The species-area relationship and why diversity matters

Bigger places have more species

Count the plants in one square metre of a field. Then count them in 10 square metres, and in a whole hectare. The count grows. But does it grow in the same way each time?

The German naturalist Alexander von Humboldt studied this. He found that, within a region, the species richness increases with the area that is explored. It increases only up to a limit.

The equation

When the species richness $S$ is plotted against the area $A$, the graph is a curve that rises steeply at first and then flattens. NCERT calls it a rectangular hyperbola. On a logarithmic scale the graph becomes a straight line. The equation of this line is

Here $S$ is the species richness and $A$ is the area. $Z$ is the slope of the line, which is also the regression coefficient. $C$ is the Y-intercept. If you take the numbers back from the logs, the same law reads $S = C A^{Z}$.

The graph above is drawn from model data. The numbers were made up for practice. They are not measurements of a real forest.

You should find that the curve flattens when Z is small, so a doubled area gives only a few more species.

The value of Z

Ecologists have found something interesting. The slope Z is in the range 0.1 to 0.2, whatever the group of organisms and whatever the region. NCERT names British birds, Californian plants and New York molluscs as examples.

The slope is much steeper when you look at very large areas, such as entire continents. Then Z is in the range 0.6 to 1.2. For the fruit eating birds and mammals of the tropical forests of different continents, the slope is about 1.15.

What the relationship tells us

If Z is 0.19, doubling the area multiplies the species by $2^{0.19}$, which is about 1.14. So the richness grows by only about 14 per cent. But cutting a forest down to a tenth leaves $0.1^{0.19}$, about 64 per cent of the species. So the loss of area costs species. This is one reason why the destruction of habitats is so harmful. The next course returns to this.

Try it in Python

The program fits the line to a table of model data. It uses the logs of the area and of the species, and finds Z and C.

The fitting by a program is for practice. NEET asks the equation, the meaning of Z, and the two ranges.

Why species diversity matters to an ecosystem

Is it only a matter of numbers? Does an ecosystem with more species work better? NCERT says that it does, and it gives two ideas.

• Stability and productivity. The ecologist David Tilman studied plots in the field for many years. The plots with more species showed less year to year variation in the total biomass. They also had a higher productivity.
• The rivet popper hypothesis. The ecologist Paul Ehrlich compared the species of an ecosystem to the rivets in the wing of an aeroplane. If a few rivets are lost, the plane still flies. But as more rivets are lost, the wing gets weak. And the loss of a key rivet may be a disaster.

A loss of biodiversity in a region may have three results. Plant production may decline. The resistance to troubles such as drought may fall. The working of the ecosystem may vary more, for example in water use and in the cycles of pests and diseases.

Practise with new numbers

Common mistakes

• Writing that the graph of S against A is a straight line. It is a curve. It is the log graph that is straight.
• Reading Z as a count of species. Z is a slope. It has no unit.
• Using the continent range for a region. Regions have Z of 0.1 to 0.2. Whole continents have 0.6 to 1.2.
• Thinking that Tilman found that many species lower the productivity. He found that more species gave a higher and a steadier productivity.

Remember these

• Humboldt: species richness rises with area, up to a limit. The graph is a rectangular hyperbola.
• $\log S = \log C + Z \log A$. $Z$ is the slope and $C$ is the intercept. Same as $S = C A^{Z}$.
• Regions: $Z$ is 0.1 to 0.2. Continents: $Z$ is 0.6 to 1.2, and 1.15 for the fruit eating birds and mammals of tropical forests.
• Tilman: more species give a steadier and higher productivity. Ehrlich: the rivet popper hypothesis.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. In $\log S = \log C + Z \log A$, which symbol is the slope and which is the intercept?

2. What is the usual range of Z for regions, and what is it for whole continents?

3. A region has $C = 7$ and $Z = 0.2$. How many species does it have in $1000$ square kilometres?

4. What did David Tilman find in his plots?

5. Explain the rivet popper hypothesis in one sentence.

References

• NCERT (2023). Biology, Textbook for Class XII, chapter 13, Biodiversity and Conservation, sections on the species-area relationships and on the importance of species diversity.
• OpenStax Biology 2e (2018), chapter 47, Conservation Biology and Biodiversity, section on the importance of biodiversity.
• Campbell Biology, 12th edition (2021), Pearson, chapter 54, Community Ecology, section on species-area curves.