Grand Valley State University
Annis Water Resources Institute
740 West Shoreline Drive
Muskegon, MI 49441
Office: 133 Lake Michigan Center
Current Research Areas — Overview
Current Research Areas — Additional Information
BIO/NRM 480/580: Techniques for Modeling Biological Systems (Fall semester in even-numbered years, 3 credits). Theories based on mathematical models have long been of fundamental importance in various subdisciplines of the biological sciences. In population biology, this importance dates back at least as far as the 1700s with, for example, Euler's work in mathematical demography. In the early to mid 20th century, there was a great flowering of mathematical approaches in many areas of biology, including ecology, population genetics, fisheries and wildlife management, biophysics, epidemiology, physiology, and biochemistry. More recently, mathematical models have become important in new areas, such as developmental biology, bioinformatics, and molecular biology.
Despite the rapidly increasing importance of mathematical theories in the biological sciences, biology students often are not required to learn the mathematical and computational skills needed to understand, assess, apply, or develop mathematical models. The main purpose of this course is to partially fill this gap by providing biology students with a set of basic mathematical, computational, and computer graphics skills that will allow them to understand and critically evaluate several of the most common types of models in the biological literature, and to develop new models of their own.
The main types of models covered in this course are difference equations, matrix models, and ordinary differential equations. No prior knowledge of any of these topics is assumed. As background, the course begins by refreshing students' memories of various topics in elementary mathematics, including the basic rules of algebra and various standard mathematical functions (power functions, exponential functions, etc.). The course also provides students with an introduction to the required parts of elementary calculus, tailored to biology students and with no prior knowledge assumed.
Students are shown how to use the R programming language to implement each technique numerically and plot the results. Applications to various branches of modern biology are illustrated with worked examples and readings from the literature. Specific applications examined during the course will be selected based on interests of the students enrolled but may include, for example, topics in animal behavior, population and community ecology, population genetics, fisheries and wildlife management, ecotoxicology, epidemiology, cell and organism physiology, biochemistry, regulation of genes and metabolism, and statistical topics such as least-squares parameter estimation and principal components analysis.
This is not a mathematics or computer programming course. Emphasis is placed on how to apply the various techniques to biological problems rather than on mathematics or programming per se.
NRM 582: Fisheries management (Winter semester in odd-numbered years, with Dr. Carl Ruetz, 3 credits). This course provides an introduction to basic fisheries science and management, with an emphasis on freshwater systems. It assumes a basic familiarity with fish but no prior knowledge of fisheries management. The course focuses on the process of managing fish populations and their habitat, the required field and laboratory methods and gear, and a variety of useful modeling and statistical tools. Specific topics include statistics for fisheries management (experimental design and hypothesis testing, regression analysis, model selection, repeated measures), length-weight relationships, condition, age and growth, estimating mortality, gear bias, abundance estimation, population growth and harvest, the yield-per-recruit model, bioenergetics models, and stocking and regulations.
BIO 580: R programming for scientific computing (Winter semester in even-numbered years, 3 credits). This course uses the R programming language to introduce students to the craft of writing computer programs for applications in the biological sciences. The emphasis is on programming concepts and constructs common to many programming languages that are widely used in scientific applications, though some of the most useful idiosyncratic features of R are included, as well. The course covers basic programming techniques, various numerical methods that are useful in scientific applications in the biological sciences, and technical graphics.