that varies greatly by area. generally, predation does play a part, but it is probably less than you think. I'd say that more damage is done to nests full of helpless young by coons, snakes, and other squirrels than by large birds of prey or hunters killing grown squirrels. even more likely is that low numbers of rats means the food is someplace else, and that is where they go. squirrels migrate, and I have seen them vanish from a farm I hunt in southern Ohio. tons of squirrels there for 30 years, 5 poor nut crops in a row there and squirrels are few in number compared to what they used to be. corn feeders and better timber a half mile away. add in some hunting with dogs and itchy trigger fingers and squirrel populations go down. one thing I've always wondered about is the dispersal of the young. squirrels have two breeding cycles a year. perhaps the young leave the area as a natural mechanism to prevent inbreeding rather than bolstering the population where they are born.