If the deer had the humans as a natural predator instead of the wolves, than the deer population would be strictly regulated, thus having the approximately same number of individuals.
The reason for this will be that the deer will have a predator which will not kill it regularly, but only in certain times of the year, because only than will be allowed. Also, the deer that will be killed will be the grown individuals, not the young ones, thus the population will constantly remain balanced.
