Why did Humperdoo inbreeding occur?

I understand the need to keep the identity of the lineage secret so how were the mates of each generation decided? Did they have each generation create a male and female child, have them mate with each other, and then kill off any extraneous offspring? Was there another inbred family whose role was to provide mates for each generation of the Jesus lineage? Otherwise, I don't see how new genetic material wouldn't flow in every generation and prevent the mental retardation we see in Humperdoo.