Capture-Recapture Sampling

Example

A classic example comes from the field of ecology. Suppose the goal is to estimate the size of a fish population in a pond. A first-stage sample of 20 fish is drawn, tagged, and released back into the pond. A second-stage sample of 30 fish is subsequently drawn. Tags are found on 12 of the 30 sampled fish, indicating that 12 fish captured in the first sample were recaptured in the second sample. This information can be used to assign actual quantities to the variables of interest in Equation 1, where n = 30, C = 20, and R = 12. Solving for N using Equation 2 yields the following estimate of the population total:

Therefore, the estimated size of the pond's fish population is 50. A more stable estimate of the population total, subject to less sampling variability, can be obtained if multiple second-stage samples are drawn, and estimated totals, computed from each sample, are averaged together.

Assumptions

In order for the capture-recapture sampling technique to produce a valid estimate of a population size, three assumptions must hold:

• 1.
  Every population element has an equal probability of being selected (or captured) into both samples.
• 2.
  The ratio between marked and unmarked population elements remains unchanged during the time interval between samples.
• 3.
  Marked elements can be successfully matched from first-stage sample to second-stage sample.

Assumption 1 holds if simple random sampling is used to capture elements into both samples. A possible violation of this assumption occurs if those who were captured in the first-stage sample have a higher probability of being captured in the second-stage sample, which would lead to overestimation of the population total. Assumption 2 follows from the relationship described in Equation 1. In general, this assumption holds if there is no change in the population, or if the population is closed during the study. However, births or deaths and immigration or emigration are permitted as long as the ratio is preserved. [Page 81]Assumption 3 holds if there is no loss of tags and no erroneous matching.

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