All animals have their own niche. Animals eat different things so they don't have to compete. Birds, squirrels and bugs can all live together because they eat separate things. The bugs eat the tree and other little things on it, the squirrels eat nuts but lives in the tree, and the bird eats seeds, nuts and the bugs so that the bugs population is controlled. They all work together and so they can all live together without running out of food.
Actually most animals do have to compete and sometimes they do run out of food. This is called competition. Competition occurs naturally between living organisms which co-exist in the same environment. Animals also compete over water supplies, mates, and other biological resources.
Sometimes an animal population may increase so much food becomes scarce then some of the animals die.
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Mainly because they aren't like humans don't overeat constantly. Also, because they ARE food.