The United States Fish and Wildlife Service may allow the hunting of antlered and antlerless deer by those holding proper hunting licenses of this State on any sea island within any federally owned or controlled game reserve, national park, or game refuge during the open season for deer hunting under the laws of this State, whenever the officials of the United States Fish and Wildlife Service determine that the deer population of the island exceeds that which can properly maintain itself on any island. The United States Fish and Wildlife Service shall notify the department, in writing, at least ten days prior to allowing such hunting, of the opening and shall also advertise it at least once in a newspaper of general circulation in the coastal area of the State at least one week before any hunting is permitted.