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# Applying the Hardy-Weinberg equation

The Hardy-Weinberg equation can help to estimate allele frequencies in a population. Dominant (p) and recessive (q) allele frequencies and genotype frequencies can be calculated using the equation p² + 2pq + q² = 1. In this video, eye color is used as an example to determine allele frequencies and genotype distribution. Created by Sal Khan.

## Want to join the conversation?

- some people have blue eyes when they are born and then gradually with time their eyes keep changing colour. How is this possible?(21 votes)
- Great question! Babies eye color changes when the pigment producing cells aren't active at birth. Over time these cells start to produce pigment and the eye color of the baby changes.(46 votes)

- So are genetic diseases like cloud blindness or hemophilia can be fixed.....? Can you knock out the genes with those mutations in a person and replace with other genes?(14 votes)
- yes they can be cured by gene therapy.the defective gene is removed and a normal gene is replaced there.but at present practically gene therapy is still in infant stage(15 votes)

- I'm a little confused, In the other genetics class I'm taking, they said that Hardy Weinberg is used to calculate the expected genotype frequency, which is then compared to the actual genotype frequency and used for things like determining gene flow. But here, it seems like Hardy Weinberg is being used to calculate the actual genotype frequency? I thought that the criteria for Hardy Weinberg could never actually be met, and one of them was infinite population size, not just a large population as stated in this video?(6 votes)
- Yes Hardy-Weinberg is mainly used to calculate the expected frequency assuming: no mutations, no gene transfer, random mating, large population, and no selection. However if we know the actual frequency of the homozygotes (i.e. p^2 and q^2) in the actual population we can compare to an expected value. So p+q should = 1 , in a real population if p^2 = .36 (p=0.6) then q would have to be 0.4. If it deviates from that value then the system isn't in H-W equilibrium. So by comparing the actual to the expected you can determine if a population is in equilibrium or if they are changing (evolving).(22 votes)

- If a person has different colored eyes, does that increase the chance that the offspring will have two different colored eyes?(8 votes)
- Yes, it's true that animals like what Dhruv Indiresh mentioned might have different coloured eyes. But this is also possible in humans. It's called Hererochromia, when a person has 2 different coloured eyes. There are several people with such a case. The list is here http://en.wikipedia.org/wiki/List_of_people_with_heterochromia.

I hope this helped and I'm sure you might be able to do more research on how this occurs in Humans now :)

Edit: Heterochromia Iridum, to be exact.(5 votes)

- how should I know which hardy Weinberg equation should use?(4 votes)
- I know that this is a late response, but for anyone else who has this question, the p+q=1 equation is used to find the allele frequencies themselves, whereas the
*p2+2pq+q2=1*equation is to find the number of individuals, or the population, that has that specific genotype, or set of alleles.(12 votes)

- In these videos we have taken the theoretical case of an eye colour gene which has only two variants and thus the Hardy-Weinberg Equation applies with such ease as in multiplication of binomials and such

But in the real world we have numerous different genes with numerous different allele possibilities so how does the Hardy-Weinberg equation apply on such large and complex scales??(4 votes)- "how does the Hardy-Weinberg equation apply on such large and complex scales??"

In short, it doesn't. There is no population where you can observe the occurrence of a particular phenotype, and then determine exactly the proportion of individual alleles.

The conditions for a Hardy-Weinberg equilibrium are pretty strict, but there are some populations that will exhibit some of these conditions a bit more than others. So in some cases, it can be used as a rudimentary predictive tool, but should not be solely relied upon.(7 votes)

- When sal was getting 2pq, how did he end up with 0.42?(2 votes)
- There are two ways of solving for this - in the video Sal plugged in the probability of "p" and "q" which were
**0.7**and**0.3**respectively into the equation. He also could have subtracted the values of p^2 and q^2 from 1. Either way, the end result comes out to 2pq =**0.42**.(3 votes)

- My professor told our class that we are not supposed to sqrt the q^2 term, since that does not give us the true q value, which he said must be solved by including the q in the heterozygotes.

