Trees, Chains, and Chances

The relatively new field of bioinformatics is undergoing explosive growth. Even before the current impetus provided by the sequencing of complete genomes and the steady increase in affordable computing speed, the discipline of biology had a well-established subfield of mathematical biology. Applications of mathematics ranging from simple statistical inference to the development of intricate mathematical models supported a wide variety of biological studies.

Now as a blurring of disciplinary boundaries occurs with the advent of such fields as informatics and cognitive science, the interaction among biology, mathematics, computer science, and these newer multidisciplinary fields is increasing. Problems encountered in one area not only borrow tools or concepts from another discipline but also sometimes drive development of new tools and theories in other disciplines.

This article focuses on a problem at the intersection of genetics, evolution, stochastic processes, and computer science. One current approach to the problem involves combining two previously independent mathematical tools. These tools relate directly to topics in the high school mathematics curriculum: matrices, probability, and computer simulation. In turn, we look at the biological problem, the two separate mathematical tools, and briefly their combination in solving a problem in evolution. This contemporary interaction involving biology, mathematics, and computer science provides a rich context in which to situate some fundamental mathematics, and can provide some students with a glimpse of where their future studies might lead them.