Another type of problem that you may see is testing if a population is in Hardy-Weinberg Equilibrium. So here, you're going to be given data from an actual population, and you want to know if it matches the Hardy-Weinberg expectation. So we're going to broadly say here to start, just to test if a population is in Hardy-Weinberg equilibrium, we need to compare those actual genotype frequencies to the Hardy-Weinberg expectations. Now, the reason you may want to do that is that Hardy-Weinberg equilibrium is sometimes used as a null model. In experimental design or statistics, a null model is the thing you compare your data to.
A null model is sort of what you would expect to happen if everything else is equal, if nothing interesting is going on. So that means that if the population is not in Hardy-Weinberg, if those two things don't match, well, we can assume one of two things. Because remember, for things to be in Hardy-Weinberg, we had some pretty big assumptions going in. So we can assume that at least one of those assumptions is broken. We can assume that there is either non-random mating in the population or that some type of evolution is going on.
Maybe there is natural selection on this gene, and it's removed alleles from the population. So in that way, we can look at populations and test whether these things are actually happening out there in the world. Now, to do this, we're given a sample from a particular population, and we see that it has 250 big A big A homozygotes.
We see that it has 100 heterozygotes and 150 little a little a homozygotes. And our question is, is this population in Hardy-Weinberg equilibrium? Well, we have these steps to solve here. They're pretty straightforward, and it's a decent amount of math, but we've actually done pretty much all this math before, so we should know how to do it.
Step 1, we are going to calculate allele frequencies. We need to calculate p and q, but we've already practiced that. Step 2, we need to plug p and q into the Hardy-Weinberg equation.
That gives us those expectations, and that gives us our p2, our 2pq, and our q2. And then, well, we need to compare it to the original. But the original here actually counts individuals. So we need to figure out what our expected counts would be. So we are going to multiply the expected frequencies by the actual number of individuals in that sample.
This will give us something to compare, and our final thing here is just to compare it to the original data. Now if you're really doing this, you'd need to use statistics and see if it's statistically significant. But in an introductory biology class, usually, they'll just make the difference big enough that you don't need statistics. It's very obvious if it is different.
Let's try this out. For our sample, the first thing we need to do is calculate the allele frequency. Again, we know how to do this:
We calculate p. We're going to take 2 times the number of big A big A homozygotes plus the number of heterozygotes and divide all of that by 2 times the total number of individuals. We calculate that 2 times 250 (number of bigA bigA) + 100 (heterozygotes) equates to 600. Dividing 600 by 1000 (total alleles) gives p = 0.6.
We already know what q equals, since p + q = 1. But again, to double-check, q calculation would be the number of heterozygotes (100) plus 2 times the number of little a homozygotes (150 each), divided by twice the total individuals (1000). This calculation confirms that q = 0.4.
Now, moving on to the genotype frequencies:
- p2 for bigA bigA will be 0.36
- 2pq for the heterozygotes will be 0.48
- q2 for little a little a will be 0.16
Now, we multiply these frequencies by the total sample size (500) to get the expected number of individuals:
- 180 expected big A big A homozygotes
- 240 expected heterozygotes
- 80 expected little a little a homozygotes
Now comparing these to the original (250 big A big A, 100 heterozygotes, 150 little a little a), we can see the population is not in Hardy-Weinberg equilibrium as the expected frequencies do not match the observed ones, indicating either non-random mating or some type of evolutionary process affecting allele frequencies.
We'll practice this more coming up. Check it out.
