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. |