Download Population Genetics

Population
Genetics
INTRODUCT ION:
An understanding of evolution depends upon knowledge of population genetics. If
you have ever asked questions such as the ones that follow, you begin to see why
studying population genetics might be useful:
1. How can O be the most common of the blood types if it is a recessive trait?
2. If Huntington's disease is a dominant trait, shouldn't three-fourths of the
population have Huntington's
while one-fourth have the normal phenotype?
3. Shouldn't recessive traits be gradually ‘swapped out' so they disappear
from the population?
These questions reflect the common misconception that the dominant allele of a
trait will always have the highest frequency in a population and the recessive allele
will always have the lowest frequency. On the contrary, there is not the slightest
foundation for the idea that a dominant trait should show a tendency to spread over
a whole population, or that a recessive trait should die out. How often a gene is
present in a population (gene frequency) can be high or low no matter how the
allele is expressed, and can change, depending on the conditions that exist. It is the
changes in gene frequencies over time that result in evolution.
In the year 1908 mathematician G. H. Hardy in England and geneticist W. Weinberg
in Germany each independently formulated the central theorem of population
genetics. This central theorem is now known as the Hardy-Weinberg Principle. The
Hardy-Weinberg Principle provides a baseline to determine whether or not gene
frequencies have changed in a population and thus whether evolution has occurred.
Recall, it is at the population level that evolution occurs. A population is a group of
individuals of the same species in a given area whose members can interbreed.
Because the individuals of a population can interbreed, they share a common group
of genes known as the gene pool . Each gene pool contains all the alleles for all the
traits of all the population. For evolution to occur in real populations, some of the
gene frequencies must change with time. The gene f requency of an allele is the
number of times an allele for a particular trait occurs compared to the total number
of alleles for that trait.
Gene fr equency = the num ber of a s pecific type of allele / the total
num ber of all eles i n the gene pool
An important way of discovering why real populations change with time is to
construct a model of a population that does not change. This is just what Hardy and
Weinberg did. Their principle describes a hypothetical situation in which there is no
change in the gene pool (frequencies of alleles), hence no evolution. This
hypothetical situation makes five assumptions that must hold true in order for
equilibrium in the population (no evolution).
1. No mutation. The alleles must not change.
2. Random mating. There is no mating preference. For example an AA male
does not prefer an aa female.
3. No genetic drift. Changes in gene pool due to chance.
4. No gene flow. Exchange of genes between the population and another
population must not occur.
5. No natural selection. Natural selection must not favor any particular
individual.
Consider a population whose gene pool contains the alleles A and a. Hardy and
Weinberg assigned the letter p to the frequency of the dominant allele A and the
letter q to the frequency of the recessive allele a. Since the sum of all the alleles
must equal 100%, then
p + q = 1 (allele frequency)
So far we have been describing only the occurrence of the alleles in a population.
As you know, in individuals, alleles occur in pairs. Thus, every individual in the
population has two genes per trait. These alleles can be arranged in one of the
following ways:
• homozygous dominant
• heterozygous
• homozygous recessive
According to the product rule of probability learned previously, the chance of
obtaining a combination of two individual alleles is the product of the chances of
receiving each individually. This leads to the second equation of Hardy-Weinberg:
p 2 + 2pq + q 2 = 1. 0 (genotype frequency)
Here, p2 = the frequency of individuals in the population having two
dominant alleles; 2pq = the frequency of those having one dominant and one
recessive allele; and q2 = the frequency of those having two recessive alleles.
Using these equations and some information about a given population, you can
determine the frequencies of individual genes as well as the frequencies of
genotypes in a population. If frequencies of alleles remain at equilibrium over
time…..no evolution. If the frequencies of alleles change….evolution!
Pre-Lab
1. The cross 2pq x 2pq describes the mating of what two kinds of individuals?
________________________________________________________
2. Match each of the following symbols with the phrase that defines it.
p
______
q
______
p2
______
2pq
______
q2
______
a. The frequency of homozygous dominant individuals
in the population.
b. The frequency of the dominant allele.
c. The frequency of heterozygous individuals in the
population.
d. The frequency of the recessive allele.
e. The frequency of homozygous recessive individuals
in the population.
3. Write the two Hardy-Weinberg equations.
4. In order for a population to be in Hardy-Weinberg equilibrium, we assume certain
conditions must hold true.
What are those conditions?
Fishy
F req uencies:
A
st ud y
of
Pop ulati on
Gen etic s
Group
I
Fact s
a bout
t he
'Fish'
1. These little fish are the natural prey of the terrible fish-eating sharks - YOU!
2. Fish come with two phenotypes, gold and brown:
• gold: this is a recessive trait (f).
• brown: this is a dominant trait (F).
3. You, the terrible fish-eating sharks, like both fish the same and eat whichever
ones you happen to catch.
4. New fish are born every 'year'; the birth rate equals the death rate. You
simulate births by reaching into the container of 'spare fish' and selecting random
fish.
