I just now picked up BioShock. I have yet to face a Big Daddy, but have been introduced to them via an in game cut scene. Before I engage in mortal combat with one I had a question about the necessity to engage them. I think I remember reading / hearing that you could complete BioShock without killing any Big Daddies or Little Sisters. It's also entirely possible that you can't and my memory is foggy.
Can you complete the game without killing any Big Daddies? If you can are their benefits to doing so? Are there disadvantages for not killing them?
I ask because unfortunately, I generally don't have time to replay games so look to complete them with the best outcome possible. I am very early on in the game so please answer with as few spoilers as possible.