Possibly Between the Dark and the Daylight by Algis Budrys. It's sort of similar to the plot you describe and it does have a character called Falconer.
Google can't find anything about the story and the Wikipedia article on Algis Budrys doesn't mention it so I may have the name wrong or it might have been published under different names. If it helps, at the time the story is set the humans have been deliberately mutated to animal like forms, and the story is about the final mutated generation who are still children at the time of the story. The base commander, Brendan, is arguing with Falconer about whether it's time to release the children to the world outside the dome. Spoiler follows:
Falconer raises a rebellion against Brendan. In the chaos Brendan releases the children, but they have been mutated so far they are little more than vicious beasts. At the end of the story the children has slaughtered all the aliens and are attempting to break back into the dome to slaughter the humans inside.