I'm slightly confused...(2 votes)- In this case q is recessive, so if someone has blue eyes, they will always have the genotype bb. If we were talking about people with brown eyes, we would have to include the 2pq term because people with brown eyes can be either BB or Bb, but a heterozygote will always have brown eyes, so we cannot include heterozygotes when we count the probability of an individual having blue eyes.(2 votes)

- just thinking, it is not completely true that an offspring must always get one of two alleles. Isn't it possible that no alleles are inherited? Let us say that in both the male and female gametes, the alleles just happened to be deleted. That means that the offspring does not inherit any allele for the gene.(2 votes)
- Only if mutation takes place, in that case, *new? allele s created. You mean gene is not expressed right?(2 votes)

- Does a green eye color allele + a blue eye color allele = blue-green eyes?(2 votes)
- First of all blue eyes are not from alleles that produce blue pigment. The eyes without pigment scatter/refract light is a similar way that the sky does making it blue. If there is some yellow pigment it produces the green color, if there is a bit of brown pigment you get hazel eyes. This video touches on this: https://www.youtube.com/watch?v=FOiV6pUF6lI(2 votes)

## Video transcript

Voiceover: Let's stick with
this idea, the simplification, that there's a gene for eye color, and it only comes with two variants. It has the dominant variant, which codes for brown eye color, and it has the recessive variant, which codes for blue eye color. So if either one of your
alleles is this capital B, you're going to have brown eyes, the only way to have blue
eyes is to have a lower case, is to be homozygous for
the recessive allele. Now let's say that in a population, it's a large population, one that meets all the Hardy-Weinberg
Equilibrium assumptions, let's say that you were to
observe that nine percent of this population has blue eyes. So now we're talking about the phenotype. You can actually observe
that they have blue eyes. Based on this, can we figure out p, which is the frequency
of the dominant allele. Can we figure this out? And can we figure out q,
which is the frequency of the recessive allele, can
we figure that out as well? I would encourage you to pause this video and based on what we saw of
the Hardy-Weinberg Equation, can we figure these things
out, given this information? Well let's revisit the
Hardy-Weinberg equation. We've worked it out in a previous video, but I'll rewrite it right now. It says, the allele frequency for the dominant allele frequency squared, plus two times the
dominant allele frequency times the recessive allele frequency, plus the recessive
allele frequency squared, is equal to one. And we saw that this
just comes from the idea that p plus q is going to be equal to one. There is a 100 percent chance,
if you were to randomly pick a gene, that it's
one of these two variants. Now when we say nine
percent has blue eyes, what does that mean? Well the only way to have blue eyes is if your genotype is
homozygous recessive. Because if you have a capital B in here then you're going to have brown eyes. So we can say that nine
percent also has this genotype. Or you can say that the
frequency in the population of this genotype is nine percent. But we've already seen, that's exactly what this term right over here is. That's this q squared term. This is the probability,
one way to think about it, of getting, q of course is the frequency of the recessive allele,
now you could view this as the probability of getting
two of the recessive alleles. In your population, it's
going to be nine percent. So we could say q squared
is equal to nine percent. Or another way to think about it, this term over here is
nine percent, or 0.09. Nine percent has this genotype, that's what this tells us right over here. So then we can solve for q. If q squared, I'll write
it as a decimal, 0.09, that means that q is going to be the square root of 0.09,
which is equal to 0.3. Just like that, we were able to figure out the allele frequency of
the recessive allele. And I could write that as a
percentage, 0.3 or 30 percent, if you were looking at the
genes in the population, 30 percent express our code for the recessive allele, or
the recessive variant. Based on that, we can figure out what percentage code for
the dominant variant. The rest of the genes must code for the dominant one, because we're assuming there's only two of them. P plus q equals 100 percent, or p plus q is equal to one. So this must be 70 percent. So just based on that, we can kind of dig a little bit deeper here. So what is p squared? P squared is going to be 70
percent squared, or 0.7 squared. So this right over here is
0.7 squared, which is 0.49. So one way to think about
it is, based on this, and once again, it's a simple equation, but these really neat ideas are starting to pop out of it based
on just this information. We're now able to say that 49 percent of the population is
going to have a genotype of capital B, they're going
to be homozygous dominant. And then we can figure
out this right over here. Two times p times q, that's going to be two times 0.7, times 0.3. So let's see, that's going
to be two times 0.21, so this right over here
is going to be 0.42. Or another way to think
about it is, 42 percent of this population is going to have the genotype upper case
B and lower case b. And you see they all add up. 49 percent plus 42 percent is 91 percent, plus nine percent all
adds up to 100 percent. So you get a little bit
of information here, and based on what we know
about allele frequencies, making a few assumptions,
we're able to get a lot more knowledge
about this population. And this is actually
very useful in real life, when people think about,
say, a recessive allele that might cause some type of a disease, based on the incidents of that disease, people can start to think about, "What percentage of the
population is a carrier?" Say they're heterzygotes for that disease. So this is actually very
useful in real life.