5. Since the gold trait is recessive, the gold fish are homozygous recessive (ff).
Because the brown trait is dominant, the brown fish are either homozygous or
heterozygous dominant (FF or Ff).
6. The fish are living in an ocean (in the middle of your table).
Procedure
1. Get a random population of 10 fish from the 'ocean.'
2. Count gold and brown fish and record in your chart; you can calculate
frequencies later.
3. Eat 3 random fish (no peaking).
4. Add 3 fish from the 'ocean.' (One fish for each one that died.) Be random. Do
NOT use artificial selection.
5. Record the number of gold and
Group I: Individual Data
brown fish.
Generation
Gold
Brow n
6. Again eat 3 fish.
1
7. Add 3 randomly selected fish, one
for each death.
2
8. Count and record.
9. Repeat steps 6, 7, and 8 two more
3
times.
4
10. Fill in the class results on your chart
and calculate
5
gene frequency and genotype
frequency.
Group I: Cl ass Dat a
Generation
1
2
3
4
5
Gold
Brown
q2
q
p
p2
2pq
Fishy
F req uencies:
A
st ud y
of
Pop ulati on
Gen etic s
Group
II
Fact s
a bout
t he
'Fish'
1. These little fish are the natural prey of the terrible fish-eating sharks - YOU!
2. Fish come with two phenotypes, gold and brown:
• gold: this is a recessive trait (f); these fish taste yummy and are easy to
catch.
• brown: this is a dominant trait (F); these fish taste salty, are sneaky and hard
to catch.
3. You, the terrible fish-eating sharks, much prefer to eat the yummy gold fish;
you eat ONLY gold fish unless none are available in which case you resort to eating
brown fish in order to stay alive.
4. New fish are born every 'year'; the birth rate equals the death rate. You
simulate births by reaching into the container of 'spare fish' and selecting randomly.
5. Since the gold trait is recessive, the gold fish are homozygous recessive (ff).
Because the brown trait is dominant, the brown fish are either homozygous or
heterozygous dominant (FF or Ff).
6. The fish are living in an ocean (in the middle of your table).
Procedure
Group II: Individual Data
1. Get a random population of 10 fish
Generation
Gold
Brow n
from the 'ocean.'
1
2. Count gold and brown fish and
record in your chart.
2
3. Eat 3 gold fish; if you do not have 3
3
gold fish, fill in the missing number by
eating brown fish.
4
4. Add 3 fish from the 'ocean.' (One
fish for each one that died.) Be random.
5
Do NOT use artificial selection.
5. Record the number of gold and brown fish.
6. Again eat 3 fish, all gold if possible.
7. Add 3 randomly selected fish, one for each death.
8. Count and record.
9. Repeat steps 6, 7, and 8 two more times.
10. Fill in the class results on your chart and calculate gene frequency and
genotype frequency.
Group II: Cl ass Dat a
Generation
1
2
3
4
5
Gold
Brown
q2
q
p
p2
2pq
ANALYSIS
&
DISCUSSION:
Make sure you have class data from both Group I
and Group II before you continue.
1. What is the basic difference between how Group I did the lab and how Group II
did the lab?
2. According to Hardy-Weinberg, what conditions would have to exist for the gene
frequencies to stay the same over time?
3. In Group I, what was the allele frequency (%) in the population?
G eneration 1
Generation 5
Homozygous Recessive: ___________
Heterozygous: ___________
Homozygous Dominant: ___________
4. In Group II, what was the allele frequency (%) in the population?
G eneration 1
Generation 5
Homozygous Recessive: ___________
Heterozygous: ___________
Homozygous Dominant: ___________
5. What happens to each of the genotypic frequencies from generation 1 to
generation 5 in Group I?
6. What happens to each of the genotypic frequencies from generation 1 to
generation 5 in Group II?
7. If Group I is experiencing any evolution, what do you think is the cause?
8. If Group II is experiencing any evolution, what do you think is the cause?
9. What happens to the recessive allele over successive generations? Would the
recessive allele disappear from the population? Explain your answer.
For the remaining questions, SH O W Y OU R WO R K and put a B OX around your
answer.
10. What is the frequency of heterozygotes in a randomly mating population if the
frequency of recessive phenotypes (aa) is 0.09? HINT: Start by figuring out the q2, q
& p.
11. A wild population of butterfly species consists of 99% orange butterflies and 1%
yellow. Genetic tests proved the yellow form to be due to an Autosomal recessive
gene. Estimate the percentage of heterozygotes in this population.
12. The frequency of the human recessive disorder cystic fibrosis is about 1 in
every 2000 births in North American Caucasians. What proportion of American
Caucasians would be expected to be carriers of the CF allele?
13. In cats, black fur is dominant to white. If 40% of all alleles for fur color in cats in
a small town are white (b), and the town has 3000 cats, how many of those cats
would be expected to be black?