Grades 9–12 · Mathematics
How can seeing some marked animals again help estimate a whole population?
Counting every animal in a habitat can be difficult. In a simple capture–recapture study, researchers first observe and safely mark a sample, then release those animals and later collect another sample.
In the diagramObserved overlap supports a population estimate40 marked initiallylater sample: 5010 of 50 markedmarked fraction10 / 50 = 1 / 540 ÷ (1 / 5) = 200 estimated animalsIdeal closed population; uncertainty remains.
The overlap between samples provides information. If marked animals are well mixed and equally likely to be encountered, their fraction in the second sample should roughly match their fraction in the population as a whole.
Suppose an invented closed population has 40 marked animals. If 10 of 50 animals in a later sample are marked, the observed marked fraction is one fifth. The simple proportional estimate is therefore about 200 animals, because 40 is one fifth of 200.
That estimate depends on assumptions and sampling variation. Animals may move, lose marks or change their behavior after capture, and some individuals may be much easier to find. Researchers choose methods and uncertainty estimates that address those effects rather than treating one overlap ratio as an exact census.
About this explanation
Starting knowledge: Understand proportions, random sampling and that many animals may remain unseen in a survey.
Sources
- U.S. Geological Survey — Capture-Mark-Recapture Science