Combining math and entomology to predict, mitigate

AMES, Iowa — At a chalkboard in his office, Rana Parshad draws a vertical y-axis for aphids and a horizontal x-axis for time. Under an exponential growth model, the associate professor of mathematics at Iowa State University explains aphids multiply quickly and indefinitely. He represents this by dragging the chalk into a sharp, upward curve.

But reality is more complicated, says Parshad. Aphid populations often crash when soybeans, their preferred host plant, dry out or “senesce” before harvest. He draws a straight line across the top of the graph; the “carrying capacity” changes the j-shaped curve into an "s."

It’s also possible to have multiple boom-and-bust cycles over a growing season, Parshad adds. Intense competition for food, which causes a drop in aphid numbers followed by a rebound, parasitoid wasps and predators, like lady bugs, could be at play. Weather and crop health are important factors, as well.

“Many of the standard population models don’t capture these complex, dynamic interactions among plants, insects and weather events,” says Parshad, whose expertise includes dynamical systems, mathematical biology and differential equations.

To fill these gaps, Parshad and his graduate students, Aniket Banerjee and Urvashi Verma, are collaborating with entomologists from Ohio State University. Funded by a $552,890 grant from the U.S. Department of Agriculture, the project’s findings could help experts predict future pest outbreaks and develop new mitigation strategies for farmers.

Over the next three years, the researchers will:

• Compare the effect of soybeans stressed from too much or not enough water on the reproductive success of aphids that are either resistant or susceptible to natural plant defenses.
• Evaluate how water-stressed soybeans impact aphid interactions with a parasitoid wasp.
• Track changes in the ratio of aphids that are resistant or susceptible to natural plant defenses under different water stress scenarios.
• Develop mathematical models to simulate changes in aphid population dynamics over the course of an entire growing season and in response to a wider array of stressors.

Andrew Michel, associate dean and entomology professor, and Margaret Lewis, postdoctoral scholar at Ohio State, are conducting lab and field trials and sharing their data with the Iowa State team.

Earlier this month, Parshad, Banerjee and Verma released a preprint of their proposed “variable carrying capacity non-local logistic model” for aphid population dynamics. Parshad says their model can capture multiple population peaks. But they’ll continue improving and expanding it to include more factors, like plant host suitability, which changes across a growing season, and the effects of drought and flooding.

Plants typically increase their protective chemicals when stressed by drought. It's less clear what happens during floods and what impact this could have on aphids, says Parshad.

Why aphids can wreak havoc

In large numbers, aphids can cause severe damage to plants. Iowa State entomology professor Matthew O’Neal says “soybean aphids can reduce pod set, seed size and plant height, resulting in yield losses as great as 40% in the Midwest.”

Part of the aphid’s success is the speed at reproducing — sexually and asexually. On soybeans, aphids can spawn up to 15 generations. They also have the ability to sprout wings and fly to other sources of food or common buckthorn, their overwintering host plant.

In response, farmers can grow aphid-resistant varieties of soybeans, but the emergence of “virulent” aphids threatens this strategy. Virulent aphids withstand the plant’s chemical defenses, passing their traits on to offspring.

In 2022, Parshad and O’Neal, along with their graduate students Banerjee and Ivair Valmorbida, published a paper exploring the dynamics between virulent soybean aphids and “avirulent” aphids, which are not resistant to new soybean varieties. Using lab experiments and mathematical models, they found virulent aphids and avirulent aphids can coexist on a resistant soybean plant. Virulent aphids alter the host plant’s chemistry, making it more hospitable to “avirulent” aphids.

“You will always have some resistant populations over time. It’s very natural. The important question is how do you manage this and keep those numbers low?” says Parshad.

In the future, Parshad and O’Neal will study predator-based bio-controls with prairie strips between crop fields. With this arrangement, beetles, parasitoid wasps and other insects that eat aphids can move between two habitats or “patches”: The prairie strip and the seasonal crop fields. Parshad says the concept is like having a restaurant close to home. You’re more likely to eat out if it’s easy to get there.