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The most uplifting moments for me are those when a biological question generates new mathematically interesting theories and results and when these results give new insights into the original biological problem.

Discovering Potentials and Possibilities

27 FEBRUARY 2004

Everything could have worked out differently. It is conceivable that I would not be a mathematician working on problems in spatial ecology at the University of Alberta in Edmonton, currently a postdoc applying for tenure-track positions in Canada. I love what I do; however, getting here was not a premeditated career path but much more a result of a continual search and chance encounters.

New Worlds Open, Literal and Metaphorical
I might not even have got into mathematics in the first place. I did want to study the subject, but at the time the non-academic job options were unappealing and an academic career didn't even occur to me. In addition, during the last years of Gymnasium (high school), I had been enjoying the variety of subjects, from Latin to physics, so much that specialising in any single one seemed like restricting myself too much. Thankfully, I received this advice: "Do what you really want to do now, be good at it, and keep your eyes open for other directions." So I took up mathematics, and a whole new world opened up in front of me, literally and metaphorically.

But by the time I got my Vordiplom (BSc), I was sure that applied mathematics was not the right thing for me. It was not the only time in my life when I was wrong about my future. Although I enjoyed writing my Diplom thesis (MSc) in an area of pure mathematics, I still was not thinking about an academic career. Frankly, I didn't consider myself good enough--in fact, everybody around me seemed to be better.

Despite those thoughts, I continued on the path into doctoral studies, for several reasons. First, at the time there were no jobs available for mathematicians that were remotely interesting to me. Second, I had been studying abroad for a year, at the University of Washington, Seattle, and the whole experience had been very positive. In Seattle I learned (among other things) how to work hard and independently. A more important lesson was the contrast between the hierarchy I had known from Germany and the almost companionship-like relationship between students and professors in Seattle. I encountered many professors who were very approachable and who took much more care of their students.

Last and most important, I was inspired by K. P. Hadeler and his courses on applications of mathematics in biology. I wanted to do something with impact beyond mathematics. In addition, I find that my fascination for mathematics is hard to convey to friends and family, but biological applications get many people interested. I was fortunate that Hadeler offered me funding to do my PhD with him.

During the 3 years of my PhD, I attended the spring quarter of the 1998-99 programme in mathematical biology at the Institute for Mathematics and its Applications (IMA) in Minneapolis, Minnesota. Every year, IMA chooses a topic in applied mathematics and invites world-class researchers to present at the many conferences and workshops on various aspects of the theme. I am grateful that my visit there was funded by the Deutscher Akademischer Austauschdienst (DAAD). Because it was for only a short period, the application for this funding was fairly straightforward.

Over the course of the many conferences and workshops, I got a glimpse of how diverse the field of biomathematics and mathematical biology is, and I enjoyed the atmosphere and building personal relationships. I met many important people in the field. Mark Lewis (then at the University of Utah) was one of them; meeting him turned out, later on, to be significant for me.

Pursuing an Academic Career
At the end of my PhD, I was still convinced that I would leave academia. But then I spotted an ad for a postdoc position with Lewis in spatial ecology. The description of research activities sounded exactly like what I wanted to do--mathematics and conservation ecology. I decided to apply for it and let the outcome determine my future: to stay in academia or not. This is my current position: with Lewis at the University of Alberta, in the newly created Centre for Mathematical Biology.

Since accepting this position, I have met many fascinating people who work in related areas, and I have decided, finally, to pursue an academic career. Over the years, I have also gradually felt more confident that I can succeed. How did I choose my mentors? At the time when I was applying, I was quite unaware of (and had not tried to find out about) the excellent international reputations of my mentors, Lewis and Hadeler. I wanted to work with them because their ways of working inspired me, and I think that counts for a lot in the end.

My research interests are mainly in ecology and conservation. The most uplifting moments for me are those when a biological question generates new mathematically interesting theories and results and when these results give new insights into the original biological problem (see box).

