In animal breeding, genetic evaluation and estimation of genetic parameters have centered primarily on normally distributed traits and linear additive genetic models. The present study examined the feasibility of estimating additive, dominance and additive x additive type epistatic genetic variances in linkage equilibrium when these types of effects exist. Computer simulation was used for this purpose. Pseudo-normal records were the sum of a stochastic genetic component and a pseudo-normal environmental deviation. Non-additive genetic components of variance are difficult to estimate due to "confounding" between additive and non-additive genetic effects. However, given an appropriate pedigree, likelihood procedure can extract the information available on these components although it is reasonable to expect that non-additive components are more difficult to estimate well than additive ones. Univariate mixed linear models were used to describe and analyze the data. With normally distributed records, likelihood procedure was used for estimation of the variance components. An average of 7 iterations were required to converge at the fifth decimal point with the Newton-Raphson algorithm for maximum likelihood (ML) in design 4 (the "most efficient" one) for all combinations of genetic parameters considered in the study. Asymptotic theory indicated that in a genetic model with additive, dominance and additive x additive effects, the most difficult parameter to estimate was the variance "due to" epistasis, and that several thousand families were required to obtain reliable estimates of this parameter. In the presence of additive x additive effects, biases, mean squared errors and empirical variances of additive and dominance variance estimators were larger; further, sampling properties mentioned above of the additive and additive x additive variance estimators were affected by linkage.

H. L Chang, Rohan L Fernando, Daniel Gianola

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume XIII. Plenary lectures, molecular genetics and mapping, selection, prediction and estimation., , 437–440, 1990
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