Definition:Capture-Recapture Sampling
Definition
Capture-recapture sampling is a statistical technique for estimating the size of animal populations.
In its simplest form, a sample of $n_1$ animals is captured, and each one tagged and released.
A second sample of $n_2$ animals is captured at a later date, and the number $m$ of animals which were tagged in the first round is noted.
If the unknown population size is $N$ and any animal is equally likely to be captured, the proportion $\dfrac m {n_2}$ of tagged to untagged animals is a reasonable estimate of the unknown proportion $\dfrac {n_1} N$ of tagged animals to the whole population.
Hence our estimate $N^*$ of $N$ can be calculated as:
- $N^* = \dfrac {n_1 n_1} N$
provided $m \ne 0$.
Warning
Capture-recapture sampling tends to overestimate the population size, especially for small $m$.
The validity of $N^*$ depends strongly upon the assumption that both the population size and the probability of capture remain constant between samples.
The former assumption ignores births, deaths and migration between sampling, and the latter does not hold if the animals decide they like being captured (perhaps because they get fed).
Alternatively, if an animal is frightened by capture, this may reduce the probability of recapture.
More sophisticated estimators take some of this into account.
Examples
Arbitrary Example 1
Let $25$ squirrels be captured, marked and released.
On a later date, let $40$ squirrels be captured and inspected.
Let $5$ of those be ones which were marked on the first capture exercise.
Then a fair estimate of the entire population of squirrels is $200$.
Also see
- Results about capture-recapture sampling can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): capture-recapture sampling
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): capture-recapture sampling