Capture-recapture method

Capture-recapture method is a statistical tool used in ecology, epidemiology, and wildlife management to estimate the size of animal populations and the incidence of diseases. This method, also known as mark-recapture, is based on capturing a sample of individuals from a population, marking them in a harmless way, releasing them back into the population, and then recapturing another sample at a later time. The proportion of marked individuals in the second sample is used to make inferences about the total population size.

Overview

The capture-recapture method involves several steps. First, a sample of individuals is captured from the population of interest. These individuals are then marked or tagged in some way that does not affect their likelihood of being recaptured and are released back into the population. After a certain period, allowing the marked individuals to mix back into the population, a second sample is captured. The number of marked individuals in this second sample is recorded. The basic premise of the method is that the proportion of marked individuals in the second sample should be representative of the proportion of the total population that was marked in the first sample.

Mathematical Model

The simplest form of the capture-recapture method can be described by the Lincoln-Petersen estimator, given by the formula:

\[ N = \frac{C_1 \times C_2}{M_2} \]

where:

• \(N\) is the estimated total population size,
• \(C_1\) is the number of individuals captured in the first sample,
• \(C_2\) is the number of individuals captured in the second sample, and
• \(M_2\) is the number of marked individuals recaptured in the second sample.

This formula assumes that the population is closed (no immigration, emigration, births, or deaths between the two sampling events), that marks are not lost or overlooked, and that every individual has the same probability of being captured.

Applications

The capture-recapture method has a wide range of applications. In ecology, it is used to estimate the size of wildlife populations, which is crucial for conservation efforts and understanding ecological dynamics. In epidemiology, it helps estimate the incidence and prevalence of diseases, especially in cases where full data collection is not feasible. The method has also been adapted for use in social sciences, for example, to estimate the size of hidden populations such as drug users or the homeless.

Limitations

While the capture-recapture method is a powerful tool, it has limitations. The assumptions of a closed population and equal catchability are often violated in real-world scenarios. Various models and modifications have been developed to address these issues, such as the Jolly-Seber model, which allows for open populations.

Conclusion

The capture-recapture method is a fundamental technique in population estimation, offering a practical approach to measuring the size of animal populations and the incidence of diseases. Despite its limitations, when applied correctly, it provides valuable insights into population dynamics and health statistics.