Mark and recapture

The recapture method is a method for estimating the size of a population of animals or other individuals. Here a sample of the measured population is caught, tagged and released. After a sample is captured and closed to the total size by the proportion of marked animals in it again. The recapture method is also known under the name of, or Peterson capture-recapture method. The Danish biostatistician C. G. J. Peterson, this method first proposed in 1896.

Calculation

The population size N can be estimated as

Where M is the number of pre- labeled individuals, n is the number of individuals in the sample and m the number of selected individuals were found in the sample. The process can be explained by the fact that the proportion of marked individuals in the sample should be the same as in the whole population:

If no marked individuals are found in the sample, no conclusion on the population size is possible.

Conditions

Thus, the result is not distorted, the following conditions must be met:

• There are between attaching the markers and the collection of the second sample not add new individuals.
• The marks go in the meantime lost ( either by replacing the labeling of individuals nor by migration of individuals ).
• The probability of being caught is the same for all individuals, with or without markings.

Mathematical derivation

It is assumed that the random variable " number of captured animals in the second sample " of a hypergeometric distribution with the following parameters ( extent of the total population ), (number of marked individuals ) and (circumference of the second sample ). The probability of having exactly marked individuals in the sample is:

In this case, the binomial coefficients called "N over n ". Since all the values ​​from the sample are known except obtained by maximizing the Peterson estimator function ( application of the maximum-likelihood method).

Other applications

The method can also be used to estimate the size of a population that is two or more instances only partially known. It attracts every instance independently of the other a sample. For example, the proportion of indexed documents to estimate a search on the WWW follows with two search engines:

However, the method is less accurate when the overlap between the search engines are generally larger.

As part of the documentation and information the method in 1981 by Walther Umstätter and Margaret Rehm has been introduced.