Introducing Transition Matrices and Their Biological Applications

The Blue Waters Undergraduate Petascale Education Program (NSF) sponsors the development of educational modules that help students understand computational science and the importance of high performance computing. As part of this materials development initiative, we developed two modules, "Time after Time: Age- and Stage-Structured Models" and "Probable Cause: Modeling with Markov Chains," which develop application problems involving transition matrices and provide accompanying programs in a variety of systems (C/MPI, C, MATLAB, Mathematica). Age- and stage-structured models incorporate the probability of an animal passing from one age or stage to the next as well as the animal's average reproduction at each age or stage. Markov chain models are based on the probability of passing from one state to another. These educational materials follow naturally from another Blue Waters module, "Living Links: Applications of Matrix Operations to Population Studies," which provides a foundation for the use of matrix operations. This paper describes the two modules and details experiences using the resources in classes.