Hi. It's Mr. Andersen. And in this video I'm going to talk about the Hardy-Weinberg equation.
Which is an equation that's used to determine the frequency of genes in a population. Before
we get to the equation, let's define a few terms. The first on is a phenotype. A phenotype
is going to be the physical characteristics that an organism has. And so the only difference
between these two individuals here is in the color of their hair. And so the difference
is going to be in their phenotypes. This person has red hair. And this person has non-red
hair. Now when you're looking at me, you're looking at my phenotypes. Now the phenotypes
however are caused by genes that we possess. And so we're going to posses two genes. And
a gene is simply a section of DNA that codes for a specific phenotype. And so the types
of genes are called alleles. And so in this case this individual has two genes. But both
of them are going to be non-red genes. Or non-red alleles. This person right here has
red hair phenotype. But its alleles are going to two red genes. And when we're solving genetic
problems we'll use letters to represent those. Big R big R stands for non-red genes. And
little r little r stands for red hair. But what happens if you were to get one of each?
What happens if an individual has one of the non-red genes and one of the red genes? What
color is their hair going to be? Well if you know anything about genetics you know that
they're going to have non-red hair. And that's because the red gene is recessive to the non-red
gene. And so these two things pictured here are the phenotype or the physical characteristics
of this individual. And the genotype, or the genes that they possess. And so let's check
our understanding. I'm going to show you a few things. And what I want you to do is tell
me if this is a phenotype or a genotype. I'll pause for a second to let you answer. And
so let's start with the first one. Let's say an individual has Huntington's disease. That's
right. That should be a phenotype because it's going to be the physical manifestation
of their genes. Let's try another one. Let's say an individual can taste PTC. Or a chemical.
That would also be a phenotype. Because it's their physical manifestation of their genes.
Let's try another one. Let's say an individual is a carrier of cystic fibrosis. That would
be their genotype. Now what that means is that they're carrying one cystic fibrosis
gene but we couldn't see that by looking at them. In other words they're not going to
have cystic fibrosis. And so this would be a genotype. And when you're solving problems
related to Hardy-Weinberg it's important that you figure out right away, are we talking
about a phenotype? Or are we talking about a genotype? Now the way I like to explain
alleles and how genes interact is using socks. And so basically you might think of it like
this. If you have a red sock. That's like having an allele for red hair. And if you
have a non-red sock that's like having an allele for non-red hair. And so basically
an individual is going to have two copies of a gene. And so if you have two red genes,
then you are going to have a genotype of red, red. And what kind of a phenotype are you
going to have? Well using socks, what we can do is if I tuck one inside the other, because
you really only see that one thing. You really see only see that phenotype of the individual.
So again, if you have two red genes, you're going to have red hair. Likewise if I have
two non-red genes, what color hair are you going to have? Well, let me tuck this in to
make our phenotype. Basically you're going to have non-red hair. And so that's pretty
easy. Two red genes you're going to have red hair. To non-red genes, you're not going to
have red hair. But what happens if we were to have an individual that has one red gene
and one non-red gene? Well since this one is dominant to this gene, that basically means
that this other gene is going to remain hidden. And so when we look at this individual, we
can't tell what that other gene is. They're going to have non-red hair. And so if I were
to pick-up another individual and look at them. So this is their phenotype. This is
physically what they look like. You don't know what this individual is going to have
for its two genes. Because that other one is hidden. And until we actually pull that
gene out, and we see that oh, this individual had one non-red and one red gene, we really
don't know what their genotype is. And so it's very important when you're solving problems
that we go to the individuals who have two of the recessive alleles. Because if you have
two of the recessive alleles, in other words you have the recessive trait, we know not
only what your phenotype is but we know your genotype. Let's look at a sample population
of ten individuals. In this case we have five individuals who have red hair and five individuals
who have non-red hair. This is their phenotype. Now what we learned from the socks is that
you only know the genotype of individuals who have both of those recessive alleles.
