# Maths in the desert

Desertification is threatening 250 million people worldwide. Ecologists have tried to predict the spread of deserts. Help is now at hand from an unexpected source: mathematicians.

Since the Second World War, more than 1.2 billion hectares of fertile land has turned to barren desert, according to figures from the United Nations. The greenhouse effect means that these arid regions will become even drier in the coming years.

### Rain and grazing

Researchers have been trying for decades to devise models that will help them predict future developments in desertification. They do this by analysing the factors that cause deserts to form, such as less rainfall and over-grazing of agricultural land.

### Complexity

One problem here is that not all ecologists are skilled mathematicians. Nonetheless, maths can provide possible solutions. For instance, clever calculations can be used to better predict how deserts form. Utrecht ecologists and Leiden mathematicians have been working together for a number of years on joint research on this issue. The research is financed from the NWO Complexity programme, that stimulates research on complex systems and processes.

### Vegetation patterns

Maths PhD candidate Eric Siero has been conducting research in Leiden and will defend his PhD dissertation on this subject on 9 February. He has been studying desertification using differential equations of vegetation patterns.

### Point of no return

The challenge is to find the critical limit, the point of no return after which the fertile soil changes irrevocably into desert. Siero and his colleagues deduce from the vegetation in a region whether that point of no return has been reached. They have now determined that there are two stages between full vegetation and barren desert.

### Tufts of greenery

Siero: ‘Without rainfall, the vegetation on a slope will change first into a pattern of stripes, with bands of vegetation that run vertically in line with the slope. That's no great problem; nature simply adapts to the reduced rainfall. But once that pattern of stripes is interrupted, and there are only a few tufts of greenery left, you are well on the way to a barren desert.’

### Sheep quota

Once that critical point has been reached, there are measures you can take. Even so, it's not easy. Siero: ‘You can't change the amount of rainfall, so I see the solution more in limiting the amount of grazing. For vulnerable areas that could mean imposing a quota on sheep, goats and cattle, limiting the numbers to an agreed maximum.'