The mark and recapture method, also known as the Lincoln-Petersen method, is a foundational technique in ecology used to estimate the size of a mobile animal population in a specific area. It is applied when studying species that are difficult to locate or too numerous to count directly, such as insects, fish, and small mammals. This procedure offers a practical way for scientists to gain a reliable population count using a simple mathematical proportion derived from a small, representative sample of the total population.
Executing the Capture and Recapture Phases
The process begins with the initial capture phase, where researchers collect a sample of animals from the target population using species-appropriate tools like traps, nets, or cages. Once captured, every individual in this first sample is given a unique and durable, yet harmless, mark. The total number of individuals marked, designated as \(M\), is carefully recorded.
Following the marking, the animals are immediately released back into their environment. A period of time must then pass during which these marked individuals can fully intermingle and disperse with the rest of the unmarked population. This mixing period is necessary to ensure the marked individuals are randomly distributed throughout the entire study area before the second sampling event occurs.
The final stage is the recapture phase, where the researchers return to the same location and collect a second sample of animals. The total number of individuals in this second collection is recorded as \(C\). Within this second sample, the scientists carefully count and record how many of the animals are carrying the original mark; this count is designated as \(R\), the number of recaptures.
Calculating the Population Estimate
The underlying logic of the mark and recapture method is based on the assumption that the proportion of marked animals in the second sample is the same as the proportion of marked animals in the entire population. The initial marked count (\(M\)) is a known figure, and the total population size (\(N\)) is the unknown value to be estimated. By setting up a simple algebraic proportion, the unknown population size can be calculated.
The Lincoln-Petersen Index, the formula used for this calculation, is expressed as \(N = (M \times C) / R\). Here, \(N\) represents the estimated total population size, and \(M\) is the number of individuals initially marked. The calculation essentially scales up the initial marked sample based on the recovery rate observed in the second capture.
For example, if a researcher initially marks and releases 50 field mice (\(M=50\)), and a second trapping yields 100 mice (\(C=100\)) of which 10 are marked (\(R=10\)), the calculation is \(N = (50 \times 100) / 10\). This results in an estimated total population size (\(N\)) of 500 mice.
Conditions for Reliable Results
For the Lincoln-Petersen estimate to be reliable, several strict ecological conditions must be met, primarily concerning the stability of the population between the two sampling periods. The first major assumption is that the population is “closed,” meaning there are no significant changes due to births, deaths, immigration, or emigration during the time between the initial capture and the recapture event. If a large number of unmarked animals enter the area, the final estimate will be inaccurately high.
A second condition requires that the marked animals fully and randomly mix back into the general population before the second capture takes place. If marked animals remain clustered near the initial release site, the second sample may contain an artificially high number of recaptures, leading to an underestimation of the total population. Furthermore, the mark must not be lost or rubbed off, and it must not affect the animal’s behavior or survival.
Finally, both marked and unmarked individuals must have an equal chance of being captured in the second sampling event. If marked animals become “trap-shy” and avoid the traps after their first experience, the recapture rate (\(R\)) will be too low. This low recapture rate causes the overall population estimate (\(N\)) to be inflated and inaccurate.