Released: Number of marked individuals released into the wild

Or:

DB1: Total number of positive individuals found in database one including those also found in database two.

Sample: Size of sample drawn later from individuals in the wild both marked and unmarked

Or:

DB2: Total number of positive individuals found in database two including those also found in database one.

Recaptured: Number of individuals marked at the earlier stage found in the sample

Or:

In Both: Number of positive individuals found both in DB1 and DB2

Prospective Capture Recapture techniques in biology are used to estimate the size of populations in the wild when it is impossible to observe all animals in the entire population. The estimation is done on the basis of the number of previously marked individuals in a sample drawn from the wild. The lower the number of marked individuals in the sample the larger the unobserved population. There are quite a large number of assumptions underlying this technique. Most important among these are first: that the population is closed, that there are no births or deaths, and that animals do not migrate into or out of the population. Second, that the capture probability is not different between marked and unmarked individuals. Third, that the marked animals recaptured in the sample do not have a higher probability to be captured compared with marked animals who are not recaptured.

Note that the capture recapture model presented here is the most basic form. Modern capture recapture models allow you to test the above assumptions, to work with open populations with population change, migration and births and deaths, to consider that marked individuals have higher or lower catch-ability compared with unmarked individuals, and other models. These newer models are also well suited for use in biology practice, were population counting and monitoring takes place continuously or is repeated with intervals overtime.

Retrospective Capture Recapture techniques in demography and epidemiology are used to estimate the size of sub-populations in the larger population when it is impossible to observe this subpopulation in its entirety. The technique is based on studying the overlap, the number of individuals observed in more than one database, between two or more databases. The less the overlap between databases, the larger the unknown population. For example, the technique can be used to estimate the size of alcohol related problems on saturday nights by studying how many individuals are arrested for drunken behavior and the number of individuals hospitalized with alcohol related problems. As for the biological models the demography models are based on quite a number of assumptions. Among these are that the probability to be included in the databases is independent on the (type of) database. Further, that the people who are not included but who are in the at risk group to be included, don't have a lesser chance to be included, compared with those who are included.

Extensions of the technique primarily have to do with the use of more than two databases. This allows for the testing of assumptions and a more precise estimation of parameters. There are few examples of demographic or epidemiological population monitoring by way of revisiting the databases, comparable with the monitoring techniques used in biology.

A completely different technique to estimate the size of populations is the use of (zero truncated) Poisson models. These are based on observing people once, twice, three, four or more times in one or more databases. On the basis of the Poisson model the number of zero's can be estimated, people who are exposed to the risk but have not yet been changed by it. The model is based on a number of assumptions, such as the assumption that the probability among the exposed of being changed is equal to the probability among those not being changed, and that the probability of being changed once, twice, three times, or more often is constant. Also, the non exposed are in no way affected by the risk.

Pollock KH, Nichols JD, Brownie C, Hines JE. Statistical Inference for Capture-Recapture Experiments. *Wildlife Monographs* 1990;107:3-97.

Hook EB, Regal RR. Capture-recapture methods in epidemiology: methods and limitations. *Epidemiol Rev* 1995;17:243-64. -> ukpmc.ac.uk

van der Heijden PGM, Bustami R, Cruyff MJLF, Engbersen G, van Houwelingen HC. Point and interval estimation of the population size using the truncated Poisson regression model
. *Statistical Modelling* 2003;3:305-322. -> igitur-archive.library.uu.nl