Table 3 Response to within and among family selection in a randomly mating population under weak selection
Level of selectionChange in frequency of A1 allele (Δp)Equilibrium values of pp = 0)Change in population mean phenotype (Embedded Image)
Among families
 Full-siblingsEmbedded Image(a + d)/2dEmbedded Image
 Maternal half-siblingsEmbedded Image(a + di)/2d(VA − covA,O(all))/4Embedded Image =Vh(dams)/4Embedded Image
 Paternal half-siblingsEmbedded Image(a + d + i)/2d(VA + covA,O(all))/4Embedded Image =Vh(sires)/4Embedded Image
Within families
 Full-siblingsEmbedded Image(a + d)/2dEmbedded Image
 Maternal half-siblingsEmbedded Image(a + d)/2d + i/6dVA/2Embedded Image + (VA + covA,O(all))/4Embedded Image = VA/2Embedded Image + Vh(sires)/4Embedded Image
 Paternal half-siblingsEmbedded Image(a + d)/2di/6dVA/2Embedded Image + (VA − covA,O(all))/4Embedded Image = VA/2Embedded Image + Vh(dams)/4Embedded Image
Total (=Among + Within)Embedded Image(a + d)/2dEmbedded Image
  • Responses to selection are shown for selection applied within and among full−sibling, maternal half-sibling and paternal half-sibling families. In each case, the response is given in terms of the change in the frequency of the A1 allele (Δp) and in terms of the change in mean phenotype (Embedded Image) observed in offspring after one generation of selection. The values for the phenotypic response to selection will be in relation to the strength of selection applied (i.e., in each case the value shown will be multiplied by the strength of selection, Embedded Image). Also shown are equilibrium values of p, where Δp = 0 (ignoring the trivial equilibria where p = 0 or 1).