The narrator learns that that the Usher family tree is unusual in that only one child every generation survives to have more children. This suggests that the family is not very healthy, as we can see in the case of Roderick and Madeline. It also means tht Roderick and Madeline have no aunts or uncles or cousins. Their father had no brothers or sisters who survived.

The implication, too, is that first cousins (the "trifling variation" in the family line), and even brothers and sisters, had had children by each other, which would lead to there being no branches. First cousin marriage was not unusual among important families in nineteenth-century Europe. Brother and sister incest would be illegal, but that doesn't mean it didn't happen, Incest would, however, lead to a physical weakening of the family line, which is what we see in Roderick and Madeline, who are both frail. Madeline, in fact, is terminally ill.

Roderick tells his friend that Madeline's death

would leave him (him the hopeless and the frail) the last of the ancient race of the Ushers.

There is no thought, apparently, of Roderick marrying a woman from the outside world to continue the family line.

Poe's "The Fall of the House of Usher" recounts the story of its narrator's visit to the secluded estate of his boyhood friend Roderick Usher.  While describing his initial knowledge of the estate, the narrator states:

I had learned, too, the very remarkable fact, that the stem of the Usher race, all time-honoured as it was, had put forth, at no period, any enduring branch; in other words, that the entire family lay in the direct line of descent, and had always, with very trifling and very temporary variation, so lain.

In the passage above, the narrator indicates that what is unusual about the "Usher race" is that their family tree does not proliferate into a multitude of family lines, "any enduring branch." Instead, Poe's narrator emphasizes that the Usher family tree is a straight line, a "direct line of decent" with little to no "variation."

The implication is that the Ushers--not unlike the European royalty of prior centuries--are the product of generations of incest.  The narrator buttresses this reading in his comparison of Roderick and his sister throughout the text, casting Madeline as the Gothic double of the more prominent Roderick.