Running head : COVARIANCE FUNCTIONS FOR EARLY GROWTH Estimates of direct and maternal covariance functions for growth of Australian beef calves from birth to weaning

Records for birth and subsequent, monthly weights until weaning on beef calves of two breeds in a selection experiment were analysed fitting random regression models. Independent variables were orthogonal (Legendre) polynomials of age at weighing in days, and orders of polynomial fit up to 10 were considered. Analyses were carried out on a phenotypic and genetic scale, fitting sets of random regression coefficients due to animals’ direct and maternal, additive genetic and permanent environmental effects, estimating up to 145 parameters. Changes in variances due to temporary environmental effects were modelled through a variance function. Results identified similar patterns of variation for both breeds, with maternal effects considerably more important in purebred Polled Herefords than a four-breed synthetic, the so-called Wokalups. Conversely, repeatabilities were higher for the latter. For both breeds, heritabilities decreased after birth, being lowest when maternal effects were most important around 100 days of age. Estimates at birth and weaning were consistent with previous, univariate results.