Back to the original question of the thread. I thought about the problem this time from the perspective of the construction of D Dorian by 3 P5s up and 3 down. Then at the Ab tritone gap you have the Ab Dorian pentatonic which is constructed by 2 P5s up and 2 down from Ab. Because of their symmetries I believe the problem is simplified. What we need is a prediction of the one by the other. To check after the fact, like for example by looking at the piano, is postdictive. So let's look at the circle of 5ths.

In green squares - D Dorian. In red squares - Ab Dorian pentatonic.

circlefifths.jpg
From this we can predict that a white key scale will have its black key pentatonic version a tritone away from its tonic. Except for F and B that already make a white key tritone.