When we think of math, we often picture numbers on a page or complex formulas on a whiteboard. But for Dr. Sophie Léger Auffrey, Associate Professor at Université de Moncton, mathematics is a powerful tool for solving real-world problems—from how tires perform on icy roads to the alarming decline of Atlantic Canada’s snow crab population.
“I’ve always been interested in applied mathematics,” she says. “Even during my undergraduate studies, I was drawn to projects that connected math with the real world—like one that explored the relationship between mathematics and music.”
Engineering Resilience
Sophie’s early work focused on tire simulation—a collaboration with industry partners to improve the numerical methods used in engineering. Her goal: to model tires rolling over everyday obstacles like potholes, mud, or curbs.
“The goal is to simulate a rolling tire that can face different real-world challenges,” she explains. “We want the tire to be able to resist all of these situations.”
That mindset—building resilience through understanding—carries into her current research, where she’s applying mathematical modeling to a much colder subject: snow crabs.
A Fragile Species, A Local Concern
“The snow crab project really stood out to me because it’s a local issue,” says Sophie. “It’s still applied mathematics, but we’re using it to understand something real and very relevant to our region.”
Snow crabs are incredibly sensitive to water temperature, preferring cold environments with very narrow tolerances. As ocean temperatures rise, their habitats shrink—posing serious risks to their survival and to the coastal economies that depend on them.
“If the snow crab population isn’t healthy, there won’t be enough for fishing,” Sophie warns. “So we’re trying to understand the current state of the population and what we can expect in the future with the climate changes already happening around us.”
Modeling a Changing Future
Currently, fishing quotas are determined by longstanding tools used by the Department of Fisheries and Oceans. Sophie and her team are developing a new, more comprehensive mathematical model—one that incorporates a broader range of biological and environmental factors.
“Our model is more global,” she says. “We represent the snow crab’s key characteristics mathematically so we can predict both short- and long-term impacts.”
For example, under normal temperatures, snow crab eggs incubate for about two years. But when the water warms, incubation may be cut to just one year. “We can incorporate that into the model,” Sophie explains, “and adjust our equations to see the long-term effects. Will it increase the population? Will it have negative consequences? What will change?”
Data-Driven Decisions
Recently, Sophie notes, scientists have observed a significant drop in one category of snow crab—a troubling sign. “A few years ago, the population was very healthy. But now, we’re seeing drastic decreases. Is it due to climate change? That’s what we’re trying to understand with our models.”
With access to real-world data from the Department of Fisheries and Oceans, her team can test and refine their predictions. “We can compare our models to real data to see if we’re on the right path, and whether we’re accurately representing the population’s essential characteristics.”
Bridging Disciplines for Impact
Understanding the snow crab population isn’t just a math problem—it’s an interdisciplinary challenge that brings together biology, statistics, and mathematics.
“We can’t control climate change by ourselves,” Sophie reflects. “But we can help manage decisions better.”
Through her work, Sophie Léger Auffrey is proving that applied mathematics isn’t just about abstract theory—it’s about creating models that inform real decisions, protect local industries, and prepare for the environmental challenges ahead.
