Estimation of Variance Components by the Expectation-Maximization Algorithm for Restricted Maximum Likelihood in a Repeatability Model for Semen Production

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Abstract
Restricted maximum likelihood by the expectation-maximization algorithm was used to estimate variance components in a mixed linear model parameterized to separate additive genetic from nonadditive genetic and permanent environmental sources of variation. In this model, heritability is not estimable unless animals are related and the inverse numerator relationship matrix is incorporated in the mixed model equations. The expectation-maximization algorithm guarantees that variance components will remain positive with positive priors. However, convergence of the algorithm tends to zero if any variance component tends to zero. In practice, some form of acceleration routine may be required to speed convergence. The procedure was applied to analyze 2,216 semen output measures for first ejaculates of volume, concentration, and total sperm on 200 young bulls from one bull stud. Heritabilities and repeatabilities were .12, .00, .02 and .24, .45, .44 for volume, concentration, and total sperm.