There main source of food either dies out as well of decreased in size.
Wolves were common in the entire American West at the time Yellowstone National Park was founded. Government agencies actually paid hunters to kill wolves (and other "bad" animals) until wolves became almost extinct in the Lower 48.
The re-introduction of wild wolves into the Yellowstone Eco-system has been a total success in that humans PARTIALLY undid the destruction they unleashed on creation. The boost to winter tourism in the region, in order to see wolves in the wild, has been a HUGE economic benefit to the region -- FAR exceeding any losses due to predation by wolves.
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Originally the wolves in the Yellowstone region were killed to near extinction on government order. The last ones were skilled off in the early 1900s. It hasn't been until recently (1995) that re-introduction acts were placed despite ranchers/farmers objections. The new wolves were brought in from Canada. Hope that answers your question.