A comparison of exact and sequential methods in multi-stage index selection.

The theory of sequential multi-stage index selection makes an implicit assumption that the correlation between indices at different stages is zero. This assumption was shown to result in errors in the estimation of genetic gain and in the proportion of the population selected by truncating the joint distribution of the indices. Knowledge of the means and volumes of truncated multivariate normal distributions was used to correct these estimates. Effects of selection intensity and the correlation between the first and second stage indices (ϱ) on the accuracy of the approximate sequential method were examined. Computational constraints limited this analysis to two-stage index selection procedures. The sequential method performed well for ϱ less than 0.6 but accuracy deteriorated rapidly as ϱ increased beyond this value. The effect of selection intensity on accuracy was smaller than ϱ. On a percentage basis, errors in actual percent selected and under-estimation of genetic gain increased with selection intensity while overestimation decreased. The types of errors which occur and their magnitude depend on the intensity of first stage selection.