If your ducks are loose at night, you're offering a free dinner to every fox, raccoon, possum, stray dog, feral cat, alligator, weasel, as well as owls. Foxes and raccoons are notorious for hunting just before sunset and they often leave no trace. To decide it is an owl, when you have no proof, and shoot a protected bird, not only is unfair to the animal, but ridiculous. Raptors are territorial. If you kill one, another will move in and claim the territory, unless you kill them all. I'm really surprised an "environmental studies major" wouldn't understand that.
If you want to keep your animals safe, for goodness sake you must realize that you need to lock them up, at least at night. That's elementary. My animals free range during the day, (in a secure fenced in acre) but all are locked up at night, and I have no losses. How sensible is it to leave your animals loose at night for every predator, then come on the board and whine about your losses ? Part of keeping animals is responsible stewardship. Provide a secure coop for your animals where they are safe from all predators, rather than blasting away at the owl just because you see it, and you can't see the real problem. The real culprits are, no doubt, too smart to show themselves when they hear, see, smell you. And after you've killed the owl, they'll be back and back, and back for the free dinner you've provided. If you're going to keep domestic animals, then be a responsible pet owner, and provide them a secure shelter. Pet or livestock ownership isn't a license to go adolescently blasting away at everything in the neighborhood because you can't bother to do the only sensible adult thing that *will* keep your ducks safe at night - build them a predator proof shelter and then take the time to lock them in it at night and let them out in the morning.