Island Biogeography Calculator
Calculate equilibrium species richness on an island using the MacArthur-Wilson theory. Find immigration and extinction rates from island size and distance from mainland.
🏝️ Ecology📐 S* = CA^z (species-area)🧬 Biology
Island area A (km²)
Constant C (from species-area curve)
Species-area exponent z
Mainland species pool P (optional)
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Island Biogeography Calculator | — | S* = CA^z (species-area) | species |
Step-by-Step Examples
Example 1
Caribbean Islands
Islands with C=5, z=0.25. Island of 100 km².
- S = 5 x 100^0.25 = 5 x 3.162 = 15.8
- ~16 species predicted
✓ ~16 species on 100 km² island
Example 2
Doubling Island Area
S increases when area doubles: by 2^z factor.
- If z=0.25: S increases by 2^0.25 = 1.19 (19%)
- Double area = 19% more species (not double)
- To double species: need 2^(1/z) = 16x more area if z=0.25
✓ Doubling area gives only 19% more species (z=0.25)
Example 3
Habitat Fragment
Forest fragment 10 km², C=8, z=0.30.
- S = 8 x 10^0.30 = 8 x 2.0 = 16 species predicted
- Original 1000 km² forest: 8 x 1000^0.30 = 8 x 7.94 = 63.5
- Fragmentation predicts loss of 63-16 = 47 species
✓ Fragmentation predicts 73% species loss
Real-World Applications
Conservation Biology
Minimum reserve size calculations use species-area relationships to predict biodiversity outcomes.
Marine Conservation
Marine protected areas: size-diversity relationships guide reserve design.
Invasion Biology
Islands and fragments are more vulnerable to invasions due to depauperate native communities.
Landscape Ecology
SLOSS debate (Single Large Or Several Small reserves) centers on island biogeography principles.
Common Mistakes to Avoid
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z varies by taxon and geography
Oceanic islands: z typically 0.25-0.35. Continental fragments: z = 0.10-0.25. Arthropods have lower z than vertebrates.
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C and z must be from relevant data
Parameters from Caribbean lizards cannot be applied to European birds. Must use data from the same taxon and biogeographic region.
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S-A relationship is log-linear
log(S) = log(C) + z*log(A). Plot log(species) vs log(area) to find C and z from your data.
Frequently Asked Questions
What is island biogeography theory? ▾
MacArthur & Wilson (1967): species richness on islands is an equilibrium between immigration (from mainland) and extinction (on island). Larger islands: lower extinction; closer islands: higher immigration.
What is the species-area relationship? ▾
S = C*A^z. Species richness (S) increases with island area (A). C is taxon-specific intercept. z is slope (usually 0.25-0.35 for oceanic islands).
What does z represent? ▾
The slope of log(S) vs log(A). z = 0.25: doubling area increases species by 19%. z = 0.30: 23% increase. Higher z = steeper species-area curve.
How is this applied to habitat fragments? ▾
Habitat fragmentation creates islands of habitat in a matrix. Predicts species loss from reserve size reduction. Used to evaluate minimum viable reserve size.
What is the rescue effect? ▾
Immigration from nearby populations reduces local extinction probability. Islands close to mainland have rescue effect -- immigration prevents extinction of rare populations. Supports corridor conservation.