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 enoughin 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 companionshiplike 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 199899 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 worldclass 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 domathematics 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 nonexpert 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 tenuretrack 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 highquality 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. Email 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.
