I'm not quite sure how far back the reach of History SE travels, but I thought I'd push my luck!
As the question asks really. Do we have any evidence that suggests homo sapiens or any of our close relatives were outcompeted in any local environment by any other animal (non-hominid species)?
From my initial thoughts, I'd guess that if this were to happen it would be unlikely to happen after the advent of agriculture so we'd be looking at the paleolithic. Unfortunately, my research thus far has turned up a dizzying array of examples of humans extirpating other animals and none the other way around (which I suppose is a finding of itself).
Appreciating the difficulty in finding evidence, does anyone know of any that exists?