Moving Toward a Mathematical Understanding of Life

New faculty member Allison Shaw blends numbers and biology to describe behavioral patterns across distantly related species. 

"The cool thing about theoretical ecology is that I get to use simple but elegant mathematical tools to understand broad biological concepts."

When you walk into Allison Shaw’s freshly minted lab, you won’t see a single microscope or petri dish. Instead, there’s a conference table and floor-to-ceiling blackboards strewn with chalky symbols—something out of a mathematician’s dream.

Shaw’s migration to CBS follows a lively career of investigating animal motion. She doesn’t need actual animals to get down to work, though. Instead of gathering and analyzing data, Shaw draws models and derives matching equations to suggest possible theories for how it all works.

“Experimental and observational work tell you about the world empirically,” says Shaw. “Theory is the scaffolding that makes sense of those data.”

Take migration, for example. If you’re a sea turtle or a salmon that must migrate to breed, how often do you risk that journey—once per year, biennially, or even less frequently?

Shaw thinks of each individual’s decision like an equation with survival costs on one side and reproductive benefits on the other, all of which can be represented by measurable numerical parameters. By having the most offspring, individuals that choose the most cost-effective strategy will eventually determine how both the species and their migratory patterns evolve over time.

If the model is robust, it should mathematically predict the particular biological behavior it was designed to describe, regardless of what species you choose. That’s what gets Shaw really excited.

"The cool thing about theoretical ecology is that I get to use simple but elegant mathematical tools to understand broad biological concepts," says Shaw. Her work suggests deep patterns in the fabric of life, even between species at opposite ends of the tree of life, like crustaceans and mammals.

Shaw’s new blackboards invite contemplation, conversation and wall-to-wall doodling—a perfect stage for the theoretical work she’ll continue here at the U of M.

Armed with software like MATLAB and tools like difference equations and individual-based models, Shaw intends to research the intersection of animal movement patterns with disease and parasites, as well as with climate change.

- Colleen Smith


All in the family

“Both of my parents, both of my grandfathers, my brother, my uncle, my aunt, they all studied physics!” says Shaw. Coming from a family full of physicists, she grew up with math. Shaw first became interested in the combination of math and biology in high school when she stumbled across the work of Jim Murray, who created mathematical models for animal coat patterns. “As it turns out, on spotted animals, you can get striped tails, but on striped animals, you'll never have spotted tails, because of the mathematics of how the boundaries work and how the chemicals are laid down,” says Shaw, of Murray’s work.