Hi.
The title of today's lecture is Natural
Selection.
What I'm going to do now is kind of switch
gears a little and leave the
cellular and molecular basis of evolution
behind and
return to the theory of natural selection,
return
to the theory of evolution that the,
previously,
we spoke about some of the major players
in the in the field of natural, natural
history and evolution and we spoke about
these
individuals from the 16th toward the 19th
century.
We learned about the contributions of
Mendel,
Darwin, Malthus, Newton, just to name a
few.
What I'd like to do now is I wanna
introduce what the major developments were
during the 20th century.
The major developments to the theory of
evolution and natural selection.
By the start of the the 20th century, the
essential foundations for evolutionary
theory had already been developed.
Darwin had already articulated the key
theory of natural selection 40 years
earlier.
And there was the rediscovery of Mendelian
genetics in the 1900s.
And this contributed another very
important
component to our understanding of natural
selection and evolution, because it
provided
a mechanism for inheritance and
maintaining variation.
We might expect that a synthesis of
these two basic contributions would have
been joined
together relatively quickly into a
consistent theory
of evolution but that was not the case.
A synthesis of these two ideas did not
occur until the 1930s, okay?
During the 1930s, biologists who were
studying mathematical models of
evolutionary change, came to realize that
small new changes in
genetic material represent the, that are
transmitted from parent to offspring
by strict Mendelian principles represent
the fuel for natural selection.
Let me say that again, small changes in
the genetic material represent the fuel
for natural selection.
Those new changes that are in the genetic
material,
are transmitted from parent to offspring,
by Mendelian principles.
This idea brought together the two major
fields in evolutionary thinking.
And together they comprise what is called
the Modern Synthesis.
So Darwin, Darwinian and Mendelian
Evolution.
The basic idea behind Modern Synthesis is
that evolution occurs in two stages.
The first stage is the production
and redistribution of variation that is
inherited
differences between individuals is what
that
is how, variation is produced and
redistributed.
The second phase of the Modern Synthesis,
is that natural
selection then has the opportunity to act
on those inherited differences.
It either acts on the inherited
differences or it acts specifically
on the variation among individuals that
differentially effects their ability to
reproduce.
I want to make it clear that natural
selection is the evolutionary force that
causes changes in allele frequencies in
populations
due to differential net reproductive
success of individuals.
That is, natural selection is what causes
changes in
the allele frequencies in populations, and
it causes it because
of differences in the reproductive
abilities of individuals, due to
those changes or differences, rather, in
those allele frequencies.
So, before when, when I first introduced
evolution, we defined evolution as change
over time.
Following the Modern Synthesis, evolution
is no longer defined as change over time.
But evolution is now defined as a change
in
the allele frequency from one generation
to the next.
These allele frequencies are, effectively,
numerical indicators
of the genetic makeup of a population.
Recall that a population is an
interbreeding group of individuals.
I also wanna remind you that populations
evolve, not individuals.
So individuals don't evolve, populations
do.
And I wanna also remind you that alleles
are one of
ver, one of, one of several forms [LAUGH]
of the same gene.
So let's look at an example of changing
allele frequencies.
Let's spec,of, effectively, that means
evolution.
We're looking at an example of evolution,
and we're
gonna look at the A, B, O blood group.
Okay.
Let's assume that we know all the blood
types of all the individuals in a
classroom.
And that this classroom represents a
population of interbreeding individuals.
Just to remind you, to be a population
of interbreeding individuals, the
individuals in this classroom
must be more likely to choose a mate
from within this group than without, from
outside it.
Let's say that Texas A and M Aggies are
more likely to choose a mate from, who's
also
a Texas A and M graduate or alum then
they are to choose one form the other
Texas university.
Let's say that the proportion of each of
the alleles in the classroom are the
following.
Let's say there are 30 individuals in the
classroom, 15 12 3.
Equals 30.
Yes.
Okay, [LAUGH] just checking my math.
And, we have three types of blood in this
classroom.
We have A blood, we have B blood, and we
have O blood.
We have fifteen individuals in the class
that have A blood.
We have twelve individuals who have B
blood,
and we have three individuals who have O
blood.
What we now need to calculate is the
proportion of alleles in the classroom.
The proportion of A alleles is 15 divided
by 30
the total number of alleles in the class,
which equals .50.
B equals 12 divided 30, which is 0.40,
which is 0.40.
And the portion of O alleles is three
divided by 30, which is 0.10.
So notice that the portion of all these
alleles equals one, 0.5, 0.4, 0.1, equals
1.0.
Let's say, God forbid, that I am teaching
this class in 25 years, and
that you are, the same students are in
this classroom 25 years from now.
So, none of us have moved on.
The proportion of the alleles, 20 and 25
years, might have changed.
The portion of the alleles might be, we
now
have, we still have 30 individuals in the
class.
But the portion of alleles is 30
individuals with I'm sorry, nine
individuals with A
blood, 9 divided by 30 equals 0.30, 12
individuals with B blood, so that hasn't
changed.
And nine individuals with O blood, 9
divided by 30 is 0.30.
So the proportion of alleles over time has
changed.
During this 25-time year period we see
that the relative proportions of A, B and
O blood have changed, A has decreased, O
has increased and B has remained the same.
Over the short-term, these changes, these
changes in allele frequencies are
relatively small.
But if they are continued and elaborated
over long periods
of time, they can and do produce
spectacular types of evolution.
[SOUND] I wanna make it very clear that we
say that a population
is evolving if frequencies of its alleles
are changing.
