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Calcimator

Fish Population Estimate Calculator

Estimate fish population size using the Lincoln-Petersen mark-recapture method with Chapman correction and 95% confidence intervals.

Inputs

Results

Estimated population (N̂)

743

95% CI lower bound373
95% CI upper bound1,112
Standard error188.4
Density (fish/ha)74.3
Recapture rate (%)12.5
How to Use This Calculator
  1. Enter the number of fish captured and marked in the first sampling event (M).
  2. Input the number captured in the second event (C) and the number of recaptures (R).
  3. Review the Lincoln-Petersen population estimate: N = (M × C) / R.
  4. Check the confidence interval — the estimate is unreliable if recapture rate R/C is below 0.05.
  5. Use the Chapman modification for small samples to reduce bias in the estimator.

How the result changes with Marked & released (M)

Marked & released (M)Estimated population (N̂)
10,00173,650
35,001257,741
65,000478,643
90,000662,734

What each input means

Marked & released (M)
Number of fish captured, marked, and released in the first sampling event.
Second capture (C)
Total number of fish captured in the second sampling event.
Recaptured (R)
Number of marked fish found in the second capture. Must be ≤ both M and C.
Survey area (hectares)
Total area surveyed, used to calculate population density per hectare.

What each result means

Estimated population (N̂)
Chapman-corrected Lincoln-Petersen population estimate.
95% CI lower bound
Lower bound of the 95% confidence interval.
95% CI upper bound
Upper bound of the 95% confidence interval.
Standard error
Standard error of the Chapman estimator.
Density (fish/ha)
Estimated number of fish per hectare of surveyed area.
Recapture rate (%)
Percentage of second capture that were marked recaptures.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Marked & released (M) = 100, Second capture (C) = 80, Recaptured (R) = 10, Survey area (hectares) = 10 = 4 input(s) provided
  2. Calculate Estimated population
    Estimated population = max(marked, round(chapmanN))
    743 = 743
  3. Calculate 95% CI lower bound
    95% CI lower bound
    373 = 373
  4. Calculate 95% CI upper bound
    95% CI upper bound
    1112 = 1112

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators.

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