscle) in terminal sire sheep breeds. There were records from over 300 000 sheep in the LAMBPLAN terminal sire dataset, predominately from Poll Dorset, Texel, Suffolk and White Suffolk breeds. The transformation methods applied to the observed data were: traits expressed as a percentage of the contemporary group mean; traits re-scaled to a common contemporary group mean in units of measurement; a logarithmic transformation; and a square root transformation. The heritabilities and other variance ratios estimated from the transformed traits were not significantly different from those using the observed data. Phenotypes transformed to a proportion of the contemporary group mean, either as a percentage or in units of measurement, resulted in the most consistent EBV across all production environments for weight and fat traits, with little effect of transformations for muscle traits. The transformation of data to the contemporary mean in units of measurement for weight and fat traits has been implemented in the Sheep Genetics evaluation system. The consistency of the progeny–sire EBV regressions around 0.5 in the data from these purebred industry flocks is heartening for terminal sire evaluation.

Effectiveness of adjusting for heterogeneity of variance in genetic evaluation of Japanese Black cattle

Heterogeneity of variance among subclasses of an effect is a potential source of bias in genetic evaluation. The objectives of this study were to quantify the heterogeneity of variance in carcass weight in Japanese Black cattle, to develop an adjustment method to account for the heterogeneity, and to evaluate the effectiveness of the method. A total of 96,950 records were collected from steers and heifers slaughtered from 1997 to 2005. These records were grouped into 2,767 farm-market-year-sex subclasses. Fourteen log-linear models for the variances were set up to estimate the heterogeneous phenotypic variances within subclasses. Schwarz's Bayesian information criterion was used for model selection. The preadjustment of records to a baseline variance was based on maximum likelihood estimates obtained from the selected model. As a result of adjustment, the SD, the CV, and the Gini coefficient for the phenotypic variance decreased by 68.6, 69.8, and 70.1%, respectively. When the top 5% of sires and top 1% of dams were selected, Spearman's rank correlation coefficients between the adjusted and unadjusted data were 0.95 for the selected sires and 0.78 for the selected dams. The effectiveness of the adjustment was evaluated in terms of the ability to predict breeding values, using the results of the successive genetic evaluations. Mean squared error between the parent averages and actual predicted values of the genetic merit for the sires whose progeny had a carcass record only from 2003 to 2005 was significantly reduced by the adjustment (P < 0.05). The results suggest that the genetic evaluation becomes more accurate by adjusting the data using the procedure developed in this study.

Estimated Heterogeneity of Phenotypic Variance of Test-Day Yield with a Structural Variance Model

First-lactation test-day milk, fat, and protein yields from New York, Wisconsin, and California herds from 1990 through 2000 were adjusted additively for age and lactation stage. A random regression model with third-order Legendre polynomials for permanent environmental and genetic effects was used. The model included a random effect with the same polynomial regressions for 2 yr of calvings within herd (herd-time effect) to provide herd-specific lactation curves that can change every 2 yr. (Co)variance components were estimated using expectation-maximization REML simultaneously with phenotypic variances that were modeled using a structural variance model. Maximum heritability for test-day milk yield was estimated to be approximately 20% around 200 to 250 d in milk; heritabilities were slightly lower for test-day fat and protein yields. Herd-time effects explained 12 to 20% of phenotypic variance and had the greatest impact at start of lactation. Variances of test-day yields increased with time, subclass size, and milking frequency. Test month had limited influence on variance. Variance increased for cows in herds with low and high milk yields and for early and late lactation stages. Repeatabilities of variances observed for a given class of herd, test-day, and milking frequency were 14 to 17% across nested variance subclasses based on lactation stage.