Application Centre Highlights
Population Biology Applications

Submitted by Matt Miller, University of South Carolina

For many years, biologists have used differential equations to analyse population trends and biological systems. At the University of South Carolina, Professor Matt Miller has implemented many of these classic models in Maple. These worksheets supplement the course notes for his undergraduate Population Biology course.

For example, in his application The Dynamics of Arthropod Predator-Prey Systems, Miller illustrates the fluctuating populations of a predator and a prey in a closed environment. Modification of the model’s parameters in Maple shows students the predicted behaviour of predator-prey populations in different environments.

Some of Miller’s applications provide Maple animations, allowing the students to visualise the full range of effects of a parameter on the behaviour of the system. For example, in the application Biological Populations with Non-overlapping Generations, Miller examines how initial conditions such as population size and growth rates affect the long-term population levels of both a single species and two competing species. As part of the analysis, Miller produces a bifurcation diagram in Maple that shows the distribution of stable points as a function of the growth rate.

Fourteen of Professor Miller’s biology applications are available at http://www.adeptscience.co.uk/go?pg=H33