Contrary to popular belief, Noah's Ark was not a little boat. Noah's Ark was an enormous boat with plenty of room for all the animals. Genesis, the first book of the Bible, gives the dimensions of the ark.
"So make yourself an ark of cypress wood; make rooms in it and coat it with pitch inside and out. This is how you are to build it: The ark is to be 450 feet long, 75 feet wide and 45 feet high. Make a roof for it and finish the ark to within 18 inches of the top. Put a door in the side of the ark and make lower, middle and upper decks." Genesis 6:14-16(The dimensions in these verses differ slightly with the picture below. In the original Hebrew the measurements are given in cubits, and there is not one set measurement for how long a cubit is. A cubit was the length of a man's arm from the elbow to the middle finger.)
Noah's Ark was an enormous boat with plenty of room for all the animals.
There were no carnivores on the ark. All living things were vegetarian until after the flood. After the initial creation God said this:
And to all the beasts of the earth and all the birds of the air and all the creatures that move on the ground-- everything that has the breath of life in it-- I give every green plant for food." And it was so. Genesis 1:30
Some time after the flood God said this:
Everything that lives and moves will be food for you. Just as I gave you the green plants, I now give you everything. Genesis 9:3
You might ask: "aren't there too many kinds of animals for them to all fit on the ark?" No, there are not too really that many kinds of animals. God created the basic types of plants and animals, and then genetic variation went on from there since the flood. For example, God made the basic types of birds including: hummingbird, woodpecker, parrot, pigeon, sparrow, duck, and so forth. Each type had a lot of capacity for genetic variability as we see in dogs so we have different types of hummingbirds, woodpeckers, parrots, and so on like we have different types of dogs. This genetic variability works within fixed limits. These animals will never turn into anything else; they will just develop into different varieties of the same thing.
There are a lot of different looking dogs, but they are all the same species. Also, wolves and coyotes can both mate with dogs and produce fertile offspring. They are all the "dog" kind of animal along with foxes and others of the dog "kind".
I have a friend who has exotic animals. One of his zebras had a fertile offspring with one of his donkeys meaning they are both the horse "kind" of animal.
Lions and tigers look different because they have isolated gene populations on different continents, but lions and tigers have mated in captivity and produced fertile offspring. They are both in the cat "kind" of animal.
Buffalo and cattle are often mated together to produce beef with less fat. These are both of the cow "kind" along with oxen.
Every animal, when it has offspring, has an offspring like it. We don't see dogs having any type of animal except another of the dog kind.
There is no evidence that if it goes on long enough that new species can be produced. In fact, each separate type of animal cannot mate with others outside of its type of animal. Bears, cats and dogs are all in the same order, carnivore, when according to evolution means that they are related.
However, bears and dogs can not mate and produce fertile offspring. Neither can dogs and cats. One has to assume that long ago and far away it was possible for an animal to have babies that was a different type than it is, but that has never been known to happen. It is assumed to have happen because of the belief in evolution.
All Noah had to have on the ark was representatives of each of the different "kinds" as stated above. There was plenty of room for representatives of all of the animals. All the dog-type animals have developed from the two on the ark. As the animals multiplied and traveled to different parts of the world they grouped into isolated gene pools so that now we have different looking dogs all over the world. Some might call this "evolution" but, no matter how much they change they are always a dog. They never were and they never will be any other type of animal.
See my page How Many Species for more information on types of animals.