The most important factor(s) which limit the number of animals that can live in a biome is/are:

Most organisms are adapted to live within a particular range of temperatures and will not survive at temperatures too far above or below their range. Precipitation limits the organisms that can be found in a biome because all organisms need water, and the bigger the animal, the more water it needs.

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The return of the wolf to yellowstone national park will probably affect the bird population to some degree, not significantly. while wolves will hunt birds when necessary, they prefer to hunt larger prey. the bird population will most likely only be affected when hunting is scarce for the wolves. birds of prey will also probably not be affected as much as other birds who spend more time on the ground hunting for food as the tend to spend more time in the air or in trees since they do not need to stay on the ground for long due to the nature of the way they hunt.