Species–Area Curve Calculator (S = cAᶻ)
Use the species–area relationship S = c·Aᶻ to predict how many species a habitat of a given area holds, fit c and z from two surveys, and estimate the species lost when habitat shrinks (the extinction debt from area loss) — with typical z values for islands, mainland plots and habitat fragments.
How it works
S = c × Aᶻ · z = ln(S₂ ÷ S₁) ÷ ln(A₂ ÷ A₁) · fraction of species remaining = (A_new ÷ A_old)ᶻ · area for a fraction f of species = A × f^(1/z)
Larger areas hold more species, but not in proportion: doubling an island's area adds a fixed percentage of species, not a fixed number, which is the power law Arrhenius described and MacArthur and Wilson built island biogeography on. The exponent z captures how fast richness accumulates — around a quarter for true islands and fragments, lower for nested samples of a continuous landscape where most species are already present in small plots. Because the relationship is a power law it can be fitted from two surveys and inverted to ask the conservation question that matters most: how many species a shrinking habitat will eventually lose, and how much area must be kept to hold a given share of them.
Worked example
A 100 km² forest with 120 bird species and z = 0.25: a 25 km² remnant is predicted to hold 120 × (25/100)^0.25 ≈ 85 species in the long run — a 75% loss of area costing about 29% of the species. Keeping 90% of the species needs about 66 km²; two surveys of 100 km² (120 species) and 25 km² (80 species) would instead fit z ≈ 0.29.
Frequently asked questions
Why is z about 0.25 so often?
It emerges from lognormal species-abundance distributions sampled at increasing area and from the colonisation–extinction balance on islands; empirical island z values cluster between 0.2 and 0.35, though scale and taxon shift it.
Does the curve say which species disappear?
No — it predicts numbers at equilibrium. Rare, large-bodied, habitat-specialist and top-predator species are the usual casualties, and edge effects can make small fragments worse than the area alone suggests.
Related calculators
Textbook ecology, forestry and quantitative-genetics formulas with simplifying assumptions. Field constants (z, k, h², efficiencies) vary by system — use locally calibrated values for management or research decisions.