Scientists are Harnessing the Magic of Math to Predict Species Extinction

By Shelby Bohn

30 August 2023

Illustration of a bird using a calculator

Illustration by Shelby Bohn


Tackling algebra homework back in high school, many of us may have wondered: “When will I ever use this in real life?” While we may not have expected that one day the answer would be “species conservation”, researchers in the Department of Integrative Biology are doing just that.

“Animal populations around the world are declining, which means we need to develop tools to help us better forecast how populations will respond to environmental change,” says Dr. Ryan Norris, a professor in Integrative Biology.

Norris and recent PhD graduate Dr. Joseph Burant, currently a tenure-track researcher at the Netherlands Institute of Ecology, have developed a powerful mathematical model to study population change in ways that would otherwise take years — or even be impossible — to do in the field or lab.

“If we think about population size, at any given time it can be represented by a variable, n, and then we can think about what might cause n to increase or decrease. There are many different ways we could try to understand changes to n, but it is all math,” says Burant.

The pair created a formula to describe population dynamics under different environmental scenarios to understand how the rate of habitat loss affects the way populations decline, the time it takes for these populations to collapse, and — most importantly — how the seasonal timing of these environmental stressors affects patterns of decline.

“Virtually all species live in seasonal environments and if we are to successfully predict how they respond to environmental change, we need to embed seasonality in our work”, says Norris.

That’s because different factors affect population size in different seasons  — something Burant says is well suited to mathematical modelling.  “For example, we showed that habitat loss during breeding versus non-breeding seasons results in different patterns of population decline.”

The results of the model have given Burant and Norris testable predictions, which they say is the next step in using mathematical modelling to advance species conservation.

“Our model is a reasonable representation of results from past experiments using fruit flies to examine early warning signals of population collapse in a seasonal environment,” explains Norris. “The next question is, do we see these same signals across a wider array of species?”

The model opens exciting doors for researchers, since data on populations from past studies is now becoming more widely accessible via online data repositories, which will make it possible to look at early warning signals of population decline in a wide range of species.

While both researchers are quick to deny being theoretical mathematicians, they admire the ways that real world occurrences can be described in simplified terms using mathematics.

“I spent a lot of time thinking about ecological theory, or how to generalize observations from nature into different circumstances, and that’s really what theory is all about,” says Burant.

Adds Norris, “There is something magical when you figure out how to represent something mathematically. It is about understanding something you study from a different perspective, like you all of the sudden know how to speak a different language.”


Read the full study in the journal Theoretical Ecology.

Read about other CBS Research Highlights.