The species–area relationship does not have an asymptote!
To attack a widespread myth.Location
Simple mathematical logical and empirical examples.Results
As both species and area are finite and non-negative, the species–area relationship is limited at both ends. The log species–log area relationship is normally effectively linear on scales from about 1 ha to 107 km2. There are no asymptotes. At the intercontinental scale it may get steeper; at small scales it may in different cases get steeper or shallower or maintain its slope.Main conclusion
The species–area relationship does not have an asymptote.