# Making Mathematical Tools to Solve Biological Problems, Like Where COVID Came From

October 31, 2023

Megan Owen, an NSF CAREER award-winning mathematics professor, analyzes “tree-shaped” data, a theoretical area with applications in fields including evolutionary biology.

Megan Owen, a professor of Mathematics at the Graduate Center and Lehman College, spends most of her time thinking about “tree-shaped” data — such as phylogenetic trees, a type of diagram that represents the evolutionary relationships among species, organisms, and genes, like the Tree of Life charts often found in natural history museums. Such trees are also used, in far more complicated forms, to trace the evolutions of viruses like COVID-19 and Zika.

Although Owen holds a Ph.D. in applied mathematics, her research leans toward the theoretical end of the pure math/applied math continuum, focusing on an area known as discrete mathematical biology: the application of math to biological problems. Owen develops mathematical tools that analyze trees as if they were individual points of data. It’s fairly straightforward to take a set of numbers and calculate the average; Owen works on whether you can take a set of trees, like gene trees, and calculate the average tree. “When people first started making phylogenetic trees back in the ’70s, they would choose the gene very carefully — it took a lot of effort to sequence the DNA,” she says. “But now you can sequence and make gene trees for thousands of genes. So the question is, how do you get a species tree? So how do you get what’s happening overall with the species, not just for any single individual gene?”

Growing up in Ottawa, Canada, Owen was mostly interested in math for its own sake. In high school, she was informed by the guidance counselor that with her skills and interests, she could pursue a career as a math teacher or an accountant. Neither appealed to her. “It didn’t seem like there were a lot of options if I got a math degree,” Owen says. Since she also liked programming — both of her parents worked in the computer industry — she wound up enrolling as a mathematics and engineering student at Queen’s University in Ontario. After casually mentioning to her adviser that she’d had a “random dream of going to MIT” for her undergraduate degree, he suggested applying to MIT’s Ph.D. program. Enrolling in a doctoral program in the United States struck her as far too expensive, but the adviser explained that it was possible to get her studies fully funded. Owen wound up applying to a number of graduate schools and decided on Cornell.

As a Ph.D. student, she worked with a professor who specialized in combinatorics, which Owen describes as the “mathematics of counting.” In simple terms: Suppose you are at the Graduate Center and want to walk to Columbus Circle. Combinatorics can tell you how many different paths you can possibly take if you follow certain rules, such as always walking either north or west.

After receiving her Ph.D., Owen completed several postdoctoral fellowships, and then joined the Graduate Center. In 2019, she won a \$412,00 National Science Foundation Faculty Early Development Program (CAREER) grant, one of the most prestigious NSF grants. She credits the NSF CAREER Bootcamp at the Graduate Center's Advanced Science Research Center with strengthening her application. “I felt like even if I didn’t get the CAREER grant, the work wasn’t wasted, because I learned so much about grants,” Owen said. As part of her proposal, Owen came up with a program to help undergraduates from Bronx Community College and Lehman get experience in data science and machine learning. So far, about 22 undergraduates have participated.

When she isn’t teaching or mentoring students in her lab, Owen works on papers, many of which are simulation-based and involve a mix of coding and analysis. Other papers are theorem-based, and involve “writing stuff down and seeing if it works.” Owen compares it to working on a painting; there are many false starts that end up as crumpled papers in the recycling bin. “But eventually, they hit on something,” she says. “I think it’s very similar. You might have an overall idea of how to prove the theorem, but there are going to be little details, you are going to have to try to wrangle different things, to get the logic to flow.” Because her work pulls in pieces from many disciplines — geometry, statistics, algorithms, evolutionary biology — there is always something new to learn and problems to figure out.

Owen, who still does much of this type of work on actual paper, enjoys this process. And then there are the hard-earned rewards. “Proving a theorem is very satisfying, because it’s absolutely 100% true,” she says. “Which can’t be said about many things in life.”