No abstract

The average daily gains of 6,420 Czech Pied bulls (dual-purpose, Simmental type) from 7 breeding stations were analyzed using single-trait animal models, a multi-trait animal model and random regression models. The effects of station, year and season were taken into account by creating herd-year-season classes (HYS) with the season being defined as a 3-month class starting with December. Legendre polynomials of the 1 st to the 4 th degree were used to describe the daily gains within the HYS classes as well as to model bull-specific gain curves. The comparison of the h 2 -values estimated with single-trait models and those gained with a multi-trait model returned only insignificant differences. The comparison of genetic parameters based on the multi-trait model to those from different random regression models shows that polynomials of at least the 2 nd degree are to be used for the genetic analysis of daily gains.

6 508 bulls of dual-purpose cattle at performance-test stations were weighed at intervals of 30 days from birth to 420 days. After all editing a total of 74 558 weight records were available. Live weight was evaluated by orthogonal Legendre Polynomial (LP) of degree 4 and by Linear Spline function (SP) with 5 knots. The fixed effects of test-day-year-station of weighing (TDS) and LP within station-year explain together 97% of variability. Variance components were estimated by REML (REMLF90 programme) taking into account heterogeneous variance during growth. The basic model included fixed effects: TDS, and fixed regression on age (LP F ), and random regression for additive genetic (SP G ) and permanent environmental of the animal (SP PE ) effects. Variability of all components increases with age. During the 50-400 day period the heritability is 0.28 on average. Heritability increases with the age of the animal; it is the highest at the end of the period. Correlations for body weights between different ages of the animal are high.

Random regression models are widely used in the field of animal breeding for the genetic evaluation of daily milk yields from different test days. These models are capable of handling different environmental effects on the respective test day, and they describe the characteristics of the course of the lactation period by using suitable covariates with fixed and random regression coefficients. As the numerically expensive estimation of parameters is already part of advanced computer software, modifications of random regression models will considerably grow in importance for statistical evaluations of nutrition and behaviour experiments with animals. Random regression models belong to the large class of linear mixed models. Thus, when choosing a model, or more precisely, when selecting a suitable covariance structure of the random effects, the information criteria of Akaike and Schwarz can be used. In this study, the fitting of random regression models for a statistical analysis of a feeding experiment with dairy cows is illustrated under application of the program package SAS. For each of the feeding groups, lactation curves modelled by covariates with fixed regression coefficients are estimated simultaneously. With the help of the fixed regression coefficients, differences between the groups are estimated and then tested for significance. The covariance structure of the random and subject-specific effects and the serial correlation matrix are selected by using information criteria and by estimating correlations between repeated measurements. For the verification of the selected model and the alternative models, mean values and standard deviations estimated with ordinary least square residuals are used.