Effect of sampling errors on efficiency of selection indices. 2. Use of information on associated traits for improvement of a single important trait

SUMMARY An analysis is undertaken of the effect of errors in estimates of parameters on the response to selection for an economically important trait (trait 1) when one or more additional traits are added in a selection index. The detailed analysis is confined to one additional trait (trait 2) which contributes useful information unless the genetic and phenotypic regressions of trait 1 on trait 2 are equal. If there are errors in parameter estimates the extra response obtained by including trait 2 will usually be over-predicted. When trait 2 actually contributes no useful information the predicted benefit equals the real loss in efficiency from its inclusion. The loss in efficiency from poor estimation of parameters, whether or not the second trait makes a contribution, is roughly one-quarter of the squared coefficient of variation of a heritability estimate of trait 1 in the same experiment.