The YEC explanation:
This is my translation of what I have read here and elsewhere. I have yet to see any creationist explanation that has any real clarity at all. They are mostly handwaving.
OK, here goes:
Before the flood there were many fewer species of living things. The exact number is not determined but it was just enough to allow for room in the ark.
Each one had a much more complex genome. They contained the genetic instructions for making all the things that would be in the same genus, family or order (not clear which one of these, varies form day to day).
After the ark landed (this would be about 4500 years ago) the creatures on it dispursed. As they rebuilt their populations the extra genetic material they had "degraded" or rather separated out. Thus allowing individual new species to appear very quickly.
Based on any evidence that is available, pictures, bones etc., all teh new species were around before 2,000 years ago.
At this point the genome had "separated" as much as it could and the rapid evolution suddenly stopped.
The evidence for this scenario is something I have never seen a trace of. I have never seen any hint of an explanation of how the genome could behave this way and this quickly.
I have never seen any attempt to take this an explain the geographic distribution of animals and plants.
No attempt have I read to explain the nature of old DNA samples as they are starting to arise. Nothing to explain the fossil record other then the sorting idea which I think is in disagreement with the scenario above.
That's the best I can do. If someone has a creationist reference that has even that much detail I would like to see it.