So in the previous example we say that the
population is evolving because the allele
frequencies have changed.
If the population is not evolving, the
allele frequencies are going to
be constant and the population is in what
we call a genetic equilibrium.
There are two main types of evolution that
I want to talk about.
The first is called microevolution, the
second is macroevolution.
Microevolution constitutes short term
evolutionary changes.
Macroevolution are long term changes
throughout fossil history
so when we're looking at changes in allele
frequencies
we're talking about microevolution when
we're talking about the
evolution of dogs from wolves we're
talking about macroevolution.
So, there are five major causes of changes
in allele frequencies.
The five changes of, causes of changes
in allele frequencies are the five
evolutionary forces.
These evolutionary forces are natural
selection,
mutation, migration, genetic drift, and
non-random mating.
These are the five evolutionary forces
that
cause changes in allele frequencies that
cause evolution.
So all five of these forces cause
evolution to occur, natural selection,
mutation, migration, genetic drift, and
non-random mating.
I'll start out with the discussion of
natural selection.
Now, we know all about natural selection
from Darwin.
Natural selection effectively filters
genetic variation.
Individuals that have certain biological
characteristics that allow
them to survive and reproduce are more
likely to
pass on their alleles for those
characteristics that allow
them to survive and reproduce to the next
generation.
Natural selection very importantly, does
not create novel genetic variation.
Natural selection does not create genetic
variation.
It only changes the relative frequencies
of the different alleles.
Those, okay, so it's a very important
point.
What we're gonna see is that mutation is
the only evolutionary force that creates
variation, natural selection acts on that
variation,
it modifies the frequency of that
variation.
The analysis of natural selection focuses
on what we call fitness.
Fitness is the probability of survival and
reproduction of an organism.
It's the proportion of individuals with
the genotype that survive and reproduce.
There are two basic components of fitness.
The first component of fitness is
reve, revolves around differential
survival or mortality.
And certain individuals have greater
survival and mortality.
Se, secondly, certain individuals have
greater fertility.
That is they produce more offspring, and
or more offspring that survive to
reproduce themselves.
So let's imagine a locust with the
genotypes, with two alleles, okay.
Allele, dominant allele and recessive
allele.
And it has three genotypes,
homozygous dominant, heterozygous, and
homozygous recessive.
All the individuals that are heterozygous
and homozygous dominant individuals
survive and reproduce.
And only half the individuals that are
homozygous recessive survive.
This means that the homozygous recessive
genotype has half
the fitness of the homozygous dominant and
the heterozygous genotype.
Fitness refers to the proportion of
individuals
with a genotype who survive and reproduce.
The fitness is always measured relative to
the other genotypes.
It's never something unto itself, okay.
Let's say we have an example.
We have individuals with the homozygous
dominant genotype have four kids.
Individuals that are heterozygous have two
kids, and
individuals that are homozygous recessive,
have one child.
Each genotype has a fitness relative to
the other genotypes.
The genotype with the highest fitness
equals one.
So, the homozygous din, homozygous
dominant genotype where they have four
kids, which is the maximum number, is a
fitness of one.
The heterozygous genotype has half the
number of kids of the maximum number of
kids that are produced in this population,
and so they have a fitness of 0.5.
The heterozygote, sorry, the homozygous
recessive genotype, has one
child out of the maximum of four chil,
children.
So it has a gene, a fitness of 0.25.
So the fitness is always relative to the
other genotypes.
Fitness is usually abbreviated
mathematically as w.
The genotype is written as w1, w2 or w3
based
on the number of different types of
genotypes in the population.
So the homozyg in this example, the
homozygous
is dominant genotype will have a fitness
of w1.
The heterozygous will have a fitness of
w2.
The homozygous recessive genotype will
have a fitness of w3.
Genotypes also have what we call a
selection coefficient.
The selection coefficient is generally
written as s.
And the selection coefficient is always
the inverse of fitness, 'Kay?
The selection coefficient is the inverse
of fitness.
So each genotype, the selection
coefficient is written as s1, s2, or s3.
The homozygous dominant is written as s1.
The heterozygote is s2, the homozygous
recessive is s3.
Fitness plus the selection coefficient
equals 1.
W plus s equals 1.
So fitness, plus the selection coefficient
equals 1.
We say that the selection coefficient s1
for the homozygous dominant
genotype equals zero, because the fitness
of population one is one.
The selection coefficient for the
heterozygous genotype is
0.5, because fitness for population two is
0.5.
We say the selection coefficient for the
homozygous recessive genotype
is .75, because fitness for population
three is .25.
Keep in mind, that there is a selection
for genotype.
Or an allele when it has a higher fitness.
There is a selection against a genotype or
allele when it has a lower fitness.
For a single trait, we generally observe
four modes of selection:
against the recessives, against dominant
alleles,
against homozygous genotypes and against
heterozygous.
I'm gonna talk about these four modes of
selection.
So, let's first start with looking at the
mode
of selection call, called selection
against the recessive allele.
Let's consider what happens when one
allele
is dominant, and one allele is recessive.
Let A be the dominant allele, and
lowercase A be the recessive allele.
Based on what we have learned so far, the
genotypes homozygous dominant and
heterozygous will both give rise to the
same phenotype because dominant A is
dominant.
Because homozygous dominant and
heterozygous specify the same
phenotype, they are going to have the same
fitness.
So these individuals here are gonna have
the
same fitness as this individual here in
this example.
Let's say that the fitness of the
homozygous dominant and the heterozygote
is 100%.
