No changes in allele frequency

We can also calculate the frequencies of $A_1$ and $B_1$ after this whole process:

$$\begin{eqnarray*} p_1' &=& x_{11}' + x_{12}' \\ &=& x_{11} - rD + x_{12} + r... ... &=& x_{11} + x_{12} \\ &=& p_1 \\ p_2' &=& p_2 \quad . \end{eqnarray*}$$

Since each locus is subject to all of the conditions necessary for Hardy-Weinberg to apply at a single locus, allele frequencies don't change at either locus. Furthermore, genotype frequencies at each locus will be in Hardy-Weinberg proportions. But the two-locus gamete frequencies change from one generation to the next.