Mark and recapture is a method commonly used in ecology to estimate an animal population's size where it is impractical to count every individual. A portion of the population is captured, marked, and released. Later, another portion will be captured and the number of marked individuals within the sample is counted. Since the number of marked individuals within the second sample should be proportional to the number of marked individuals in the whole population, an estimate of the total population size can be obtained by dividing the number of marked individuals by the proportion of marked individuals in the second sample. The method assumes, rightly or wrongly, that the probability of capture is the same for all individuals. Other names for this method, or closely related methods, include capture-recapture, capture-mark-recapture, mark-recapture, sight-resight, mark-release-recapture, multiple systems estimation, band recovery, the Petersen method, and the Lincoln method. Another major application for these methods is in epidemiology, where they are used to estimate the completeness of ascertainment of disease registers. Typical applications include estimating the number of people needing particular services (e.g. services for children with learning disabilities, services for medically frail elderly living in the community), or with particular conditions (e.g. illegal drug addicts, people infected with HIV, etc.).
Field work related to mark-recapture
Typically a researcher visits a study area and uses traps to capture a group of individuals alive. Each of these individuals is marked with a unique identifier (e.g., a numbered tag or band), and then is released unharmed back into the environment. A mark-recapture method was first used for ecological study in 1896 by C.G. Johannes Petersen to estimate plaice, Pleuronectes platessa, populations. Sufficient time should be allowed to pass for the marked individuals to redistribute themselves among the unmarked population. Next, the researcher returns and captures another sample of individuals. Some individuals in this second sample will have been marked during the initial visit and are now known as recaptures. Other organisms captured during the second visit, will not have been captured during the first visit to the study area. These unmarked animals are usually given a tag or band during the second visit and then are released. Population size can be estimated from as few as two visits to the study area. Commonly, more than two visits are made, particularly if estimates of survival or movement are desired. Regardless of the total number of visits, the researcher simply records the date of each capture of each individual. The "capture histories" generated are analyzed mathematically to estimate population size, survival, or movement. When capturing and marking organisms, ecologists need to consider the welfare of the organisms. If the chosen identifier harms the organism, then its behavior might become irregular.
Notation Let
N = Number of animals in the population n = Number of animals marked on the first visit K = Number of animals captured on the second visit k = Number of recaptured animals that were marked A biologist wants to estimate the size of a population of turtles in a lake. She captures 10 turtles on her first visit to the lake, and marks their backs with paint. A week later she returns to the lake and captures 15 turtles. Five of these 15 turtles have paint on their backs, indicating that they are recaptured animals. This example is (n, K, k) = (10, 15, 5). The problem is to estimate N.
Lincoln–Petersen estimator
The Lincoln–Petersen method (also known as the Petersen–Lincoln index or Lincoln index) can be used to estimate population size if only two visits are made to the study area. This method assumes that the study population is "closed". In other words, the two visits to the study area are close enough in time so that no individuals die, are born, or move into or out of the study area between visits. The model also assumes that no marks fall off animals between visits to the field site by the researcher, and that the researcher correctly records all marks. Given those conditions, estimated population size is:
N ^ = n K k , {\displaystyle {\hat {N}}={\frac {nK}{k}},}
Derivation It is assumed that all individuals have the same probability of being captured in the second sample, regardless of whether they were previously captured in the first sample (with only two samples, this assumption cannot be tested directly). This implies that, in the second sample, the proportion of marked individuals that are caught ( k / K {\displaystyle k/K} ) should equal the proportion of the total population that is marked ( n / N {\displaystyle n/N} ). For example, if half of the marked individuals were recaptured, it would be assumed that half of the total population was included in the second sample. In symbols,
k K = n N . {\displaystyle {\frac {k}{K}}={\frac {n}{N}}.}
A rearrangement of this gives
N ^ = n K k , {\displaystyle {\hat {N}}={\frac {nK}{k}},}
the formula used for the Lincoln–Petersen method.
Sample calculation In the example (n, K, k) = (10, 15, 5) the Lincoln–Petersen method estimates that there are 30 turtles in the lake.
… excerpt ends here. Continue reading the full article.