That is all the individuals that are
purple, have 100% fitness, and the fitness
of the homozygous recessive individual,
this individual down here, is zero.
And what this means is that no individuals
that are homozygous
recessive survive to reproduce, and that
the homozygous recessive condition is Ao.
Okay, so this is how I like to write it
out so that in, it flows better
I think in your notes and other places
where you write it out in this manner.
This is the original population.
We have the genotype, the fitness, and
it's the total population size.
A is the frequency of the dominant allele,
and
recessive A here is the frequency of the
recessive allele.
We start out with just the genotypes, and
we know that the fitness of the homozygous
dominant
and the heterozygous is one, and we know
that the fitness of the homozygous
recessive is zero.
And we have 50 individuals that are
homozygous dominant, 100
individuals that are heterozygous, and 50
individuals that are homozygous recessive.
Now we need, so we have a total of 200
individuals in the population.
The first thing we need to do in
order to determine how selection is
operating against this
recessive allele, or how it affects the
allele
frequencies when selection is operating
against a recessive allele.
And many recess, homozygous recessive
genotype has a fitness of
zero, but the heterozygote is still
maintained in the population.
We have to first the allele frequencies.
The frequency of the dominant and the
recessive allele in these populations.
So, we start out, individuals with the
homozygous
dominant genotype; there 50 of them, and
the
each have two, two dominant alleles, so 50
times 2 is 100; they have no recessive
alleles.
The heterozygotes, there 100 individuals;
they have
100 dominant alleles and 100 recessive
alleles.
The homozygous recessives, there are 50
individuals; they had no dominant alleles.
And they, since they have two alleles, two
recessive alleles, 2 times 50 equals 100.
So the frequency of the dominant allele is
100 plus 100 plus 0 is 200.
200 divided by the total number of alleles
in the population, which is 400.
So, 200 divided by 400 equals P, equals
0.5.
Q is for the recessive allele, 0 plus 100,
plus 100 is 200.
200 divided by the total number of alleles
in the population, 200 by
200 is 400, so 200 divided by 400 equals Q
equals 0.5 also.
So here we did it; A equals the allele
frequencies, 200
dominant alleles, 400 total alleles, P
equals 0.5.
A is the allele frequencies; there are 200
recessive alleles
out of 400 total alleles from population,
so Q equals 0.5.
So let's look at what happens after
selection,
after one generation of selection against
the recessive.
We said that the homozygous have a fitness
of zero.
So in the next generation, there gonna be
no individuals.
So instead of having 200 individuals in
the population, we now have 150.
So we still calculate our alleles, the
freq, homo,
the frequency of the dominant alleles are
100, because 50
times 2, the frequency of heterozygotes,
is 100, and
100, so we have 300 total alleles in the
population.
The frequency of the dominant allele is
now 200 divided by 300.
The frequency of the recessive allele is
now 100 divided by 300.
So what, what does this amount to?
Then now, we have the frequency of the
dominant
allele is 200 A dominant alleles divided
300 total alleles.
The frequency of P is now 0.667.
The frequency of the recessive allele.
We have 100 recessive alleles from the
heterozygous, even though the homozygous
recessives were
all eliminated, and we have 300 total
alleles so the frequency of Q is .333.
So, after selection against the homozygous
recessive genotype, there
are only 150 individuals, and the allele
frequency has changed.
This demonstrates the effect of selection
against a homozygous recessive genotype.
The frequency of the recessive A allele
has dropped from 0.5 to 0.333.
[BLANK_AUDIO].
The recessive A allele is harmful in the
homozygous form.
And as such the fitness for in the
homozygous form in
that, it was, was zero, and it was
eliminated; however, the recessive
A allele is not going to be eliminated
completely from the population, and this
is because the heterozygote condition is
not eliminated through selection.
Because that has a fitness of one because
of the dominant allele.
So the A allele, the recessive A allele is
continued to be maintained in the
population, and it is not going to be
eliminated from a single generation.
Okay the frequency of the recessive A
allele
does not decrease at the same rate over
time.
In fact, it slows down.
The amount of reduction in the recessive A
allele slows down over time.
And as the frequency of the recessive A
approaches zero, an increasingly
lower percentage of the allele frequency
will be homozygous recessive.
That is fewer individuals are going to be
eliminated every generation.
So, however, that said, the reduction in
the recessive A is
going to be offset by new mutations from
dominant to recessive A.
The mutations are slow, so the frequency
of the
recessive A will only be slightly greater
than zero.
And ultimately, a balance will be reached
as the reduction in the recessive
A, due to selection, is offset by new
mutations from dominant to recessive A.
So the effects of natural selection, I
want to make
it very clear, are dependent on both the
initial allele frequencies,
whether an allele is dominant or not, and
the exact
values of fitness for each genotype, not
just for one genotype.
Okay, let's look another example against
homozygous recessive genotypes.
So we have there are three
genotypes: homozygous dominant,
heterozygous and homozygous recessive.
We have three finesses.
Homozygous dominant and heterozygous still
have a fitness of one.
But in this case, instead of having
the homozygotes, homozygous recessive
having a fitness
of zero, they have a fitness of 0.75, just
slightly less than the other genotypes.
The selections are thus if you have
a fitness of one, selection coefficient
zero.
Fitness of one, selection coefficient of
zero.
Fitness of 0.75, your selection
coefficient is 0.25.
These are your genotype frequencies, okay,
for the population, 0.36, 0.48 and 0.16.
We now, the first thing we need to do is
calculate the allele frequencies for the
dominant and the recessive alleles.
