University of Tennessee, Knoxville

Supported by National Institutes of Health Award GM59924-02

For related NIH programs see NIGMS Complex Systems Initiatives

2003 Short Courses

The 2003 series of Short Courses will be held at the University of Tennessee and as with earlier ones, these are oriented towards biologically-trained individuals. The overall objective is to provide a rapid introduction to the mathematical and computational topics appropriate for understanding current research in biological complexity. These Courses will each last four days. The Courses will be led by a group of distinguished faculty with particular expertise in biological modeling. Each Course will include computer-based workshops in addition to formal lectures and discussion sessions. Each Course is organized separately, though some individuals will benefit from attending two or more of them, depending upon their research interests. Significant financial support for travel, registration and housing expenses are available to qualified applicants (particularly graduate students, post-doctoral fellows and faculty without externally-funded projects).

Course 1: Introduction to the Mathematics of Biological Complexity:
March 30 - April 2, 2003

Course 2: Optimal Control Theory in Application to Biology: 
July 9-12, 2003
Course Home Page with Lecture Notes

Course 3: Modeling the evolutionary genetics of complex phenotypes: a hierarchical approach from sequences to populations:
September 7-10, 2003 (note changed date)

In addition to the above, the following Courses are planned to be held over the next year, pending approval of funding:
4. Quantitative Assessment of Stress on Systems: Modeling, Risk and Decisons (Dr. Thomas Hallam, organizer)
5. Nonlinear Dynamics, Bifurcations, and Chaos in Biology: an introduction to the formulation, parameterization, analysis, and simulation of nonlinear models of biological systems (Dr. Aaron King, organizer)
6. Statistical Data Mining in Biology (Dr. Hamparsum Bozdogan, organizer)
7. Bioinformatics and Computational Biology of Genome Sequences: compartive analysis and evolution (Dr. Jay Snoddy, organizer)
8. Workshop: An Introduction to Biocomplexity and Quantitative Education (Dr. Louis Gross, organizer)

Lecture notes and other materials from previous Short Courses are at:

2002 Course Home Page

2000 Courses Home Page

2003 Courses



The Faculty

The Courses

Further Information

Application Form


Interested individuals are invited to apply for admission to these Courses. Attendance will be by invitation only and will be limited to forty participants for each of the Courses. Preference will be given to individuals without extensive prior mathematical training, particularly for the first of the Courses.

These Courses are supported by a grant from the National Institutes of Health, which will cover most local expenses, including hotel, meals and the registration fee, for participants from colleges and non-profit organizations. Additionally, travel grants are available for those who cannot obtain travel funds from other sources. Preference for these grants will be given to graduate students and those who can obtain some support from their home institution, but grants of full travel support are also available. All those requesting travel grants will be expected to make travel arrangements at the lowest possible fare through our local travel agent. Generally, individuals from private, for-profit institutions will be expected to cover their own expenses. Discounted lodging rates are available at the hotel for these Courses (Knoxville Hilton, Downtown) which is adjacent to the University of Tennessee Conference Center where all Courses sessions will be held.

Applicants should complete the application form and email  it to the Director of the Courses as per instructions. Applicants will be notified of their acceptance by email, and given details regarding travel and lodging arrangements. Applicants for Course 1 will start to be accepted immediately with a final deadline of March 20 for this Course - individuals are urged not to delay in applying. Applicants for Courses 2 and 3 will start to be accepted 3 months before the start of the Course, with a final application deadline 1 month before the start of each of these Courses.


The registration fee for each Course is $300, which includes all Course materials as well as all meals during the Course (breakfast, lunch and dinner for days 1-3 of each course and breakfast and lunch on day 4). There is an additional non-refundable deposit of $50 for all participants required within two weeks of acceptance. The negotiated lodging rate is $70 per day plus tax for a single room. 

The Faculty:

Course 1:

Course Organizer: Dr. Louis J. Gross
Professor of Ecology and Evolutionary Biology and Mathematics
Director, The Institute for Environmental Modeling
University of Tennessee
Dr. Sharon Lubkin
Assistant Professor of Statistics and Biomathematics
North Carolina State University
Dr. Holly Gaff
Postdoctoral Fellow
Department of Ecology and Evolutionary Biology
The Institute for Environmental Modeling
University of Tennessee

Course 2:

Course Organizer: Dr. Suzanne Lenhart
Professor of  Mathematics
University of Tennessee
Dr. Renee Fister
Associate Professor of Mathematics
Murray State University
Dr. Hem Raj Joshi
Postdoctoral Fellow
Department of Ecology and Evolutionary Biology
The Institute for Environmental Modeling
University of Tennessee

