A small town wanted to know how many stray cats lived in it. Counting them directly was impossible: cats move, hide, and look like other cats.
The method they used is one biologists have relied on for a century. A group of cats was caught, marked harmlessly, and released. Some weeks later a second group was caught, and the proportion of marked animals in that second group was counted.
The reasoning is a single step. If the marked cats have mixed evenly back into the population, then the fraction of marked cats in the second catch should match the fraction of marked cats in the town as a whole. Twenty marked out of a hundred caught suggests that the originally marked group was about a fifth of everything.
The method has assumptions, and they are where it goes wrong. The marked animals must mix back in, which fails if being caught makes a cat avoid traps. No cats may arrive or leave between the two catches. Marked and unmarked must be equally catchable, which fails if the hungriest cats are caught first and are then better fed.
The town's estimate turned out roughly right, checked later against a much more expensive survey. What is worth taking from it is not the number but the shape of the idea: when you cannot count everything, you can sometimes count a sample twice and let the overlap tell you the rest.
Vocabulary in this text
- century /ˈsɛntʃɚi/ — a period of one hundred years
- proportion /pɹəˈpɔɹʃən/ — a part of a whole, often as a share
- reason /ɹˈizən/ — why something happens
- fraction /fɹˈækʃən/ — a part of a whole, such as one third
- whole /ˈhoʊl/ — complete, all of something
- suggest /səˈdʒɛst/ — to offer an idea for someone to consider
- assumption /əˈsʌmpʃən/ — something accepted as true without proof
- avoid /əˈvɔɪd/ — to stay away from something
- estimate /ˈɛstəmət/ — to say approximately how much or how many
- turn out /ˈtɝn ˈaʊt/ — to happen in a particular way, often unexpectedly