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Hello.
Welcome back to Introduction to Genetics in Evolution.
In the previous videos we talked about some of the fundamentals associated
with natural selection.
I reintroduced that is a mathematical inevitability, we talked about the three
conditions for it, and we looked briefly at changes in allele frequencies and
genotype frequencies associated with the action of natural selection.
Now one point I stressed in the last video was the importance of dominance.
That dominance affects how natural selection shapes allele and
genotype frequency.
Now in the last example I showed you in the last video,
we had all adult, little a, little a, individuals die.
So we said that at age 10 all little a, little a, individuals just die off.
Let's follow up on this with a couple of different examples.
I'm going to change, in this case, the alleles from big A and
little A to M and N.
That way there's no implication of capital being dominant or recessive or
anything like that.
So let's say now we are looking at the relative fitness of three possible
genotypes.
And again, there's two alleles.
Genotype MM has a fitness of 1.0.
So again, relative fitness.
Genotype MN has a relative fitness of 1.0.
And genotype NN has a relative fitness of zero
as in all individuals that are NN are dead.
Now which allele is dominant or which allele is recessive?
Well we define dominance by what the heterozygote has the same phenotype as.
The phenotype we're looking at in this case is the relative fitness.
So which homozygous does the heterozygote have the same relative fitness as?
In this case the MM homozygous have the same relative fitness as
the MN heterozygotes.
In this case,
this must necessarily be dominant, this must necessarily be recessive.
2:08
Here's a different example.
So in this case MM has relative fitness 1.0.
MN has relative fitness of 0, NN has relative fitness of 0.
So what do we think is going to happen in this case?
Well, first of all, which one is dominant?
In this case again we look at the heterozygote.
Which one has the same relative fitness asset?
In this case, it is the NN homozygote.
So, N is actually dominant now.
N is still that, so in this case, the dominant one, this one is dominant,
N is dominant.
And what will selection do differently?
While we might guess in this case, selection will actually be much more
quick, because in this case you're eliminating all
Ns from the population at once, instead of just a subset of Ns from the population.
Here are some Ns are sheltered.
Here no Ns are sheltered, they are all exposed to natural selection so with
a dominant detrimental, the heterozygotes will always respond to select.
Let's do a third example.MM is 1.0, for it's relative fitness.
MM is .5 and MN, zero.
In which case, which one is dominant?
Well, the simple answer is neither, because
no homozygote has the same relative fitness as this particular heterozygote.
So we can call this a case of no dominance.
In all three of these cases we assume that the NN heterozygote is the worst one.
This is what's often referred to as directional selection because selection
will preferentially push towards the elimination of the N allele over time
whereas MN is always perfectly healthy.
But the rate will be very different, in this case,
selection will be very slow to eliminate N's.
In this case selection would be very fast to eliminate N's and
in this case it would be intermediate.
3:58
Now we can see this.
Here is the effect of dominance with directional selection.
This is using that allele A1 software that I mentioned before.
So let's look at the case.
Now the alleles in this case are called the A1 and A2.
So if we have genotype A1A1 has a fitness of 1.0,
genotype A1A2 has a fitness of 0.5.
So we're not eliminating all of them,
we're just eliminating half the relative fitness.
Genotype A2A2 has a fitness of 0.5.
This would be a case of a dominant detrimental.
We say it's dominant because, again, you look at the heterozygote.
It has the same fitness as this one.
Okay so, A2 is dominant, A2 is bad.
A2 will be going away from the population.
In this case, since no A2s can hide, it goes away pretty quickly.
4:41
In contrast, when you have the recessive detrimental.
Now, this one is dominate, A1 is dominant but A2 is the bad one.
So you can eliminate these pretty readily from the population but
these are perfectly okay.
So as you can see what happens here if you look at the change over time
the x axis here is time in generations.
The y axis is the frequency of the A2 allele.
You see the A2 allele is going down in frequency but
it's going down somewhat gradually near the end because a lot of these
individuals when you're down here, a lot of the A2s are hiding as A1A2.
Whereas over here, none of them can hide,
they're immediately exposed to selection, boom.
Whereas here, the A2s can stick around.
And therefore you maintain some A2 in the population,
over a fairly long period of time.
In fact, this is actually what happens for many bad mutations.
As I mentioned a long time ago when we were talking about inbreeding depression,
many bad mutations are either completely or mostly recessive.
Some examples of genetic diseases like this are Tay-Sachs, cystic fibrosis, etc.
They're maintained in the population by carriers.
Selection is inefficient at getting rid of them.
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Which of these depicts the change in lactose intolerance allele?
This is the big A we talked about in a previous lecture by selection.
So I'm giving you here the relative fitnesses.
So big a big a has a relative fitness of .95, that is when it's lactose intolerant.
That's also the ancestral type.
Big A little a has the relative fitness of 1.0.
And little a little a has fitness of 1.0.
Again, these pictures are showing time generations on the x axis and
the frequency of big A, make sure you know that.
Frequency of big A on the y axis.
