Whither Mathematical Biology?

Some Remarks upon becoming President of the Society for Mathematical Biology - August 2003

Lou Gross
Department of Ecology and Evolutionary Biology
Department of Mathematics
University of Tennessee
Knoxville, Tennessee 37996-1610

The Dundee Conference and Annual Meeting of our Society was superb not just due to the phenomenal cuisine, cameraderie, illuminating mathematical discussions on topics from cancer to divorce, and the availability of a plethora of single malts, but also because it readily illustrates why the field of math biology is so relevant today. The diversity of topics presented, the excitement of the younger researchers there, and the attention paid by the popular press to the presentation by Jim Murray are all a testament to the vibrancy of the field. We all owe a debt of gratitude to the outstanding efforts by our colleagues at Dundee, most particularly Mark Chaplain, who so ably managed this gathering.

As I remarked at the Annual Meeting, the field of mathematical biology, and therefore the SMB, might best be viewed as a "big tent". It embraces all those who wish to provide a firm basis in mathematics for studies of biological systems, be they highly computationally-oriented or highly analytically-oriented, or anywhere in between. This firm basis in mathematics includes model formulation and analysis in addition to concern for working on problems that are of direct interest to biologists. As presentations at the Dundee Conference illustrated in profusion, this is not math for math's sake or math in the service of computation, but math contributing to biology.

Since biology inherently includes observation and experiment, this implies that connection to data is an inherent part of the practice of math biology. Indeed Jim Murray remarked to me at the Dundee gathering how wonderful it was that there was so much application work going on. This is a major change from many years ago when there were rare papers which dealt with data and its connection to model evaluation. Math biologists today care about providing results of interest to biologists, hence we must relate our work to the data upon which much of biology is built.

In addition to the trend towards application in our work, another hallmark is the acceptance of the great diversity of math and quantitative methods to address questions. It wasn't long ago when some math colleagues would say "I know x (PDE's, ODEs, etc.) and so I'm going to apply x to this particular problem". Now it is much more common for us to choose the methods appropriate to address a particular biological problem, learning new techniques or approaches as we go, or collaborating with experts as needed. This is true applied mathematics in that we let the underlying scientific questions drive the choices of mathematical approaches we use. I do not mean to imply by this that our efforts do not drive new and interesting mathematics. This may not be our scientific objective, but it arises because our work often pushes the limits of mathematical knowledge.

The splintering of biology that has occurred over the past century has begun to affect our Society as well. Several colleagues, when I asked if they were attending the Dundee meeting, informed me that they preferred to attend gatherings of theoreticians in their own particular sub-discipline of biology, and that they didn't see the need for overall math biology conferences anymore. While I can't readily perform an experimental test of the hypothesis, I would guess that had they attended the Dundee Conference, two factors might have changed their opinion (leaving aside the single malts!).

First, biology, as all of science, is done by people. Unlike the popular notion that science is driven by unfeeling, creative automatons, it is in reality a very human enterprise, and very affected by the personalities of those who practice it. For biology to continue to expand, highly quantitative people are needed with sufficient skills to understand both the biology and the mathematics (as evidence, see the large number of ads in recent issues of Science and Nature for quantitatively-oriented biologists). However the pool of creative people with strong quantitative skills is quite limited. We need to do everything we can to attract these people to the life sciences and maintain their interest.

Gatherings such as the one at Dundee therefore provide a unique guide for these young researchers, opening a window on the applications of quantitative approaches across a diversity of biological subdisciplines, and the people who work in these areas. Math biology is now so expansive that no institution of higher learning can offer its students access to the research-level expertise across biological applications that is available at gatherings such as Dundee. The success of the SMB Mentoring Program illustrates the importance of obtaining advice from outside a particular young researcher's cadre of interactions. So these gatherings serve a unique role in preparing the researchers who will be the leaders of math biology in the future.

Second, you never can tell when an application in another sub-discipline will lead to that "Aha" and you realize it applies to something you've been working on (or were stuck on) in a completely different context. This is part of the power of mathematics, but mathematical techniques and approaches have become so expansive that it would be difficult for any of us, no matter how broadly versed we attempt to be, to see all the potential connections. Keeping strictly to meetings in our own sub-disciplines could lead to inbreeding of ideas and approaches. A bit of a mutation from exposure to outside influences is likely good for all our science. The reverse is also true of course - something you have been working on may be ideally modified to apply in some other sub-discipline and then watch out - you might be coerced into an entirely different area of research. Some cross fertilization benefits all areas of the life sciences.

In sum, our field and our Society have tremendous opportunities available to us in the near and long-term. The advantages of mathematical approaches are now evident and accepted throughout biology. Our challenge is to not let this opportunity be dispersed among the numerous scientific societies, but rather gather together, as the Society has accomplished so ably in the past, so as to foster cross-fertilization of approaches, and a broad education for the math biologists of the future. This requires leadership, and it is appropriate for me to end this essay with a special thanks to Mark Lewis who so ably served as President of SMB over the past two years and whose research efforts epitomize my above points regarding the benefits of taking a broad perspective in science.

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