APPROXIMATING SELECTION DIFFERENTIALS AND VARIANCES FOR CORRELATED SELECTION INDEXES

Empirical formulae were derived to approximate selection differentials and variances of the selected estimated breeding values when the esti mated breeding values of the candidates for directional selection are multinormally distributed and correlated in any manner. These formulae extended the well-known exact basic form for the equicorrelated case, taking into account selection pressure, average pairwise correlation coefficient and average standard deviation of pairwise correlation per observation, through polynomials fitted to simulated data. Simulation s were carried out for different correlation structures (1, 2 or 3 dif ferent intra-class correlations per family, ranging from 0.3 to 0.99), for different numbers of independent families (1, 2, 5 or 10), for co nstant or variable family size and for selection pressures ranging fro m 0.5 to 50%. On average, 90% of the bias occurring when ignoring corr elations between observations was removed by our prediction formula of selection differential or variance of selected observations. Comparis ons with other correction methods, which assume special correlation st ructures, were also carried out.