MathBench > Population Dynamics

Mystery of the Missing Housefly

You write the equation

I prefer action to words, and I prefer words to numbers, and I prefer just about anything to formulas, but the two century notes she laid on my desk were having the desired effect.

If I was going to crack this case, I'd have to use my head for something other than a battering ram. Just how many of Ms. Domestica's relatives were missing, and how much insurance money did that add up to?



OK, let's give it a try. I'm going to pick some small numbers, so as not to overwhelm your calculator. Let's say you start with 3 flies, and each fly lays 2 eggs at a time, which take 1 month to mature. After 1 month, all of the new flies lay eggs and die on the spot.

Your assignments are:

  1. write an equation for this process,
  2. write the initial condition
  3. iterate the equation for 12 months (use a calculator!), and
  4. graph the population dynamics

houseflies reproducingIn case you need some hints:

  1. To write an equation, think about how fliest (number of flies at time t)
    relates to flies t-1 (number of flies the month before).
  2. The initial condition is simply how many flies there are at the Beginning of Time (fliest=1)
  3. To iterate your equation, start at time 0 and work forward for 12 months,
    making a table with months and flies as headings
  4. To graph the dynamics, just graph the table of numbers you created in the third step.