Multibreed designs 3. Inter-breed relationships

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Abstract
Experimental designs with optimal allocation of animals within and between breeds are given for investigating inter-breed relationships between different traits. Optimal designs are given for estimating the following between-breed parameters: the genetic regression with breeds random, the genetic correlation, the ratio of genetic standard deviations for two traits and also the comparison of regressions within and between breeds. As in the case of between-breed variation, these turn out to be multibreed designs with a few animals per breed and usually as many different breeds as possible. Formulae are given for obtaining optimal numbers and estimation errors for traits with intra- and inter-breed correlations lying within restricted ranges. If an exepriment with a multibreed design is to be effective, the optimum number of animals (or sires) per breed would normally lie between two and 10. If the optimum number per breed is much greater than 10, the experiment is unlikely to be worthwhile unless the total number of animals is large (at least several thousand).