Mathematical ecology has been a formally recognized academic subdiscipline at the University of Tennessee, Knoxville (UT), since 1977. The program was developed as an interdisciplinary collaboration of the mathematics department and the graduate program in ecology at UT, with close connections to the environmental sciences division of Oak Ridge National Laboratory and Oak Ridge environmental consulting groups.

Since its inception, the primary goal of the program has been to produce graduates who are prepared to bridge the gap between ecology and the quantitative methodologies typically taught in computer science, math, and statistics departments. We have endeavored to meet this objective while offering something to students with primary interest in either of the relevant subdisciplines. Students primarily interested in mathematics or computer science are enticed to work on problems that develop biological theory, while students with laboratory or field interests are provided training in a diversity of quantitative approaches and computational tools that are useful in addressing major biological questions.

A flexible and successful program

Indeed, a unique aspect of this program has been its flexibility; students are able to pursue several alternative routes to a degree--through math, ecology, computer science, or environmental toxicology--all within the mathematical ecology program. One indication of the success of this effort is the fact that some program graduates who obtained their Ph.D.s in mathematics now have faculty appointments in biology departments, and some with Ph.D.s in ecology have faculty appointments in mathematics.

Graduate students in the program have interdisciplinary interests but typically come from one of two backgrounds. Some of our students have strong quantitative skills and wish to contribute to ecology, while others are primarily trained in biology or environmental science, yet they realize the importance of math to the biological questions that intrigue them. Degree routes are determined by student interest, although the majority of students complete formal degrees through the department of ecology and evolutionary biology or the mathematics department. The mathematics department has a specialty track for students in math ecology that includes a set of preliminary examinations distinct from those in the traditional math degree.

Despite their diverse backgrounds, all our students are required to take a 2-year course sequence of mathematical ecology, a one-semester course on mathematical evolutionary theory, and a mathematical biology seminar that meets each Fall and Spring semester. The first year of mathematical ecology covers an introduction to data and the modeling and analysis of ecological populations and communities. This foundational course provides a broad overview of approaches in applied mathematics, covering both deterministic and stochastic methods, with an emphasis on ecological questions, and is taken by general mathematics students who wish to obtain an introduction to graduate-level applied math, as well as by our students who are specifically interested in mathematical biology. The second-year course is more specialized and emphasizes topics such as ecotoxicology, epidemiology, individual-based models, or spatial analysis of ecological systems.

Undergrad, graduate, postdoc, and outreach components

Our program also includes an extensive undergraduate component, an outreach component that provides short-term opportunities for biologists to enhance their quantitative training, and opportunities for graduate students to do collaborative research with full-time staff and postdoctoral researchers at UT in computational ecology, or with a variety of researchers at Oak Ridge National Lab and private firms.

Educational and research opportunities for postdoctoral research with our faculty are available. The number of postdoctoral positions varies according to levels of external funding, with a current group of six postdoctoral associates supported by the mathematical biology faculty. Approximately half of our past postdoctoral associates have gone on to faculty positions, with the others pursuing careers in private industry, government agencies, or nonprofit environmental organizations. We occasionally also have funding to support visiting faculty members.

UT has been a leader in the development of quantitative courses appropriate for undergraduates in life sciences. These teaching opportunities have allowed our graduate students to hone their teaching skills while enhancing the appeal of math courses for biology undergraduates via an applied focus and the inclusion of relevant biological examples. Many undergraduates have spent summers or part of their academic year collaborating on research projects with faculty.

Currently a mixed group of undergraduates--both biology and math majors--are collaborating on a range of projects, mentored collectively by graduate students, postdoctoral associates, and faculty. We have a long history of presenting courses in mathematical ecology that are open to and attended by scholars from all over the world; see a photo of the Spring 2004 seminar participants below. Over the past several years we have offered an extensive series of short courses on the mathematics of biological complexity.

Lessons for students, faculty, and scientists

The UT program in mathematical ecology has been around for more than a quarter century, but the wide recognition of the great potential for mathematics and computational science to contribute to modern biology is much more recent. This recognition has led to the initiation of numerous interdisciplinary and multidisciplinary programs at institutions all over the world. Our long experience with educating mathematical ecology students provides some lessons that are likely to be useful to potential students who wish to compare training opportunities, as well as for young independent researchers who are seeking an institution with which to affiliate themselves in order to develop their own interdisciplinary research and training programs.

Here are some suggestions that we hope will be helpful to students as they search for programs, new scientists as they develop an education philosophy, and faculty groups as they formulate a new program.

* Program components should be discipline-specific and not overly broad. To cover the complete spectrum (or even a reasonable fraction) of biological sciences stretches resources, limits faculty time for fruitful interactions, and can lead to "burnout" of students who have more directed interests. The existence of a strong disciplinary program and a strong quantitative support group is necessary if students are to become well grounded in the discipline and have the training in theoretical and computational tools they need to pursue their investigations. A disciplinary focus will help to assure the critical mass of faculty and students that is necessary for peer-learning and support regular seminars. Although a few broad-based math biology programs exist, the rarity of these is an indication of the difficulty of building and maintaining such programs.

* Collaborative efforts that bring together those with primarily biological training and those with primarily quantitative training are invigorating to all concerned. In our experience, a diverse peer group of students, collaborating in a research team on projects arising from biology, is an effective means of cross-disciplinary skill transfer. This approach is enhanced by seminars that bring these students together with faculty and postdocs with diverse skill sets. Whether joint manuscripts are written and accepted, and whether joint funding proposals are developed and funded, are measures useful in assessing the success of these collaborative projects.

* While a disciplinary focus is critical, flexibility is no less so. A program should be flexible in terms of courses taken, the types of comprehensive examinations required of students, and the range of degree options available. Interdisciplinary research should be at the core of the program, and affiliation with research projects should start early, generally in the first year of the graduate program. Interdisciplinary programs should not take significantly more time to complete than traditional programs. Research teams should be congenial, with respect by all for the diverse skills that others bring to the table. We screen prospective students not only by their academic credentials, but also for their apparent team-orientation. We look for students for whom it is fun to share ideas and who have the patience to learn the language and culture of different areas of science.

* New faculty members who participate in interdisciplinary programs should have agreements, made in advance, about expectations for promotion. This includes an understanding of the characteristics of the journals they intend to publish in as it relates to assessment for tenure. Those within disciplinary subject areas sometimes have not recognized interdisciplinary interactions as worthwhile scientific endeavors. Even a minority of faculty with this attitude can have a negative influence on efforts to evaluate an individual's interdisciplinary research accomplishments. Interdisciplinary studies can produce multi-authored papers, which means that the old standard of primary authorship is often inappropriate for interdisciplinary scholars. Hence, young scholars should seek evidence that administrators and senior colleagues who will be evaluating them for tenure--especially those with a more disciplinary focus--are supportive of interdisciplinary research and aware of the challenges of evaluating interdisciplinary and multidisciplinary science.