If the population was too high to support them, then a natural reduction is better than a planned hunt. It seems the mechanism to adjust population to the terriortory by natural means is in effect.

Many animals die from distemper. If you want a wild population that means you do not vaccinate.

Vaccination in human population areas by leaving out food with rabies vaccination is done to reduce rabies in rabbits, foxes and skunks to name a few and to reduce the possibilty of contamination into pets such as cats and dogs.

In a park are it is not ecofriendly to vaccinate wild animals.