The “kinds” of animals that were chosen are not the same as the modern day term “species.” The account says they were chosen “according to their kinds.” In fact, over a million species can be reduced to a few “kinds.” You have the dog “kind”, the horse “kind” and the cow “kind”, to mention just a few. With this in mind, it is estimated that there were 43 kinds of mammals, 74 kinds of birds, and 10 kinds of reptiles, which over the last 4,400 years has produced the variety of species that we now have. Moreover, the sea animals could have stayed in the sea. Finally, Noah could have taken most of the larger “kinds” in when they were small, and there would have been plenty of room.