Equations for biological invasions: Mathematician takes on the emerald ash borer

Posted on Wednesday, May 3, 2017

Frithjof Lutscher, professor at the University of Ottawa’s Department of Mathematics and Statistics, in front of a dead tree covered in equations

Photo credit: Dave Weatherall, University of Ottawa

Damage caused by the emerald ash borer, a highly destructive beetle native to Asia, is visible across several U.S. states and large parts of Quebec and Ontario. The insect, first detected in Canada in 2002, typically kills 99% of ash trees in a given area within six years and has caused the destruction of tens of millions of trees. Its spread has also resulted in hefty bills for the treatment or removal of countless ash trees.

As chainsaws slice through dead logs, governments are trying ways to stop the pest in its tracks, such as culling healthy trees and altering landscapes. Now, Frithjof Lutscher, a professor at the University of Ottawa’s Department of Mathematics and Statistics, has used math to investigate the effectiveness of such measures, and has discovered that some might actually be doing more harm than good.

In a study published in Ecology, Lutscher and former student Jeff Musgrave replaced some typical insect dispersal models, which disregard particular landscape features, with a more specific model that includes observations of movements of individual insects in response to forest edges and other features. They then explored how fast the emerald ash borer might spread across different landscape configurations.

They found that the biological invaders spread considerably faster in areas where trees are not uniform, even in landscapes with a lower overall density of trees, for example, due to government culls.

“We may think that the population of host trees, which act as a food source and breeding ground, is the most important driver of an insect’s invasion. But insects can adapt their behaviour according to tree availability and exploit their host trees much more efficiently. This explains why removing trees or other landscape alterations to slow the spread might be having the opposite effect,” explains Lutscher.

Lutscher and Musgrave’s new model is based on a “random-walk model,” relating the complex probabilities of individual insect dispersal to the landscape and applying the model to an entire insect population. It incorporates three observations on the emerald ash borer’s behaviour:

  • Faster movement in resource-poor areas
  • Lower ovipositioning, or laying of eggs, in resource-poor areas
  • Movement preference for resource-rich areas

When forest management experts decide on measures such as tree removal, stand thinning or increased biodiversity, they need to be aware of the insects’ ability to adjust their movement, and should avoid measures that insects can detect easily and adapt to. “The insects move more quickly between ash tree stands, but stay longer within these stands, and as a result, the overall invasion front moves faster. Our research shows that we need to study the small-scale movement behaviour of invading species to better target measures to stop their spread,” notes Lutscher.

About the emerald ash borer:

 Detected in Ontario, Quebec, and 21 U.S. states / Image of dead tree: Kills trees in 1 to 4 years / Image of piggy bank: cost for treatment, removal and replacement of trees could reach $2 billion over 30 years

       Infographic data: Natural Resources Canada

Read the study in Ecology

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