MathBench > Population Dynamics

Mutation and Equilibrium

>Episode 1: The Blue Hair Backstory

Simulating the Genotype

At the Assistant's the next meeting with the ME, he presented his findings: between 0 and 30% of people will have Bluehair, between 0 and 60% will be carriers, and between 40 and 70% will be unaffected.

The ME's narrowed-eye stare was hair raising. “I was expecting a more exact answer! “ he snapped, “and all you can give me are probabilities? You're going to have to do better than this. I'm getting pressure from upstairs.”

“The Mayor's office?”

“No, the people upstairs. They're tired of hearing me yell at you.”

“I won't let you down, Boss. I'll try every test.”

Dump out the m&m's again, just in case you, um, missed anything. This time, try taking a handful of m&m's, 6 blue and 14 brown. Mix them up in a cup, then draw them out in pairs. How many of each kind of pair do you get?


In case you don't have enough m&m's (anymore?), here is an applet that does the same thing, only we use 200 digital m&m's, instead of 20 real ones. In addition, the applet shows you how the results differ from the predicted maximum and minimum for each type.

The 200 alleles sort out like this:

  min possible actual max possible
brown-hair (homozygote) 40   70
carrier (heterozygote) 0   60
blue-hair (homozygote) 0   30


Try it a few times – how much do the results vary?