Download Hardy Weinberg

FORM GROUPS OF FOUR
1. Stream A and Stream B are located on two isolated islands with similar
characteristics. How do these two stream beds differ?
2. Suppose a fish that varies in color from a light shade to darker shade is introduced
from Stream A into Stream B. How might the color of the fish population in Stream B
change over time?
GENETICS AND EVOLUTION
• Genes determine most of an individual’s
features, such as tooth shape or flower color.
• If an organism has a feature that is poorly
adapted to its environment, the organism
may be unable to survive and reproduce.
GENETICS AND EVOLUTION
• Evolution occurs as a population’s genes and their
frequencies change over time.
•This can take millions of years for a species to change
GENETICS AND EVOLUTION
• How can a population’s genes change over time?
• Picture all of the alleles of the population’s
genes as being together in a large pool called
a gene pool.
• The percentage of any
specific allele in the gene pool
is called the allelic frequency.
GENETICS AND EVOLUTION
• They refer to a population in which the frequency
of alleles remains the same over generations as
being in genetic equilibrium.
• A population that is in genetic equilibrium is NOT
evolving.
A
The Hardy-Weinberg principle is
a
like a Punnett square for
populations, instead of individuals.
A
a
AA Aa
Aa aa
A Punnett square can predict the probability of
offspring's genotype based on parents' genotype.
Likewise, the Hardy-Weinberg principle is a tool
we can use to calculate the frequency of
particular alleles in a population.
Evolution is simply a change in frequencies of alleles in
the gene pool of a population.
B=brown
• Alleles:
b=blonde
One of two or more forms of a gene that
code for different versions of the same trait.
•Gene Pool:
All possible genes and genetic
combinations in a population.
• Population:
A group of organisms from the same
species and the geographic location.
Let us assume that there is a trait that is determined by
the inheritance of a gene with two alleles--B and b.
If the parent generation had 92% B and 8% b and their
offspring collectively had 90% B and 10% b, it would be
evident that evolution had occurred between the
generations.
This definition of evolution was developed in the early
20th century by
Godfrey Hardy, an English mathematician, and
Wilhelm Weinberg, a German physician.
Hardy
Weinberg
Hardy-Weinberg Equilibrium maintains five basic
assumptions:
1. the population is infinitely large, and that genetic drift is not an issue within
the population.
2. there is no gene flow, or migration in or out of the population
3. mutation is not occurring
4. all mating is totally random
5. natural selection is not occurring
Under these conditions it is obvious that evolution
would not occur.
There are no mechanisms of evolution acting on
the population, so the process cannot happen-the gene pool frequencies will remain unchanged.
However, since it is highly unlikely that any one of these
seven conditions, let alone all of them, will happen in the
real world, evolution is inevitable.
Hardy and Weinberg went on to develop a simple equation that
can be used to discover the probable genotype frequencies in a
population and to track their changes from one generation to
another.
This is the Hardy-Weinberg equilibrium equation.
p² + 2pq + q² = 1
p is defined as the frequency of the dominant allele
q is the frequency of the recessive allele
In other words, p equals all of the alleles in individuals who are
homozygous dominant (AA) and half of the alleles in people who
are heterozygous (Aa) for this trait in a population. In
mathematical terms, this is
p = AA + ½Aa
Likewise, q equals all of the alleles in individuals who are
homozygous recessive (aa) and the other half of the alleles in
people who are heterozygous (Aa).
q = aa + ½Aa
Because there are only two alleles in this case,
the frequency of one plus the frequency of the
other must equal 100%, so…
p+q=1
Since p+q=1, then logically p=1-q
There were only a few short steps from this knowledge for Hardy
and Weinberg before they realized that the chances of all
possible combinations of alleles occurring randomly is
p² + 2pq + q² = 1
In this equation:
p² is the predicted frequency of homozygous dominant (AA)
organisms in a population.
