Island Biogeography Calculator
Predict species richness from island area and distance using the species-area relationship (S = cA^z) from MacArthur & Wilson's theory.
About this calculator
This calculator applies the species-area relationship, S = cA^z, one of the most consistently observed patterns in ecology: the number of species a habitat can support scales with its area, raised to a fractional power z, times a constant c that depends on the taxonomic group and region being studied. The relationship traces back to Olof Arrhenius's 1921 work and was formalized as the centerpiece of Robert MacArthur and E.O. Wilson's 1967 theory of island biogeography, which explains species richness on islands (or any isolated habitat fragment) as a balance between immigration of new species and extinction of existing ones.
Published z-values commonly cluster around 0.20-0.35 for true oceanic islands and a lower 0.12-0.17 for habitat patches within a mainland, reflecting that isolated islands lose species to extinction more easily than well-connected mainland patches of the same size — this calculator's default inputs sit inside that typical oceanic-island range. Beyond the core species-area calculation, this calculator also estimates immigration rate, extinction rate, and an equilibrium species count using a simplified, illustrative version of MacArthur and Wilson's immigration-extinction equilibrium model; these three outputs use fixed scale constants for teaching purposes rather than reproducing any single published, taxon-specific parameter set, so treat Species Richness (from the verified S = cA^z relationship) as this calculator's most defensible output, and the immigration/extinction/equilibrium figures as illustrative of the underlying theory's shape rather than a citable prediction.
Inputs
Results
Predicted Species Richness
26.6
Figures current as of 1967. Source: MacArthur, R.H., Wilson, E.O. The Theory of Island Biogeography. Princeton University Press, 1967.
How to Use This Calculator
- Enter Island Area (km2) and Distance from Mainland (km).
- Set the z Exponent (typically 0.20-0.35) and c Constant from the species-area relationship.
- Review Predicted Species Richness, and the species count at half and double the current area.
- Check % Lost if Area Halved to evaluate the conservation impact of habitat fragmentation.
- Use Immigration and Extinction Rates to understand equilibrium dynamics on the island.
How the result changes with c Constant
| c Constant | Predicted Species Richness |
|---|---|
| 5 | 13.3 |
| 7.5 | 19.9 |
| 15 | 39.9 |
| 25 | 66.5 |
What each input means
- Island Area
- Total area of the island or habitat fragment in square kilometers.
- Distance from Mainland
- Distance from the nearest mainland or large source habitat in km. Affects immigration rate.
- z Exponent
- Species-area exponent. Typical values: 0.20-0.35 for oceanic islands, 0.12-0.17 for mainland habitats.
- c Constant
- Taxon- and region-specific constant. Depends on the taxonomic group and biogeographic region.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersIsland Area = 50, Distance from Mainland = 100, z Exponent = 0.25, c Constant = 10 = 4 input(s) provided
- Calculate Predicted Species RichnessPredicted Species Richness26.6 = 26.6
- Calculate Species at Half Area22.4 = 22.4
- Calculate Species at Double Area31.6 = 31.6
Figures and sources
- Species-area relationship (S = cA^z) and the immigration-extinction equilibrium theory of island biogeography (1967) — MacArthur, R.H., Wilson, E.O. The Theory of Island Biogeography. Princeton University Press, 1967.
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does increasing Island Area always raise Predicted Species Richness?
The species-area relationship, S = cA^z, is a power function of area with a positive exponent z (typically 0.1 to 0.5 in real ecological studies), so richness rises whenever area rises, for any positive z. This matches one of the most robust patterns in field ecology: bigger islands and habitat patches reliably support more species than smaller ones of similar type and isolation, all else being equal.
Why does the c Constant move Predicted Species Richness so directly?
In the formula S = cA^z, c is a multiplicative scaling factor applied to island area raised to the z power, so richness scales linearly with c for any fixed area and z. Ecologically, c reflects the size of the regional species pool available to colonize the island — a taxonomic group or region with more total species to draw from (a higher c) predicts more species on an island of any given size than a group with fewer available species.
Why does Predicted Species Richness not change at all when I adjust Distance from Mainland?
Species Richness is calculated purely from the species-area relationship (island area, the z exponent, and the c constant) — distance never enters that formula. Distance from Mainland instead drives this calculator's separate Immigration Rate output, reflecting a different part of island biogeography theory: how far new colonizing species have to travel, not how many species the island's area can ultimately support.
Why does Immigration Rate fall as Distance from Mainland increases?
Immigration Rate uses an exponential decay model, since farther islands are harder for colonizing species to reach — fewer individuals successfully cross a longer stretch of ocean or unsuitable habitat to establish on a remote island than a nearby one. This mirrors the core insight of MacArthur and Wilson's equilibrium theory: near islands receive new species faster than far ones, all else being equal.
How reliable are the Immigration Rate, Extinction Rate, and Equilibrium Species outputs compared to Species Richness?
Species Richness rests directly on the well-established species-area relationship with the z and c values you provide, so it's this calculator's most defensible number. Immigration Rate, Extinction Rate, and Equilibrium Species illustrate the shape of MacArthur and Wilson's immigration-extinction equilibrium theory using simplified, fixed scale constants rather than a specific published, taxon-and-region-calibrated parameter set, so treat them as educational illustrations of the theory rather than citable predictions for a real island.
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