At the Museum of Natural History, there is a room filled with butterflies. Patrons can come into the room and watch the butterflies from close up. The butterfly caretaker, Aubrey, decides to approximate the population of the butterflies. She uses a net to capture 22 butterflies, marks them, releases them, and then later catches 800 butterflies. Of those 800 butterflies, 16 are marked. To the nearest whole number, what is the best estimate for the butterfly population?