Order statistics of correlated variables and implications in genetic selection programmes.

Formulae are derived and examples given for the expected values of the order statistics from a sample of several groups or families of equal size where the group members have intra-class correlation t. As t increases from O the means of the highest ranking individuals are little reduced initially, but as t approaches 1 the change becomes more rapid, the total reduction depending on the number of groups. The effect on selection differentials of the intra-class correlation of family members is generally small for t less than 0.5, such as if selection is practised on individual performance. If, however, family mean performance is used in an index, the selection differentials may be substantially reduced.