My input into this process is modelling and mathematical analysis. I look for simple and simplified models that explore and explain a basic underlying mechanism. More realistic models tend to be intractable by mathematical analysis, at least at first, and require elaborate computing power. A combination of both approaches will eventually lead to deeper understanding.

How can mathematics answer biological questions? Frithjof explains in non-expert terms.

The biological question that stimulated my current research is known in the literature as the "drift paradox": Insects living in rivers and streams, such as mayflies, cannot actively swim against the water current, yet populations of these insects manage to persist in upper reaches of streams. The most widely cited biological explanation for this paradox is that although insect larvae are transported downstream, insect adults emerge from the water and fly upstream to lay their eggs, starting the cycle over. Yet, not all species emerge from the water as adults. How do their populations persist?

We started by writing down a model for how a single insect moves. Most of the time it holds on to the bottom of the stream, but quite often it lets go, "jumps up" into the current, and gets transported away before it settles down at a new location. We came up with a formula for the probability of a given jump distance and direction. Taking into account turbulence in the water, it is actually possible that the insect settles upstream from where is started. We then assumed that in a population of such insects, every one moves, on average, in the same way and that each insect can produce offspring. The analysis of the model showed that if the population growth rate is high enough and the water velocity is small enough, then the population can persist in upper reaches of the stream.

Currently, we are working on extending the model to incorporate availability of and competition for food. So far, this project has been collaborative, between mathematics and theoretical ecology. But in the future, we hope to actually measure how far these insects "jump" and whether our prediction of how slow the water has to be is accurate. In the future I hope to be present at the field site at which these measurements are taken, but most of my work is done with a pencil and paper or in front of a computer or, of course, by way of discussions with colleagues.

Based on my experience, what is important to be aware of before you embark on a career in mathematical biology? Mathematics is a tough subject, one that requires a high frustration threshold, but I find it rewarding, and friends and study groups have helped me through the rough times. I would say it is difficult to acquire deep mathematical skills if mathematics is not the first area of study, although I have met biologists who are quite good in certain areas of mathematics related to their work. Good communication skills are also extremely important to succeed at the interface between mathematics and biology, for example to collaborate with people in different fields.

Future Plans
So what comes next? I have applied for several tenure-track positions at Canadian universities, and I hope to get one of them. I have been here for over 2 years, and I enjoy the work environment. Compared to my experience in Germany, the environment here is more demanding but also more rewarding. The hierarchies are leaner, I feel I receive more support, and the administration seems more flexible.

I enjoy teaching at both the undergraduate and graduate levels. I find that much more emphasis is put on high-quality teaching here than in Germany. I find it a particularly striking difference that undergraduates are already encouraged to participate in research through summer projects with appropriate funding. One of the most important points in the decision to apply for a permanent position in Canada, however, was that I consider my chances here to be better.

The funding agencies and universities in different countries place different emphasis on different areas of mathematical and interdisciplinary research. As far as I know, funding and open positions for mathematical biology/spatial ecology are rare in Germany, whereas these fields enjoy a high priority in Canada and also in the U.S. (Detailed information on the European situation is available from the European Society for Mathematical and Theoretical Biology.)

Moving to a country so far from home comes at a price. On a cultural level, the differences might not be obvious at first, but eventually they will surface. Visiting friends and family is difficult and more expensive. E-mail and phone are ways to keep friendships alive, but this requires effort. What if, as happened to me, a close family member becomes severely sick?

Mathematical biology is an exciting field that is growing inside and outside of academia (for example, in drug and biotech companies). I feel that there will be an ever increasing demand for mathematical modellers. I plan, in the coming years, to establish my own group with people from different backgrounds working together on challenging problems at the interface between mathematics and biology.

Related Articles
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    By Andreas Deutsch, 12 Mar 2004
  2. Mathematical Biology: An Evolving Discipline and Career Over 15 years
    By Thomas Hillen, 20 Feb 2004
  3. Biology Outside the Box
    By Mark Lewis, 13 Feb 2004

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