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.
