What this is for: Mark–recapture population estimates (Lincoln–Petersen and Chapman), quadrat density with confidence intervals, and exponential vs logistic growth projections.
The formula: N = (M × C) ÷ R; logistic N(t) = K ÷ (1 + ((K − N0)/N0) × e^(−rt))
How to use:
- In Mark–Recapture, enter M, C and R, and report the Chapman N with its standard error and 95% confidence interval.
- In Quadrat Sampling, enter one row per quadrat — individuals of the target species, species richness — and the quadrat size in m².
- Read total individuals, mean density per quadrat and per m², the standard error, frequency and mean richness.
- In Population Growth, enter N0, r and K, then enter a year to read off.
- Compare the exponential and logistic N at that year and in the growth table and chart.
Mark–Recapture Population Estimate (Lincoln–Petersen & Chapman)
Mark and release M animals; later catch C animals of which R carry the mark. Chapman is the bias-corrected version to report, with its standard error and 95% CI.
Lincoln–Petersen N = M × C / R
CHAPMAN N (report this)
Variance (Chapman)
Standard error
95% CI — lower
95% CI — upper
Marked share of second catch (R/C)
Quadrat Sampling — Density, Frequency & Richness
One row per quadrat: individuals of your target species and the total species richness of that quadrat.
m²
Total individuals counted
Mean density (individuals per quadrat)
Mean density (individuals per m²)
Standard error of the mean (per quadrat)
Frequency (share of quadrats with species present)
Mean species richness per quadrat
Population Growth — Exponential vs Logistic
N grows from N0 with intrinsic rate r; the logistic curve bends toward carrying capacity K. The read-off box evaluates both models at any year you choose.
/year
Doubling time (years)
N exponential at that year
N logistic at that year
Prefer to work offline or keep a copy? The download link is right below.
Download the Ecology & Population Calculator workbook (.xlsx)
Download the Ecology & Population Calculator workbook (.xlsx)
Notes & limits (from the workbook): Mark–recapture assumes a closed population (no births/deaths/migration between samples), marks not lost, and marked animals mixing fully and as catchable as unmarked. With R below ~10 the CI is very wide. Quadrat density per m² assumes every quadrat is the stated size, and the SE needs 10+ quadrats placed randomly or on a fixed grid. The logistic model assumes r and K are constant — real populations overshoot, cycle, or shift K with the environment.