Now, let’s get to the meat of this issue, the Hardy-Weinberg equation. You’ve seen it before, I’m certain.
This is how we’re going to derive our genotypic frequencies from the allelic frequencies that we see
in the population. It’s a little bit more tricky to go around this way because we have to use this
fancy equation which I could show you the derivatives of but it’s not really important.
What you need to know is that in this case, p squared equals the frequency of the dominant allele
or one of the alleles. It's really pretty arbitrary whether you assign it to p or q. Q is the frequency of the other.
So, 2pq is the frequency of the heterozygote and q squared is the frequency of the other gene form
or by default, we’ll just call it the recessive form. So p squared, 2pq, and q squared covers all three
of the genotypes that we were observing in the table. Now, you have a complete understanding, right?
Anyway, we can then break it down and say that if we are looking at the allelic frequency, we can say
the p is equal to the frequency of A and q is equal to the frequency of little a, such that the whole
population is covered by this little guy at the bottom, the ratio of p squared, the ratio of 2pq,
and the ratio of q squared. That covers our population. That’s how we might note these things.
Again you might ask, why on Earth do I need to know this Hardy-Weinberg principle equation
when I’m going to be a doctor, not a population geneticist? Well, the bottom line is you need to know it
because it’s going to be on your exam. You see the exclamation point at the top there.
We know it’s going to be on the exam. So, we need to understand how to work with it and what it all means.
Let’s take a look then at the Hardy-Weinberg law and where this equation came from and why
because it can be a little bit confusing to understand why we have some statement like this.
Hardy-Weinberg law, I need you to understand first that it is a theoretical case, right? It doesn’t really
exist in nature. Hardy-Weinberg equilibrium states that a population at equilibrium has an allelic
and genotypic frequencies that remain constant from generation to generation.
Now, as you probably recall, populations change, right? Allelic frequencies change in populations.
So, why have this crazy statement that’s totally theoretical? Well, the point is this is a standard
by which to compare evolution is happening or allelic frequencies are changing in a population.
If we set a standard that says what does it look like when they’re not changing, we can then say,
well, they might be changing because the frequencies have changed. Then we can look at
what things caused those changes. Again, that’s where we consider societal things as well as genetic
factors and environmental factors that might influence the prevalence of a particular allele.
Going back to the example that I introduced you to earlier in the lecture with the CCR5 receptors,
you could see that perhaps this spontaneous mutation that’s become hereditary has an advantage
when individuals are exposed to the HIV virus. Perhaps, when they experienced this plague
that we think that it might have selected for it in the beginning, it was also an advantage.
That’s why it has a prevalence in that population.