Feeding wild animals increases their populations to account for the new food source, and makes them dependent on the new food source. You'd need to wean them off human food to prevent starvation. So, stop feeding them, but maybe over a couple seasons.Jebus wrote: Do you mean that starvation would/should control the population?
Calorie restriction absolutely reduces fertility. The body enters a calorie restricted state where non-vital systems are shut down. Males and females metabolize body fat and muscle, and reduce activity. For females, they stop ovulating, for both sex drive reduces drastically.
Reducing animals' food sources isn't the same as starving them to death, since the reductions is generally distributed throughout the population, particularly for foraging animals like deer whose food sources are non-centralized and thus can not be monopolized by the strongest and best fed (creating feedback, and locking out others).
Human feeding habits create serious problems with this functional mechanism in overpopulated countries due to their motility, monopolizability, and inflexibility.