Course 3:

Course Organizer: Dr. Jason Wolf
Assistant Professor of Ecology and Evolutionary Biology
University of Tennessee
Dr. William Atchley
Professor of Genetics and Statistics
North Carolina State University
Dr. Charles J. Goodnight
Professor of Biology
University of Vermont

The Courses:

Course 1: Introduction to the Mathematics of Biological Complexity

This Course will provide an overview of mathematical and computational approaches useful in analyzing complex biological systems including: continuous dynamical systems, discrete dynamical systems, matrix approaches including structured population models and Markov chains, and stochastic process models. This is designed for biologists who require a rapid, broad overview of modern quantitative techniques that appear again and again in many biological contexts. The focus will be on modeling methods, conceptual foundations and biological applications rather than detailed computations. The concepts will be motivated by numerous biological examples, chosen from physiology, genetics and infectious diseases. An objective is to ensure that participants for whom the first short course is appropriate would have been exposed to the basic mathematical background materials required for either of the second or the third Courses. Another objective is to enable attendees to read with comprehension the modeling literature in their own fields of biological interest.

Topic coverage will include the below, but will emphasize topics of particular interest to attendees. Accepted attendees will be polled to ensure that topics of particular interest to many attendees will be covered.

An overview of calculus with focus on differential equations in preparation for the section on dynamical systems and diffusion.
An overview of linear algebra in preparation for the section on Markov Chains and the section on dynamical systems.
An overview of basic probability in preparation for the section on stochastic models.
How to model it - examples of basic discrete and continuous models in application to chemostats, population genetics, and physiology. Application of non-dimensionalization methods to reduce the number of parameters in a model.
Introduction to dynamical systems - Discrete and continuous compartment models, phase-plane analysis.
Transport and diffusion - partial differential equations, the conservation equation, steady-states and traveling waves.
Stochastic models - birth and death processes, branching processes, Markov Chains. Applications to genetics and evolutionary theory.

Course 2: Optimal Control Theory in Application to Biology

This short course will focus on optimal control of systems of ordinary differential equations modeling biological systems. Here the differential equations model the dynamics of system response with some component of the system being under direct control, such as the rate of infusion of a drug. The optimal control problem requires a criterion (the objective) that is to maximized or minimized, such as minimizing tumor size, under constraints such as a limited total infusion due to limited tolerance for the drug. The mathematical theory then provides methods for how to best apply the control in time (e.g. the time-course of infusion) and stay within the constraints of the problem. The basic ideas of optimal control theory will be covered, and applications to disease, cancer and bioreactor models will be presented. Numerical solutions for simple control problems will be demonstrated in a computer lab setting.

Course 3:  Modeling the evolutionary genetics of complex phenotypes: a hierarchical approach from sequences to populations

The major goal of evolutionary and epidemiological genetics is to understand the architecture of genetic variation in and among populations. In evolutionary analyses understanding this architecture allows one to predict or reconstruct evolutionary genetic changes in response to selection at the level of phenotypes (e.g., Grant & Grant 1995). In epidemiological analyses it allows one to predict the incidence and distribution of various inherited pathologies (e.g., Sing & Boerwinkle 1987). However, understanding the genetic architecture underlying trait variation, and its implications for various processes, can be extremely difficult because there can be many levels of organization mediating the mapping from DNA sequence to phenotype.  As a result, researchers studying these complex phenotypes have relied heavily on theoretical models to assess the implications of various patterns of genetic variation (e.g., Barton & Turelli 1991). 

Because theoretical approaches have been so important in the advancement of understanding of complex phenotypes it is critical that non-theoreticians doing empirical genetics be able to comprehend the models that are being developed. This course will provide these researchers with the tools required to understand the various modeling approaches that are being used in this area. In order to achieve this goal we will utilize a hierarchical perspective, covering modeling approaches that have examined the implications of variation at various levels of organization. The course will span the hierarchy, from models that focus on single loci and their RNA or protein products (e.g., Atchley et al 2000) to those that include multi-locus interactions (see Wolf et al. 2000), developmental organization such as modularity (Atchley et al. 1994) and the resulting modular interactions (Wolf et al. 2001), up to those that include phenomena above the level of the individual such as genotype interactions (Moore et al, 1997), population processes (e.g., founder events [Goodnight 1987]) and metapopulation dynamics (Goodnight 2000).

Further Information:

Any questions about the Courses should be directed to

Return to The Institute for Environmental Modeling Home Page

Last Modified: April 23, 2003