The frequency of the dominant allele
equals 0.36,
is the frequency of the homozygous
dominant genotype, plus
this is the frequency of the heterozygote,
and we
divide it by two because they have both
alleles.
When we get 0.6, the frequency of the
recessive allele is 0.16.
This is the frequency of the homozygous
dominant genotype
plus half the frequency of the
heterozygote, gives you 0.4.
The question we now ask is, what is the
loss in genotype and
allele frequencies in this population due
to
selection, selection against the
homozygous recessive genotype.
Okay, to calculate the loss due natural
selection, what we do is we
multiply the selection coefficient S by
the genotype frequencies.
So, here we have the genotypes.
We have our S, our selection coefficient,
based on, calculated from our fitness.
And we have our genotype frequencies.
First thing we do is we calculate,
multiply S by the
genotype frequencies, 0 time 0.36 equals
0; 0 times 0.48 is 0.
So you'll see that there's no loss in the
homozygous dominance; there's
no loss in the heterozygous because
we're looking for selection against
homozygous recessive.
Now we have 0.25 times 0.16, and it gives
us a loss of 0.04.
Okay, so this is a loss in, geno, in the
homozygous recessive genotypes.
So, what happens after one generation
of selection against the recessive
homozygous genotype?
We have three genotypes; we have the
homozygous dominant, the heterozygote, and
the homozygous recessive.
The original frequencies of the homozygous
dominant was .36.
The original frequency of the heterozygote
was 0.48, and
the original frequency of the homozygous
recessive was 0.16.
We calculated the loss due to selection,
and we said that there was no loss in the
homozygous dominance or in the
heterozygous because there
was no because they have a fitness of one.
And we said that the loss due to the, in
the homozygous recessive genotype was
0.04, bringing us a new frequency of 0.12
for the homozygous recessives.
We note that 0.36, 0.48, and 0.12 do not
add up to 100.
It adds up to 0.96.
So we need to create corrective
frequencies
by dividing each genotype frequency by
0.96.
So the homozygous dominant frequency,
which was
originally 0.36, we divide it by .96,
so we know the frequency of the homozygous
dominant in this population is now 0.375.
The frequency of the homozygote, 0.48
divided by 0.96 is now 0.50.
And the frequency of the homozygous
recessive 0.12 divided by 0.16 equals
0.125.
These new corrected frequencies add up to
one.
So the new allele frequencies, full after
one generation of selection, the frequency
of the dominant allele, 0.375 plus one
half of 0.05 equals 0.675.
And the frequency of the recessive allele
is
0.125 plus one half of 0.5 equals 0.375.
These values right here, the 0.375; this
is
the frequency of the homozygous dominant;
this 0.125 is
the frequency of the homozygous recessive;
these 0.5
in both situations is the frequency of the
heterozygous.
So what we're seeing is that where as
before, the frequency of the
dominant alleles was 0.5, and the
frequency of the recessive allele was .5.
After one generation of selection, A has
increased, and
dominant A has increased, and recessive A
has decreased.
If this is continued over multiple
generations, A,
dominant A is going to increase towards
one.
Recessive A will decrease towards zero.
Let's look at a case of selection against
recessive homozygotes.
An example in humans of a case of
selection against
recessive homozygous is a medical
condition called Tay Sachs disease.
Tay Sachs is caused by metabolic disorder.
And that results in blindness, mental
retardation, destruction of the central
nervous system.
Children with Tay Sachs generally die
within the first years of life.
They rarely live past five.
The disease is caused by a recessive
allele,
and it occurs in individuals who are
homozygous.
So, generally, you have normal parents but
they happen to
be carriers, and they have a child who is
now homozygous.
The heterozygotes, of course, carry the
allele, but they are not affected.
When deleterious alleles are recessive
such as with Tay Sachs,
the frequency of the recessive allele is
generally not zero.
Because heterozygotes continue to pass the
allele on
from generation to generation with no
impact on phenotype.
Nonetheless, the frequency of the
recessive allele
is still going to be very low.
This low frequency is maintained by
mutation,
but is kept from increasing by natural
selection.
So and in selection against dominant
alleles, let's consider this example.
As an example, considering the starting
point as in the
previous example, we have 50 individuals
that are homozygous dominant.
We have 100 individuals that are
heterozygous and
we have 50 individuals that are homozygous
recessive.
The allele frequencies we're starting with
are the
dominant A is .5, recessive A is also .5.
Let's complete, we have complete in this
example.
We'll have complete selection against the
dominate allele.
And what this means is that, any
individual
with a dominant allele is going to die,
okay?
He's not gonna survive and reproduce.
So the fitness will be 0
for homozygous dominant genotypes and
heterozygous genotypes.
The fitness will have be 100% for
individuals that are, that are homozygous
recessive.
So in this example with the peas, these
three individuals would have a fitness of
0, this individual with the heterozygous
genotype is gonna have a fitness of 1.
So, let's look at selection against the
dominant allele.
We have our three genotypes:
homozygous dominant, heterozygous,
homozygous recessive.
The homozygous dominant has a fitness of
0.
Heterozygous, fitness of 0 because we're
looking at selection
against the dominant allele, and they both
have dominant alleles.
And then we have the homozygous recessive,
is a
fitness of one cuz it has no dominant
alleles.
There are 50, 100, and 50 individuals, 200
individuals total.
We calculate the allele frequencies the
frequency of
the dominant allele, we have 100 dominant
alleles from
homozygous dominant individuals, we have
100 dominant alleles
from the heterozygous individual and 100
from the recessive.