And so now let's take a look at their genotypes. And what we'll find is that all the individuals
who had red hair are going to have both of those red alleles. But if you have non-red
hair you might have one of the alleles for red and one of the alleles for non-red. Or
you might have both of those the non-red allele. And so these are their genotypes. Now the
alleles in a population when they're all combined make something called a gene pool. So the
gene pool is simply a collection of all of the alleles in a population. And when you're
solving these problems it's important that you calculate the frequency of each. And so
frequency is simply going to be a ratio. The number of those alleles compared to the total
number of alleles in the population. And we use letters to represent these two frequencies.
p will always represent the frequency of the dominant allele. And q is going to represent
the frequency of the recessive allele. So it's kind of hard to count these. So let me
stack them up so we can look at them. And so basically what this means is that p is
going to be the frequency of the dominant alleles. And so what was dominant? Remember
the non-red genes are going to be dominant. So if I count those there are six of those
non-red alleles divide by a total of 20 alleles. And so that's going to be 0.3. q then is going
to give us the frequency of the recessive alleles. Well there are 14 total recessive
alleles. Divided by a total number of 20. And so our q value is going to be 0.7. And
what you should notice right away, this is very important, that p plus q will always
equal one. In other words, 0.3 plus 0.7 is going to equal 1. And in any problem that
you solve, p plus q will always equal 1. And that allows you to solve some tough problems.
And so basically let's get to the Hardy-Weinberg equation. Hardy-Weinberg equation is going
to tell us the frequency of different genotypes in a population. And so it's written as this.
p squared plus 2pq plus q squared equals 1. Now lots of times when biology students are
trying to solve problems related to Hardy-Weinberg equilibrium, they will simply try to plug
numbers in and then solve this equation. And that's not how it works. Basically p squared
is going to represent the frequency of the individuals in a population that are homozygous
dominant. Now that's a new term. What does it mean? They have both copies of this dominant
gene. q squared is going to tell us the individuals who are homozygous recessive. That means they
have both copies of the recessive gene. And 2pq is simply going to tell us the frequency
of individuals in a population that have one of each. And we call those heterozygous for
this trait. And so let's get to a problem. And so let's say the problem presented is
this. Two percent of humans on the planet have red hair. What percent of humans are
heterozygous for this trait? Well the first thing you need to do is figure out what the
question is giving us. And so they're saying that 2 percent of humans have red hair. And
so what are they telling us? Well they're telling us a number here. But when they're
telling us the individuals have red hair, are they telling us a phenotype? Or are the
telling us a genotype? Well red hair is going to be a phenotype. And so they're telling
us that. But the nice thing is that since this is a recessive trait, red hair is recessive,
not only are they telling us the phenotype, but they're telling us the genotype. And so
in this case that's going to be q squared. Since red hair is recessive, q squared is
going to be the individuals who have red hair. And so when you're solving Hardy-Weinberg
problems you want to make sure that you always convert that to a decimal value. Otherwise
you're going to get results that really won't make sense. And so we've got q squared equals
0.02. Why did I use q squared? Well we know that these are the individuals who are homozygous
recessive for that trait. So how do I solve this? Well basically I could take the square
root of this and I could take the square root of that. And so q is going to equal the square
root of 0.02. And so that's going to be roughly 0.14. Once I've figured out my q value, and
I know in the back of my head that p plus q will always equal 1. I automatically know
what p is. In this case p is going to be 0.86. Okay. So now I've already determined p and
q. When you're solving Hardy-Weinberg equations the first thing you want to do is find your
p and your q value. So let's kind of talk about what this means. If 2 percent of the
humans on the planet have red hair. That means if we were to take all the alleles of all
the people on our planet and put them together in this one gene pool we'd find that 0.14
or 14% of those genes are going to be actual red hair. Now let's get to the question that
they're asking. They're saying what percent of individuals are heterozygous for that trait?
Well look back to our Hardy-Weinberg problem we know that the heterozygous individuals
are always going to equal 2pq. And so that's going to be 2 times our p value, which is
0.86 times our q value which is going to be 0.14. And if I plug that into my calculator,
I'm going to get a value of around 0.24. Or since they're asking as a percent, about 24
percent. And so on the planet 24 percent of the individuals or almost one-fourth of the
individuals on our planet are going to be heterozygous for that trait. Or they're going
to be carriers of that trait. So now let me give you a problem. Let's say that 12 percent
of the individuals in Ireland have red hair. What percent of this population is going to
be homozygous for non-red hair? And so what you should do is figure out what the question
is asking. You should figure out what they're giving you. And then you should use the Hardy-Weinberg
equation to give this a try.