changes of allele frequency with selection

[nena77]

I have a problem with the article of Lebowitz in Theor Appl Genet, 1987
"Trait based analysis for the detection of linkages between marker loci and quantitative trait loci in crosses between inbred lines"

in a F2 population with genotypes AA Aa aa at the QTL ( only one QTL is supposed to exist) the difference in allele frequency as a result of one step selection , carried out at both tails of the phenotypic normal distribution, is
=iD/4
where i is the standardized selection differential
D= is the proportional effect of the QTL equal 2d/δ, where d is the additive effect of the QTL and δ the phenotypic standard deviation of the all population ( equal lso to standard deviation of the distribution of the three genotypic classes AA Aa aa)
my question is
why is it everythinf divided by 4?

for a BC population the same foruma would be divided by 8 instead of 4.....why?
thanks

Elena