The city oversaw 720 vasectomies last year, when the project launched, and they estimate that about 92 percent of the sexually active male deer on the island were sterilized. Last month, a six-person team began searching for the remaining adult bucks, as well as younger males, which they estimated to be about 250 in August.

For years, environmental officials and local leaders, including the Staten Island borough president, have said that the increased deer population was a nuisance and health hazard. Deer can put drivers in dangerous situations during the fall mating season, when the frisky animals cross roads in search of a mate. Last year, the Health Department confirmed 93 new cases of Lyme disease in Staten Island, a record high, and residents have complained about chewed-up flower beds and gardens. The parks department has fenced off parks and planted deer-resistant vegetation to keep the city’s greenery out of the mouths of hungry deer.

The parks department first began receiving regular reports of deer in the borough in 2000. With no natural predators, and hunting outlawed in the city, the population grew rapidly. The department estimates there are now about 2,000 deer on Staten Island — in 2008, a study by the state counted 24.

In 2015, Mayor Bill de Blasio assembled an interagency task force to deal with the deer. Last year, the parks department hired White Buffalo, a nonprofit organization led by Anthony DeNicola that works to conserve native species and ecosystems, to perform the vasectomies as part of a research project. The nonlethal experiment to reduce the deer population will cost the city $3.3 million over three years.

Because bucks can travel great distances to breed, sterilizing them requires covering a lot of ground. So cities with deer sterilization programs have mostly focused on sterilizing the female deer, which are more stationary. But on Staten Island, Dr. DeNicola saw an opportunity to do something different.

Namely, because it is an island, finding all of the males is possible, Dr. DeNicola, said.

The borough’s suburban geography also helps. Dr. DeNicola and his team cannot chase deer through backyards or dart them in populated areas. Instead, he waits for them to arrive at bait sites in wooded areas throughout the island.