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Biodiversity Explorer

Explore island biogeography theory, species-area relationships, habitat fragmentation, and biodiversity indices. Adjust island size, distance, and fragmentation to see how they affect species richness and ecological equilibrium.

Parameters

Island Area100 km\u00B2
Distance from Mainland50 km
Mainland Species Pool200

Results

S^=P⋅Imax⁡e−d/d0Imax⁡e−d/d0+Emax⁡/A\hat{S} = P \cdot \frac{I_{\max} e^{-d/d_0}}{I_{\max} e^{-d/d_0} + E_{\max}/\sqrt{A}}
Equilibrium Species
177
Turnover Rate at Eq.
0.0886
Max Immigration Rate
0.7788
Max Extinction Rate
0.1000
Mainland Pool (P)
200
Fraction of Mainland
88.6 %

Immigration & Extinction Rate Curves

ImmigrationExtinctionEquilibrium

Reference Guide

Island Biogeography Theory

MacArthur and Wilson's equilibrium theory (1967) predicts that the number of species on an island is determined by a balance between immigration from the mainland and local extinction.

Immigration decreases as species accumulate
I(S)=Imax⁡⋅(1−SP)⋅e−d/d0I(S) = I_{\max} \cdot \left(1 - \frac{S}{P}\right) \cdot e^{-d/d_0}
Extinction increases with more species
E(S)=Emax⁡⋅SP⋅1AE(S) = E_{\max} \cdot \frac{S}{P} \cdot \frac{1}{\sqrt{A}}

Equilibrium species count occurs where the two curves cross. Larger, nearer islands support more species because immigration is higher and extinction is lower.

Species-Area Relationship

One of the most consistent patterns in ecology. Species richness increases with area following a power law, appearing as a straight line on a log-log plot.

Power law
S=c⋅AzS = c \cdot A^{z}
Log-linear form
log⁡S=log⁡c+z⋅log⁡A\log S = \log c + z \cdot \log A

The exponent z typically ranges from 0.15 to 0.35. Island biotas tend toward z = 0.25, while continental samples give z = 0.15. The constant c depends on taxonomic group and region.

Diversity Indices

Biodiversity is measured in two dimensions. Richness counts how many species are present. Evenness measures how equally individuals are distributed among those species.

Shannon-Wiener Index
H′=−∑i=1Spiln⁡(pi)H' = -\sum_{i=1}^{S} p_i \ln(p_i)
Simpson's Diversity Index
D=1−∑ni(ni−1)N(N−1)D = 1 - \frac{\sum n_i(n_i - 1)}{N(N - 1)}
Pielou's Evenness
J=H′ln⁡SJ = \frac{H'}{\ln S}

Habitat Fragmentation & Corridors

When continuous habitat is broken into smaller patches, each fragment behaves like a small island. Edge effects degrade habitat quality near boundaries, reducing the effective interior area available to species.

Edge-to-area ratio increases with fragmentation
Edge ratio=2nπAA=2nπA\text{Edge ratio} = \frac{2\sqrt{n\pi A}}{A} = \frac{2\sqrt{n\pi}}{\sqrt{A}}

Wildlife corridors connect fragments, allowing species to move between patches. This partially restores the effective habitat area and reduces the isolation effect, increasing biodiversity relative to unconnected fragments.

Conservation strategies apply island biogeography: prefer one large reserve over several small ones (SLOSS debate), and connect fragments with corridors where possible.