MathBench > Population Dynamics

Mutation and Equilibrium

>Episode 3: Revenge of the Mutants

The HW Genotypic Equilibrium Still Holds

“You're late,” said the ME as the Assistant entered his office.

“I couldn't find a taxi, so I had to take the Blue Line,” explained the Assistant.

“That's funny, I thought the only sure things in life were death and taxis,” said the ME. “So, do we have any theories on the cause of the increased Blue Hair Syndrome?”

“The major suspects are sunspots, global warming and Survivor reruns.”

“None of those are going to be ending anytime soon,” replied the ME. “How soon before we hit equilibrium?”

“Well, sir, we don't really 'hit' allelic equilibrium. It's more like a gradual approach. But I can tell you what the population will look like at equilibrium -- what the distribution of genotypes will be. ”

 

No matter what allelic frequencies we started with, the equilibrium frequencies (after 10 or so generations) was 333:167. In other words,

and

So contrary to the first Hardy-Weinberg predictions, the allelic frequencies (p and q) have changed.

But the second part of the Hardy-Weinberg predictions (the genotypic frequencies) depends only on random mating. And we're assuming that mating is still random.

taxiTherefore: