There are deer on Staten Island, not really the suburbs. Unfortunately the only real predators left to take down deer are hunters and cars. People (often hunters) even freak out if a dog chases one.

They freak out for a good reason. A pack of dogs will pull down a deer, eats it hind quarters and leave it to die. I had a relative who worked for the Department of Lands and Forest. When he was the FNG he would get called out every few weeks to kill them. After the third one he started carrying a rifle whenever in the woods and shot every unaccompanied dog he saw.

In addition to taking out their predators, we have also fragmented ecosystems.

Certain species like deer thrive in the boundaries between two different ecosystem types because they get different resources from both ecosystems.

Humans do not only reduce forest size, but also change the geometry of forests: fragmentation makes the edges more pronounced (increases the perimeter:area ratio)

This harms some animals like large solitary predators who require vast ranges, but helps other species like deer who prefer the edges.