I have the same problem with Rats, here in Florida Rats nest and live in Sabal Palms , I have cut down many Sabals and when they hit the ground you see several Rats take off. Before I get attacked, FOR EVERY Sabal WE CUT DOWN , WE MUST REPLACED IT WITH ANOTHER ONE.
Most people blame other animals, the fact is when a Fruit has a Hole on it, ( eaten by a rat at night) the smell attract other critters.
If rats are your problem, and your Fruits are getting eaten go outside after Sunset when it starts to get dark and you should see them running.
Carlos