Math may hold the key to eco-friendly pest control
edited by Brain Case
What happens when a sterilized fly mates with its female counterpart? Ideally—nothing, at least in terms of offspring.
Now imagine this on a much larger scale in nature. If sterilized male flies out-competed wild (and virile) flies in mating with wild females, it could cause an entire population to collapse. This is a theory behind the Sterile Insect Technique (SIT), which has been in development since the 1950s. It has been a passion of UVic alumnus Hugh Barclay (PhD Biology ’78), since the 1980s. He says SIT can be used to control the spread of pests that cause agricultural and health consequences.
The SIT method is an environmentally friendly, targeted form of pest control. The main disadvantage is that until recently it was deemed uneconomical. Today, the method is being effectively used to keep the Mediterranean fruit fly, a pest that destroys coffee crops, out of the United States and Mexico. This is accomplished through control programs being implemented in Guatemala through the “Moscamed” Program, a tri-national effort between the three nations.
The program involves dropping insects from airplanes. But effectiveness questions remain. When? Where? How many? And for how long?
In order for the Sterile Insect Technique program to be effective, another question needs to be answered—what is the optimal spacing and frequency of plane flight lines for airborne release of sterilized insects to maintain a uniform minimum coverage of steriles?
Dr. Barclay realized that he needed to enlist some more advanced mathematicians to answer this question, so he called upon UVic Emeritus Professor Pauline van den Driessche for help. She in turn knocked on Robert Steacy’s office door. He is a professor of Mathematics, and an expert in what are called “partial differential equations” .
Steacy mused over the question for months. Surprisingly, he had his “ah ha” moment at home while he was sleeping.
“Knowing that every normal distribution changes concavity from concave down, to concave up, at a distance of one standard deviation from the average value, I awoke at 3 am realizing that if the flight lines were spaced exactly two standard deviations apart—so that the point where the concavity change taking place from one flight line links up with the one from the next flight line—then we would obtain a distribution which is sufficiently close to uniform coverage, for real-world purposes,” Steacy says.
This results in the insect density at the line halfway between flight lines being over 97 percent of the density at the
flight lines, from one single flight. This then improves with repeated flights, he calculates.
By solving this ‘simple’ equation, one only needs a hand-held calculator and a few inputs to answer our original question so that farmers across the world who want to implement the SIT technique can easily do so, says Dr. Steacy.
Both Barclay and Steacy believe SIT can be effectively adapted in other similar health situations, such as the recent Zika virus outbreak by releasing sterile mosquitos. In the 1990s, SIT was used to eradicate the Tsetse fly from the whole island of Zanzibar. It posed a serious health risk for cattle and humans alike.
Steacy believes that one of the perceived barriers to effectively implementing SIT is the math. But by creating what he calls a ‘pancake mix’ equation—just add water— you don’t need to be a mathematician because that work is done for you.
Making calculations for optimal SIT more accessible may be a key to increasing the method’s impact in health and agriculture.
For more information, see the recently published article: “Modelling diffusive movement of sterile insects released along aerial flight lines” in the International Journal of Pest Management, by Drs. Hugh Barclay, Robert Steacy, Walther Enkerlin and Pauline van den Driessche.
This article originated from Science Matters - Spring 2016 (PDF).