This is obviously much less than the 125,000 that could easily have been carried. There was also ample room for food storage and for living quarters for Noah and his family. In fact, the ark was so commodious that the whole story makes sense only if the Flood were a universal flood. The ark was far too large for only local animals. The problem of preserving human and animal life could have been solved far more easily by merely moving out of the endangered flood plains.
Animals can migrate long distances, especially when impelled to do so by imminent weather changes.
Once they were safely on board, lodged in their stalls, and properly fed, most of them very likely settled down for a long period of dormancy, or hibernation. Modern biologists, despite much study, have still been unable to provide a satisfactory explanation for the origin and operation of these fantastic capabilities. Before the Flood, it is likely that there was a worldwide warm, pleasant climate. Thus, before the Flood, animals had no need for migration and hibernation, and probably all kinds of animals were dispersed more or less uniformly all over the world. When the thermal vapor blanket condensed and precipitated at the time of the Flood, there was a rapid change of climate, which led finally to the ice age and then eventually to the present climatologic regimes of the world.