The reproductive potential of a sheep system is much reduced by the failure of released ova to be fertilized and to survive to parturition. This paper looks at currently available information on fertilization failure and early embryonic deaths. Separate hypotheses are proposed for fertilization and for early embryonic mortality. For fertilization, the hypothesis is that a ewe that mates with a ram will end up with either all or none of her released ova fertilized. For embryonic mortality, the hypothesis is that the survival of a fertilized ovum depends only on how many ova were released with it and is independent of the survival or death of those released with it. A mathematical model is constructed on these hypotheses and its predictions are compared with published experimental results of other workers. INTRODUCTIONIn the process of constructing a model of the population and nutritional characteristics of a sheep system, several sub-models have been investigated. One of these is a model for fertilization failure and embryonic mortality, the greatest causes of wastage of potential lambs that exist in a typical sheep system. An investigation of the literature showed that, although considerable progress has been made in experimental techniques for estimations of the total prenatal mortality in sheep, still many of the results appear at first sight to be contradictory, and it is difficult to fit them into a single conceptual framework. The model described below attempts a simple description in mathematical terms of the biological situation for fertilization and embryonic mortality and follows the consequences of the assumptions made, in order to assess the predictions of the model against published experimental results.

An analysis of the records of ewe weight and condition at mating together with subsequent lambing performance for several commercial flocks in the UK revealed no significant relationship between lambing performance and size, measured by weight transformed to a standard condition. The relationship between mating weight and body condition score at mating was linear though there was considerable variation in weight at a fixed body condition, suggesting a substantial spread in skeletal size. Increases in ovulation rate were not discernible from lambing figures over the range of body conditions observed in these flocks.

A computer program is described which allows the calculation throughout pregnancy of the energy requirements of a ewe of any weight carrying any number of foetuses. The calculations rely on a prediction of potential lamb birth weight, from which a foetal growth curve of weight against time from conception is generated. Tied to the foetal growth curve are the growths of the placenta and fluids, while growth of the uterus is related to the ewe's weight at mating. Weights are converted to energy through energy density curves applicable through pregnancy for each component. An efficiency factor converts this energy requirement into a metabolizable energy requirement. With assumptions on the maintenance requirements for the ewe-foetus system, the total requirement for energy during pregnancy is calculated.Predictions from the model are compared with other estimates of energy requirements available in the literature. The sensitivity of the predictions of energy requirements for the pregnant ewe to variations in the assumptions made in the construction of the model is discussed. The most important assumptions are those on the maintenance requirements for the ewe-foetus system. Effects on the predicted energy requirements of varying either the efficiency for foetal growth or the gestation length are also discussed.

A computer-based model of the response of the ewe to energy nutrition during pregnancy is described, based on a previous analysis of energy requirements. A ewe of specified weight and body condition 30 days from conception, carrying a known number of lambs, is predicted to grow them to an optimal weight if the nutritional regime allows. Daily energy requirements of the ewe-foetus system are calculated as the sum of requirements for maintenance and for growth and are compared with the daily energy supplied. If the feed provides energy surplus to requirements, the ewe herself gains weight; otherwise, the ewe mobilizes her own reserves, within limits, to protect the foetus. If this does not produce the energy required for optimal growth, foetal growth is reduced. Published experimental results are compared with predictions of the model when run under similar conditions; in general, predictions of total maternal weight at the end of pregnancy are within 5 % of those observed in the experiments. Model predictions of the effects of some particular nutritional regimes during pregnancy are presented and the sensitivity of the predictions of the model to certain of the assumptions made in its construction are discussed. 357

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