Abstract
A selection index is developed which maximises genetic gains in some characters while controlling the gains made in others. More specifically, if there are m characters for selection, and 4 of these are to be altered by an amount ki, j=1,..r, to bring them to their optimum values, then a conditional selection index is constructed so that genetic gains are proportional to kj for the r "restricted characters", while maximum gains are made in the remaining (m-r) characters. As an application of this index, consider the selection of animals for meat production. In this case, maximum progress in the amount and economy of production may be required, accompanied by minor changes in certain carcass characteristics.

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