Additive genetic variance $V_A= 2pqa^2$ ... what is $a$?
This information is given in p.118.

In essence $a$ represents the deviation from the population mean due additive genetic effects.

Say a trait is controlled solely by locus X with the effect alleles X impacting the phenotype Y in an additive manner (no dominance and epistasis effect), then we can calculate the effect size of carrying the X allele, called $a$, and representing the distance from the population phenotypic mean of homozygote XX. Based on this definition, the distance from the mean for individual with the following genotype is given by:


XX: $a$
Xx : 0
xx: $-a$


This makes more sense using the genetic model:

$P=G+E=BV+I+E=A+D+I+E$ (parameters listed at the bottom)

In the example, the locus has only an additive effect then D=0 and assuming there is no epistasis then I=0 as well which gives $P=BV+E=A+E$ therefore $BV=A$

In this case $a$ can be computed directly from the BV, with p=f(X) and q=f(x), as:


$BV(XX)=2qa$
$BV(Xx)=(q-p)a$
$BV(xx)=-2pa$


Now for the complete case of both additive and dominant effects, i.e. $BV=A+D$, you can refer to table 7.3 in p.118 which describe that XX individuals are given the value $a$, Xx -> $d$ and xx -> $-a$ with the corresponding relationship to the BV given by (care here it's not $a$ but alpha $\alpha$):


$BV(XX)=2q\alpha$
$BV(Xx)=(q-p)\alpha$
$BV(xx)=-2p\alpha$


with $\alpha=a+d(q-p)$




P=phenotype
BV=A+D=Breeding value
G=Genotypic effect
E=Environmental effect
A=Additive genetic effect quantified by $a$
D=Dominant genetic effect quantified by $d$
I=Epistasis effect