Which of these would be an accurate depiction of what we expect to
see over time?
7:29
Again.
There are many types of selection that can happen.
There is, in fact, many types of what is referred to as directional selection.
And this is what we've been looking at so far.
In directional selection, one allele eventually replaces the other.
That everybody in the population eventually,
if you wait a long enough time, will be either big A, big A or little a, little a.
So what you have is something like this where the fitness of big A,
big A is less than or equal to the fitness of big A, little a is less than or
equal to the fitness of little a little a.
Or the opposite, where the fitness of big A.
Big A is greater than or equal to the fitness of Big A little a,
is greater to or equal to the fitness of little a little a.
8:24
This particular example again, everybody eventually will be big A big A, and this
is a case of no dominance, or intermediate dominance as some people call it.
In this particular example now, we have little a little a has higher fitness than
the other two, so eventually everybody in the population will be little a little
a and here's the example of lactase resistance, or lactose intolerance.
Then eventually everybody in the world can wait long enough periods of time,
everybody should be allele, allele, or lactose tolerant, or lactase resistant.
You know this may not happen in real life, for this particular example,
because we now can purchase lactase over the counter, but
that's the direction that things happen.
9:02
So, these are all cases of directional selection where eventually you go to one
form, eventually you go to monomorphism.
Here's a different type of selection, this is the case of heterozygote advantage,
this is often called overdominance.
In that particular case, the most fit genotype is the heterozygote or the Aa.
So this one is more fit than both kinds of homozygous.
The two homozygotes may differ in fitness from each other, but
the highest fitness is associated with the heterozygote, okay?
In this case, unlike with directional selection,
one allele does not replace the other.
This does not lead to monomorphism over time.
A classic example of this, that people always site is that of
sickle cell anemia and malaria resistance, so let me introduce this to you briefly.
Malaria is a big threat for a large part of the developing world.
In fact, in places like sub-Saharan Africa,
your odds of death by malaria are around 4%, that's pretty high overall.
Now, malaria is transmitted by mosquito bites,
which are giving this Plasmodium protozoa, which is what actually causes malaria.
Now, how does this relate to sickle cell anemia?
Well, sickle cell anemia is not a great thing, either.
This is a recessive genetic disease, so only aa individuals are fully afflicted.
In this particular case, the sickle cells die faster than normal red blood cells.
They deliver less oxygen to cells.
So people who have this disease are tired all the time, they have chronic pain.
They have, quote unquote,
episodes where they sometimes have to go to the hospital associated with this.
So this is clearly not a good thing.
Interestingly the heterozygote, so the big A little As,
these people are often called having the sickle cell trait.
They are usually okay, sometimes they can have some sickling in their cell
when they're exercise very hard and have some type of intense physical exertion.
But overall they're good.
But interestingly, these individuals who are heterozygous for
sickle cell are actually more resistant to malaria than
individuals that are heterozygous for the non sickle allele.
Now, the thought a long time ago with this was that invasion, growth and development
of Plasmodium was actually somehow reduced in these heterozygous blood cells.
But more recently, I cite two studies down here.
You're welcome to look them up if you'd like.
One thought is the heterozygote is more tolerant to sickle cell symptoms, but
actually still retains a connection.
Whereas another study showed that the infected Heterozygous cells,
are more likely to be eliminated by the spleen.
12:06
They don't really get malaria, they don't have sickle cell disease.
So they'll have the highest relative fitness of 1.00.
And little a,
little a's have a sickle cell disease which is extremely debilitating.
So we'll say their relative fitness is something like .05.
Well what would be the fate of a little a allele if
it arose as a mutation in a big a big a population?
Well it seems like little a little a is really bad,
on the other hand, big a little a is pretty good.
So what should happen?
Well we can simulate this using little A1, and
12:52
Interestingly, we can actually apply the math ourselves and see what happens.
So the frequency of little a, this is the prediction from what you should see in
terms of changes and real frequencies and the equilibrium allele frequencies.
So this is at equilibrium.
A little hat over this to indicate equilibrium.
At equilibrium, what should the frequency of little a be?
Well we'd say it's 1- the relative fitness of AA divided by 1- the relative
fitness of aa + 1- the relative fitness of AA.
We have all these numbers here right?
So the fitness of AA so 0.85, the fitness of aa 0.05.
It's a big A big A again, 0.85.
So we can substitute these numbers into this very simple formula.
13:39
So there we go, they're put in there.
And this calculates out to 0.136.
That number may look familiar to you because
that was exactly where we saw this equilibrium drawn.
So the important thing, this is actually a stable equilibrium.
Essentially, if you're not at the equilibrium allele frequency,
selection pushes you towards it.
If you're above it, you go down to it.
If you're below it, you go up to it.
You're drawn to this equilibrium allele frequency.
And again, this is called overdominance.
Both alleles are retained, and
if you're not at equilibrium frequency, you will move to it.
Now let me show you a graphical representation of that.
Here it is. Here's a graphical representation of
changes in allele frequency associated with overdominance.
