- [Voiceover] In the introductory video
to the Hardy-Weinberg equation,
I gave some conditions for the Hardy-Weinberg equation
to hold, and what I wanna do in this video is
go into a little bit more depth,
and have a little bit 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 the gene,
say for eye color, and let's say that gene
comes in two versions, one is the allele that produces
blue, one is the allele that produces brown,
if p is the frequency of the blue allele,
q is the frequency of the brown allele.
Well, and if they're the only two versions,
if you add the frequency of p, of the blue,
plus the frequency of the brown,
they're gonna add up to 100%, or one.
And if you square both sides of this,
you would get this expression right over here.
And we talk about that this is the probability,
or you could say, the frequency,
of being a 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 cause you can get a blue from your mom
and a brown from your dad,
or a blue from your dad and a brown from your mom.
So there's two ways to get that pq combination.
Now the key idea is Hardy-Weinberg assumes
a stable allele frequency,
so let me write that really big.
Because all of these other conditions that you might see
are really like, well, what are all the different ways
that you could somehow not have stable allele frequency?
So let me write this down, the stable allele frequency.
Stable allele frequency.
So a lot of times there's a temptation to memorize
a bunch of this stuff, you might wanna do that.
But the more important thing is to get the underlying idea.
And the underlying idea is, well, will something somehow
cause the allele frequency to be unstable?
And actually, another way to say stable allele frequency
is no evolution.
No evolution.
Evolution is a change in the inheritable traits
in a population, and that will include a change
in allele frequency.
And if you think about the two ways that you could have
a population evolving, well, you can have selection.
So we're gonna assume no selection.
Actually, there's more than two ways,
you could have genetic engineering and all sorts of things.
So we're gonna assume the mainstream ways,
I guess you could say, we can assume no selection,
we can assume no genetic drift.
Remember, selection is certain traits that make
that organism more fit for that environment,
well those traits are more likely to be passed on.
Genetic drift is random chance changes
in the 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,
some natural disaster that really gets you
to that small population.
So that's the big picture.
But given that big picture,
I wanna dive deep into some of the assumptions
that you might see in your biology class,
just so you feel comfortable with them
and you see that we're talking about the same thing.
So the ones that I mentioned in that
introductory video are no selection,
and that's consistent with no evolution.
I also talk about no net mutation,
also consistent with no evolution.
Once again, we don't want to change the allele frequency.
If there was net mutation, one of those,
maybe some of those blue versions of the gene
got a mutation and they're now maybe a different version,
or they're definitely not blue anymore,
so the allele frequency would change.
The reason why we care about large population
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.
The other conditions that you will often see
are things like random, random mating.
That whether an organism has the blue or the brown version
of the gene, that that doesn't make them any more
or less desirable to a member of the opposite sex.
And if you think about, 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, that you don't have,
the population isn't growing by other organisms
entering it or isn't shrinking by other organisms
leaving or there's not a mixing of population
between two populations.
And once again, it's all in, it's all because
we care about stable allele frequencies.
Now if we wanna 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, no genetic drift.
But sometimes, we are assuming that we are dealing
with diploid organisms, that you're getting one set
of chromosomes from your mom, one set of chromosomes
from your dad, one version of an allele from your mom,
one version of an allele from your dad.
And you might say well, how can you be other than diploid?
Well you could be a, there are tetraploid populations,
especially this can happen in plants.
Or you could get two sets of chromosomes from your mom,
and two sets of chromosomes 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 that's not correlated with what sex you are.
So allele frequency, allele frequency same in all sexes,
in all sexes.
And we're assuming sexual reproduction, once again,
we're assuming one where there's 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 that the, where you could no longer
apply the Hardy-Weinberg.
Where this is with two alleles,
we're assuming sexual reproduction,
diploid, you're getting from your mom, from your dad,
and just here are all the conditions
that help us ensure that we have a stable allele frequency.
Now the one thing you're saying, okay,
I can, diploid, sexual reproduction, okay.
But isn't there always a chance for a little bit
of genetic drift?
Isn't there just, the history of the world,
is that we have this evolution,
and the answer is yes.
And so the actual reality is that there's very few
places where you can 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.