MathBench > Population Dynamics

Mystery of the Missing Housefly

...and an equation

I poured myself a stiff one, to clear my head. The numbers were crashing into each other like a county fair demolition derby, but the answer was still coming out the same. “And…” I said.

 

Let's look at the equations in a little more detail:

flies t = 120* flies t-1 - .99 * 120 * flies t-1, which simplifies (using algebra only) to

flies t = (120 - .99 * 120)* flies t-1 , and doing some math I get

flies t = 1.2* flies t-1

dead houseflySo, I can simplify the growth-and-death equation into something that looks a lot like an exponential growth equation -- in fact, it is exponential growth. In both cases, the number of flies in a certain month equals the number of flies the month before multiplied by some constant number.

So we can say that these two models have the same functional form , and therefore the same shape on a graph. The form is

flies t = r * flies t-1

where r is the "rate of growth", taking mortality into account.