The Caribbean Islands, especially the smaller ones, had few animals when Europeans arrived, as few could cross the water.
Trinidad had the best range, including sloth , anteater, tiger cat, raccoon, small deer. Other isles their only mammals apart from bats, rodents included the large, tasty hutia, similar to a of rabbit, and 1 frog species. Various reptiles thrived included caiman and crocodiles. Only Cuba had a range of reptiles, ie, snakes, lizards, giant iguana.
Natives added very few domesticated animals over the years. Caribs kept muscovy ducks, Arawaks may have raised guinea pigs & small dogs which were non barking, so very old species.
Spanish colonists initially introduced plants & especially animals, from home. Some European animals immediately took to the region, free of natural predators. The tough Spanish pig multiplied at an incredible rate. Cats chickens, goats, Spanish cattle also. Horses were more fragile, and slower to breed but also widespread by 1530s.
Only sheep failed to establish. Why?