Estimation and identifiability for a dynamic model of maternal nutrition and fetal growth in sheep : a thesis presented in partial fulfilment of the requirements for the degree of Master of Applied Statistics at Massey University, Albany, New Zealand

Abstract

The optimal maternal nutrition intake is extremely important in the second half of pregnancy for fetal development in mammals. It affects the health and wellbeing of the offspring. The purpose of this study was to determine the optimal daily nutrition intake for sheep during the second half of their pregnancy, to achieve a pre-determined desirable birth weight for lambs. By achieving the optimal birth weight, the postnatal development of the animals is likely to be improved. In this study, pregnant sheep carrying singletons or twins were considered. There were two levels of nutrition, low and high. Various dynamic mathematical models were proposed to obtain the optimal daily nutrition intake. The model parameters were estimated by weighted least-squares. Bootstrap simulations were used to check the reliability of each estimated parameter. Finally, the optimal daily nutrition intake was obtained by solving the boundary value problems, with pre-determined parameter values. The results suggested that the optimal daily nutrition intake for sheep in the second half of their pregnancy was a constant. For the particular breed of sheep, with target weight 6.5 kg for singletons, the optimal nutrition intake was 1.36 kg of dry matter per day. For twins, with a target weight of 12 kg, the optimal nutrition intake was 1.93 kg of dry matter per day. In addition, a comprehensive and generic ‘black-box’ algorithm was produced using the software MATLAB. It could return the optimal daily nutrition intake for any type of mammals given a time series of fetal weight and maternal nutrition.