2pq is the predicted frequency of heterozygous (Aa) organisms
q² is the predicted frequency of homozygous recessive (aa)
ones!
Tudaaaaaaah!
Albinism is a rare genetically inherited trait that is
only expressed in the phenotype of homozygous
recessive individuals (aa).
The most characteristic symptom is
a marked deficiency in the skin and
hair pigment melanin.
This condition can occur among
any human group as well as
among other animal species.
The average human frequency of
albinism in North America is only
about 1 in 20,000.
The Hardy-Weinberg equation (p² + 2pq + q² = 1),
and the frequency of homozygous recessive
individuals (aa) in a population is q². Therefore,
in North America the following must be true for
albinism: q² = 1/20,000 = .00005
By taking the square root of both sides of this equation, we get:
q = .007 (rounded)
Knowing one of the two variables
(q) in the Hardy-Weinberg equation,
it is easy to solve for the other (p).
p=1–q
p = 1 - .007
p = .993
The frequency of the dominant, normal allele (A) is,
therefore, .99293 or about 99 in 100.
The next step is to plug the frequencies of p and q into
the Hardy-Weinberg equation:
p² + 2pq + q² = 1
(.993)² + 2 (.993)(.007) + (.007)² = 1
.986 + .014 + .00005 = 1
This gives us the frequencies for each of the three genotypes for
this trait in the population:
p² = AA = .986 = 98.6%
2pq = Aa = .014 = 1.4%
q² = aa = .00005 = .005%
You have sampled a population in which you know
that the percentage of the homozygous recessive
genotype (aa) is 36%. Using that 36%, calculate
the following:
1. The frequency of the "aa" genotype.
The frequency of the “aa” genotype is given in
the problem as 36%!
2. The frequency of the "a" allele.
The frequency of aa is 36%, which means that q2 = 0.36,
by definition.
If q2 = 0.36, then q = 0.6, again by definition.
Since q equals the frequency of the a allele, then the
frequency is 60%.
3. The frequency of the "A" allele.
Since q = 0.6, and p + q = 1, then p = 0.4;
the frequency of A is by definition equal to p, so the
answer is 40%.
4. The frequencies of the genotypes "AA" and "Aa."
The frequency of AA is equal to p2, and the frequency of
Aa is equal to 2pq.
So, using the information above, the frequency of AA is
16%
(p2 = 0.4 x 0.4 = 0.16)
and Aa is 48%
(2pq = 2 x 0.4 x 0.6 = 0.48)
5. The frequencies of the two possible phenotypes if "A"
is completely dominant over "a."
Because "A" is totally dominate over "a", the dominant phenotype will
show if either the homozygous "AA" or heterozygous "Aa"
genotypes occur.
The recessive phenotype is controlled by the homozygous aa
genotype. Therefore, the frequency of the dominant phenotype equals
the sum of the frequencies of AA and Aa, and the recessive phenotype
is simply the frequency of aa.
Therefore, the dominant frequency is 64% and, in the first part of this
question above, you have already shown that the recessive frequency
is 36%.
GENETICS AND EVOLUTION
• Any factor that affects the genes in the gene pool can
change frequencies of a certain trait.
• This disrupts a population’s genetic equilibrium,
which results in the process of evolution.
GENETICS AND EVOLUTION
• One mechanism for genetic change is mutation.
• Environmental factors, such as radiation or
chemicals, cause many mutations, but other
mutations occur by chance.
GENETICS AND EVOLUTION
• Many mutations are lethal.
• However, occasionally, a mutation results in a useful
variation, and the new gene becomes part of the
population’s gene pool by the process of natural
selection.
GENETICS AND EVOLUTION
• Another mechanism that
disrupts a population’s
genetic equilibrium is
genetic drift—the alteration
of allelic frequencies by
chance events.
• Genetic drift has been observed in some small human populations
that have become isolated due to reasons such as religious practices
and belief systems.
PRACTICE
HARDY-WEINBERG!