Discussions of conditions for Hardy Weinberg | Biology | Khan Academy

In the introductory video to the Hardy-Weinberg equation, I gave some conditions for the Hardy-Weinberg equation to hold. What I want to do in this video is go into a little bit more depth and have a little more of a discussion on the conditions for the Hardy-Weinberg equation.

Now, just to review what the Hardy-Weinberg equation is all about: if we have a population with a gene, say for eye color, and let's say that gene comes in two versions. One is the A allele that produces blue, and one is the a allele that produces brown. If p is the frequency of the blue A allele and q is the frequency of the brown a allele, well, if they're the only two versions, if you add the frequency of p (the blue) plus the frequency of the brown (q), they're going to add up to 100% or 1.

If you square both sides of this, you would get this expression right over here. We talk about this as the probability, or you could say the frequency, of being homozygous for the blue. This is the probability of having two alleles for the brown, and then right here in the middle, this is the probability of being a heterozygote. And why is that? Well, because you could get a blue allele from your mom or a brown allele from your dad, or a blue from your dad and a brown from your mom, so there are two ways to get that Pq combination.

Now, the key idea here is that Hardy-Weinberg assumes stable allele frequency. So let me write that really big, because all these other conditions that you might see are really like, "Well, what are all the different ways that you could not have stable allele frequency?" So let me write this down: stable allele frequency.

A lot of times, there's a temptation to memorize a bunch of stuff. You might want to do that, but the more important thing is to get the underlying idea, and the underlying idea is that something, somehow, could cause the allele frequency to be unstable. Actually, another way to say stable allele frequency is "no evolution."

No evolution means evolution is a change in the heritable traits in a population, and that will include a change in allele frequency. If you think about the two ways that you could have a population evolving, well, you can have selection. So we're going to assume no selection. Actually, there are more than two ways—genetic engineering and all sorts of things. So we're going to assume... but the mainstream ways, I guess you could say, are: we can assume no selection, we can assume no genetic drift.

Remember, selection involves certain traits that make that organism more fit for that environment. Those traits are going to be more likely to be passed on. Genetic drift is random chance changes in allele frequency. It could be due to small populations; it could be due to members of the population migrating or some type of bottleneck effect, or a natural disaster that really gets you to that small population.

So that's the big picture. Given that, I want to dive deep into some of the assumptions that you might see in your biology class, just so you feel comfortable with them and see that we're talking about the same thing.

The ones that I mentioned in that introductory video are "no selection," and that's consistent with "no evolution." I also talked about "no net mutation," which is also consistent with "no evolution." Once again, we don't want to change the allele frequency. If there was net mutation, maybe some of those blue versions of the gene get a mutation and they're not, maybe a different version, or they're definitely not blue anymore. So the allele frequency would change.

The reason why we care about large populations is mainly for genetic drift. If you have a very small population, just due to random chance, it's more likely that the allele frequencies can change appreciably.

Now, other conditions that you will often see are things like random mating. Whether an organism has the blue or brown version of the gene does not make them any more or less desirable to a member of the opposite sex. If you think about it, you might say, "Well, isn't that a form of selection?" And you'd say, "Well, yes, it kind of is," but this is sometimes broken out as another way.

Now also, no migration means the population isn't growing by other organisms entering it or isn't shrinking by other organisms leaving. There’s also not a mixing of populations between two populations. Once again, it’s all because we care about stable allele frequencies.

Now, if we want to go even further than that—and sometimes you will hear these types of things mentioned—although I just mentioned the five mainstream things, which all boil down to stable allele frequency, no evolution, no selection, and no genetic drift. Sometimes, we are assuming that we are dealing with diploid organisms—that you're getting one set of chromosomes from your mom and one set from your dad, or one version of an allele from your mom and one version from your dad.

You might say, "Well, how can you be other than diploid?" Well, there are tetraploid populations, especially this can happen in plants, or you could get two sets of chromosomes from your mom and two sets from your dad. We are assuming sexual reproduction—that we're not dealing with cloning or just budding where you're just a copy of another organism from generation to generation.

We're assuming that whether you are blue or brown, whether you have those versions, that’s not correlated with what sex you have or what sex you are. So, allele frequency should be the same in all sexes, and we're assuming sexual reproduction. Once again, we’re assuming there are only two sexes.

So you could, you know, if you were to think about... if you were to let your imagination go wild, you could imagine a lot of other constraints to put here or other ways where you could no longer apply the Hardy-Weinberg principle. We have two alleles; we're assuming sexual reproduction, diploid, you're getting a version from your mom and a version from your dad.

Here are all the conditions that help us ensure that we have a stable allele frequency. Now, the one thing you're saying is, "Okay, I can, you know, diploid sexual reproduction, okay," but isn't there always a chance for a little bit of genetic drift? Isn't there, you know, just the history of the world is that we have this evolution? The answer is yes.

The actual reality is that there are very few places where you could point to—very few populations, if any—where you can say, "Oh, that's a pure..." we can purely apply Hardy-Weinberg there. But, like a lot of things in the applied sciences, it's a very good approximation for many populations, and so that's why it is useful.