And then we have from the homozygous
recessive individuals, we
have no dominant alleles, and we have 100
recessive alleles.
There are 200 total A alleles, 200 total
recessive alleles.
200 divided by 400 gives you P equals 0.5.
200 divided by 400 equals Q equals 0.5.
Okay.
So the next thing we need to do, is we
need
to calculate the loss in genotype and
allele frequencies due to selection.
To calculate the loss due to selection,
the first thing
we do is we multiply the selection
coefficient by genotype frequencies.
Okay.
So, these are our genotypes.
Homozygous dominant, heterozygous,
homozygous recessive.
We now know the selection coefficient for
the
homozygous dominant must be 1, because
fitness equals 0.
We know the selection coefficient for the
heterozygous
has to be 1 because fitness is 0.
We know the selection coefficient for the
homozygous
recessive has to be 0 cuz fitness is 1.
We have, these are our genotype
frequencies
that we've calculated from our P's and
Q's, and now we calculate and multiply
our selection coefficient by our genotype
frequencies.
1 times 0.36 equals 0.36.
1 times 0.48 equals 0.48.
0 times 1.6 equals 0.
So, the loss of the homozygous dominance
is gonna be 0.36.
The loss of the heterozygote is gonna be
0.48.
The loss of the homozygous recessive is
gonna
be 0.
We now have to do, create corrected
frequencies.
We now have 0.36 minus 0.36 is 0.
0.48 minus 0.48 is 0.
So these are the frequencies of these
genotypes after one generation
of selection, and the homozygous recessive
0.16 minus 0 is 0.16.
Will, they are all at 0 plus 0 plus 0.16
equals 0.16.
Does not add up to 1.0.
We divide these all by 0.16.
0 divide by 0.16 equals 0.
0 divide by 0.16 equals 0.
0.16 divide by 0.16 is 1.
So the frequency of the homozygous
recessives is now 1.
So we now calculate the loo, new allele
frequencies in
the population after one generation of
selection against dominate alleles.
A equals 0 cuz this is the frequency of
the dominate allele of the homozygous
dominates plus 0, divided by 2 because the
0 was the frequency of the heterozygote.
New frequency of the dominant allele is 0.
The frequency of the recessive allele is 1
cuz is the frequency of the
homozygous, homozygous recessive genotype,
plus 0 cuz
is the frequency of the heterozygous
genotype.
So, we see A has decreased, dominant A has
decreased, recessive A has increased.
Actually, you wouldn't even just say
dominant A
has decreased, would say dominant a has
been eliminated.
The dominant allele has been eliminated
after
one generation because the selection
coefficient was one.
No further change will occur in this
population, unless the allele,
the dominant allele, is reintroduced into
the population through mutation or
migration.
Let's look at another, less severe example
of selection against dominant alleles.
In this example
we see that we have three genotypes.
Once again, homozygous dominant,
heterozygous and homozygous recessive.
The fitness of the homozygous recessive is
still 1.
But the fitness of the homozygous dominant
and the heterozygous is less than 1.
It's not 0, it's 0.75.
The selection coefficients, therefore, are
0.25, 0.25 and 0.
These are our genotype frequencies, okay?
We calculate our dominant allele frequency
0.36 plus one-half of 0.48 is 0.6.
The recessive allele, 0.16 plus, 0.48
divided by 2 equals 0.4.
So, the P equals .6, Q equals .4.
[BLANK_AUDIO].
Okay, we now want to calculate the loss
due to selection.
We're gonna multiply, once again, the
selection coefficients by the genotype
frequencies.
These are our selection coefficients, and
once again, they are
the opposite of the fitness, the inverse
of the fitness.
We know that the fitness of the homozygous
recessive is 1, so it's 0.
The fitness of the heterozygous was 0.75.
Selection coefficient's 0.25.
The selection coefficient of the
homozygous
dominant is .25 cuz fitness was 0.75.
We now calculate the loss due to one
generation of selection.
We multiply the genotype frequency by the
selection coefficient, 0.25 times 0.36
equals 0.09.
The loss for the heterozygote is 0.25
times 0.48 equals 0.12.
And the loss of the homozygous recessive,
0 times 0.16 which equals 0.
So, let's calculate this out.
We have the gene, we have our three
genotypes.
We have our original, genotype
frequencies.
We have the loss due to selection right
here.
So 0.36 minus 0.09, our new frequency of
the homozygous dominant genotype is 0.27.
I'm sorry, I need to go forward.
The new genotype, the heterozygous
genotype, the original frequency was
0.48, the loss due to selection is 0.12,
so the new frequency is
0.36, for the homozygous recessive, it was
originally 0.16.
We had 0 due to loss to selection so the
new frequency is 0.16.
But we add up 0.27, 0.36, and 0.16, and it
only adds up to 0.79.
So we need to correct to a hundred.
So 0.27 divided by 0.79 equals 0.34.
So the new frequency of the homozygous
dominant is 0.34.
The new frequency of the heterozygote 0.36
divided by 0.79 equals 0.46, and the new
frequency of the homozygous recessive
equals 0.20.
Okay, so the new allele frequency is based
on, let me
go back to the previous slide, based on
these new corrected frequencies.
Okay, 0.34, 0.46 and 0.20 are, are now
calculated.
The dominant allele is homozygous
dominant, allele frequency is 0.34.
The heterozygote is 0.46.
So, the frequency of the dominant allele
is 0.434 plus one-half of 0.46 equals
0.57.
