Island Biogeography Simulator: MacArthur-Wilson Equilibrium Model

simulator intermediate ~10 min
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~47 species at equilibrium on a 100 km² island 50 km from mainland

A 100 km² island 50 km from the mainland reaches equilibrium at approximately 47 species, where the declining immigration curve meets the rising extinction curve. This dynamic equilibrium involves constant species turnover.

Formula

S_eq = P * i / (i + e * d / A^z)
Immigration rate: I(S) = i * (P - S) / P * exp(-d/d0)
Extinction rate: E(S) = e * S / A^z

The MacArthur-Wilson Theory

In 1967, Robert MacArthur and E.O. Wilson proposed one of ecology's most elegant theories: the number of species on an island is determined by a dynamic equilibrium between immigration from the mainland and local extinction. This theory transformed how ecologists think about biodiversity, applying not just to oceanic islands but to any isolated habitat — forest fragments, mountain tops, or lake patches.

Immigration and Extinction Curves

The immigration rate decreases as more species colonize the island (fewer mainland species remain to arrive), while the extinction rate increases with species count (more species means more competition and smaller populations). Where these curves cross defines the equilibrium species number. The key insight is that this equilibrium is dynamic — species constantly turn over even as the total number remains roughly stable.

Area and Distance Effects

Two primary factors control island diversity. Area affects extinction: larger islands provide more habitats, support larger populations, and buffer against stochastic extinction. Distance affects immigration: remote islands receive fewer colonists. This creates a predictive framework: large, near islands are species-rich; small, remote islands are species-poor. The theory correctly predicted species counts on islands worldwide.

From Islands to Conservation

The theory revolutionized conservation biology. Habitat fragments act as ecological islands, and their species richness follows the same area-distance rules. This has profound implications for reserve design: a single large reserve preserves more species than several small ones of equal total area (the SLOSS debate). Understanding these dynamics is essential for managing biodiversity in an increasingly fragmented world.

FAQ

What is the theory of island biogeography?

Proposed by MacArthur and Wilson in 1967, the theory predicts that island species richness reaches a dynamic equilibrium where the rate of new species immigrating equals the rate of resident species going extinct. Larger, closer islands support more species.

How does island area affect species richness?

Larger islands support more species because they offer more habitats, larger population sizes (reducing extinction risk), and a bigger target for colonizers. The species-area relationship follows S = cA^z, where z is typically 0.2-0.35.

Why does distance from the mainland matter?

Distance reduces immigration rates because fewer organisms can disperse across larger water gaps. Remote islands like Hawaii have fewer species but higher endemism because successful colonizers evolve in isolation.

What is species turnover on islands?

Even at equilibrium, species composition changes continuously. New species arrive while others go extinct, maintaining a roughly constant total but shifting identity. This turnover rate is highest on small, near islands.

Sources

Embed

<iframe src="https://homo-deus.com/lab/ecology/island-biogeography/embed" width="100%" height="400" frameborder="0"></iframe>
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