36 K
. Meyer Livestock Production Science 65 2000 19 –38
slight downward trend in variance for later ages, stone et al. 2000 found that parametric curves fitted
indicating that the upwards trend in estimates on the the data best, but produced negative estimates of
untransformed scale was associated with the increase genetic correlations between early and late lactation
in average weight. As the cyclic pattern on the while RR on orthogonal polynomials did not. The
logarithmic scale shows, seasonal variation in vari- rationale for concentrating on variances or standard
ances clearly could only partially attributed to scale deviations in this study was that it seemed futile to
effects. Moreover, Fig. 11 suggests that the non-size examine covariances, unless variances had been
related, seasonal differences became more important modelled correctly.
at later ages, presumably because variation in the RR models proved well capable of describing the
ability of cows to cope with dearth increased with existing, complex pattern of variation. Not requiring
age. any prior knowledge about the shape of curves to be
modelled, RR on orthogonal polynomials of age performed admirably. While they required more
4. Discussion parameters to achieve the same degree of fit mea-
sured by log + values than other curves, they Results showed a seasonal pattern in growth of
appeared to be least susceptible to convergence animals, determined by high winter rain falls and
problems, even for analyses involving well over 200 summer droughts and corresponding levels of pasture
parameters to be estimated. Alternative curves in- availability. With almost complete confounding be-
volving segmented polynomials or sine and cosine tween age at weighing and season, average growth
functions required knots to be specified or the curves showed a corresponding, sinuous pattern Fig.
assumption that a sinusoidal curve of given period- 1. Fixed effects fitted, i.e. year-week-paddock of
icity 12 months was appropriate. Analyses for recording and a fixed, cubic regression on age,
models involving segmented polynomials were gen- accounted for differences in mean weights, but had
erally slow to converge. In a few cases there were little effect on variances Fig. 2.
doubts whether convergence was real and had indeed Analyses identified a distinct cyclic pattern in
achieved a global maximum. Future work should variances, both between animals and for temporary
consider the use of orthogonal rather than ordinary environmental effects. As a transformation to loga-
polynomials to model individual segments, and rithmic scale showed, this could only in part be
investigate the joint estimation of knots. attributed to scale effects. This implied that there
Attempts to separate age-determined from season- was substantial variation between animals in their
ally influenced variation between animals by fitting reaction to seasonal effects. Moreover, seasonal
an additional RR on polynomials of month of fluctuations in variance independent of size appeared
recording failed. Clearly, with the degree of con- to become more pronounced at later ages Fig. 11.
founding between age and season in the data, there Modelling this variation adequately presented a
was insufficient information to do so. Nevertheless, seemingly unending task. With considerable numbers
the second set of RR coefficients invariably resulted of records per animal, log + values increased
in a better fit of the model considered, presumably to significantly whenever any additional parameters
some extent by accounting for differences in tempor- were added, even though differences in estimates of
ary environmental variation. variances appeared insubstantial in various instances.
Measurement error variances were clearly not Clearly, variances alone do not represent the whole
homogeneous. The cyclic pattern found indicated picture, estimates of covariance functions provided
that this heterogeneity was primarily due to seasonal by RR model analyses give a description of co-
effects. A model fitting 12 different, cyclically variances between all ages in the data. These need to
repeating components thus appeared adequate. When be taken into account before deciding on the ‘best’
comparing models involving the same type of curve model. In comparing parametric curves and ortho-
e.g. orthogonal polynomials, however, estimates of gonal polynomials of days in milk in RR analyses of
the between animal components were little affected
2
test day records of dairy cows, for instance, Brother- by the number of s
fitted. This suggested that
e
K . Meyer Livestock Production Science 65 2000 19 –38
37 tock breeding. In: Proc. Sixth World Congr. Genet. Appl.
orders of fit could be compared assuming a single
Livest. Prod., Vol. 23, Armidale, Australia, pp. 32–39.
component, thus reducing computational require-
Jamrozik, J., Schaeffer, L.R., 1997. Estimates of genetic parame-
ments.
ters for a test day model with random regressions for pro- duction of first lactation Holsteins. J. Dairy Sci. 80, 762–770.
Jamrozik, J., Schaeffer, L.R., Dekkers, J.C.M., 1997. Genetic evaluation of dairy cattle using test day yields and random
5. Conclusions
