First up: how did all the animals fit on the ark? AiG makes the following points: there were 16,000 animals total, these animals were young (but not newborns), most animals are small, the largest of them would only be a few hundred pounds, and many of them could have been housed in groups.
Let’s grant the 16k number for the sake of argument (at least for the moment), and do some math. The ark was 300 x 50 x 30 cubits (Gen 6:15). Cubits were likely either 18 inches, or 20.7 inches. Let’s even use the longer cubit. So, the available space on the ark is: 6210 x 1035 x 621 inches = 517.5 x 86.25 x 51.75 feet = 2309828.90625 cubic feet. Let’s round up to 2.31 million cubic feet. That certainly seems like a lot, doesn’t it? It is a pretty good sized amount of space.
I’m not going to attempt to guess at the average size of an animal on the ark; because there’s a much bigger problem with this than whether the animals themselves could fit. The problem is fresh water. I’m going to make the assumption that Noah didn’t have a desalinization plant on the ark. I’m also going to make the assumption that during the “40 days and 40 nights”, he could have used rainwater for both his family and the animals. The problem comes afterwards – this went on for a year after the rain stopped. There’s 7.48 gallons of water in a cubic foot. Noah would have needed at the very least 5000 gallons of water a day for drinking and cleaning, and this is being extremely conservative. 5000 x 365 = 1825000 gallons / 7.68 = 237,630 cubits of space taken up just by the water. So now we’re down to roughly 2 million cubic feet of space.
He would have needed food too. Let’s say a cubic foot of food a day for each animal on average, which is again extremely conservative. So that’s 16,000 x 365 = 584,0000 cubic feet of food. Now we’re down to 1.42 million cubic feet for the animals.
We also need to knock off a certain amount of space taken up by supply storage, the construction of the inner decks, waste disposal systems, etc. It’s hard to quantify how much space this would take up, so let’s make a conservative guess and knock it down to 1.2 million cubic feet for the animals.
And finally, of course animals aren’t perfect cubes. They need at least a little bit of space to move around. In terms of area, let’s say each animal needs an enclosure twice its body size to move around. So that’s going to cut the space in half, to 0.6 million cubic feet. That’s only a quarter of the ark’s total space, or roughly 130 x 86 x 51 feet. This only leaves 37 cubic feet for each animal on average. That’s about a 3.3 foot cube space for each animal.
Of course, these numbers are all extremely conservative. ICR says, “Noah was told to take two of each “kind” of animal on board, probably represented by today’s “families” or “genera” rather than species.” Here’s a list of various amounts of families, genera, and species:
Stinkbugs – 896 genera 
Frogs and Toads – 31 families, 300 genera, 5000 species 
Turtles – 14 families, 97 genera, 300 species 
Lizards and Snakes – 50 families 
Birds – 235 families 
Spiders – 111 families, 3747 genera, 40288 species 
Mammals – 155 families, 1243 genera, 5773 species 
Flies – 209 families 
This is far from a complete list, but it serves to illustrate a point: “kinds” cannot be species, obviously; there’s no way Noah had 80,000 spiders crawling around, along with 10,000 frogs and over 10,000 mammals. If kinds are genera, there’s still well over 16,000 animals that need to be on the ark (remember, I haven’t even included every genera in this list). So, kinds have to be families, or a higher taxon. But this can’t work, as it would require a bizarre, super accelerated hyper-evolution to give us the huge number of species (in the millions) that we see today. Every birth after the flood would have to be a speciation event for years and years. To get 5000 species of frogs from just 31 pairs in such a short time is ridiculous.
The problem of space just gets worse and worse, though.In addition to all these animals, Noah would also had to have plants on the ark. Many plant species cannot survive a year of submersion, especially not at the depths of the flood. He would need fish too, as well as tanks to keep them in, and equipment to keep the temperature, lighting, oxygen, and salt levels within tolerable levels. Most fish require very specific water compositions to survive, conditions which the flood would have extraordinarily upset.
ICR says “It’s well known that all animals can survive on a meatless diet.” Ok, maybe – with modern food processing techniques which let us produce nutritional animal feed. But Noah didn’t have any meow mix to feed his tigers. But anyway, let’s move on to the post-flood world.
So, the waters finally subside and Noah steps off the ark with his family and all these animals. He looks around, and sees the ultimate dystopia. Everything is dead – not just animals, but plants too. The world is now a barren wasteland. There’s nothing to eat, and the land is ruined. Nothing will grow for decades anywhere. What’s worse, due to all the water, the entire world now has a tropical climate that will remain for hundreds of years. Life which requires any other climate is doomed.
He decides to eat the polar bears first.
The wolves pick at some decaying corpses they found. Flowering plants seem doomed, because the bees all died on the ark. He had a male drone and a queen, but didn’t take any female worker bees. Noah sees the lions take down a gazelle, and a frog snatch a fly out of the air. This could be a problem.
A few months later, the rabbits are looking kind of funky. Many of them are being born with twisted jaws, some of them are bleeding for no reason, and some of them just die at birth. Maybe reproducing with siblings isn’t such a good idea.
The plants go extinct first. The cows, which somehow managed to avoid the lions, ate all the grass. The giraffes ate all the leaves off the trees. The herbivores soon follow. If they’re not eaten by the carnivores, they die of starvation. Finally the carnivores die out. They lasted a good long while, but most of them can’t eat decaying meat. Noah’s family dies too. The host of viruses, bacteria, and parasites that can’t live outside the human body get the better of them after a year on the ark followed by a few months of starvation. Due to a lack of fruits and vegetables, one of his sons actually dies of scurvy before the malaria he contracted from close proximity to the mosquitos on the ark does him in.
The bears finally die – hibernation can’t be permanent. The buzzards and hyenas are doing well, though, at least for now. In a few years there won’t even be any carrion left for them to eat. And even if there was, they’re being born with two heads, or no feathers, after a few years.
Almost everything is now dead. There’s only a few dozen species left, including a small tribe of Noah’s grandchildren; about 8 of them. There were more, but these people have gone feral and fight to the death for food or mating privileges when there’s not enough to go around; and there almost never is. After seeing the rabbits years ago, they at first were very careful about breeding, but the conditions of the post-flood world have created a lord of the flies situation.
One of them was born with a harelip today.