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One Person's Path to Mathematical Biology


When I was an undergraduate at the University of Toronto I was interested in a research career, but I wouldn't have believed you if you had told me I would end up doing biological research.

It's not that I didn't find living things fascinating---who could not? But I accepted the notion that biological systems, and their bewilderingly complex behaviour, could ultimately be understood from more fundamental physical laws. So it seemed logical to concentrate on studying those more fundamental laws, presumed to be found in physics and mathematics.

As it happened, I found that I generally enjoyed courses in math more than physics; consequently I focussed much more on math in my final 2 years. But when I started thinking about graduate school, my desire to understand the real world resurfaced and I decided to study applied mathematics and theoretical physics. The research area that seemed most exciting at the time was quantum gravity.

After only a few months at the University of Cambridge, U.K., my enthusiasm for research that might resolve the inconsistency between general relativity and quantum theory was waning. Many of the world's greatest physicists had been working on this problem for years and finding it very difficult. And there I was just starting graduate school. This was not the right problem for me. At the same time, it was clear that there were plenty of interesting problems in theoretical physics that a graduate student was more likely to solve or contribute to in a substantial way.

Evolution of a different kind

The specific issues that I addressed in my Ph.D. thesis were all associated with, or at least motivated by, problems in theoretical astrophysics, gravitational dynamics in particular: the evolution of the orbits of planets in the solar system and the evolution of structure in galaxies. As a postdoc, I also began to investigate the evolution of large-scale structure in the universe.

During that postdoc in theoretical astrophysics, evolution of a different kind diverted my attention in a way that I thought would be temporary.

My wife, Sigal Balshine, is a behavioural ecologist, which means that she tries to make sense of the observed behaviour of living organisms as a consequence of natural selection operating in real ecological environments. While she was writing up her Ph.D., Sigal sat me down one day with a serious expression on her face.

"I'm trying to use game theory to make a model that can explain the evolution of parental care in my fish. You're a mathematician--you should be able to solve this!"

"But I don't know anything about game theory."

"Don't you love me?"

"Umm, OK, I'll try."

I soon discovered that the major challenge for me was not that I wasn't familiar with game theory. It was that Sigal's problem required a completely different kind of thinking than the sorts of things I had been researching until that moment. There were no laws of physics from which we could derive appropriate equations. And even if I had been an expert in game theory, it wouldn't have helped much. The key challenge was to figure out what the right question was, and then to formulate a model that could both answer it theoretically and lead to predictions that would be testable through observations and experiments with real animals.

I found that I really enjoyed that challenge. It forced me to be creative in a new and very interesting way. Rather than trying to devise a technical solution to a fairly well-defined problem, we were really not sure how to define the problem in the first place. As it turned out, the models we ultimately developed didn't require a lot of mathematical sophistication to analyze, but it was far from obvious at first how to write down a useful model.

Having recognized that biology could be tremendously fun and rewarding, I began to scan biology journals, especially for mathematical papers. Rapidly, it became clear that there were many interesting and important problems in biology that could benefit from mathematical analysis, but they seemed to have received much less attention than problems of equal importance in physics. This got me thinking that there was a lot of scope for a fascinating career if I were to change focus and start thinking seriously about biological problems.

I started noticing job advertisements in theoretical biology and wondering whether one of these could become a way for me to enter the world of biological research. Eventually, I started admitting to friends that I was considering such a change, and admitting this to one particular person really got the ball rolling.

One of our friends in Cambridge was Bryan Grenfell, a faculty member in the zoology department, who was already well known for his research applying mathematics and statistics to ecological and epidemiological problems. Bryan could not have been more supportive and enthusiastic, and he went to considerable efforts himself to facilitate the change I was considering. I ended up getting a research fellowship from The Wellcome Trust to work with him in Cambridge.

Change now or wait until granted tenure?

I didn't exactly jump at the opportunity to change fields. I was nervous. What if it didn't work out? It might then be tough to rejoin the path I had been on so far. I also had attractive second postdoc offers to continue in theoretical astrophysics, so it was a difficult choice to make, and friends and mentors gave mixed advice. I recall one colleague saying emphatically, "Don't do this now. If you want to change fields then wait until you have tenure. Now is not the time." Others encouraged me to follow my interests and, with some hesitation, that's what I did.

During my 3-year fellowship in Cambridge, I worked on a variety of ecological and epidemiological problems, and also continued applying evolutionary game theory to animal behaviour, with Sigal and with other biologists. Bryan sparked my keen interest in childhood disease dynamics, and more generally in developing mathematical models that can explain the real epidemic patterns evident in historical surveillance data. It was especially satisfying to find that relatively simple mathematical models and analyses could explain puzzling changes in the epidemic patterns of measles in large cities in the 20th century.

Near the end of my fellowship in Cambridge I was lucky to have the opportunity to spend several months with Simon Levin and his group in the department of ecology and evolutionary biology at Princeton University. This visit led to very enjoyable and productive collaborations on synchrony in population dynamics and the ecology and evolution of influenza.

Sigal and I have been back in Canada at McMaster University since January 2000. The department of mathematics and statistics, where I am based, now occupies the historic Hamilton Hall, which has recently been completely renovated to become the state-of-the-art James Stewart Centre for Mathematics. The math centre has a very friendly and open atmosphere and there are faculty representing a wide variety of areas of pure and applied mathematics. The Mathematical Biology Research Group currently includes two faculty, four postdocs, three grad students, and several undergrad research associates, and we usually have opportunities at all levels every year.

In addition to an attractive campus that borders beautiful conservation lands, McMaster has a number of features that make it an excellent place to do research in mathematical biology. Within the Faculties of Science, Social Sciences, and Health Science, there are researchers in a variety of departments with a serious interest in collaborating with mathematicians to make progress on biological and medical problems.

Apart from my current collaborations with faculty members in clinical epidemiology and biostatistics, the Centre for Health Economics and Policy Analysis, pathology and molecular medicine, and psychology, I have been discussing possible collaborations with faculty in biology, physics and astronomy, geography and geology, and anthropology. The genuine spirit of enthusiastic interdisciplinary collaboration at McMaster is outstanding.

Nearby resources at other universities and institutions in southern Ontario also provide endless opportunities for mathematical biologists. In particular, McMaster is one of the six principal sponsoring universities of the Fields Institute for Research in Mathematical Sciences in Toronto and a primary member of the SHARCNET high-performance computing consortium. Both Fields and SHARCNET have programs that provide funding for students and postdocs at McMaster.

Before returning to Canada, Sigal and I had often heard that the funding situation was much poorer than in the U.S.; however, we were pleasantly surprised by the real, current situation for new faculty members in Canada. In particular, Canadian universities can leverage very large start-up grants for new faculty from the Canada Foundation for Innovation's New Opportunities Fund. If their research interests include a health connection, faculty members in mathematical biology have more potential funding sources than other applied mathematicians, the key source being the Canadian Institutes of Health Research (CIHR).

Editor's note: CIHR is a Next Wave sponsor

Of course, not everyone who is considering a career in mathematical biology has academic research in mind. There are many other possibilities, because there is a great need for mathematically and computationally competent individuals to work on health-related problems in industrial and governmental organizations. (Examples of the latter include Health Canada and Statistics Canada.)

There is every reason to believe that embarking on a career in mathematical biology is likely to be exciting and very rewarding.