Hi. It's Mr. Andersen and in this podcast I am going to hopefully show
you how to solve Hardy-Weinberg problems. Here's Hardy, here's Weinberg. They came up
with this wonderful idea of Hardy-Weinberg Equilibrium. It's used by geneticists and
evolutionary biologists. But little did they know they would plague biology students forever
as they try to solve these problems. And so this would be a typical Hardy-Weinberg problem.
We've got 16% of the population unable to taste a chemical. And they're asking a number
of questions like how many people are heterozygous? What's the allele frequency? And when I have
students who struggle with this, basically all these terms are kind of swimming around
in their head and they have no idea what's what or where to even start. And so I want
to kind of go back to basics and show you what a gene pool is. And then show you how
to solve some of these problems. And so let's start with a sample population. Let's make
this population really really small. Let's say we have ten people. So we've got ten people
here. And half of them have red hair. And so to have red hair you have to have two red
alleles. So this would be a person with red hair, red hair, red hair, red hair, red hair.
So half of the people have red hair. And then half of the people don't. And so this would
be somebody who maybe has black hair. Or this could be somebody who has blonde hair. Or,
it doesn't matter. But they don't have red hair. And since it is a recessive, you have
to have two copies of it. Okay. So this would be the population and this would be their
phenotypes, physically what they look like. But if I take all of those genes in a population
and scramble them up and put them in a pool, then it becomes a gene pool. Now they're not
associated with one individual anymore. And so basically, this is a gene pool. And so
there are two values that I want to throw out. The first one is p. And the second one
is q. p is going to be the allele frequency of the dominant trait. Okay. So what's the
dominant trait? That's going to be this non-red. And so I'm going to say one, two, three, four,
five, six. There's six of them. And there are 20 total alleles here. There are 20 total
genes. And so our p value would be 0.3. And so now how do we figure out the q value. Well
the q value I could count up all of the red ones, it's going to be 14. And then I divide
that by 20 and it's going to be 0.7. Another quick way to do that is if you figure out
that this is 0.3, p plus q will always equal 1. And so I could've just taken 1 minus 0.3
and that would have given me my q value. And so what does this mean? Well, in a gene pool
this means that 30% or 0.3, be cautious of percents because they can get you in trouble
when you're solving the problem. But 30% of the individuals are going to be of the genes
are going to be on the dominant and 70% are going to be of the recessive. Now if you know
anything about genetics, we can figure out where the rest of the Hardy-Weinberg comes
from. So what are the odds, if I were to just grab one of these. If I were to just randomly
grab one of these genes out of the gene pool, what is the odds that that is going to be
recessive? In other words, what are the odds that it's going to be red? Well the odds would
be 7 out of 10. What are the odds, if I pulled two of them out? That they're going to be
red? Well knowing anything about the law of multiplication, that's going to be 7 out of
10 times 7 out of 10. And so that's going to be 49 out of 100 or that's going to be
0.49. So grabbing two of the reds, it's going to be 0.49. Let's do that again with the blues.
What are the odds of me pulling a blue out and then another blue out? It's going to be
3 out of 10 times 3 out of 10, and that's going to be 9 out of 100 and that's going
to be 0.09. Okay. So for me to get two of the recessive, it was 0.49. For me to get
two of the dominant it's going to be 0.09. So what are the odds of me pulling out a blue
and then a red? Well to do that it would be a 7 out of 10 of the red times a 3 out of
10 of the blue. So that's going to be 21 out of 100. But I don't have to necessarily pull
out a red on the first time and a then a blue on the second. I also could do it by getting
a blue on the first time, 3 out of 10 times 7 out of 10 and so that would be a 21 out
of 100. And so I have to add these two because I could get a red and a blue one in two ways.
And so when we look at the equation for Hardy-Weinberg Equilibrium, let's go to that, where do we
get this p squared 2pq q squared? p squared is basically taking the allele frequency of
the dominant when we were solving this problem, that was 0.3. And then we simply square it.
And that's going to tell me how many individuals are homozygous dominant. In other words they
have one of each of the genes. What are the odds of me doing this one? In this case our
recessive value is 0.7 squared. So that's going to be 0.49. That's the homozygous recessive
individuals. And then the heterozygous individuals are going to be 2 times p times q. Because
you could get it either red, blue or blue, red. So either of those. And so this is where
this term comes from. And so basically even though I may have lost you at this point,
the big thing to remember is that if they talk about the allele frequency, then they're
talking about the p value and the q value. If they're talking about individual people
or individual organisms, or individual phenotypes, then they're talking about p squared 2pq and
q squared. Because it's vital when you're trying to tackle one of these problems that
you know what you're given on day one, or on the first step. And so let's try this problem
again. So what does it say? It's says, let's break down this thing. 16% of a population
is unable to taste this chemical. These non tasters are recessive for the tasting gene.