The frequency of the recessive allele is
0.20 plus one-half of 0.43 equals 0.43.
So what we're seeing is the dominant
allele has decreased slightly from 0.6.
And recessive allele has increased
slightly from 0.4
due to minor differences in the, in the,
in the fitness between dominants and
recessives.
This is due to some selection against the
dominant allele.
There are examples of, these types of
dominant alleles
in humans, where we do see selection
against dominant alleles.
An example of a dominant allele in human
populations is achondroplastic dwarfism.
This type of dwarfism results in small
size, and abnormal body proportions.
It's caused by a dominant allele, a rare
dominant
allele, that's found in very low
frequencies in human populations.
0.00005, very, very low.
Because the allele is dominant,
individuals with one
or two of the alleles show the condition.
So, that means that virtually all dwarfs
are heterozygous.
This condition is usually caused by a
mutation
that occurs in the sex cells of the
parents.
And we know this because 80% of the
dwarves are born to
heterozygous, homozygous, heterozygous
normal parents, okay?
So, it usually occurs in a mutation, and
it
usually founds 80% of dwarfs have two
normal parents.
Because if the parents were heterozygous,
they would have one
of those dominant alleles and they would
exhibit the condition.
So we know that 80% of dwarfs have two
normal parents.
In cases, where dwarfs mate the offspring
can be either homozygous
for the disease and they generally die
before, before or shortly after birth.
The low frequency of this condition, is
the result of
natural selection acting to remove the
harmful allele from the population.
Although there is no major risk or
mortality
for heterozygous condition, selection acts
on differential reproduction.
The third type of natural selection, that
way that natural selection
operates on allele frequencies is
selection for the heterozygote.
Selection for the heterozygote is often
referred to as selection against the
homozygote.
Selection against the homozygote increases
the frequency of
one allele and decreases the frequency of
other alleles.
And over time, allele frequencies are
expected to approach 0 or 1 depending
on which allele is selected for and which
allele is selected against.
So we might expect that most populations
have allele frequencies,
either close to 0 or 1, and few
populations with intermediate values.
But what we see is that studies of human
genetic
variation demonstrate that most traits
allele frequencies have intermediate
values.
Values such as 0.3, 0.5, 0.8.
Why is this the case?
Some people have suggested that the reason
we see so
many intermediary values of these allele
frequencies, is that natural
selection is not yet complete and over
longer periods of
time, the allele frequencies would move
closer to 0 and 1.
Populations at 0.3 would move towards 1.
Populations at 0.8 would move towards 1.
The majority of information regarding
allele frequencies
in human groups makes this very unlikely.
So the question is why do so
many intermediary alleles show
intermediary allele frequencies?
Is there a way that natural selection can
produce intermediary allele frequency?
A classic example of intermediate allele
frequencies in human's populations
can be seen with a disease called sickle
cell anemia.
Sickle cell anemia is a disease that
results
from a single amino acid substitution, a
mutation.
It's called a point mutation.
And it's at position six within the
hemoglobin beta chain.
And this hemoglobin beta chain has 146
amino acids, and it is only
at position six that there is a single
change in the amino acids.
For example, look at the following graft,
the following figure.
This is normal, this is the first 1, 2, 3,
4, 5, 6, the first 7 amino acids-.
In, the hemo, hemoglobin chain, okay?
And, this is what it, this is the, this,
the three bases.
We see CAC, GTG, GAC, TGA, GGA, CTC and
CTC.
And they code for these specific ameno
acids.
Okay?
When we have, when an individual has
Sickle Cell Anemia, they have the first 5,
amino acids are exactly the same as what
we see in people with normal hemoglobin.
However, position number six has a single
change, instead of CTC it has CAC.
So instead of this amino acid it produced
this amino acid.
Okay, now, why is this relevant at all?
Well, hemoglobin is a protein, found in
our red blood cells and it
transports oxygen from our lungs to the
various tissues in the body.
And every red blood cell, contains
millions of hemoglobin molecules.
In Sickle Cell Anemia what happens is
at normal hemoglobin molecules packed
together to
form rods, this causes the red blood cells
to become crescent or sickle shaped.
So you can see that our, a normal red
blood cell
looks like this a sickle red blood cell
looks like this.
These deformed blood cells they break very
easily they're,
they are often removed from circulation
which produces anemia.
Cuz you no longer have enough protein in
your blood,
and these sickled cells also result in
clogged blood vessels.
Individuals that are homozygous for this
mutate-orial and we say.
They have Hbs/Hbs are likely to die very,
very early in life.
Even in the United States, with aggressive
medical intervention, life expectancy for
individuals with Sickle Cell allele,
Anemia, is often less than thirty years.
So on the surface, this cl, appears to
be a classic example selection against the
homozygote.
You don't want individuals to have both
alleles
for Sickle Cell Anemia because then you'll
exhibit it.
So the expectation would be that sickle
cell allele frequencies should be close to
zero.
However, we find that many populations do
have
sickle cell frequencies near or close to
zero.
However, there are a number of populations
in Africa, in
India and in the Mediterranean that have
much higher frequencies.
Some West African groups, the frequency of
sickle cell alleles is greater than 20
percent.
In Gambia, in West Africa, 40 percent of
the population is heterozygous.
That means 40 percent of the population
has at least one sickle cell allele.
So the question is, how can these
harmful allele frequencies exist at such
high frequencies?
The answer to that question is the form
of a selection known as selection for the
heterozygote.
The way the selection maintains very
harmful alleles
at high frequency is selection for the
heterozygote.
