The Black Robin or Chatham Island robin (Petroica traversi) from the Chatham Islands off the east coast of New Zealand, cannot fly very well. With the introduction of rats and cats, the population of these birds crashed down to one fertile female, named Old Blue. She has since become the mother of her entire species, hatching out progeny which, in turn, have hatched out more. Today, there are 250 Black Robins on the Chatham Islands, and the status of the species has been raised from Critically Endangered to Endangered.
How could the Black Robin survive despite having such a narrow gene pool? Some have speculated that previous bottlenecks may driven out any bad alleles, but this is just nonsense as genes drift and destruction will eventually enter the best of gene pools. The real answer has to do with the marvelous fecundity and relatively short life span of birds which generally allows them to out breed, or breed through, the destruction caused by a very small gene pool, same as mice, rats, and cats do when they are introduced onto islands.