Counting on squirrels for help

SOME of Scotland’s rarest species of wildlife could find themselves in debt to an unlikely saviour: mathematics. The discipline is being put to use in Heriot Watt University in Edinburgh to gain a more sophisticated understanding of animal populations than was ever possible before.

Already the research has proved that Scotland’s rare red squirrels are being wiped out not by their failure to compete for food with bigger grey squirrels but because of a disease carried by the greys.

Another researcher hopes to produce a mathematical model that will allow him to see what happens to animals if he alters their virtual environment drastically - in ways that would be inadvisable in real life.

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"Maths is a way of thinking about things that are too hard to think about," says one of the researchers, Professor Jonathan Sherratt. "History is full of people who tried to solve problems just through thought where the problems were just too complicated. Maths is a way of dealing with those problems."

Populations of anything, from animals to plants to people, are exceedingly difficult to model because of the large number of variables involved. Sherratt and his colleague Dr Andrew White are conducting separate research programmes to attempt to create rules that can be applied to more than one population of animal.

"We set up a model by writing down equations that represent the key biological issues involved in population changes," says Sherratt. "Then using data we can use a computer to simulate behaviour which we then study."

For his research, Sherratt chose groups of field voles that live in Kielder Forest in the Borders. "I studied these voles, not because they are highly important, but because there happens to be historical data on them going back years," he explains.

The computer modelling discovered that there are oddly cyclical peaks and troughs in the population of the voles and that, over time, groups of voles moved away from the side of a reservoir located in the forest. On the computer, Sherratt was able to remove the reservoir completely. The vole population became more ordered without the presence of the reservoir, a thesis that could never have been tested without the computer model.

Although useful, this kind of computer simulation is relatively simple.

Sherratt is hoping for a more elusive result, the beginnings of a model applicable to other animal populations: "The other thing we try and do is apply what I call ‘old-fashioned mathematics’ to it. We try to reduce the model and the equations down to their bare bones and understand on a fundamental level what is causing behaviour."

Using the Kielder Forest data, which spans several decades, Sherratt produced patterns that can now begin to be adapted for other populations: "We’re trying to do something difficult, to trim it down and really understand what we see. The aim is to develop more general tools. The hard part is the ideas, not the inputting of specific data."

White’s mission is perhaps more urgent. He is using similar models to investigate fluctuations and geographical patterns in the red squirrel population. Red squirrels are native to Britain but have become an endangered species since the introduction 100 years ago of the American grey squirrel, which is now more prevalent.

"People thought that it was just to do with diet and competition, that the smaller reds just didn’t compete as well for food," says White. "Then it became known that greys carry a disease that is only fatal to reds, but nobody thought it was a major cause of death. But our models did not make sense unless it was."

White’s figures made no sense without disease as a major factor in declining populations, and using simulations he plugged a gap in scientific understanding. Disease deaths were not being picked up in field observations because animals died quickly. Diseased reds died inside two weeks, says White, and would have been scavenged too quickly for bodies to be discovered in sufficient numbers to indicate the scale of the problem. A mathematical model has made the cause of plunging red numbers clearer than normal field biology could ever have.

White is now trying to work out how many refuges are needed for red squirrels and what action needs to be taken to protect them. "At the moment there is no real strategy behind refuges," he says.

The system can model animal movements between refuges and help conservationists find out where to place them.

The mathematicians are using simple ecological systems to develop tools that may one day be used for more complex population groups. What about the most complex group of all, humanity?

"Human populations are very complicated, uniquely complicated," says Sherratt.

"In certain cases, though, like the study of the spread of HIV, people are using models to see the effect of human behaviour."