Some great points have already been made, with hibernation, food storage on the ark, and God being in charge.
And in the end only the point about God being in charge makes sense. God could have, I suppose, caused a global flood 4,000 years ago and then completely and utterly wiped the earth of all evidence. That is certainly within His power. But the creation ministries are claiming no such thing, and it is their scientific claims that we are discussing, not claims about God and what He could have done.
Did you forget that the bird brought back an olive branch before the ark ever landed. Vegetation was growing and no need for irrigation.
"No need for irrigation"! The problem here would not have been too little irrigation, it would have been too much! And this is relevant to me because over-irrigation is precisely what is damaging a lot of Australian agriculture. Water dissolves salt, and "overcharging" the water table brings these salts to the surface where they essentially thirst plants on the surface soil to death. Now, the whole earth being underwater for an entire year would have pretty much salinized the soil as much as it possibly could be. How that olive plant grew at all would be a very good question!
Another thing, I bet God put pregnant animals on the ark to speed the recovery, and some, like the Dinosours and dragons did not survive long after the flood.
Yet we have plenty of amphibians, reptiles and birds alive today.
The other thing is, for the sake of space and handling God most likely put very young animals on the ark (if the meat eater came on as young and the prey as older and giving birth?), those who could be fed the milk of other animals like the cow or goat for instants. The prey could have a couple litters before the lion began eating them (and some like the bears are not strictly meat eaters and there would be fish to supliment)
Firstly, this entirely ignores non-mammalian carnivores. What would the snakes have eaten? (According to creationists, evolution can only cause features to be lost and not gained. Therefore nonvenomous, noncarnivorous snakes must have evolved from the degradation of venom and predatory systems in carnivorous snakes, so that the snakes on the Ark must have been venomous and carnivorous.) Or Komodo dragons, or Gila monsters?
Secondly, even if the prey bore "a couple of litters" before the carnivores began eating them, this would not have been enough. Of the energy transferred between trophic levels, only 10% builds new biomass; it takes 10kg of herbivore to support 1kg of carnivore. Would the 300g ancestor of the cat kind have had 3kg of rabbit waiting for it as it descended?
An entirely new argument is the problem of introduced species. Introduced species are species which in their natural environment are controlled by predators that have evolved to destroy them, but which thrive beyond control when they are transferred to different environments where those predators don't exist. Now, evolution can explain why introduced species exist: natural selection in the new areas hasn't had the input required to evolve predators to the introduced species, while it has had time to evolve them in the old areas.
But how can creationism explain it? After all, according to them, all animals dispersed from Mt. Ararat. As they did, predator would have followed prey; moreover, evolution according to them would not have had the time or the ability to design novel predatory mechanisms. So either: a) introduced species cause problems because no predators have evolved to prey upon them - but predators
have evolved to prey upon them in their native regions!, or b) introduced species cause problem because they were introduced to areas where their natural predators don't exist. But why should they have needed human intervention to get to those areas? Take rabbits in Australia for example: the kangaroo and the dingo got from Ararat to Australia well enough, so given the rabbit's current success in Australia, why did it need human transport instead of hitching a ride with hapless Europeans?
When all other factors run out there is the will of God which created and sustains all things.
If only the creationists infected by scientism would realize that all the other factors ran out long ago!