Mark and Recapture: Counting Animals You Cannot See at Once

A quadrat works because plants stay put. Animals move, hide and flee, so you can never see all of them at once — and counting the ones you do see tells you more about your own searching than about the population. Pierre-Simon Laplace used the idea to estimate the population of France in 1802, and C. G. Johannes Petersen applied it to fish in 1896. Catch a sample, mark them, release them, wait, catch a second sample. If a tenth of the second catch carries marks, then your marked animals are about a tenth of the population — so the population is about ten times the number you marked. The arithmetic is trivial. The assumptions are not, and every one of them can be violated in a way that makes the answer confidently wrong. Most of this blueprint is about those assumptions, because that is where the real work is.