So if you think you know how to do this, you may want to pause the video and try to work
it out. And then I'll show you how I would work it. Pause video. Okay. So here we go.
So basically what are they telling me? They're saying 16% of a population. So are they talking
about genes? Or are they talking about people? Well they're talking about in a population.
They're saying 16% of the people are unable to taste it. And so what are they telling
me? They're telling me, you know, p squared 2pq or q squared. Almost always when you're
solving one of these problems they have to tell you the individuals who are homozygous
recessive. And the reason why is if you're dominant for the trait we can't tell if you're
homozygous or heterozygous. So they almost always start with q squared. So they're telling
me q squared equals, and now we want to get rid of the percent. We're going to say equals
0.16. Okay. So 16% or 0.16. So now my goal in any problem, even though I haven't even
looked at the questions here and what they are, is to get to p and q. Because if I can
get to p and q I can solve any problem. Okay. So how do I get to q? I could take the square
root of this side. I could take the square root of that side. I could say q equals 0.4.
I could say p equals 0.6. And now I can just smile to myself because I know I can solve
any problem that they ask me with just a little bit of common sense. So I've got my p and
q values. So let's look over the questions they ask. Number 1. What percent of individuals
in the population are tasters? Well let's use a little common sense. They're saying
that 16% are non-tasters. And so that means that everybody else has to be a taster. So
I would say 84% on this first one. Okay. Let's look at the next question. What is the frequency
of the dominant allele? And what's the frequency of the recessive allele? Well the frequency
of the dominant allele, we've already solved that. That's going to be our p value. So that
would 0.6. And then what about the recessive allele? That's going to be 0.4. That's going
to be my q value. So I'm golden so far. Now let's go to the next one. What percent of
the population are heterozygous for the trait? So now we have p and q. We can solve for this.
Heterozygous remember are always going to be those individuals that are 2pq. So it would
simply be 2 times p, which is 0.6, times q which is 0.4. So this is going to be .24.
So I would say the total is going .48. Or if we're looking for a percentage here I would
say it's 48%. Okay. So the majority of questions you get when you're solving Hardy-Weinberg
questions, they're almost always going to start by telling you the individuals who are
q squared. And so if you remember that and it's an individual, then you're going to do
well. Let's go to another problem though. Because this is another way you can be asked
this question. Let's look at this one. This one the delta-32 mutation, a recessive gene
gives humans protection from HIV. The allele frequency in a town in Sweden is 20%. Okay.
So what are they telling you here? This is another thing that they can tell you. They
could tell you the allele frequency. So this is super important. They're telling me the
allele frequency and they're also saying that that's recessive. Okay. So what have they
told me? I know right away that they've told me q. In this case they're telling me that
q equals 0.20. I say p equals 0.80 and we know that immediately right away. And so now
I again smile to myself because I can solve any problem they ask me. Okay. So let's look
at this one. What percent of the population have two copies of the gene and are therefore
immune to HIV? So now they're saying 2 copies of this recessive gene, so what are they telling
me? Now they're saying solve for q squared. So q squared equals 0.2 squared. And so q
squared equals .04. Now a common mistake that people make when they're solving this is that
they take 0.2, they square it and in their head they somehow think that's going to be
0.4. And why is it not 0.4? Well if you have that mistake, trust me, put it in your calculator.
I'm right. If we take 0.2 squared, a good way to check that is to write 2 over 10 times
2 over 10. And that equals 4 over 100. And so that equals 0.04. Okay. So we've solved
this one. It's going to be 0.04. Let me clear that out. Next one they're saying what percent
of the population are less susceptible to the disease since they are heterozygous? Oh.
So to solve that one again, it's going to be 2 times p times q. So that's going to be
2 times 0.8 times 0.2 and so I get like 0.32. Or if they're asking what percent I would
call that 32%. Okay. And so that's how you solve Hardy-Weinberg problems. Remember pay
attention because they're going to tell you specifically either a q squared value or give
you a way to figure out a q squared value. Or they're going to start by telling you allele
frequency. And you want to work to p and q. And then you can solve anything else. And
so I hope that's helpful.