Shoot every one of them you see. Here's a short list of some invasives we are dealing with.
http://www.tsusinvasives.org/home/database/birds-mammals.htmlBirds
Cattle Egret - Bubulcus ibis
Common Myna - Acridotheres tristis
Common Sparrow - Passer domesticus
Eurasian Collared Dove - Streptopelia decaocto
European Starling - Sturnus vulgaris
Monk Parrots - Myiopsitta monachus
Mute Swan - Cygnus olor
Rock Pigeon - Columba livia
Mammals
Axis deer - Axis axis
Barbary Sheep - Ammotragus lervia
European Rabbit - Oryctolagus cuniculus
Feral Pig - Sus scrofa
Gambian Rat - Cricetomys gambianus
Norway rat - Rattus norvegicus
Nutria - Myocastor coypus
Sika Deer - Cervus nippon
Small Indian Mongoose - Herpestes javanicus