Species-Area Relationship Calculator
Estimate species richness from habitat area using MacArthur and Wilson's S = cA^z equation.
Calculate how habitat loss reduces biodiversity in any ecosystem.
The species-area relationship (SAR) is one of ecology’s most consistent empirical patterns. Larger habitats support more species. The relationship follows a power law, first formalized by MacArthur and Wilson in 1967 as the theory of island biogeography.
The equation:
S = c x A^z
where S is the number of species, A is area, c is a constant that depends on the taxon and region, and z is the scaling exponent.
The z exponent. For true islands isolated by ocean, z is typically 0.25-0.35. For habitat fragments on land (forest patches in an agricultural landscape), z is lower, around 0.12-0.25. The difference matters. A lower z means species are more resilient to area reduction.
The c constant varies widely by taxon and region. For birds in tropical forests, c might be 5-20. For insects on a single island chain, it could be 0.1 or 500. It is best calibrated with local data.
Habitat loss prediction. If you halve the area of a forest patch, you expect to lose a fraction of species: S_new = S_old x (0.5)^z. With z = 0.25, halving the area loses about 16% of species. With z = 0.35, it loses about 22%.
This is why conservation biology focuses on maintaining connected habitat corridors. Fragmented patches behave as islands and suffer species loss at rates predicted by the SAR. A single large reserve often supports more species than several small reserves of equal total area.