There already is a form of birth control called PZP. It is given in vaccine form which causes the female's immune system to produce antibodies that attach to the egg and prevent fertilization. It isn't 100% but it comes close. It is reversible and can be used on many species. It would have to be injected (which means capture) or darted with a specialized gun and dart. It has to be boostered the first year so you would have to use some kind of lasting dye that is highly visible and then it would be given once a year after that. Certainly cheaper I would suspect in the long run than what we have now. It is being used to control deer populations in a few areas.