Genetics and a Mathematically Indefensible Historical Moment

Mathematical modeling is an important tool in both governmental policy decision-making and in industrial planning. In mathematical modeling, we develop a function, a graph, an equation, or a simulation based on assumptions about a situation. The results often give insight into the situation. The expense of making a mathematical model is usually significantly less than making a prototype. Even more importantly, a math model can sometimes help us avoid making decisions that may have disastrous effects on humans and our environment.

In this article, we are going to develop and analyze some models related to population genetics. In particular, we are going to study how the genetic makeup of a population changes over time as a result of natural and manmade influences.

We begin by developing models related to the failed "eugenics movement" of the late ninteenth and early twentieth century. This worldwide movement promoted forced sterilization of individuals deemed to have harmful genetic traits. The movement particularly targeted mental retardation, with the goal of eliminating mental retardation.