Mark–Recapture

How many snails live in the pond? Catch some, mark them and let them go. Later, catch again and count how many carry a mark. The share of marked animals in the second catch tells you how big the whole population is — with the Lincoln–Petersen and the Chapman estimate and a 95% range.

EcologyPopulation sizeField work

Inputs

Input examples

First visit: catch and mark M animals and release them. Second visit: catch C animals and count the R among them that carry a mark. Give the marked animals time to mix in with the rest, and use a mark that does not fall off or make them easier to catch.

Marked and released M — first visit

Caught on the second visit C

Of those, already marked R

How does Mark–Recapture Work?

You cannot count every snail in a pond, but you can count a share. If 8 of the 50 snails in your second catch are marked, about 8/50 = 16% of all snails carry a mark. You marked 40, so the pond holds about 40 / 0.16 = 250 snails. That is the Lincoln–Petersen estimate.

With few recaptures it overestimates the population, and with none it gives infinity. The Chapman estimate adds 1 to each count and is nearly unbiased once R is about 7 or more. The method assumes a closed population (no births, deaths or migration between the visits), marks that stay on, and that marked animals are as easy to catch as the rest.

R ≥ 7reliable estimate

R = 0only Chapman works

trap-shyestimate too high

trap-happyestimate too low

How Likely is Each Population Size?

chance of finding exactly R marked, for each population size

Chapman estimate

95% range

Result

Enter the counts above

Worked Techniques

Lincoln–Petersen

The marked share in the second catch equals the marked share in the whole population.

Example: 120 fish marked, 18 of 150 recaught: 1000 fish.

Chapman Correction

Adding one to each count removes most of the bias of small samples and works even when no marked animal is caught again.

Example: the fish: (121·151)/19 − 1 = 961.

95% Range

The range shrinks as R grows. It never goes below M + C − R: you have seen that many different animals yourself.

Example: the snails: 231 ± 115, so roughly 116 to 347.

Sources & Verification

References

C. J. Krebs, Ecological Methodology, 2nd ed., Benjamin Cummings, 1999 — Ch. 2 (Estimating abundance: the Petersen method and the Chapman estimator, with its variance).
D. G. Chapman, “Some properties of the hypergeometric distribution with applications to zoological sample censuses”, University of California Publications in Statistics 1 (1951) 131–160.
G. A. F. Seber, The Estimation of Animal Abundance and Related Parameters, 2nd ed., Griffin, 1982 — Ch. 3 (Closed population: single mark release).