On the x axis here I have the frequency of the big allele and on the y access
I have the predicted change in frequency of the big allele next generation.
Don't worry about this too much if you're not exactly following.
But this just depicts the same sort of thing.
So imagine that you're at, let's say in this case the predictive allele frequency
equilibrium allele frequency is .6.
if you're at .4, if you're at actual frequency of 0.4,
your predicted change in frequency of big A is what?
In this case, your predicted change is positive, so
it'll push you toward equilibrium.
If you're over here at 0.8, your predicted change in allele frequency is negative,
so that pushed you in this direction.
So you can see, anytime you're anywhere but
at equilibrium frequency, or we have no variation.
Then you will always be drawn to that equilibrium.
Unless you are at either 1.0 or 0.0 where there is no variation.
And selection requires variation to act.
So this is just a graphical representation of what told you in words.
You don't worry about that.
And the important thing heterozygote advantage, or overdominance, is there
is this predictable equilibrium allele frequency the population will be drawn to.
15:32
Now let's talk about the opposite, heterozygote disadvantage.
Whatever, the heterozygote has the lowest fit.
There aren't very many good cases of this,
but we can at least show mathematically what should be expected.
One of these cases, again, the least fit genotype is the heterozygote.
I just made up some numbers here.
What this does, this actually leads to an unstable equilibrium,
like this fellow standing on the chair here.
That if you start below the equilibrium allele frequency.
So again, the equilibrium allele frequency is 0.27, so
you're just a tiny bit below it there.
If you start below it, it'll just go away completely,
you'll lose one allele completely.
If you start above it, you'll lose the other allele,
one of them goes to fixation.
It's only if you're right at equilibrium allele frequency that both alleles can
persist.
But in a real population, you probably can't do that, because unless you have
an infinite population size, you can't stay exactly at that allele frequency.
So unlike the previous example, this is a graphical representation of allele
frequency change with underdominance.
If you're not at the equilibrium point, let's say, for
example again the equilibrium allele frequency is 0.6.
If you're starting at 0.8, again,
your predicted change allele frequency is positive.
If you start at 0.4, your allele frequency predicted change is negative.
Negative, it pushed away.
So again, you lose variation in the population.
16:53
Only if you're right at that equilibrium allele frequency can it stay,
so it's a very unstable equilibrium point.
It probably doesn't happen very much, or if it does,
it's eliminated so quickly that we never see it, okay?
So those are three kinds of single locus selection we've talked about.
Directional selection, where one allele is just consistently favored, overdominance,
where variation is retained in a stable way, underdominance,
where variation can be retained temporarily in an unstable way, but
eventually you lose variation and it's unpredictable which one you would lose,
unless you know that you're above or below the equilibrium allele frequency.
There's one more type I was going to introduce, and that is that of frequency
dependent selection, specifically negative frequency selection.
Now, the previous examples all assume that fitness was independent of what was going
on in the rest of the population.
That you're big A big A, you're better than big A little a, no matter what.
Or if you're a little a little a, you're better than being a big A, no matter what.
Sometimes, it's actually better to be rare, that your fitness may
depend on your relative abundance or frequency of the population.
Now, being better makes you more common, right?
That if you're better it means you're having more kids,
you're more likely to survive, so you become more common, but if it's better to
be rare, it's kind of this funny thing where you have these opposing forces.
What this does, and
this is the case specifically of negative frequency dependent selection,
we're not going to talk about positive frequency negative selection.
If you have negative frequency dependent selection this assumes that it's better to
be rare, but being better makes you become more common.
This eventually leads to an equilibrium.
Let me give you an example, let's use the case of sex ratio.
18:31
So, in many species, you know sex is determined genetically,
as you know, in mammals we talked about the sex chromosomes,
that XY is what causes maleness.
You're kind of locked into this by transmission.
But there are other species where alleles at one gene can cause an individual to
become a male versus a female.
That you can have this sort of variation within it.
Now, if females are very rare in a population, and you need both male and
females to make offspring, is it better for you to produce male or
female offspring?
Is it better to produce the abundant type or is it better to produce the rare type?
Essentially, in this particular example would selection favor the male or
female allele?
19:09
It's probably better to produce the rare type, because you're more likely to mate.
If you produce the common type, you're very likely not to mate.
When you're rare, this rare allele has an advantage.
As it becomes more and more common, it loses its advantage, and
eventually can go to a disadvantage.
This will maintain genetic variation in a population.
And you might guess, if you have two alleles what would you predict that
equilibrium allele frequency to be, if you assume it's symmetric?
20:57
All of these are affecting genotype in allele frequencies, but
they're acting through the phenotype.
Now this discussion,
we're looking at everything in the context of the effect of alleles at one gene.
Obviously, that's not what Darwin did.
And it's obviously not what people do when they're
applying artificial selection, right?
They're looking at the traits as a whole.
They're looking at the phenotype, the variance.
So let's tie this back to the principles we talked about earlier,
in terms of heritability and things like that.
Well, we'll start doing that in the next video.
Thank you.