The Midge Problem

In 1981, two new varieties of a tiny biting insect called a midge were discovered by biologists W. L Grogan and W. W. Wirth in the jungles of Brazil. They dubbed one kind of midge an Apf midge and the other an Af midge. The biologists found out that the Apf midge is a carrier of a debilitating disease that causes swelling of the brain when a human is bitten by an infected midge. Although the disease is rarely fatal, the disability caused by the swelling may be permanent. This is no insect to mess with! The other form of midge, the Af, is quite harmless and a valuable pollinator. In an effort to distinguish the two varieties, the biologists took measurements on the midges they caught. The two measurements taken were of wing length and antennae length, both measured in cm.

Af Midges

Wing Length (cm) / 1.72 / 1.64 / 1.74 / 1.70 / 1.82 / 1.82 / 1.90 / 1.82 / 2.08
Antenna Length (cm) / 1.24 / 1.38 / 1.36 / 1.40 / 1.38 / 1.48 / 1.38 / 1.54 / 1.56

Apf Midges

Wing Length (cm) / 1.78 / 1.86 / 1.96 / 2.00 / 2.00 / 1.96
Antenna Length (cm) / 1.14 / 1.20 / 1.30 / 1.26 / 1.28 / 1.18

Is it possible to distinguish an Af midge from an Apf midge on the basis of wing and antenna length? In your work, determine a method for distinguishing the two varieties of midges. Write a report that describes to a naturalist in the field how to classify a midge he or she has just captured. The following are some questions that you might want to consider.

  1. If you make an error in your classification, would you rather call an Af midge and Apf or an Apf midge an Af? How does this affect your classification scheme?
  1. There seem to be more Af midges than Apf midges, so if a midge is captured it is more likely to be an Af midge. How can this be taken into account?
  1. Would using some combination of the measurements (sum, difference, product, quotient, sums of squares, or other combination) help distinguish the midges?
  1. The variation for the Apf midges is different than the variation for Af midges. The average residual for the Apf midges is not the same as that of the Af midges. How can this difference affect the boundary defined between the two types of midges?

It is important to know if a midge is dangerous or not. Suppose five additional midges were found in traps today. Their measurements are:

Midge A / Midge B / Midge C / Midge D / Midge E
Wing Length (cm) / 1.70 / 2.02 / 1.88 / 1.96 / 1.78
Antenna Length (cm) / 1.36 / 1.32 / 1.30 / 1.54 / 1.22

How would you classify each new midge? Which classifications do you have the most confidence in and why? Support your answer.

This is to be submitted as a project report from the group ( one copy only per group), neatly typed, double spaced. It must include everything needed to support your conclusions. Be accurate and specific in your findings.

Grading Rubric: 100 point project

25 pts Neatly typed, double spaced report with correct spelling & sentence structure

25 ptsReport is in scientific form as reporting to a group of scientists in the field.

25 ptsMathematical model is accurate, detailed, and clearly explained.

25 ptsFive new midges are accurately classified (they cannot all be classified as Apf).

Final Report is due at the beginning of class on March 27 ( 3rd) or March 30 (6th)