Mathematical group's calculations can plot the path of Sars, smoke or seedlings

By SIMON COLLINS, science reporter

A group that used mathematics to predict the spread of diseases such as Sars and smallpox is now trying to stop unwanted pine trees spreading across prime New Zealand farmland.

The expert mathematicians group, led by Professor Graeme Wake at Massey University's Albany campus, has developed a mathematical model for the spread of pine seedlings in Canterbury based on wind directions, the local landscape and the weight of seed dispersed from each tree.

Environment Canterbury ecologist Dr Philip Grove said the pine seedlings model confirmed his intuition that the best way to stop pines spreading was to eradicate the youngest and most distant seedlings first.

"The pine forests are spread all over the region," he said.

"A lot were put in by the old Electricity Department around lakes such as Tekapo. There are pine forests at Hanmer, and there was erosion control planting in the 1950s and 1960s."

He said Canterbury's high country had 60,000ha of unwanted trees which were a potential threat to up to a million hectares - "a quarter to a third of the region".

The seedlings problem was one of six presented in January to a transtasman "mathematics in industry" study group which has met in Australian state capitals for the past 20 years.

It met in New Zealand this year for the first time, and will stay at Albany for the next two years.

Associate Professor Mick Roberts, a former AgResearch mathematician hired by Massey last year, said it was "a purely logical exercise" to turn the seedlings problem into mathematical equations.

"You ask how many seeds does a conifer produce a day, then you have to count where they go to and where they land," he said.

"You have to look at how they spread, which is down to what is going to blow them.

"The problem of spreading seeds is very similar to the problem that someone is working on here on the spreading of volcanic ash, and you have other people working on dirt coming out of a factory chimney."

The spread depended on the size of the particles, the direction of the wind and the local landscape.

Near Lake Coleridge in Canterbury, for instance, Mt Barker acted as a launching ramp for pine seeds, releasing them 200 metres above the surrounding land.

"The mathematical model will give you a general set of guidelines such as 'If the seeds have these dimensions, then 50 per cent of them will go no further than this and 75 per cent will go no further than that'," Dr Roberts said.

"Then if you say, okay, look at this particular valley or this particular clump of trees, then you have to take those same equations but tailor them into a much more complicated model, for which you'd have to use a computer."

Dr Roberts, who worked at AgResearch on the spread of tuberculosis in possums, was asked first by New Zealand's Health Ministry and then by the World Health Organisation to model the potential spread of Sars when the disease broke out in Asia last year.

"I could produce a model quickly because I was working on one for the Ministry of Health on smallpox - what would happen if that got into the country," he said.

The main conclusion for Sars and smallpox was that anyone showing possible symptoms of the disease should be isolated immediately.

Sars victims showed symptoms after about four days, but were infectious for up to two weeks.

"If you isolate them within a day or two [of showing symptoms], then you have prevented about two-thirds of the infection they were going to pass on," he said.

"The object is to make sure a person infects an average of less than one other person, because then the numbers infected will gradually drop.

Massey's Centre for Mathematics in Industry is seeking new problems for January's study group.

How they use it

The mathematical model can track the spread of:

* Pine tree seedlings across farmland.

* Volcanic ash from an eruption.

* Dirt from a factory chimney.