A biologist catches 20 fish, tags them, and releases them back into a lake. A week later, they catch 30 fish and find 5 are tagged. Somehow, this tells us there are roughly 120 fish in the entire lake — no need to drain it. Here the lake really is hidden: set the size of the second catch, or catch again, and the estimate is worked out only from the tagged fish that actually turn up in your net.
Capture-recapture relies on a simple proportion: if tagged fish make up a certain fraction of our second sample, they should make up that same fraction of the whole population. We use the formula: Population = (First catch × Second catch) ÷ Tagged in second catch. In our example, (20 × 30) ÷ 5 = 120 fish. The key assumption is that tagged fish mix evenly back into the population, so our second sample is a fair random grab. This method is used by ecologists worldwide to estimate populations of fish, birds, insects, and even endangered species without disturbing the whole habitat.