How to use it
- On the first visit, mark and release M animals.
- On the second visit, catch C animals and count how many carry a mark, R.
- Enter the three numbers and read the population estimate and its 95 % interval.
The formulas
- Lincoln–Petersen: N = M × C ÷ R.
- Chapman: N = (M + 1)(C + 1) ÷ (R + 1) − 1.
- Variance (Seber): (M + 1)(C + 1)(M − R)(C − R) ÷ ((R + 1)² (R + 2)); the standard error is its square root.
- 95 % interval: Chapman ± 1.96 × SE, not below M + C − R.
Worked example
50 fish marked, 40 caught a week later, 10 of them marked:
- Lincoln–Petersen: 50 × 40 ÷ 10 = 200;
- Chapman: 51 × 41 ÷ 11 − 1 = 189;
- variance 51 × 41 × 40 × 30 ÷ (121 × 12) = 1,728.1, standard error 41.6;
- 95 % interval: 189 ± 1.96 × 41.6, about 108 to 271;
- a quarter of the second catch was marked, and 80 different fish were handled.
Planning a survey
- Aim for at least 7 to 10 recaptures; fewer gives a very wide interval.
- Mark enough animals: the estimate is most precise when M and C are both a good share of the population.
- Leave time for marked animals to mix, but not so long that births, deaths or migration change the population.