F. Phocas et Jj. Colleau, APPROXIMATING SELECTION DIFFERENTIALS AND VARIANCES FOR CORRELATED SELECTION INDEXES, Genetics selection evolution, 27(6), 1995, pp. 551-565
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.