An Experimental Approach to Mathematical Modeling in Biology

The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context. We then describe Bugbox-population, a virtual insect laboratory that allows students to make observations and collect quantitative data easily, thereby learning mathematical modeling in the context of its use in scientific research. Creating a mathematical model for boxbugs involves the same intellectual work as creating a mathematical model for real insects, but without the difficulties involved in collecting real biological data. The analysis of the Bugbox-population data leads to the development of the eigenvalue problem for population projection matrices.