Decision rules and variance of response in breeding schemes

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Abstract
Selection decisions in breeding schemes can involve choices between candidates evaluated to different accuracies. A Bayesian framework is put forward for choosing among candidates, and it is shown that attaching loss functions for estimation errors makes this process different from selecting upon best linear unbiased predictions alone. Examples are given using both linear and quadratic loss to show that when estimation errors are penalized, the selection process tends to select more unrelated and more accurately evaluated individuals. In a dairy cattle breeding scheme response was only slightly lower than that from selection on expected breeding values but with a much reduced coefficient of variation. However, if prediction errors are preferred, with the hope of selecting individuals whose breeding value are higher than expected, extra genetic progress could be obtained by favouring the selection of individuals with low accuracy. This requires consideration of more than a single generation. With discrete generations and equal measurements on candidates the decision framework was shown to be equivalent to a single quadratic restriction on the selection scores of parents in the previous generation. A framework based on Bayes decision theory could be simply applied to produce a flexible means for producers to select according to their individual risk preferences.