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"Estimates of genetic and phenotypic covariance functions
for postweaning growth and mature weight of beef cows"

K. Meyer

* Journal of Animal Breeding and Genetics * **116 ** : 181-205.

### Abstract

Annual weights of of cows from 19 to 119 months of age in two herds
were analysed fitting a random regression model, regressing on
orthogonal polynomials of age in months. Estimates of covariances
between random regression coefficients were obtained by restricted
maximum likelihood, and resulting estimates of covariance functions
used to construct covariance matrices for all ages in the data.
Analyses were carried out fitting regression coefficients
corresponding to overall animal effects only and fitting regressions
for animals' additive genetic and permanent, environmental effects.
Different definitions of fixed effects subclasses were examined.
Models were compared using likelihood ratio tests and estimated
standard deviations for the ages in the data.
Cubic regressions were
sufficient to model both population trajectories and individual grow
curves. Random regression coefficients were highly correlated, so that
estimation forcing their covariance matrices to have reduced rank (2
or 3) did not reduce likelihoods significantly, allowing parsimonious
modelling. Results showed that records were clearly not repeated
measurements of a single trait with constant variances. As cows grew
up to about 5 years of age, variances increased. Estimates of genetic
correlations between three year old and older cows were close to unity
in one herd but more erratic in the other. For both herds, genetic
correlations between weights on two year old cows and older animals
were clearly less than unity.

**Key words** : Growth, beef cattle, covariance function

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K.Meyer, July 2000