The Synergy of Math and Science

Written By: 
Brian Hydefrost

Recently our Algebra 1 class had a great opportunity to look at Applied Mathematics in relation to an experiment they conducted in Biology.  The experiment was a simulation of natural selection in the wild.  They had taken 290 pistachios and colored the shells as follows: 100 Tan, 100 Black, and 90 Brown to simulate genetic variation within a generation.  Our students scattered these pistachio "bugs" outside and then went "hunting" for them on four different occasions.  They counted how many of each color they found in each hunt and calculated the percent found and different survival rates for each of the different variations.  Looking at this data they were able to see how color impacted survival.  But how could they simulate reproduction and see how the population would change over time? Natural selection occurs over many generations...

Math to the Rescue!

Having collected all their data it was now time to bring the project over to Math class for the next level of analysis.  We decided that we wanted to use this data to make a prediction about what would happen to these populations over time. Since we were studying the fictional pistachio bug we had to begin by defining the life cycle (and reproductive patterns) of our make believe bugs.  This allowed us to derive a formula for each variation that predicted the population after x years.  They students used these formulas to graph the populations over time. 

For the final phase of the project we analyzed and talked about our findings.  One student pointed out that it was interesting to note that although the Brown bugs had started out as the smallest percentage, after only two years it would be the most common.  Another student started looking at what the populations must have been in the past by putting negative values into our formulas.  This led him to discover how long ago the original mutation occurred that spawned the brown variety of pistachio bugs. Students had a much easier time writing up their scientific format papers with the data and ideas they generated in Math Class.

All in all, it was a fun and exciting way to look at how Mathematical Models can be used to make predictions, and the role that Math plays in the realm of Biology.  But more importantly we produced some ground breaking research on the little known North American Pistachio Bug.