From Science:
Even predators have enemies, and having a set of claws and sharp teeth isn’t a guarantee against attack. But just which killers do predators have to watch out for? A rare look into carnivore-on-carnivore violence indicates that size matters: Predators tend to strike only those species somewhat smaller than themselves, while avoiding true pipsqueaks and similarly sized or bigger animals.
The survey of 59 different predatory mammal species–including tigers, leopards, foxes, and wolves–revealed thousands of instances of one species slaughtering another. The researchers then combined these data with several biological factors for each species, including body mass, diet, and geographic range.
Not surprisingly, the team found that if one predator was bigger than the other, the fight was on.
More here.