Island Biogeography

Empty a small mangrove island of every insect, spider and mite, and in one Florida Keys experiment most such islands held about as many arthropod species as untreated islands within roughly 250 days. The species on each island, though, were not all the ones present before treatment, and arrivals and extinctions continued.

That result is what a theory published in 1963 predicted. It treats the number of species on an island as a balance between two ongoing processes, so the count can be steady while its membership keeps turning over. This lesson builds the model, calculates its equilibrium, reads the experiment that tested it, and then asks what it can and cannot say about patches of habitat on land.

The idea: two curves and a crossing

Call the number of species living on an island its species richness, S. The species that could reach it, from a mainland or nearby islands, form the species pool, P species in all.

In 1963 Robert MacArthur and Edward O. Wilson proposed in the journal Evolution that S is set by two rates. Immigration, in their model, means the arrival of a species not already on the island. When the island is empty, every arriving species is new. As S rises, more arrivals belong to species already present, so the immigration rate falls, reaching zero when all P species are resident. Extinction here means local extinction, the disappearance of a species from that island. If each resident species has the same, independent chance of disappearing, the total extinction rate rises in proportion to S.

Think of a bath with the plug half out. The tap slows as the water rises and the drain runs faster, so the level settles where inflow equals outflow, even though the water itself keeps changing. In the model:

dS/dt = I(S) - E(S), and at equilibrium I(S) = E(S)**

The equilibrium richness S* is where the curves cross. It is stable: above S*, extinction exceeds immigration and richness falls; below it, immigration wins and richness rises. Two predictions follow. A more distant island receives fewer immigrants at every S, which lowers the immigration curve and S*. A smaller island loses species faster at every S, which raises the extinction curve and lowers S*. So near, large islands hold more species than far, small ones. A smaller pool also lowers S*. The 1963 paper added speciation on the island as a further source of species, which matters on large, remote islands and not on the small ones below. MacArthur and Wilson developed the theory at book length in The Theory of Island Biogeography in 1967.

This is a model: it says what follows if its assumptions hold. Real species do not have equal extinction chances, and residents can change one another’s chances, so real curves need not be straight lines.

Worked problem. These numbers are invented teaching inputs, not estimates for any real island. An island draws on a pool of P = 100 species. Immigration is I(S) = 10(1 - S/100) species per day and extinction is E(S) = 0.1S species per day. Assume continuous, deterministic change, constant coefficients, no speciation, and an empty island at time zero.

1. Equilibrium. dS/dt = 10 - 0.1S - 0.1S = 10 - 0.2S. Setting this to zero gives S = 50 species*.
2. Turnover. At S = 50, I = 10 x 0.5 = 5 species per day and E = 0.1 x 50 = 5 species per day. Net change is zero, yet about 5 species are replaced each day (10 events per day if you count gains and losses separately).
3. Approach. Solving the equation from S = 0 gives S(t) = 50(1 - e^(-0.2t)). Richness reaches 90% of S*, 45 species, when e^(-0.2t) = 0.1, so t = ln 10 / 0.2 = 11.5 days. Check: at S = 45, I = 5.5 and E = 4.5 species per day, so richness is still rising by 1 species per day.

immigration I(S) = I₀(1 − S/100) extinction E(S) = eS

Immigration at S = 0, I₀ 10 species per day (lower for a more distant island) Extinction per species, e 0.10 per day (higher for a smaller island)

Resample a random run

Inset: richness S filling from an empty island (day 0)

S(t) = S*(1 − e^−kt), k = I₀/100 + e one random run

Equilibrium S* (I = E)

Turnover at S*

Richness reaches 90% of S*

Net change at that richness

Expected (deterministic curve) beside simulated

Quantity	Expected	Simulated (this run)

In this sketch: the curves assume continuous, deterministic change; the random run adds chance. Constant coefficients, no speciation, an empty island at day 0, pool P = 100 species; the numbers are invented teaching inputs, not estimates for any real island. In the random run each absent species arrives at the same rate I₀/100 per day and each resident goes extinct at rate e per day, independently.

Rule to keep: richness settles where immigration equals extinction, and at that point species are still arriving and leaving at the turnover rate.

Testing it: emptying islands in the Florida Keys

The model is about rates, but natural islands were colonised long ago and cannot be watched filling. Daniel Simberloff and Wilson chose islands small enough to empty: six small islands of red mangrove, Rhizophora mangle, in the Florida Keys, each supporting a community of terrestrial arthropods (insects, spiders, mites and their relatives). They censused each island’s arthropods, removed them by fumigation with methyl bromide, and censused the islands repeatedly for a year. The full report appeared in Ecology in 1969.

By day 250, all the experimental islands except E1, the most distant, had species numbers similar to those of untreated islands. Population densities, however, were still abnormally low, so richness recovered before the communities were demographically normal. The authors inferred that most arrivals came through the air, by flight or carried on the wind. They also considered physical causes important in the extinctions of early colonists, so not every loss can be read as one species excluding another. Treatment had its own side effects: on island E7, fumigation killed 85% of the mangrove tree.

