# Adding to the Sum of Biological Knowledge

Whoever said that mathematics is esoteric, detached from reality, and only open to those with strong will? For the life sciences, mathematics provides the framework to identify what is potentially (biologically) plausible from what is not. In fact, it is amazing to realise how useful mathematics is for understanding patterns in the natural world, from the helical structure of DNA, to the alternation of leaves on stems, to the dynamics of populations.

It is an exciting time to be at the interface of mathematics and biology. Consider the release of genetically modified organisms, or outbreaks of avian influenza and foot-and-mouth disease: What management strategies should we implement? Is it best to cull or vaccinate in the face of an emerging disease? Although these are clearly biological problems, formulating solutions relies on the application of mathematics.

And both maths and biology stand to gain. Mathematics provides a common language that allows cross-fostering of ideas between subdisciplines in the biological sciences. Combining maths and biology not only allows us to solve particular biological problems, but it can also facilitate the development of novel applied mathematics. Our detailed knowledge of nonlinear dynamical systems and chaos, for example, has resulted from interaction between population biologists and mathematicians.

Deeper and Richer Understanding of Biological Problems

For me, mathematical biology is the way forward. I did my first degree in biology. However, during my Ph.D. I was able to combined both experimental biology and mathematics. With the help of a good mentor, I was able to develop some of the quantitative skills that I learnt as an undergraduate. Using maths allowed me to gain a deeper and richer understanding of the biological problem I was working on.

After my Ph.D., I was able to continue along this route of doing both experiments and mathematics. I completed two research-council-funded postdoctoral positions. In these posts I aimed to understand the population dynamics of ecosystems, in other words what governs fluctuations in numbers of species, both by developing mathematical models and designing experiments to test these models.

Currently I hold a Royal Society Research Fellowship, and I am looking into the broad research question of how species live together in time or space or both. This research programme takes place at the interface of maths and biology, with mathematical models developed and applied to problems in population biology. However, it does not stop there. This is an iterative process in that biological experiments and observations are taken to test mathematical models, and maths is developed and refined to achieve an insight into the dynamics of how species interact. In fact, theory and experiments are developed so that to make progress, you have to go right around what can often be a complex loop.

Routes Into Mathematical Biology

Broadly, there are two routes into mathematical biology: Biologists enter the field by developing a range of quantitative skills, and mathematicians by learning biology. As I mentioned, I originally trained as a biologist but was really lucky to have a mentor who was patient enough to take me through the basic methods I needed to learn, and I would definitely advocate this as a start into mathematical biology.

Biologists can no longer ignore the quantitative aspects of their discipline. Often biology is chosen as the science course at the undergraduate level as the best way to avoid maths. However, this is often not the case. Many undergraduate courses now include maths as part of the curriculum. Developing these good quantitative and analytical skills should be a fundamental part of any biological training.

Applying these quantitative mathematical skills at a research level is more complicated than the maths most biology undergraduates experience. Often undergraduate courses only scratch the surface and do not give sufficient mathematical details. However, many maths courses exist to fill the gaps in knowledge. A number of good distance learning centres, the Open University, for example, provide modular courses that address specific maths topics that are relevant to biologists. These are often general undergraduate level courses and may not be specifically billed as "maths for biologists." However, their broad remit provides a range of skills in mathematics applicable to biology.

In addition, short courses, tutorials, seminars, and focused workshops are becoming increasingly common, especially at mathematical biology research centres. These courses have the potential to be great resources but may not be widely known. U.K. groups that offer them include those at the universities of Oxford, Bath, and Strathclyde (where there is a master's course in mathematical biology). A good comprehensive guide to mathematical biology institutes and departments in the U.K. is available from the Centre for Mathematical Biology in Bath.

Practising maths is really the best way to understand it. Having access to maths books (and a good mentor) to learn maths from is probably the route I would encourage. But because it may be hard (although not impossible) to learn maths from books, it is equally important to be prepared to ask for help and to use lots of different resource media and discussion forums to develop the skills necessary for the biological problem at hand. Often, unless you are already familiar with the techniques in a particular area, it may be difficult to know how to solve a particular problem--a potential pitfall for budding mathematically inclined biologists. However, by being prepared to discuss ideas with peers and mentors and to use discussion forums, it is possible to overcome these difficulties.

For the mathematician wishing to learn biology, the first problem is that undergraduate mathematics courses predominantly focus on the physical applications. As a result, mathematics undergraduates are rarely exposed to the biological application of maths. Convincing mathematicians that problems in the life sciences provide a challenge when the marriage between the physical sciences and mathematics has a long lineage is a dilemma currently being wrestled with at many different levels, undergraduate, postgraduate, and research council. However, I would encourage all of those interested in mathematical biology, with either a mathematics or biology background, to get involved with the local mathematical societies and particularly the biologically relevant groups such as the Society for Mathematical Biology.

Funding and Research Fellowships

Several of the U.K. research councils (NERC, BBSRC, EPSRC) run schemes specifically aimed at attracting talented mathematical biologists. Grant funding is also to be had outside of dedicated mathematical biology schemes. However, researchers looking to develop their careers would be well advised to pay particular attention to the fellowships available. Becoming more popular, these provide an alternative approach to the traditional progression from postdoctoral research assistant to lecturer and onward.

The most prestigious of these fellowship schemes are the two run by the Royal Society. Dorothy Hodgkin fellowships were established in 1995 and are aimed at people in the early stages of their academic careers, particularly women. The University Research Fellowship ( URF), which I was lucky enough to be awarded in 2000, aims to attract and retain the best and brightest scientists in the U.K.

The scheme was established in 1983 to stop the U.K.'s "brain drain," and it is open to E.U. citizens who are either currently employed in the U.K. or have been resident in the U.K. for a continuous period of 3 years (other than for the sole purpose of full-time education). Tenure on this scheme can last for up to 10 years, and holders are absolved from departmental administration and teaching duties to pursue interesting (and potentially risk-prone) research questions. The expectation is that individuals will have completed at least one postdoctoral research position before applying, and about 40 URFs are appointed each year from across all the scientific disciplines.

The fantastic benefit of holding one of these fellowships is that it allows me to focus on my research and not be too concerned about my short- to midterm career prospects. My long-term goal is, of course, to secure a permanent academic job in a biology or applied maths department. The URF puts me in a good position to do this and explore exactly what possibilities are available.

A Field Wide Open

The application of mathematics to the life sciences is not confined to my own particular area of research. Understanding the broad spatial and temporal dynamics of biological systems provides exciting challenges for mathematical biology. Areas of recent and unprecedented growth in the application of mathematics include bioinformatics, epidemiology, population ecology, and immunology.

Moreover, the application of mathematics to large-scale patterns (e.g., oceanic productivity and flows) down to the fine-scale patterns (e.g., gene regulation and expression) is revealing detailed insight into the underlying biological (and sometimes physical) phenomena that generate the patterns. The challenge remains wide open to all those who are motivated to become mathematical biologists.

### Mike Bonsall

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