Defending crops with maths

The world faces a potential food crisis in the coming decades as the population grows inexorably and as climate-related changes intensify pressures on food production. Given that the most productive land is already being used around the globe, simply increasing crop production is not the answer. One way to safeguard food security is to increase the yield of crops from the same amount of land and also to minimise the amount lost to pests and pathogens – the so-called untaken harvest.

Moreover, outbreaks of disease can sometimes reach epidemic proportions, wiping out entire crops, often with substantial social and economic consequences. Today, epidemics such as cassava mosaic disease, citrus canker, sugar beet rhizomania and a particularly alarming new wheat pathogen, Ug99, threaten important agricultural and food crops in regions across the globe.

‘Each year, despite remarkable improvements in crop-protection strategies such as breeding disease resistance, a quarter of the global crop production is still lost in the untaken harvest, and plant pandemics are a constant threat,’ explains Professor Chris Gilligan of the Department of Plant Sciences. ‘One way to reduce these losses is to develop mathematical models that can help regulators, policy makers and growers to track disease and to develop surveillance and eradication strategies.’

This is precisely what Professor Gilligan, a Biotechnology and Biological Sciences Research Council (BBSRC) professorial fellow, and his team of mathematicians and statisticians have developed. Their mathematical toolkit not only provides a new way of predicting the associated risks and hazards but also, crucially, generates intelligence on the cost-effective management and control of that threat.

Uncertain behaviour

When the invasion and persistence of a disease reaches a level where it requires monitoring and controlling, working out where to look for it and how frequently, and then predicting what will happen and how best to control it, can be fraught with challenges.

Not only can the scale of an epidemic be hidden – for instance some infected plants might be symptom-free and yet transmit infection – but, as Gilligan explains, there is also an element of uncertainty: ‘Dealing with complicated systems that have a biological, economic and social component is inevitably challenging. In addition to this ‘noise’ is the potential for the disease to take what you might imagine to be an unlikely turn. The art of modelling is to identify as simple a model as possible that captures the inherent features of the system and then to use it to explore the certainties – and the uncertainties – in disease spread.’

As the Cambridge scientists have discovered, the secret has been to allow many possible scenarios to play out through the model. Bayesian methods of statistical inference are used to allow for uncertainty in understanding how an emerging epidemic spreads, and the model is then updated as new data become available. This allows the Cambridge group to predict the most likely future spread of disease based upon current knowledge.

Working in collaboration with the UK Department for Environment, Food and Rural Affairs and the United States Department of Agriculture, the Gilligan group has successfully integrated fundamental biological understanding of how certain diseases spread into epidemiological models that incorporate data from geographic information systems about landscape and weather. The result is a toolkit that enables end-users to identify the risks and hazards of disease detection, spread and control.

Balancing detection and eradication

Any form of disease control involves costs and crucial decision making. Where mathematical modelling can help is to enable regulators to use resources strategically in the most effective way.

One recently published report from the team looked at Asiatic citrus canker, a bacterial disease of the economically important citrus crop of the USA, Brazil and Australia. Eradication attempts have already proved to be extremely costly – a decade-long attempt in Florida which began in 1995 cost in excess of $1 billion and led to the removal of millions of citrus trees.

The new results flagged up an important point that informs a political dilemma concerning the removal of diseased trees to eradicate the disease when the pathogen infects both residential and commercial trees. The two constituencies, home owners and growers, are linked by dispersal of the pathogen, and what happens in one constituency affects the other. Hence, an eradication effort must be co-ordinated in both areas.

‘It is precisely this type of intelligence about disease dynamics that is so important for regulatory bodies to be aware of,’ explains Gilligan. ‘With this knowledge, it would be possible to choose a control strategy that satisfies the objectives of both commercial and residential citrus tree owners.’

Often the recommendations of the models are counter-intuitive. ‘Contrary to expectations, for some diseases, the best strategy is to operate an intermediate level of detection rather than a high level of vigilance,’ he says. ‘In fact, even

a slight change in the balance between the resources allocated to detection and those allocated to control may lead to drastic inefficiencies in control strategies.’

For some diseases, the best control method for an outbreak in two regions is to control the smaller outbreak first and then to concentrate on the larger one. ‘The common assumption would be to treat both at the same time but for some diseases this is the worst you can do – much better to concentrate resources on eradicating in the region with the lower infection,’ explains Gilligan. ‘The models allow us to identify where best to deploy control and where there would be wasted effort.’

As well as for studying plant pests and pathogens, the models have also been used to study the spread of pesticide resistance, and the transfer of genes from genetically modified crops to wild populations. And, because the underlying mathematics and epidemiological modelling are similar regardless of the disease, the toolkit can also be targeted towards the surveillance of human diseases and pandemics.

Communicating disease threats

A key aim of the research programme has been to develop a resource within which end-users can easily try out and simulate a range of control scenarios – juggling parameters such as how often surveys are conducted, how successful detection is, what level of eradication is aimed for, and which control strategy to use.

Professor Gilligan anticipates one particularly important use for the toolkit in the near future: ‘A new strain, Ug99, of stem rust, a wheat pathogen, emerged in Uganda in 1999 and has been spreading north, across the Red Sea and into the Middle East. We don’t yet know when it will arrive in major wheat-growing areas such as Europe and the Indian subcontinent, but we are at least five years away from having a wheat variety that can resist the pathogen. When the pathogen arrives, and it is very likely that it will, it could inflict severe shortages in wheat production costing billions of pounds. We need to be ready – and this means having the capability to detect, track and control the disease effectively.’

For more information, please contact Professor Chris Gilligan (cag1@cam.ac.uk) at the Department of Plant Sciences (www.plantsci.cam.ac.uk/).