And when you have selection for
the heterozygote, you're selecting against
the homozygote.
Let's consider the following example.
We have fit, the following three fitness
values.
We have three genotypes,
homozygous dominant, heterozygote,
heterozygous recessive.
70% of the population has homozygous
dominant.
100, sorry let me rephrase that.
7, of the fitness for the homozygous
dominant is 70%, the fitness for the
heterozygote is 100% and the fitness for
the homozygous recessive is 20%.
What this means is that 70% of the people
that have homozygous dominant alleles
die, survive and 20% of the homozygous
recessive
alleles survive for every 100 people with
the heterozygous genotype.
This is selection for the heterozygote and
selection against the homozygous.
So let's look at it in this matter, we
have our three genotypes,
homozygous dominant, heterozygote,
homozygous recessive.
We calculated our, we have our fitness
values already.
0.7, 1.0, and 0.2 for the three genus
types
respectively from which we can calculate
our selection coefficient.
When the fitness is 0.70, selection is
0.30.
Fitness is 1.0, selection is 0.
Fitness is 2.0, selection is 0.80.
We now know, we know our genotype
frequencies.
Of the frequency of the homozygous
dominant is
0.25, the frequency of the heterozygote is
0.5,
the frequency of the homozygous recessive
is 0.25,
from which we can calculate our allele
frequencies.
And we note that the allele frequency for
the dominant
allele P, A, is 0.5, so Q, P equals 0.5.
Q, the frequency of the recessive allele,
also equals 0.5.
Okay, so what happens before selection.
In the first population, we have 200
individuals.
And before selection, we have 50
individuals that are homozygous rece,
homozygous dominant.
We have 100 individuals that are
heterozygous.
And we have 50 individuals that are
homozygous recessive.
After selection, the allele frequencies
are going to be
the dominant allele will have 170 divided
by 290.
Equals 0.586.
The recessive allele will have 120 divided
by 290 equals 0.414.
[BLANK_AUDIO].
So how do we, how did we calculate that?
To calculate the loss due to selection
after one generation, we have here,
we have our selection coefficients from
the
previous slide, and the other genotype
frequencies.
We now look at, we multiply the selection
coefficient by the genotype.
0.30 times 0.25 equals los of 0.08 for the
heterozygote.
0 time 0.50 we have a loss of 0.
For the homozygous recessive 0.80 times
0.25 equals 0.20 is our loss.
So those are our losses.
We now calculate the, subtract the
original
frequency, the loss from the original
frequency.
The original frequency of the homozygous
dominant was 0.25,
minus due to select, one generation of
selection, is 0.08.
Equals 0.17 is the new frequency.
0.150 minus 0 is 0.50, and for the
homozygous recessive, we
started with 0.25, we lost 0.20, so our
new frequency is 0.05.
.17, .50 and .05 equal .72.
So we need to create corrective
frequencies.
.17 divided by .72 is .24.
.50 divided by .72 is .69.
.05 divided by .72 is .07.
So our new frequencies are 0.24, 0.69,
0.07.
And those are the new frequencies.
So we originally had 0.25 for homozygous
dominant, now we have 0.24.
We originally had 0.50 for the
heterozygote, we now have 0.69.
We originally had 0.25 for the homozygous
recessive, we now have .07.
We then take these values and go back to
.25, 4.69 and .07 and we
calculate our new allele frequencies, the
ones I showed you before.
We have 0.24 plus one-half of 0.69 divided
by two equals 0.585.
The frequency of the recessive allele is
0.7 plus 0.069 divided by two equals
0.415.
So we're seeing it, the frequency with the
dominant
allele has increased, and the excessive
allele has decreased.
The question is, why has that occurred?
Selection for the heterozygote, both
alleles are being selected
for both the dominant allele and the
recessive allele.
But what we're seeing is that every
homozygous recess, I'm sorry, every
heterozygous individual.
It's still contributing, alleles to the
next generation.
Also, both alleles are being selected
against.
The heterozygotes are being selected
against and het,
homozygotes recessive people die and fail
to reproduce.
So we're seeing selection against the
homozygotes
involves selection for and against both
alleles.
Because the fitness of homozygous
recessive is
greater in this example, than the fitness
of
the heterozygote, proportionally more
individuals with homozygous recess,
homozygous dominant, will survive than
homozygous recessive individuals.
So there'll be more dominant A alleles in
the next generation.
Eventually, a balance will be reached
between
selection for and against the two alleles.
The, the exact value of this balancing
point
will depend on the fitness of the
homozygous genotypes.
Selection for heterozygotes is often
referred to, I apologize, selection
for the heterozygote is often referred to
as balancing selection.
Given this model, the distribution of
sickle cell anemia frequencies makes
sense, in all environments, there is
selection, against the sickle cell.
Homozygous because people died before
reproducing and it has a low frequency.
However, when Malaria is common, in
environment where Malaria is common,
the heterozygous have an advantage because
they are less susceptible to Malaria.
Malaria is a disease caused by a protozoan
parasite.
Predominantly called plasmodium
falciparum, although
there are other varieties of it.
This disease is transmitted to humans by
infected mosquitos and
affected individuals suffer recurring
episodes of illness throughout the life.
They're also more likely to contract other
diseases often fatal diseases.
So what say is that malaria victims have a
reduced fitness.
They're more 2 million people that die
from malaria every year.
And more than 3 million people are
infected by malaria each year.
Prior to ethics, there was a very
interesting study that was conducted on
Malaria.
