Genetic parameters of Legendre polynomials for first parity lactation curves

Variance components of the covariance function coefficients in a random reg ression test-day model were estimated by Legendre polynomials up to a fifth order for first-parity records of Dutch dairy cows using Gibbs sampling. T wo Legendre polynomials of equal order were used to model the random part o f the lactation curve, one for the genetic component and one for permanent environment. Test-day records from cows registered between 1990 to 1996 and collected by regular milk recording were available. For the data set, 23,7 00 complete lactations were selected from 475 herds sired by 262 sires. Because the application of a random regression model is limited by computin g capacity, we investigated the minimum order needed to fit the variance st ructure in the data sufficiently. Predictions of genetic and permanent envi ronmental variance structures were compared with bivariate estimates on 30- d intervals. A third-order or higher polynomial modeled the shape of varian ce curves over DIM with sufficient accuracy for the genetic and permanent e nvironment part. Also, the genetic correlation structure was fitted with su fficient accuracy by a third-order polynomial, but, for the permanent envir onmental component, a fourth order was needed. Because equal orders are sug gested in the literature, a fourth-order Legendre polynomial is recommended in this study. However, a rank of three for the genetic covariance matrix and of four for permanent environment allows a simpler covariance function with a reduced number of parameters based on the eigenvalues and eigenvecto rs.