Lincoln-Petersen Estimate
Population size from mark-and-recapture sampling.
Formula
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Example
M=50,C=40,R=10 ⇒ 200
How it works
The Lincoln-Petersen estimate is used to infer the total size of a population when you cannot count every individual directly. You first mark a sample of individuals, then later take a second sample and see what fraction of that sample is marked; if the marked fraction in the second catch matches the marked fraction you originally released, the total population can be estimated by scaling up from the sample sizes. The formula assumes the marks are not lost, the population is effectively closed between samples, and marked and unmarked individuals are equally likely to be caught.
When to use it
Use this in ecology or wildlife studies when estimating the number of fish, insects, mammals, or other mobile organisms in a habitat using capture and recapture data. It is also useful in public health or conservation surveys when a full census is impractical.
Worked example, step by step
Suppose 80 animals are marked in the first sampling. In the second sampling, 60 animals are captured. Of those 60, 12 are found to be marked. Use the formula: N = (M × C) / R Substitute the values: N = (80 × 60) / 12 Calculate the numerator: 80 × 60 = 4800 Divide by the recaptured marked animals: 4800 / 12 = 400 Estimated population size: N = 400
Common mistakes to avoid
- Using the number marked in the first sample as the total population instead of just one sample size
- Forgetting that R must be the number of marked individuals recaptured in the second sample, not all captured individuals
- Applying the formula when the population changes between samples or the marking affects capture probability
Did You Know?
Ecologists estimate wild animal populations by tagging some, releasing them, and seeing how many turn up again.
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