Mark-Recapture Population Survey (2D)

Field Setup

True population size 80

Sample 1 size (marked, M) 20

Sample 2 size (recapture, C) 20

Wander speed 1.0×

Set your sample sizes, then run ① Capture & Mark to tag a first random sample.

Live Readouts

Marked (M)

Recaptured marked (R)

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Estimated population N̂ (Chapman)

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True N vs estimate error

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How it works

Mark-recapture is the standard field method for estimating a wild population you cannot count directly. Capture a random sample of size M, tag every individual, and release them to remix with the population. Later, capture a second independent sample of size C and count how many of those R already carry a tag.

Lincoln-Petersen:  N̂ = (M × C) / R

Chapman's correction (used here, avoids
division by zero and bias at small R):
  N̂ = (M+1)(C+1) / (R+1)  −  1

Intuition: marked individuals should turn up in the second sample in roughly the same proportion they make up of the whole population — R/C ≈ M/N — so solving for N gives the estimator above.

① Capture & Mark — randomly selects M animals from the current population and tags them red.
② Recapture Sample — randomly selects C animals (any animal, marked or not) and flashes them blue/amber; any that are already red count toward R.
↺ Reset Population — regenerates a fresh, unmarked population at the chosen size.

Key assumptions this method relies on (and why real surveys can go wrong): the population is closed (no births/deaths/migration between samples), every individual is equally catchable, marks are not lost, and marked animals mix back in fully before the second sample. Ecologists use this exact technique — capture-mark-recapture — for fish stocks, small mammals, birds and insect populations worldwide.

Unmarked Marked (tagged) In current sample

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