An algebraic formulation of the problem

The above calculations tell us what's happening for this particular data set, but those of you who know me know that there has to be a little math coming to describe the situation more generally. Here it is:

Genotype	Number	Sex
$A_1A_1$	$F_{11}$	female
$A_1A_2$	$F_{12}$	female
$A_2A_2$	$F_{22}$	female
$A_1A_1$	$M_{11}$	male
$A_1A_2$	$M_{12}$	male
$A_2A_2$	$M_{22}$	male

then

$$\begin{array}{cc} p_f = \frac{2F_{11}+F_{12}}{2F_{11}+2F_{12}... ...ac{2M_{22}+M_{12}}{2M_{11}+2M_{12}+2M_{22}} \quad , \end{array}$$

where $p_f$ is the frequency of $A_1$ in mothers and $p_m$ is the frequency of $A_1$ in fathers.³

Since every individual in the population must have one father and one mother, the frequency of $A_1$ among offspring is the same in both sexes, namely

$$p = \frac{1}{2}(p_f + p_m) \quad ,$$

assuming that all matings have the same average fecundity and that the locus we're studying is autosomal.⁴

Question: Why do those assumptions matter?

Answer: If $p_f = p_m$, then the allele frequency among offspring is equal to the allele frequency in their parents, i.e., the allele frequency doesn't change from one generation to the next. This might be considered the First Law of Population Genetics: If no forces act to change allele frequencies between zygote formation and breeding, allele frequencies will not change.