Predictions in quantitative genetics have mostly been restricted to additive genetic effects. The flexibility of Henderson's mixed model methodology allows for straightforward consideration of dominance effects if there is no inbreeding. The proper treatment of inbreeding and dominance involves three parameters beside additive and dominance genetic variance. Tabular methods can be used for calculating genotypic covariances. The algorithm involves writing out animals in terms of pairs of gametes and, if necessary, considering also new combinations of gametes. The matrix is called an extended genomic table. The inversion of this matrix requires inverting several block diagonal matrices corresponding to a particular gamete.

A. Maki-Tanila, S. P Smith

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume XIII. Plenary lectures, molecular genetics and mapping, selection, prediction and estimation., , 293–296, 1990
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