No abstract

The milk production of 63 5-year-old Merino ewes was measured over a 16-week period after lambing. The purpose was to find a suitable mathematical model to represent the lactation curve of Merino sheep and to estimate the parameters of the model for an individual ewe from a single data point in early lactation. Three models were considered, the three-parameter Wood model, yn = nb exp(a + en), the four-parameter Morant model, yn = exp(a + bn + en2 + d/n and the six-parameter Grossman model, yn = a1b1 - [tanh2 (b1n - c1))] + a2b2[1 – tanh2 (b2(n -c2,))].The Grossman model was found to be inappropriate for the available data, while there seems to be little difference in the suitability of the other two models. The Wood and Morant models both seem adequate to represent the lactation curve. A pattern in the estimated residuals suggests possible autocorrelations in the errors, but this is inconclusive due to the limited number of data points per animal.The correlation between the estimated parameters of the model and the daily yield measured during the 1st week of lactation enabled us to use linear regression to estimate the lactation curve of an individual animal based on the 1st week's yield. Confidence and prediction intervals for the yield during the rest of the lactation period may then also be constructed. This makes it possible to extend incomplete milk records for use in genetic evaluation, formulation of rations and economic evaluations.

No abstract

Bayesian theory is applied to compare the characteristics of the estimated lactation curves of two groups of 5-year-old Merino ewes. The diets of the two groups were supplemented respectively by DL-methionine and maleyl-DLmethionine. The purpose is to illustrate the Bayesian approach when analysing for the effect of supplement on the lactation pattern of the sheep. Using Wood's model, the posterior distributions of the model parameters are determined for the two groups. This is achieved by assuming a hierarchical Bayes model and applying the Gibbs sampler, a sampling based computer intensive algorithm that is very efficient in obtaining marginal distributions of functions of parameters. The Gibbs sampler enables us to obtain marginal posterior distribution of characteristics of the lactation curve such as peak yield, time of peak yield, persistency and total milk yield. The results are notable differences in the marginal posterior distributions of mean peak milk yield and mean total yield. The posterior probability that the mean peak milk yield of the group supplemented by maleyl-DL-methionine is higher than that of the group with DL-methionine supplement is 0·98, while the same probability for mean total yield is 0·83.

Bayes Risk, Hypothesis Testing, Posterior Probability,