Twenty progeny tested sires from each of two countries - Canada and the US, were used to demonstrate the use of quadratic programming (QP) for maximizing the utility function. Utility functions maximize net present value (NPV) of sire selection decisions considering attitude towards risk. NPV were calculated for each sire based on the semen cost, interest rate and production to type selection policy. NPV expressed the value of genetic contributions to descendants over 3 generations. Estimated transmitting abilities (ETA) of US sires were converted to Canadian equivalents. Selection accuracies on US sires were adjusted to account for accuracy of the conversion formulae. Risk represents the variance in NPV and is a function of selection accuracy. Variances and covariances of sire NPV were considered. Inclusion of covariances, based on sire additive genetic relationships had little or no effect on utility functions. Sires included in the portfolio remained the same; however, with increasing aversion to risk, matings to sons of a particular sire decreased when relationships were considered. When aversion to risk increased, the number of sires included in the optimal portfolio increased and sires with high selection accuracy receive increased usage. Associated reductions in risk were up to 47.6% with small (5.2%) reduction in NPV. When interest rates were increased by 4%, NPV and risk decreased by 27.2% and 25.2%, respectively. Increasing selection pressure on type relative to production increased risk by 17.5% with a 193% increase in NPV; sire selection and usage changed significantly. The use of QP is an effective tool for sire selection when risk is to be considered. A difficulty arises in generalizing sire usage recommendations because selection decisions are based on personal utility functions.

H. W Leitch, John P Gibson, Jack CM Dekkers, E. B Burnside

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume 17. Genetics and breeding of dairy and beef cattle, swine and horses, , 50–53, 1994
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