AT THE BEGINNING of the year, Doug Corwin’s duck farm was thriving. By January 13, one of his barns held 12,000 two-week-old ducklings. It was cold, but they looked healthy. Another flock of 800 birds, six to seven weeks old, was doing well too. “They were absolutely beautiful,” Corwin says, sitting at his desk in Aquebogue, just east of Riverhead. On the walls are a framed photo of duck farmers posing outside John Duck’s Restaurant and a few aerial shots of Crescent Duck Farm, which Corwin’s great-grandfather Henry founded in 1908 on land the family had lived on since the 1640s. On Tuesday, January 14, though, those flocks were hurting: Hundreds of the 12,000 ducklings were dead. Concerned, Corwin called Dr. Gavin Hitchener, the director of Cornell’s Duck Research Laboratory.…