Mark-Recapture Calculators

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Mark-recapture estimates population size when direct counting is impossible. In the Lincoln-Petersen method: M animals are captured, marked, and released. After mixing, a second sample of C animals is captured, of which R bear marks. Population estimate: N̂ = (M × C) / R. Key assumptions: marked animals mix randomly with unmarked; marks are not lost; no births, deaths, or migration between samples; marked and unmarked individuals have equal capture probability. Modern multi-sample methods (Cormack-Jolly-Seber) relax many assumptions.

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Lincoln-Petersen Formula

N̂ = (M × C) / R

M = marked and released; C = total in second capture; R = marked in second capture. Example: tag 50 fish (M=50); recapture 40 (C=40); 8 tagged (R=8): N̂ = (50×40)/8 = 250 fish. Chapman modified estimator for small samples: N̂ = [(M+1)(C+1)/(R+1)] − 1.

Assumptions and Violations

  • Closed population: no births, deaths, immigration between samples
  • Equal catchability: marked and unmarked equally catchable — violations cause over/underestimates
  • Random mixing: marked animals don't have different habitat use from unmarked
  • Mark retention: tags must not fall off or increase mortality

Modern Methods

MARK program: CJS (open populations); Huggins models (heterogeneous detection). Genetic mark-recapture: DNA fingerprinting as non-invasive marks for wolves, bears, whales.

Glossary

Lincoln-Petersen Estimator
N̂ = (M × C) / R; estimates population size; M = marked released; C = total recaptured; R = marked among recaptured; assumes closed population and random mixing.
Closed Population
A population with no births, deaths, immigration, or emigration during the study; required for Lincoln-Petersen; open-population models (Cormack-Jolly-Seber) relax this assumption.
Genetic Mark-Recapture
Non-invasive mark-recapture using DNA genotypes as individual marks from hair, feces, or skin; eliminates need for physical capture; used for elusive or dangerous species.

Frequently Asked Questions

Mark-recapture captures, marks, and releases animals, then re-samples the population. The Lincoln-Petersen estimate: N̂ = MC/R. Logic: if marked animals mix randomly, the proportion marked in the second sample (R/C) equals the proportion marked in the whole population (M/N). Solve for N. Example: mark 60 deer (M); recapture 80 (C); 12 are marked (R): N̂ = 60×80/12 = 400 deer.

Four critical assumptions: (1) Closed population — no births, deaths, immigration, or emigration between samples. (2) Random mixing — marked animals distribute randomly among unmarked throughout the habitat. (3) Equal catchability — all animals have the same probability of being captured in the second sample; trap-happiness or trap-shyness violates this. (4) Mark persistence — marks must not fall off or cause higher mortality. Violations lead to biased estimates: trap-happy animals → R too high → N underestimated; trap-shy → R too low → N overestimated.

Mark-recapture guides: harvest management — fish and deer population estimates set catch limits and hunting quotas; survival estimation — recapture rates across multiple periods estimate annual survival (Cormack-Jolly-Seber models); population trend monitoring — compare N̂ between years to detect decline or recovery; dispersal mapping — track where marked individuals appear to estimate home ranges. Pacific salmon: coded wire tags or PIT tags in hatcheries; recover tags at dams and in commercial catch to estimate run size.

Instead of physical tags, each individual's DNA genotype serves as a unique, non-invasive mark. Collect DNA from hair snares, feces, shed skin, or biopsy darts; genotype to identify individuals. Advantages: no capture needed; no trap-related behavioral effects; works for elusive, dangerous, or hard-to-capture species (wolves, bears, marine mammals). Photo-identification is a similar approach using natural markings (whale flukes, shark fins, big cat spots). Software like Wildbook uses pattern-matching algorithms to automate individual recognition from photographs.