Mark and Recapture Calculator
Estimate a population size using the Lincoln-Petersen mark-recapture method.
Estimated Population Size (Lincoln-Petersen)
Lincoln-Petersen Estimate
N = (M × C) / R
Chapman Estimate
N = ((M + 1)(C + 1) / (R + 1)) − 1
Interpretation
How Mark and Recapture Works
Mark and recapture (also called capture-mark-recapture) is a method used by ecologists to estimate the size of a wildlife population that cannot be counted directly. A first sample of animals is captured, marked (with tags, bands, or paint), and released back into the population. After the marks have had time to mix uniformly through the population, a second sample is captured.
The proportion of marked animals found in the second sample reflects the proportion of marked animals in the whole population. If marked animals make up a small fraction of the recaptured sample, the total population must be large; if they make up a large fraction, the population is small.
- M = number of animals marked and released in the first capture
- C = total number of animals captured in the second sample
- R = number of marked animals recaptured in the second sample
Key Assumptions
The accuracy of a mark-recapture estimate depends on several assumptions being met. Violating them leads to biased estimates of population size:
Closed Population
The population does not change between the two sampling events. There are no births, deaths, immigration, or emigration during the study period.
Marks Do Not Affect Recapture
Marking does not change an animal's chance of being captured again or its survival. Marks are not lost or overlooked, and marked and unmarked animals are equally catchable.
Random Mixing and Sampling
Marked animals mix randomly back into the population, and every individual has an equal probability of being captured in the second sample.
Lincoln-Petersen vs Chapman
Lincoln-Petersen Estimate
The classic estimator, N = (M × C) / R, is simple and intuitive. However, it is biased upward (it tends to overestimate) when sample sizes are small or when few marked animals are recaptured, and it is undefined when no marked animals are recaptured (R = 0).
Chapman Estimate
The Chapman estimator, N = ((M + 1)(C + 1) / (R + 1)) − 1, is a modification that is less biased for small samples and remains defined even when R = 0. For large samples both estimators converge to nearly the same value, so Chapman is often preferred as the default.
Related Calculators
Educational Disclaimer: This mark and recapture calculator is provided for educational purposes to illustrate the Lincoln-Petersen and Chapman population estimation methods. Real ecological studies require careful field design and may use more advanced models that account for open populations, unequal catchability, and multiple sampling occasions. For research or management decisions, consult qualified ecologists and appropriate statistical methods.