Recent studies seem to indicate that the real effect on brown anoles on the native green anoles is that they have driven the green anoles to higher trees and brush rather than totally displacing them. Their diet consists of various insects including spiders, grasshoppers, crickets, cockroaches, mealworms, and wax worms. They may also feed on smaller lizard species like the green anoles and their eggs. They also feed the population living near water feed on arthropods and small fishes as well.
Brown anoles (De La Sagra’s Anole, Bahaman Anole) are the most common lizard I see everywhere in Florida and are so numerous that we literally have to avoid stepping on the when leaving our place. They're small and native to Cuba and the Bahamas. This species is said to be highly invasive and have the altered behavior and triggered a negative effect on populations of the native green anole (Carolina anole) but this is based on casual observation.