Self Contained Space Habitats and "Zoo Devolution"

A big problem on the generational ship headed to Tau Ceti in KSR's "Aurora" was something called "zoo devolution". Over the centuries of star flight the life forms (animal and human) confined to the ships various biomes experienced genetic "regression to the mean" and even what appeared to be the effects of inbreeding. Apparently the ship's biome compartments were not big enough.

Is it merely a question of size and numbers?

If so, how big would an enclosed biome have to be to avoid this problem indefinitely?