Biogeography

Humboldt explained where plants grow by climate. He could not explain why places with the same climate hold different species. Why are there no bears in Australia and no kangaroos in Africa, when both have grassland and forest? Charles Darwin gave the answer in On the Origin of Species (1859). Species live where their ancestors lived, or where they could spread to. Distribution is a record of history as much as of climate.

Alfred Russel Wallace made that record visible. Collecting in the Malay Archipelago between 1854 and 1862, he found that the birds of Bali were Asian, while those of Lombok, across a narrow strait, were largely Australian: cockatoos and honeyeaters instead of barbets and woodpeckers. He traced a boundary through the islands that follows deep water. When sea level fell in the ice ages, the islands west of it joined Asia and those east of it joined Australia, but the gap between them never closed. Thomas Huxley named it the Wallace Line. In 1876 Wallace divided the whole world into zoological regions, and his map, with small changes, is still in use.

Some patterns defied every explanation. The same fossil reptiles and seed ferns turned up in South America, Africa, India and Antarctica. Biologists invented land bridges that had since sunk. Alfred Wegener proposed instead, in 1915, that the continents themselves had moved. Geologists rejected the idea for half a century, until the discovery of sea-floor spreading in the 1960s made plate tectonics the consensus. Many distributions that had puzzled Darwin turned out to be the pieces of a broken supercontinent.

Islands had always fascinated biogeographers, because they are natural experiments. Naturalists had long noticed that larger islands hold more species. The Swedish scientist Olof Arrhenius showed in 1921 that the number of species grows as a power of the area, and in 1962 the engineer turned ecologist Frank Preston found the same law across the world's archipelagos.

In 1963 Robert MacArthur, a mathematically minded ecologist, and Edward O. Wilson, an expert on ants, explained why. Imagine an island near a mainland that holds a pool of species. Species arrive by flying, swimming or rafting, and the rate of arrival falls as the island fills, because most arrivals are already present. Species also die out, and the rate of extinction rises as the island fills, because each population is squeezed smaller. Where the two curves cross, the number of species settles. A large island has lower extinction, and a near island has higher immigration, so both hold more species. The species themselves keep changing, even when their number is steady.

The theory predicted something testable: turnover. Daniel Simberloff, Wilson's student, tested it. In 1966 he had tents raised over tiny mangrove islets in the Florida Keys and fumigated them, killing every insect and spider. Over the following year he counted the arrivals. The islets filled back up to about their old numbers, and then species kept coming and going. The theory held.

The species–area law is usually written

$$S = c\,A^{z},$$

where $S$ is the number of species, $A$ is the area, and $c$ and $z$ are constants for a given group of organisms and region. The constant $c$ sets the scale. The exponent $z$ says how fast species accumulate with area. For isolated islands it is typically between 0.25 and 0.35. The zoologist Philip Darlington summed up the rule of thumb for Caribbean reptiles and amphibians: ten times the area, twice the species.

That rule is just $z = 0.3$, because

$$10^{0.3} \approx 1.995 .$$

Take $c = 5$ and $z = 0.3$, with area in square kilometres:

Island area (km²)	Predicted species
10	10.0
100	19.9
1,000	39.7
10,000	79.2
100,000	158.1

Each row is ten times larger than the last and holds almost exactly twice as many species. A thousandfold difference in area yields only an eightfold difference in species.

The law also works in reverse, and this is why it matters to conservation. Suppose a forest is cut down until only a tenth of it remains, and treat the remnant as an island. The fraction of species that the remnant can hold is

$$\frac{S_{\text{new}}}{S_{\text{old}}} = \left(\frac{A_{\text{new}}}{A_{\text{old}}}\right)^{z} = 0.1^{0.3} \approx 0.50 .$$

Losing 90% of the habitat eventually costs about half of the species. Losing half the habitat costs about 19% ($0.5^{0.3} \approx 0.81$). Within a continuous mainland, where $z$ is nearer 0.15, the same 90% loss costs about 29%. The losses are not immediate. Populations in the remnant can linger for decades before dying out, a delay ecologists call extinction debt. Estimates of this kind, and arguments about how reliable they are, sit at the centre of conservation biology.

Biogeography asked where species live. Answering it raised a second question: how many individuals of each species a place can support, and what makes those numbers rise and fall. That question belongs to population ecology, which grew up alongside the mathematics of differential equations.

The largest pattern on Humboldt's map is still unexplained. Species are packed most densely in the tropics and thin out towards the poles, in almost every group of living things. Why is still argued, more than two centuries after he first noticed it.