Capture Recapture Sampling

TL;DR

Method: capture a sample, mark and release those individuals, then recapture another sample and count marked individuals.
Practical when counting every individual is infeasible; typically quicker, less invasive, and less expensive than full counts.
Accuracy can be reduced by factors such as movement into/out of the population, the marking process, and small sample sizes.

Definition

Capture-recapture sampling is a statistical method used to estimate the size of a population. It commonly involves capturing a sample of individuals, marking them, releasing them back into the population, and later capturing a second sample to count how many marked individuals are present.

Explanation

The procedure begins by capturing a sample from the population and marking those individuals (for example, with a tag or dye), then releasing them. After some time, a second sample is captured and the number of previously marked individuals in that second sample is recorded. The proportion of marked individuals in the second sample is used to infer the total population size: if marked individuals make up a known fraction of the second sample, that fraction is assumed to reflect the fraction of the total population that was marked in the initial sample. The method is widely used in ecology and other fields when direct counting of every individual is impractical.

Examples

Fish in a lake

A biologist captures a sample of fish from a lake, marks them with a small tag or dye, and releases them. After some time the biologist captures another sample and finds 50 marked fish out of 100 total fish in the second sample. From this information the biologist estimates there are 200 fish in the lake (because 50 marked fish were caught in a sample of 100 fish, so there must be twice as many fish in the lake overall).

Homeless population in a city

A researcher conducts a survey of homeless individuals, marks them with a unique identifier (such as a wristband or a card), and then releases them back into the city. After a period of time the researcher conducts another survey and counts how many of the homeless individuals are wearing the marked wristbands or carrying the marked cards. This count is used to estimate the total size of the homeless population in the city.

Use cases

Estimating animal populations in ecology, especially when direct counts are impractical.
Estimating dispersed or hard-to-count human populations (example: homeless populations).
Applied when individuals are migratory or populations are spread over large areas.
Informing conservation and management decisions.

Notes or pitfalls

Not always accurate; estimates can be biased by movement of individuals into or out of the population, effects of the marking process, and the sizes of the samples used.
Advantages include being relatively quick, inexpensive, and less invasive than methods requiring complete enumeration.

Tagging / marking (e.g., small tags, dye, wristbands, cards)