It was this guy, this guy named Allison,
and he conducted in an
experiment on 30 volunteers in a village
called Luo in West Africa.
He injected malaria into patients with the
following genotypes.
Hbs/Hbs, so they're homozygous, recessive
for
the genotype for the sickle cell anemia.
Hbs/Hb, so they are heterozygous.
An Hb/Hb, So they're homozy, homozygous,
normal for the, for not having Malaria.
And what he did, was he injected Malaria
into patients
that had those three genotypes, and the
results were very interesting.
None of the individuals that were
homozygous for sickle cell anemia
developed malaria.
They all developed sickle cell anemia, but
none of them had malaria.
One in ten individuals that was
heterozygous with the Hbs/Hb genotype
developed malaria.
And all of the individuals with the
non-sickle cell anemia hemoglobin genotype
developed malaria.
These results, are very instructive.
basically, they suggest that mutated
hemoglobin confers some protection against
malaria.
But this is expected, because once an
individual is bitten by a Plasmodium
parasite.
The parasite sets up residence in the red
blood cells,
and eventually goes through a
developmental process that destroys the
cell.
Cells containing sickle cell hemoglobin
are not conducive to the parasite's
development making heterozygotes less
susceptible to malaria.
Research demonstrates that parasite
infects the
red blood cells of hemoglo, of
heterozygous.
But when the sickle cell begins to sickle,
it develops
that sickle shape instead of that nice,
round, plump shape.
The potassium levels in that cell drop and
the parasite dies.
So basically what we see is that
homozygotes for sickle cell anemia allele
die.
Homozygotes for normal hemoglobin are
likely to get malaria and possibly die.
So what we're seeing is selection against
both homozygotes.
You don't want to be homozygote for sickle
cell anemia, and you don't wanna
be homozygote and not have a sickle
cell allele, because then you're gonna get
malaria.
So, we're seeing selection for the
heterozygote.
A balance of sickle, and non-sickle cell
allele frequencies
has been found in many of these human
populations.
We can calculate the equilibrium
frequencies by, from the
genotype fre, fit, fitness using the
following formula.
S1 p-hat equals s3 q-hat.
So s1 is the selection coefficient in
population 1.
P hat is the, frequency,
of the genotype frequency in the
equilibrium population.
s3 is, the equilibrium frequency for the
dominant allele.
s3 is the selection coefficient.
For the third genotype, and q-hat
equals the equilibrium frequency for the
recessive allele.
Now, we really don't want this formula, we
want
this one, where we're solving for p-hat
and q-hat.
What is the frequency of the, what is the
equilibrium frequency for
the dominant allele, and what's the
equilibrium frequency for the recessive
allele?
And we can calculate this, you don't need
to know how we go from here to here.
But we can calculate it from S3 divided
by S1 plus S3, these are your selection
coefficients.
And the frequency of q hat is S1 over S1
plus S3.
And once again, so the, we
can calculate equilibrium frequencies from
selection coefficients.
Equilibrium occurs when S1p-hat equals
S3q-hat.
And this equilibrium represents a balance
between selection against the two alleles.
When you have a stable equilibrium,
there's gonna be no further changes
in those alleles, in those gene
frequencies or allele frequencies.
So, let's look at a specific example
because it's easier to understand.
We have our three genotypes:
homozygous dominate, heterozygote and
homozygous recessive.
We know what our fitness is, okay?
The fitness of the heterozygous is one.
The fitness of the homozygous dominant is
0.75,
and the fitness of the homozygous
recessive is zero.
From that, we can calculate what our
selection coefficients are.
Fitness is 0.75, the selection coefficient
is 0.25.
Fitness is 1, selection is 0.
Fitness is 0, selection is 1.
We now calculate our, value for what the
equilibrium frequency for,
the dominant allele, and the equilibrium
frequency for the recessive allele.
S3, equals 1, divided by S1, plus S3, so
that's .25, plus 1, 1 divided by 1.25
equals .8.
So the equilibrium frequency of the
dominant allele is gonna be 0.8.
The equilibrium frequency of the recessive
allele in this example will be 0.2.
What this means is at these, equilibrium
frequencies, the
gene frequencies will remain the same,
generation after generation.
Regardless of the strength of natural
selection, we can start at
p equals .8 and q equals .2, and let's
test this out.
We have our original genotype frequencies,
okay?
And, we see loss due to selection.
Okay, we calculate point two five times
point six four.
Our new frequency equals point one six.
We correct it to point four eight.
We subtract it and we get point four
eight.
And then we have point four eight divided
by eight equals point six.
And then this is point four and
the frequency of the homozygous recessive
is 0.
We now calculate our New Allele
Frequencies,
even though we've had another generation
of selection.
A equals 0.60.
Okay?
Cuz that's the frequency of the dominant
alleles plus 1 half of the Heterozygote.
O.4 divided by 2 is still 0.8.
Frequency of the recessive allele, 0 plus
one half of .4 is .2, so even though
we've had some really strong selections,
especially against
these hetero, homozygous recessives and
the homozygous dominants,.
The allele frequencies are not going to
change because it is
now at an equilibrium where the selec,
selection is operating on
both of them, and their selection for the
heterozygous, pretty cool, This represents
what we call a balanced polymorphism,
selection for the homozygote.
When you have selection for the
heterozygote, when you can use the formula
S1 p hat equals S3 q hat to determine the
selection coefficient of one homozygote.
When you know the equilibrium gene
frequencies
and selection coefficient of the other
homozygote.
So it's very easy to to, to calculate out.
okay.
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