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A population of size 40 was simulated 1,000 times for 10 generations. Five out of twenty males were selected each generation, and each male was mated to four females to have two progeny. The additive genetic variance (sigma 2a) before selection was 10, and the initial heritability was .5. Due to covariances among animals, inbreeding and gametic disequilibrium, the genetic variance was reduced to 6.72 after 10 generations of selection. Reduction of variance was lower in another population simulated with size 400 and 10% of the males selected. Restricted Maximum Likelihood was used to estimate sigma 2a using an animal model. The estimate of sigma 2a was empirically unbiased when all data and all relationships were used. Omitting data from selected ancestors caused biased estimates of sigma 2a due to not accounting for all gametic disequilibrium. Including additional relationships between assumed base animals adjusted for inbreeding and for covariances. Bias from gametic disequilibrium decreased slightly with the use of more relationship information, and it was smaller in the small population and(or) when selection had been practiced for just a few generations.
Werf et al. (Mon,) studied this question.