Changes in $D$

You can probably figure out that $D$ will eventually become zero, and you can probably even guess that how quickly it becomes zero depends on how frequent recombination is. But I'd be astonished if you could guess exactly how rapidly $D$ decays as a function of $r$. It takes a little more algebra, but we can say precisely how rapid the decay will be.

$$\begin{eqnarray*} D' &=& x_{11}'x_{22}' - x_{12}'x_{21}' \\ &=& (x_{11} - rD... ...} + x_{12} + x_{21} + x_{22}) \\ &=& D - rD \\ &=& D(1-r) \end{eqnarray*}$$

Notice that even if loci are unlinked, meaning that $r = 1/2$, $D$ does not reach 0 immediately. That state is reached only asymptotically. The two-locus analogue of Hardy-Weinberg is that gamete frequencies will eventually be equal to the product of their constituent allele frequencies.