- [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.