Mark-Recapture Calculator
Estimate wildlife population size using Lincoln-Petersen mark-recapture method. Calculate N from marked animals released (M), total recaptured (C), and recaptured marked (R).
🌳 Ecology📐 N = M·C / R🧬 Biology
Marked animals released M
Total captured in 2nd sample C
Marked recaptured in 2nd sample R
Confidence level (95 or 99)
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Mark-Recapture Calculator | — | N = M·C / R | individuals |
Step-by-Step Examples
Example 1
Fish population
M=100 tagged fish released. Second catch: C=80, R=20 marked recaptured.
- N = M×C/R = 100×80/20 = 400
- SE = √(100²×80×60/(20²×21)) = √(174.6) = 13.2
- 95% CI: 400 ± 1.96×13.2 = 374 to 426
✓ N ≈ 400 fish (95% CI: 374-426)
Example 2
Deer census
M=50 tagged deer. Recapture: C=60, R=15.
- N = 50×60/15 = 200
- Capture rate: 15/50 = 30% of marked recaptured
✓ N ≈ 200 deer
Example 3
Accuracy check
If R/M < 5-10%: estimate unreliable. If R/C close to M/N: good estimate.
- Check: R/M = R/M should ≈ C/N
- More R (more recaptures) = better precision
- Aim for R ≥ 10 for reasonable precision
✓ Larger R values give more precise estimates
Real-World Applications
Wildlife Biology
Standard method for estimating population size of fish, birds, mammals, and insects.
Fisheries Management
Tag-recapture estimates stock sizes to set sustainable catch limits.
Entomology
Mark-recapture estimates insect populations for pest management and conservation.
Ecology Research
Population size is a fundamental measurement; mark-recapture is the standard for mobile animals.
Common Mistakes to Avoid
⚠️
Animals must mix randomly
Marked and unmarked animals must mix randomly between sessions. If marked animals avoid traps: N is overestimated.
⚠️
No births, deaths, immigration, emigration between samples
Closed population assumption. Use open models (Jolly-Seber) if population is open.
⚠️
Larger R gives more precise estimate
Aim to mark ≥ 20% of the population and capture ≥ 10 marked individuals in recapture for reasonable precision.
Frequently Asked Questions
What is the Lincoln-Petersen method? ▾
N = M×C/R. Assumes: equal capture probability for all individuals, population closed, marks not lost, marks recognized. Simple and widely used.
What is the Chapman modification? ▾
N = (M+1)(C+1)/(R+1) - 1. Less biased when R is small. Use when R < 7 or when M+C > N.
What is an open population model? ▾
Jolly-Seber model allows births, deaths, and migration between capture occasions. Estimates survival and recruitment rates as well as population size.
How many marks are needed? ▾
For CV < 20%: need R ≥ 25. For CV < 10%: need R ≥ 100. Mark a fraction (p) of population; then recapture fraction p to get expected R = p²N.
What is PIT tagging? ▾
Passive Integrated Transponder: implanted microchip read by scanner. Permanent, individual ID, no mark loss, and can be read without recapture (remote readers).