Noah's Ark - Mice

A pair of mice produces a litter of about six, and those can be sexually active in 30 days. Assuming just half of those are female, and that there is adequate food on the Ark (Noah was required to provide food for all the animals), over ten months just one pair of mice can multiply to over a million. But when you start to think about all the different kinds of mice, rats, and other rodents in the world, there are more than 2,000 species. With each of these breeding at the normal rodent rate, there would be no physical space left for anything else before landfall on Ararat. (I wonder if the mountain was named for all the rats that swarmed off the Ark?)