By Jillian Kunze
The spotted lanternfly is an invasive species in the eastern U.S., first introduced to Pennsylvania in 2014. While these pests are not directly harmful to humans, their droppings attract fungi that damage trees, crops, and grapevines — causing major issues for the agricultural and lumber industries. While there have been incidents in which shipments have arrived at the west coast of the U.S. containing dead spotted lanternflies, no living lanternflies have established a foothold there yet.
At the 2024 SIAM Conference on the Life Sciences, which is taking place this week in Portland, Ore., concurrently with the 2024 SIAM Conference on Mathematics of Planet Earth, two contributed presentations focused on different aspects of mathematically modeling the spread of spotted lanternflies. Benjamin Seibold of Temple University first explained a model of the lanternfly life cycle, then Jacob Woods of Temple University described the insect’s spatial spread.
“I’ll be highlighting our work with ecologists to understand the spotted lanternfly,” Seibold began. “We want to understand their behavior so that stakeholders, like the U.S. Department of Agriculture, can perform interventions.” Seibold created a principled mathematical model of the life cycle of spotted lanternflies (see Figure 1) to explore whether they would be able to establish themselves in particular locations given the local climatic conditions, and calibrated the model based on laboratory and field data (see Figure 2).
Since the insects are cold-blooded, temperature dominates everything in the model. A single generation of spotted lanternflies generally synchronizes with one year, since only the eggs can survive the winter (though that may no longer be the case if the insects established themselves somewhere that is warm year-round, like Florida). There is a fixed background rate of lanternfly death in the model, as well as a correlation between mortality and temperature; both the cold and extreme heat can be deadly for lanternflies. Seibold was particularly curious how diapause—the suspension of egg development during the cold winter months—would change in different climates. It was also important to find the basic reproduction number, knowing that each female can lay up to 100 eggs across multiple clutches. “In the model, we want to capture all of these things,” Seibold said.
Even if a clutch of lanternfly eggs all hatch at the same time, the insects may go through the ensuing stages of development at different times. Seibold used a linear partial differential equation model to allow for a continuum in the developmental age of the insects, and incorporated laboratory data on the development and diapause speed versus the temperature.
Figure 2. Benjamin Seibold (left) and Jacob Woods document spotted lanternfly nymphs on the Temple University campus. Photo courtesy of Fatma Betul Seker of Temple University.
Through this model, it is possible to create maps of the lanternfly’s establishment potential at specific locations within the U.S. based on their real temperature profiles, approximated as sine curves. Seibold first simulated the changes in the lanternfly population in Berks Country, Pa., which was ground zero of spotted lanternfly introduction to the U.S.; the model clearly produces a change in distribution that synchronizes to the year. However, modeling lanternflies in Los Angeles, Ca., produces quite different results — the winters are not as cold, so the yearly synchronization effect is not as strong. The simulation indicates that spotted lanternflies would still be able to establish themselves in Los Angeles, but their population would not blow up as much.
“With this model, you can look at the whole U.S. based on temperature and see where you get lanternfly establishment,” Seibold said. Some areas of concern, like Seattle, Wa., do not have temperature profiles that are friendly to lanternfly growth — though about half of the U.S. does have a climate that enables lanternfly development.
Next, Woods expanded on Seibold’s presentation to discuss nuanced principled models of spotted lanternfly movement that could help stakeholders determine the best methods to control them. “I’m going to be focusing on spatial spread,” Woods said. “I’m really curious about the geometry of what’s happening in the real world.” Woods particularly investigated vineyards, as grapevines make a great host for spotted lanternflies and provide them with food at all of their life stages. Vineyard owners generally perform pest treatments in October, but adult lanternflies then invade the vineyard again the following July through October, which coincides with the time of grape harvest.
Spotted lanternflies generally follow a host-hopping model: They ascend a host (like a tree or a telephone pole) and remain there for a while, then move pseudo-randomly off the host (they are not particularly good flyers) and find a new host. The pests tend to congregate in edge ecosystems that fall on the boundary between two different areas. “To model this, we need an idea of our landscape,” Woods said. He assigned potential hosts an attractiveness function; the insects head directly to the most desirable host—which is generally whatever structure appears tallest from their point of view—but may change their trajectory along their journey if something more compelling comes into sight. To simplify, Woods reduced this behavior to a random walk between the hosts, then calibrated the model functions based on spotted lanternfly data from experiments.
Animation 1. A simulation with the host hopping model at 1723 Vineyards in Landenberg, Pa., with geometry based on satellite imagery. All of the spotted lanternflies are initialized in the forest and invade the vineyard over the course of 70 days. Animation courtesy of Jacob Woods.
In Animation 1, the model simulates the spotted lanternfly spread at 1723 Vineyards in Landenberg, Pa.; the invasion occurs quickly and the lanternflies favor the edge between the vineyard and forest, which comports with the observations of the vineyard’s owner. “What are the key large-scale implications of a host-hopping model like this?” Woods said. “How would this scale up to the state level?” Woods fed the small-scale hopping model into a larger-scale model to investigate how spotted lanternflies might spread across long distances—like the entire state of California—through human mediation, such as by hitching a ride on trains.
“Overall, we see that this model can quantitatively reproduce behavior that is seen in the field and at vineyards,” Woods concluded. In the future, he aims to calibrate the model based on more data, simulate control strategies for spotted lanternflies, and combine this model with the life stage model that Seibold initially described.
Acknowledgements: Benjamin Seibold and Jacob Woods acknowledged collaborators Stephanie Lewkiewicz (University of Pennsylvania) and Matthew Helmus, Jocelyn Behm, and Sebastiano De Bona (Temple University), as well as support from the U.S. and Pa. Departments of Agriculture.
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Jillian Kunze is the associate editor of SIAM News. |