Partial diallel crossing designs are in common use among evolutionary geneticists, as well as among plant and animal breeders. When the goal is to make statements about populations represented by a given set of lines, it is desirable to maximize the number of lines sampled given a set number of crosses among them. We propose an augmented round-robin design that accomplishes this. We develop a hierarchical Bayesian model to estimate quantitative genetic parameters from our scheme. For example, we show how to partition genetic effects into specific and general combining abilities, and the method provides estimates of heritability, dominance, and genetic correlations in the face of complex and unbalanced designs. We test our approach with simulated and real data. We show that although the models slightly overestimate genetic variances, main effects are assessed accurately and precisely. We also illustrate how our approach allows the construction of posterior distributions of combinations of parameters by calculating narrow-sense heritability and a genetic correlation between activities of two enzymes.
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