Home Statistical Dictionary Capture-Recapture Method
Capture-Recapture Method
A method for estimating the size of a population that cannot be directly counted, based on capturing (or otherwise identifying), marking, and releasing a first sample, then capturing a second sample and observing how many of the second sample were already marked from the first.
In Plain English
Capture-recapture, originally developed by wildlife biologists to estimate animal population sizes without being able to count every individual directly, works on a simple logical trick: capture some animals, mark them, and release them back into the population. Later, capture a second sample. If marked animals make up a large fraction of the second capture, the total population is probably not much bigger than what you've already sampled, if marked animals are rare in the second capture, the population is probably much larger than either sample alone would suggest. The same underlying logic now shows up well beyond wildlife biology, epidemiologists use it to estimate the true size of hard-to-count populations like people with a particular undiagnosed condition, by treating separate administrative records or case-finding efforts as the two 'capture' events.
Definition
The capture-recapture method estimates the size of a closed population that cannot be enumerated directly by capturing a first sample of size , marking and releasing those individuals, then capturing a second, independent sample of size and observing , the number of individuals in the second sample that were already marked from the first capture. Under the assumption of a closed population (no births, deaths, immigration, or emigration between captures) and equal catchability (every individual has the same probability of capture in each sample, independent of whether it was previously captured), the classical Lincoln-Petersen estimator uses the proportion of marked individuals in the second sample, , as an estimate of the first sample's true proportion of the population, , yielding ; violations of the closed-population or equal-catchability assumptions (such as trap-shy or trap-happy behavior, where being previously captured changes an individual's future capture probability) are well-documented sources of bias, and more advanced multi-sample capture-recapture models exist specifically to relax and test these assumptions.
Properties
- The capture-recapture method's validity rests entirely on its two core assumptions, a closed population between captures (no entries or exits) and equal catchability (capture in the first sample does not change an individual's probability of capture in the second), violations of either assumption are well-documented sources of substantial bias in real applications.
- Beyond wildlife biology, capture-recapture methodology (sometimes called dual-system or multi-system estimation in this context) is widely used in epidemiology and official statistics to estimate the size of hard-to-count populations, undiagnosed disease cases, undercounted census populations, using overlapping administrative lists or case-finding efforts as the 'capture' events instead of physical marking.
- Modern extensions to the basic two-sample capture-recapture design use three or more capture occasions and log-linear or mixture models to explicitly test and relax the equal-catchability assumption, allowing for heterogeneous capture probabilities across individuals, a substantial refinement over the simple Lincoln-Petersen estimator's assumption of homogeneity.
At a Glance