Species-Area Relationship Simulator: Power Law of Biodiversity

simulator intermediate ~10 min
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~112 species predicted for a 1000 km² island with z=0.25, c=20

With z=0.25 and c=20, a 1000 km² island supports approximately 112 species. Halving the area to 500 km² reduces this to ~94 species — a 16% loss, not 50%, demonstrating the nonlinear species-area relationship.

Formula

S = c * A^z (species-area power law)
log(S) = log(c) + z * log(A)
Extinction debt: delta_S = S_old * (1 - (A_new/A_old)^z)

The Power Law of Biodiversity

The species-area relationship is one of the most fundamental patterns in ecology, first quantified by Olof Arrhenius in 1921. The observation is simple yet profound: larger areas contain more species, and this relationship follows a remarkably consistent power law across ecosystems worldwide. From tropical islands to temperate forests, from coral reefs to soil microbiomes, S = cA^z describes biodiversity with striking accuracy.

Understanding the Parameters

The exponent z controls the slope on a log-log plot and varies systematically by context. Oceanic islands typically show z = 0.25-0.35 because isolation limits recolonization after local extinction. Continental mainlands have lower z = 0.12-0.17 because species can recolonize from surrounding areas. Habitat fragments often have the highest z values because they combine isolation effects with edge effects and degraded habitat quality.

Extinction Debt and Habitat Loss

When habitat is destroyed, the species-area relationship predicts how many species will eventually be lost — but not immediately. This delayed extinction, called extinction debt, means that current species counts overestimate the long-term diversity that a fragmented habitat can support. Studies suggest that many tropical forest fragments carry substantial extinction debts that will play out over decades to centuries.

Conservation Implications

The nonlinear nature of the SAR has critical conservation implications. Because S = cA^z with z < 1, the first half of habitat destroyed causes less than half the species loss, creating a false sense of security. But as destruction continues, each additional hectare lost removes proportionally more species. This nonlinearity means that protecting the last remaining fragments of habitat is disproportionately valuable for biodiversity conservation.

FAQ

What is the species-area relationship?

The species-area relationship (SAR) is one of ecology's oldest and most robust patterns: larger areas contain more species. It follows a power law S = cA^z, where S is species count, A is area, c is a constant, and z typically ranges from 0.15 to 0.35.

What does the z-exponent mean?

The z-exponent controls how steeply species richness increases with area. Islands typically have z = 0.25-0.35, mainland regions z = 0.12-0.17, and habitat fragments z = 0.25-0.50. Higher z means species are more sensitive to area changes.

What is extinction debt?

Extinction debt is the future biodiversity loss that is committed by habitat destruction but hasn't yet occurred. Species persist temporarily after habitat loss because extinction takes time. The SAR predicts how many species will eventually be lost.

How is the SAR used in conservation?

Conservation biologists use the SAR to predict species loss from habitat destruction, estimate minimum reserve sizes, and prioritize areas for protection. If 90% of habitat is lost, the SAR predicts roughly 50% of species will eventually go extinct (with z=0.25).

Sources

Embed

<iframe src="https://homo-deus.com/lab/ecology/species-area/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub