Buck’s Hollow, in Staten Island’s Greenbelt, might sound like a natural home to whitetail deer, but the New York City parks department is doing its best to keep them out.

The department, which is restoring the forest in the area, has surrounded six acres with eight-foot fencing intended to keep the deer away. In the past year, workers removed invasive species like Japanese honeysuckle and Chinese wisteria from the parcels. Next year, the department will enlist volunteers to plant 8,000 trees and shrubs — native species like red maple, beech, cherry, sweet gum and spicebush. The plan is to keep the fence around the four plots of land, called exclosures, until the saplings are 10 feet tall or big enough to survive the deer’s voracious appetites.

Deer are a relatively new presence in Buck’s Hollow, which is named after the Dutch word for goat, bok. While the city has a robust population of small mammals like raccoons, groundhogs and skunk, deer were scarcely seen in the five boroughs before 2000.

As recently as 2008, a state count of deer on Staten Island put their numbers at just 24; the animals were believed to have swum from New Jersey. But that number has exploded: An aerial count of the herd last winter, using infrared technology, put the number of deer in the borough at 763.