Island Biogeography

The equilibrium model

Picture two curves on the same axes. The horizontal axis is the number of species currently on the island, S. The vertical axis is a rate, in species per year.

The immigration curve starts high and slopes downward. When the island is empty, every species in the mainland pool is a potential new arrival. As S grows, fewer mainland species remain to colonize, and the per-year immigration rate falls. It hits zero when every mainland species has already arrived.

The extinction curve does the opposite. When the island is empty, no one can go extinct, so the rate is zero. As S grows, more species are at risk and competition tightens, so the per-year extinction rate climbs.

The two curves cross at one point. There the rate of arriving balances the rate of dying out, and S sits at equilibrium species richness, S*. The model is dynamic: at S* the identities of resident species keep turning over even though the count holds steady. Empirical turnover rates on small islands sit near 1 to 3 percent of species per year for birds.

Four corners of the model

Now shift the curves. Distance from the mainland scales the immigration curve up or down: a far island starts with the same intercept but every per-species rate is smaller, so the whole curve drops. Area scales the extinction curve: a big island has more habitat, lower density per species, and lower per-species extinction risk, so the curve drops too.

	Immigration rate	Extinction rate	Equilibrium S*	Example
Large & near	High	Low	Highest	Trinidad
Large & far	Low	Low	Medium-high	Madagascar
Small & near	High	High	Medium-low	Coronado Islands
Small & far	Low	High	Lowest	Easter Island

The four corners give a one-glance prediction. Bird counts on Indonesian islands (Diamond, 1972) sit on the predicted ranking; so do beetle counts on West Indies islands and reptile counts on California Channel islands.

The species-area equation

Plot the equilibrium count S* against island area A on log axes. The points fall on a line. That line is the empirical species-area law:

S = c · A^z

Or, taking logs, log S = log c + z · log A. The slope z and intercept c are fit per dataset. Across hundreds of studies:

• Oceanic islands (Hawaii, Galápagos, West Indies): z ≈ 0.20 – 0.35.
• Habitat fragments (forest patches in farmland): z ≈ 0.15 – 0.25.
• Mainland sample plots (nested quadrats): z ≈ 0.12 – 0.18.
• Habitat-island lakes and mountaintops: z ≈ 0.20 – 0.30.

The intuition: doubling area roughly multiplies species count by 2^z. With z = 0.25 that is a 19 percent gain. With z = 0.35 it is 27 percent. A 10× area increase gives 1.78× species at z = 0.25 — meaningful but sublinear.

Worked example: Galápagos

The Galápagos archipelago has sixteen named islands ranging from Daphne Minor (0.34 km²) to Isabela (4640 km²). Plant species counts span 7 (Daphne Minor) to 347 (Isabela). Fit the power law on log-log axes and you get z ≈ 0.33, c ≈ 28. The model predicts:

• Pinta, area 60 km² → S ≈ 28 · 60^0.33 ≈ 105 plant species. Observed: 119.
• Santa Cruz, area 986 km² → S ≈ 28 · 986^0.33 ≈ 270. Observed: 287.

The fit is rarely better than ±20 percent on individual islands because volcanism age, elevation range, and ash-fall history all add noise to a clean two-parameter law. The point is the regularity, not pinpoint prediction.

MacArthur-Wilson vs other diversity theories

	MacArthur-Wilson (1967)	Habitat heterogeneity	Hubbell neutral theory (2001)
Driver of richness	Immigration / extinction balance	Number of habitat types	Random drift in equivalent species
Role of area	Reduces extinction rate	More area → more habitats sampled	More area → more individuals, slower drift
Species identities	Interchangeable in the math	Tied to specific niches	Functionally identical
Predicts species-area curve	Yes (power law)	Yes (sampling effect)	Yes (zero-sum dynamics)
Predicts turnover	Yes — central feature	Weakly	Yes — drift-driven
Conservation use	Reserve area & spacing	Habitat-mosaic design	Background extinction estimates
Empirical fit	Good for fauna on true islands	Good for plants in heterogeneous land	Good for tropical forest plot data

The three are not mutually exclusive. Real systems blend all three: bigger islands sample more habitats, lose fewer species to drift, and lose fewer species to deterministic extinction. Modern biogeography fits hybrid models with area, isolation, elevation, and habitat-richness all as predictors.

The empirical case

• Krakatau recolonization (1883–present). The 1883 eruption sterilized the Krakatau islands. Bird species count climbed from 0 to about 30 within fifty years, hovered near that ceiling for the next half century, and showed continuous identity turnover. Textbook validation of the equilibrium prediction.
• Simberloff & Wilson defaunation (1968–1969). Six tiny mangrove islands off the Florida Keys were tented, fumigated to remove every arthropod, then watched. Species counts returned within 6 to 12 months; species lists kept rotating for years. The cleanest experimental confirmation of dynamic equilibrium ever run.
• Hawaiian honeycreepers. One ancestral finch radiated into more than 50 species across the Hawaiian chain, far exceeding immigration-extinction prediction. The discrepancy spotlighted in-situ speciation as a third process MacArthur-Wilson did not capture.
• African elephant range fragmentation. As savanna fragments shrink, elephant counts fall along a species-area curve with z ≈ 0.20; extinction debt models predict further losses from already-completed fragmentation.

Conservation lessons

Reserve design draws four canonical rules from MacArthur-Wilson: bigger reserves lose species more slowly; reserves close to source populations gain more; round shapes minimize edge effects; and shrinking habitat creates extinction debt that pays out over decades as the population converges to the lower S* the species-area law predicts.

Diagram sketch

The canonical figure has three panels.

• Panel A. Two curves on (S, rate) axes. Immigration drops from a left-axis maximum to zero at S = pool size; extinction rises from zero to a right-axis maximum. They cross at S*.
• Panel B. Four pairs of curves shifted by area and distance, marking S*_large-near > S*_large-far > S*_small-near > S*_small-far.
• Panel C. Log S vs log A scatter with a fitted line of slope z. Galápagos plant data sit cleanly on it.

Pitfalls and modern critiques

• Habitat heterogeneity is not in the model. Two islands of the same area but different habitat counts will host different species totals; treating them as equivalent is the model's biggest omission.
• Speciation is missing. On young, isolated archipelagos like Hawaii or the Canaries, in-situ adaptive radiation generates more species than immigration. The original 1967 model assumes a fixed mainland pool.
• Mainland is not always a reservoir. Some "islands" are habitat fragments embedded in a hostile but porous matrix. Source-sink dynamics and metapopulation theory often fit better.
• Overfit to neutral assumptions. Hubbell's neutral theory reproduces the species-area curve from drift alone, undermining the claim that immigration-extinction balance is the unique cause. Distinguishing the two requires fine-grained turnover data.
• z is not a constant. z varies with taxon, latitude, and sampling scheme. A literature average is not a forecast for your study system.

Variants and extensions

• Target area effect. Big islands also catch more migrants per unit area because they are easier to hit. Adds a small upward bias to the immigration curve for large islands.
• Rescue effect. Frequent immigrants top up dwindling populations before extinction completes, so islands close to the mainland have lower extinction rates than area alone predicts. Brown and Kodric-Brown 1977.
• General Dynamic Model (Whittaker et al., 2008). Adds island age and ontogeny — young islands gain habitat as they grow, then erode and lose it. Predicts a hump-shaped diversity-vs-age curve seen on volcanic chains.
• Habitat-island metapopulation. Levins' patch-occupancy framework recasts MacArthur-Wilson at the species level — each species is a metapopulation across patches.