Capturemarkrecapture

Capture-recapture is a method used in ecology and wildlife biology to estimate the size of a population. The basic principle involves capturing a sample of individuals from a population, marking them, and then releasing them back into the population. After a period of time, a second sample is taken. The number of marked individuals in the second sample is then used to estimate the total population size.

There are several variations of the capture-recapture method, each with different assumptions and formulas. The simplest form is the Lincoln-Petersen estimator, which is suitable for closed populations where there is no immigration, emigration, births, or deaths between the two sampling periods. The formula for the Lincoln-Petersen estimator is N = (M * n) / m, where N is the estimated population size, M is the number of individuals initially captured and marked, n is the total number of individuals captured in the second sample, and m is the number of marked individuals recaptured in the second sample.

More complex models exist to account for open populations, where individuals can enter or leave the population between sampling events. These models often use techniques like Jolly-Seber or Cormack-Jolly-Seber to estimate survival rates and population sizes over time. The effectiveness of capture-recapture methods relies heavily on meeting certain assumptions, such as the marks being permanent and not affecting the animal's survival or behavior, and the marked individuals mixing randomly with the unmarked population. Violations of these assumptions can lead to biased estimates. This technique is widely used for studying a variety of species, from fish and insects to mammals and birds.