Hardy Weinberg Equation and Equilibrium

Описание: This video walks through the Hardy-Weinberg equation and a sample problem.

** If there are any pictures used in this video, they are NOT MINE and I will not take credit for them. **

TRANSCRIPT:
In an AP biology course, you’ll come across a lot of Hardy-Weinberg problems and you might even see a few on the AP exam. Essentially, the Hardy-Weinberg equation is used to see if a population’s allele frequencies are in equilibrium. This doesn’t mean that the dominant and recessive alleles are at the same frequencies, it just means that the frequencies are the same from year to year. There are five factors that keep a population in Hardy-Weinberg equilibrium, and these are: no natural selection, no gene flow, no mutations, random mating, and a large population. If you think about it, each of these makes sense: no natural selection ensures that the alleles don’t have an advantage over the other, or else one would increase in frequency. No gene flow ensures that there aren’t any new alleles coming in from immigration or emigration, no mutations means that there aren’t going to be any new random alleles, random mating means that organisms aren’t choosing mates based on specific traits, and a large population ensures that any changes from generation to generation don’t have as big as an influence. Here’s the Hardy-Weinberg equation.
So you’ll see here that we have p-squared plus 2pq plus q-squared equals one. Another part of the equation is the fact that p plus q equals one. See how both of these equations equal one? Now, the variable p stands for the frequency of the dominant allele. On the other hand, q stands for the frequency of the recessive allele. Alright, so now that you know that, let’s get to this bigger equation over here. P-squared stands for the frequency of those who are homozygous for the dominant allele, meaning that the individual has two dominant alleles. Let’s take this eye color example for a moment. The brown allele is dominant, and the blue allele is recessive. If you get two brown alleles, then you have brown eyes. If you get one brown allele and one blue allele, then you still have brown eyes because brown is the dominant allele. If you get two blue alleles, then you end up with blue eyes. Simple enough, right? Well, if you get two of the same alleles, that means you’re homozygous for it. If you get two different alleles, such as one brown and one blue, that means you’re heterozygous. Going back to what I said earlier, p-squared stands for the frequency of those who are homozygous for the dominant allele, so in this case, it would be people with two brown-eyed alleles. That’s why it’s p-squared: they have two of the same thing. It’s the same for q-squared: they have two recessive alleles.
Now let’s take a look at the middle term, 2pq. It makes sense because there’s a p here and a q here, meaning they have one dominant allele and one recessive allele. But where does the 2 come from? Actually, this means that there are TWO ways to get heterozygous offspring. Take a look at this Punnett Square. If you cross two heterozygotes, there are two ways to get another heterozygous child. That’s because the mother might be giving a recessive allele and the father might be giving a dominant allele, or vice versa.
Now that you know what each term stands for, let’s take a look at a sample problem. In a certain population, 16% of people have blue eyes. Find the value for each term of the Hardy-Weinberg equation.
One of the answers is right in the problem. It says that 16% of people have blue eyes. When you write 16% out as a decimal, you get .16. And, it says that 16% of the people have blue eyes, so they’re referring to the amount of people with a particular genotype. We know that when you have blue eyes, you must be homozygous recessive, since blue eyes is a recessive trait and you can only have blue eyes if you have two recessive alleles. That means that we should assign q-squared the value of .16. Now, we can work out the rest of the problem, first by finding q. Q is just the square root of q-squared, so the square root of .16 is .4. This makes sense because .4 times .4 is .16, which is the same thing as saying q times q is q-squared. Now that we’ve got q, we can use .4 as a value to figure out what p should be. .4 plus .6 is 1, so p must be .6. And, since we know that p is .6, we can find out p-squared by squaring .6, which gives us .36. See, we’re almost done! The last thing to do is find out 2pq, which is easy since we already know what p and q are. So, we just have to plug in p and q into the equation, and you get this.
So that’s it for Hardy-Weinberg! If you have any questions, feel free to comment below. Thanks for watching!