A second report, in 1970, followed four islands to the end of the second year. Species numbers had changed little from the year before, while immigrations and extinctions continued at high rates. That combination, steady count with continuing replacement, is what the model calls a dynamic equilibrium.

The rates themselves were hard to measure. Most observed immigration and extinction rates lay between 0.05 and 0.50 species per day, while a simple noninteractive model predicted about 0.1 to 1.0. Censuses were intermittent, and a species that arrived and vanished between two visits left no record, so the observed rates undercount the events.

Simberloff then tested area directly. In a study published in 1976 he censused eight mangrove islands, removed sections to reduce their area, and censused them again. Richness tracked island area independently of habitat diversity in that system, though the sample was too small to test whether smaller islands also turn over faster.

Same number, different species

Richness is a count; it does not say which species are present. To compare identity, use the Jaccard similarity: the number of species two lists share, divided by the number of species found in either list.

Worked problem, continued. The 1969 appendix records, for each island and census, whether each species was seen, inferred present or inferred absent. Take three mite taxa from island E9, chosen because their records before treatment and on day 364 are unambiguous. Bdella sp. was present before and on day 364. Carpoglyphus lactis was absent before and present on day 364. Amblyseius sp. was present before and absent on day 364.

4. Richness and identity. Before: Bdella and Amblyseius, 2 taxa. Day 364: Bdella and Carpoglyphus, 2 taxa. Shared: 1. Found in either list: 3. Jaccard similarity = 1/3, or about 0.33. Richness is unchanged, while two of the three taxa differ.

Read this subset carefully. It is a selection, not the whole community and not a random sample. Bdella being present at both censuses does not mean it survived fumigation; it was recorded again after recolonisation. And you cannot divide these changes by 364 days and call the result the island’s turnover rate, because other arrivals and losses between censuses are not counted here.

The broader point carries to any community: a stable richness can hide a changing membership. For more on comparing communities by identity rather than count, see diversity and succession.

Fragments, area and connectivity on land

A forest remnant surrounded by farmland looks like an island, and the species-area pattern is often summarised as S = cA^z, where A is area and c and z are fitted constants. The exponent z varies among taxa and sets of islands, so treat any single value as illustrative.

Worked problem, continued. Take z = 0.25 as an illustrative value.

5. Habitat loss. A habitat holding 50 species is cut from 100 to 10 km^2. Richness is multiplied by (10/100)^0.25 = 10^(-0.25) = 0.56, so the expected richness falls toward about 50 x 0.56 = 28 species. This is the expected long-run value after relaxation, the slow loss of species that a smaller area can no longer hold, not an immediate loss on the day the habitat is cut.

Fragments are not true islands. The surrounding land, the matrix, is not open sea: some species live in it, some cross it readily and some cannot cross it at all. That ties the model to the metapopulation view, in which a metapopulation is a set of local populations linked by dispersal, each subject to local extinction and recolonisation.

Experiments show that rates move before counts do. In calcareous grasslands in the Swiss Jura, Jasmin Joshi and colleagues isolated patches of 0.25 to 20.25 square metres by mowing around them from 1993 to 1999. Plant colonisation was 30% lower than in unisolated controls of the same sizes, yet after seven years the isolated patches had only marginally fewer species.

Connectivity has been tested over a longer span. In an experiment in longleaf pine savanna habitat reported by Ellen Damschen and colleagues in Science in 2019, patches joined by corridors had annual colonisation about 5% higher and annual extinction about 2% lower than unconnected patches across 239 plant species. After almost two decades, connected patches held nearly 14% more species, and richness was still rising. A study that stopped after five years would have seen much less of the effect. For how these results enter reserve planning, see conservation.

Design problem

A planner must choose between one 100 ha reserve and four 25 ha reserves, or decide whether to link existing patches with corridors. Design a study that tests whether connection itself changes the species found in patches.

One way to do it

Island biogeography alone does not settle the reserve choice: one large reserve may hold more area-sensitive species, while several small ones may sample more habitat types and spread the risk of a local disaster. So test the mechanism.

1. Replicate equal-area patches in the same kind of habitat and matrix, and assign them at random to connected or unconnected treatments.
2. Control for the corridor’s own area. A corridor adds habitat and edge. Give unconnected patches dead-end side strips of the same area, as some of the unconnected control patches in the longleaf pine savanna experiment had, so that a difference can be attributed to connection.
3. Census species identity repeatedly, at a fixed effort and season, for many years. Record which species are present as well as how many.
4. Estimate colonisation and local extinction separately, from changes in each species’ presence between censuses, and say how many events between visits you could have missed.
5. Report both richness and composition (for example Jaccard similarity to a reference patch), and expect the effect to keep growing: the 2019 experiment found connected patches nearly 14% richer after almost two decades, still without a plateau.

The result applies to that habitat, matrix and set of species. Whether it transfers to a different matrix or to animals with other dispersal modes is a separate question to test.