Genetic parameters for a population selected with a sib index

Xm, Xf dNumber of male and female parents and mating ratio d = Xf/Xm
nm, nf, noNumber of male and female offspring in a full-sib family, no = nm + nf
P, Embedded Image , Embedded Image Phenotype of candidate and its full- and half-sib family means
I, b1 b2, b3Index and weights for selection Embedded Image
pm, pfSelection proportions for males and females: pm = (nmd)−1, pf = nf−1
Vm, Vf, im, if, km, kfTruncation points, intensities of selection, and variance reduction coefficients
Embedded Image Variance of the index, total genetic variance, and accuracy of selection
Embedded Image Genetic variance among selected sires and dams and residual variance
Ai(hs), Aj(fs)Mean breeding value of the half-sib family of sire i and the mean breeding value of the full-sib family of dam j expressed as a deviation from the half-sib family
V(Ai(hs))Variance of Am and similarly defined for Embedded Image
ρFS, ρHSCorrelation of indices among full-sibs and half-sibs, respectively: Embedded Image
  • In the initial unselected base population, the phenotypic variance was assumed to be 1 and the initial heritability Embedded Image