Harnessing the power of mathematics for northern ecosystems
Published on 22 Jan 2025
Modelling experts use new mathematical approaches to better understand the many complex systems in the North. They may well be confined to their respective laboratories at Université Laval in Quebec City, but Antoine Allard and Patrick Desrosiers nonetheless work together to advance research in the North. The mathematical modelling tools developed by the two physicists and their teams give meaning to the research data collected through various projects supported by Sentinel North. The result is a better understanding of systems which a priori could seem to be as relatively dissimilar as northern ecosystems and neural networks.
“Ironically, I’ve never stepped foot in the places I help to characterize!” says Antoine Allard, a professor in the Department of Physics, Engineering Physics and Optics at Université Laval and holder of the Sentinel North Research Chair on the Applications and Theory of Network Analysis. This does not mean, however, that they work on their equations alone and independently. “It’s very much the opposite: I’ve never before conferred with so many researchers from different backgrounds,” points out Patrick Desrosiers, a researcher at the CERVO Brain Research Centre and associate professor in the Department of Physics, Engineering Physics and Optics at Université Laval.
Through the power of mathematical abstraction, they simplify phenomena of unbelievable complexity without distorting them. The goal is to produce intelligible representations, in the form of networks, to be able to assess the interactions between different elements. These models in turn allow experts in fields as diverse as ecology and neurobiology to exchange their views and address problems from a new perspective. “This fresh outlook has led them to conduct unprecedented analyses,” Professor Allard adds.
Applied and fundamental
This is what happened, for instance, with a project on boreal caribou led by Daniel Fortin, a professor in Université Laval’s biology department. With his collaborators, which include Antoine Allard and Patrick Desrosiers, he assessed the effectiveness of conservation measures which seek to mitigate the impact of human activity on this endangered species. The conclusion is implacable: protecting this herbivore also simultaneously benefits the entire biodiversity that coexists in this same northern ecosystem, thus confirming its status as an umbrella species.
The study of interactions within the same food web also made it possible to deploy models for predicting the abundance of dozens of bird and beetle species in the boreal forest of the North Shore region over the course of the next century. “The predictive methods used are based on network theory,” explains Professor Desrosiers. “This research is crucial to fauna and flora conservation efforts as the effects of climate change become increasingly felt.”
Legend: Mathematical modeling approaches can be used to study complex interactions in a given environment, for example in the boreal forest, where network science is supporting wildlife conservation efforts.
Some of the initiatives linked to Sentinel North are more fundamental in nature. This is the case with a project which examines how the brain geometry of the zebrafish, a vertebrate that has the unique characteristic of being transparent in the larval stage, influences cerebral activity. “We deployed models which incorporate neural networks, stimuli and movement,” says Patrick Desrosiers. “Such a high level of detail is unheard of.” In the long term, this could lead to a better assessment of the impact of exposure to various contaminants on the brain.
And it doesn’t stop there
The cross-cutting approach to research taken by Antoine Allard and Patrick Desrosiers helps decompartmentalize areas of expertise, one of Sentinel North’s core objectives. Although initially there may have been a wide gulf between the various disciplines, this gap is gradually bridged once dialogue is initiated. “By getting to know one another, you become familiar with the other person’s field, and you end up speaking a common language,” Professor Allard points out. “It’s a real challenge,” Professor Desrosiers adds, “but I would never turn back.”
Legend: Photo of Antoine Allard and Patrick Desrosiers' research group taken at their annual symposium in September 2024.
Indeed, both have initiated numerous projects in recent years which are set to continue well into the future, above and beyond Sentinel North. Antoine Allard is particularly pleased with the opportunities the student researchers he supervises have seized. “They had the chance of being exposed to alternative ways of conducting science, which for many of them has opened up new horizons,” Patrick Desrosiers says. “Their career is certainly going to benefit from this experience.”