In today's video we're going to
introduce the Hardy-Weinberg equilibrium
and selection.
Let's say that we have a species of
caterpillar whose color depends on a
single autosomal gene on the "A" locus.
A homozygous dominant caterpillar will
have the dark green phenotype,
a heterozygous caterpillar will have the
light green phenotype, and a homozygous
recessive
caterpillar will have the yellow
phenotype.
In our initial population of
caterpillars we have 36 that are
homozygous dominant,
48 that are heterozygous, and 16 that are
homozygous recessive for a total
population of 100 caterpillars.
The first step to determine whether the
current population is in Hardy-Weinberg
equilibrium is to calculate the
frequency of each allele in the
population.
To calculate the frequency of the big "A"
allele we multiply two times the number
of AA individuals plus the
number of Aa individuals and
divide that number by two times
the total population. In this case we see
that the frequency of the big "A" allele is
sixty percent.
you can determine the frequency of the
little "a" allele in a similar manner or
you can simply subtract the frequency of
the big "A" allele
from one since the two frequencies must
add up to one. Here we see that the
frequency of little "a" is forty percent.
The Hardy-Weinberg equilibrium states
that the allele and genotypic
frequencies will arrive at equilibrium
after one generation of random mating so
long as the population meets certain
criteria.
If the population is at equilibrium then
the frequencies of the genotypes can be
determined by the equation above where p
is the frequency of the big "A" allele and
q is the frequency of the little "a"
allele.
If we plug in the corresponding
frequencies calculated earlier we will
find that our population of caterpillar
satisfies the equation for the Hardy-Weinberg equilibrium. But what if the
phenotype of the caterpillar influenced
the likelihood
that it can find another mate to
reproduce? For instance, let us assume
bright yellow caterpillars are the
easiest to spot on a leaf and that 50%
of all the bright yellow caterpillars
are eaten by predators before they are
able to reproduce.
Likewise, 70 percent of light green
caterpillars are eaten before
reproducing while virtually all
dark green caterpillars are able to
survive predation and reproduce due to
their ability to blend in with the dark
green leaves on which they live.
Using the original frequencies and
fitness values for each genotype we can
determine the frequencies of the
genotypes after selection occurs.
This is done by multiplying each
frequency by its corresponding fitness
value and then dividing by the average
fitness.
The average fitness is the sum of the
products of multiplying each genotypic
frequency by its fitness value.
Here we can see the genotypic
frequencies and the calculations that led to
them.
Now if we look at the genotypic
frequencies after selection has occurred
we will see that the genotypic
frequencies for AA,
Aa, and aa are
0.464,
0.433, and 0.103 respectively.
If we compare these frequencies with the
original population before selection we
will see that the frequency for the
homozygous dominant genotype increased
while the frequencies of the other two
genotypes decreased. This is an example
of directional selection because
selection favors one extreme over the
other.
If this type of selection were to
continue, what we would expect to see is
the frequency of dark green caterpillars
increasing while the frequencies of
light green and bright yellow
caterpillars decrease.
Eventually if there are no changes we
could potentially see one of the
genotypes disappear entirely from the
gene pool.
