Anybody know anything about Darwin's finches?

When Darwin discovered the finches it supported evolution through "natural selection" or "survival of the fittest." Say you are one of these little birds that got blown by a storm clear over to these remote islands. There are only a few food sources that you are used to eating. One of your offspring (babies) has a weird mutation, a beak that is a little shorter but very strong, strong enough to eat the nuts that you and your other offspring can't crack. Suddenly this offspring has a big food source you can't use and it grows up and has more offspring that carry the gene for this mutation of a strong beak. Later another offspring of one of the finches has an offspring with a long skinny beak that can reach insects hiding in trees, now this offspring has an untapped food source and so do all of it's offspring. These finches start to stay close to the islands or areas that offer the food source they can take advantage of and begin to change over generations from the other types of finches until they become a new species. Changes in climate may have changed the food sources which would have favored finches with beaks to take advantage of whatever happened.