The critters would be deigned to express themselves within limits, as they do to this day. The biblical text indicates they were created after their kinds, which could reasonably be understood to mean that, where evolutionists find groups of animals having similar features, these all indeed have a common ancestor, the genetic makeup of which was rich enough to give wide expression over a relatively short period of time.
Take the current form of the human species. If we were to fossilize the skulls of everyone living today the variety would be astonishing, and could easily be interpreted as different "species" that developed over long periods of time. Yet they are all human. Having come from the first humans, it stands to reason that the first humans were designed with a compression of genetic data that would express itself in wide ranging patterns.
That is not to say environmental factors would not also have an effect. I am of the opinion that the weather patterns prior to the worldwide deluge were far less extreme. I would also seriously entertain the notion that pangaea preceded the deluge as well. Lastly, I think the greater part of the geological record we observe today is the result of catastrophic events that attended the flood.
Although I often come across as one who acerbically criticizes the theory of evolution, my criticism has more to do with the bigger picture certain people seem to draw from it, and the notion that it should for some reason be illegal or out of bounds to discuss intelligent design in a scientific context.