Species-Area Relationship (Power Law) Calculator

Formula first

Overview

The Species-Area Relationship (SAR), often expressed as a power law, describes the empirical relationship between the area of a habitat or region and the number of species found within it. This fundamental ecological pattern, S = $c{A}^z$, shows that larger areas generally contain more species. The constant 'c' represents the species richness of a unit area, while the exponent 'z' indicates how rapidly species richness increases with area, typically ranging from 0.1 to 0.5 for continental areas and 0.25 to 0.55 for islands.

Symbols

Variables

c = Constant, A = Area, z = Exponent, S = Species Richness

Apply it well

When To Use

When to use: Use this equation to estimate species richness in different-sized habitats, predict biodiversity loss due to habitat destruction, or compare biodiversity patterns across different regions or taxa. It's particularly useful in conservation biology for setting reserve sizes or understanding island biogeography.

Why it matters: The SAR is a cornerstone of ecology and conservation, providing a quantitative framework for understanding biodiversity distribution. It informs conservation strategies, helps predict the impact of habitat fragmentation, and is crucial for designing protected areas to maximize species preservation.

Avoid these traps

Common Mistakes

• Using inappropriate 'c' and 'z' values for the specific ecosystem or taxonomic group being studied.
• Extrapolating the relationship far beyond the range of areas for which 'c' and 'z' were derived.
• Confusing the power law model with other SAR models (e.g., exponential, logarithmic).

One free problem

Practice Problem

A study in a tropical rainforest found that for a specific group of insects, the constant 'c' is 3.5 and the exponent 'z' is 0.28. If a conservation area is established with an area of 1500 km², how many species of this insect group would be predicted to be present according to the power law species-area relationship?

Solve for: $S$

Hint: Remember to calculate $A^z$ first before multiplying by c.

The full worked solution stays in the interactive walkthrough.

Keep going

Related Formulas

References

Sources

1. Wikipedia: Species-area curve
2. Begon, M., Townsend, C. R., & Harper, J. L. (2006). Ecology: From Individuals to Ecosystems. Blackwell Publishing.
3. MacArthur, R. H., & Wilson, E. O. (1967). The Theory of Island Biogeography. Princeton University Press.
4. Ricklefs, R. E., & Relyea, R. (2014). The Economy of Nature (7th ed.). W. H. Freeman and Company.
5. Begon, M., Townsend, C. R., & Harper, J. L. (2006). Ecology: From Individuals to Ecosystems (4th ed.). Blackwell Publishing.
6. Rosenzweig, M. L. (1995). Species Diversity in Space and Time. Cambridge University Press.
7. Lomolino, M. V. (2000). Ecology's most general pattern? Species-area relationships and the new biogeography.