Unit 4 Populations and environment
7 Population genetics and allele frequencies
So far we have considered the inheritance of alleles from a single pair of parents. In population
genetics the genes of the entire population of organisms is considered.
The Hardy-Weinberg Principle
In 1908 G. Hardy and W. Weinberg independently proposed that the frequency of alleles and
genotypes in a population will remain constant from generation to generation if the population is
stable and in genetic equilibrium
The Hardy Weinberg principle involves two concepts –
1. The gene pool ___________________________________________________________________________
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2. Allele frequency – the number of times an allele occurs within the gene pool (Frequency is
always a fraction of 1 expressed as a decimal)
The Hardy-Weinberg principle predicts that the proportion of dominant and recessive
alleles of any gene in a population remains the same from one generation to the next
provided that five conditions are met
Name the 5 conditions:
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Unit 4 Populations and environment
The Hardy Weinberg equations can be used to
1) Predict allele frequency
2) Predict genotype frequency
3) Predict the percentage of a population that has a certain genotype.
1) Estimating Allelic Frequency
If a trait is controlled by two alternate alleles, how can we calculate the frequency of each allele?
For example, let us look at a sample population of pigs.
The allele for black coat is recessive to the allele for white coat. Can you count the number of
recessive alleles in this population?
Answer: There are 4 individuals with black coat, so it might seem that there are 8 copies of the
recessive allele.
In fact, some of the individuals with white coat may be heterozygous for the trait. So you cannot
estimate the number of recessive alleles simply by looking at the phenotypes in the population –
unless, that is, you know that the population is at Hardy-Weinberg equilibrium. If that is the case,
then you can determine the frequencies of alleles and genotypes by using what is called the
Hardy-Weinberg equation
To estimate the frequency of alleles in a population, we can use the Hardy-Weinberg equation.
According to this equation:
p = the frequency of the dominant allele (represented here by A)
q = the frequency of the recessive allele (represented here by a)
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Unit 4 Populations and environment
For a population in genetic equilibrium:
p + q = 1.0 (The sum of the frequencies of both alleles is 100%.)
(p + q)2 = 1
so
p2 + 2pq + q2 = 1
The three terms of this binomial expansion indicate the frequencies of the three genotypes:
p2 = frequency of AA (homozygous dominant)
2pq = frequency of Aa (heterozygous)
q2 = frequency of aa (homozygous recessive)
When completing questions based on Hardy Weinberg principle always read the question
carefully and decide what equation to use
If the question is telling about numbers of individuals in a population (start with p2, 2pq or
q2 - usually q2 as it is the recessive characteristic)
If the question is telling about the frequency of an allele then p+q are being used
Sample Problem 1
The allele for black coat is recessive. We can use the Hardy-Weinberg equation to determine the
percent of the pig population that is heterozygous for white coat.
Calculate q2 Count the individuals that are
homozygous recessive in the illustration above.
Calculate the percent of the total population they
represent. This is q2.
2. Find q. Take the square root of q2 to obtain q, the frequency of the recessive allele.
3. Find p. The sum of the frequencies of both alleles = 100%, p + q = l. You know q, so what is p, the
frequency of the dominant allele?
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Unit 4 Populations and environment
4. Find 2pq. The frequency of the heterozygotes is represented by 2pq. This gives you the percent of the
population that is heterozygous for white coat:
Sample Problem 2
In a certain population of 1000 fruit flies, 640 have red eyes while the remainder have sepia eyes.
The sepia eye trait is recessive to red eyes. How many individuals would you expect to be
homozygous for red eye color?
Hint: The first step is always to calculate q2! Start by
determining the number of fruit flies that are homozygous
recessive. If you need help doing the calculation, look back at
the Hardy-Weinberg equation.
Answer:
Allelic Frequency vs. Genotypic Frequency
Allelic Frequency
If you are told that the frequency of a recessive allele in a population is 10%, you are directly
given q, since by definition q is the frequency of the recessive allele. This comprises all the copies
of the recessive allele that are present in heterozygotes as well as all the copies of the allele in
individuals that show the recessive phenotype. What is q for this population?
Answer:
2. Genotypic Frequency
Genotypic frequency is the frequency of a genotype — homozygous recessive, homozygous
dominant, or heterozygous — in a population. If you don't know the frequency of the recessive
allele, you can calculate it if you know the frequency of individuals with the recessive phenotype
(their genotype must be homozygous recessive).
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Unit 4 Populations and environment
3. Predict the percentage of a population that has a certain genotype - Working out the
actual frequency of an allele
Alleles are either Dominant or Recessive
They are found in homozygous dominant, homozygous recessive and heterozygous conditions
e.g. AA, Aa and aa
When asked to work out the actual frequency of a recessive allele then you have to follow the
following procedure:
In a population of 100 there are 35 AA, 50 Aa and 15 aa. What is the actual allele frequency of a?
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As the population is 100 then the gene pool is 200 (a and A allele)
Remember gene pool is all the alleles in the population therefore in this case the alleles are A or a
so total number in 100 people is 200
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So we have in 35 people AA – 35 + 35 = 70 alleles
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In the 50 people Aa have 50 A allele and 50 a allele
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In the 15 people aa have 15+ 15 = 30 alleles
The actual frequency of a allele is then 50 + 15 + 15 = 80 out of 200 alleles
Allele frequency of a = 0.4
Question
Homozygous purple-stemmed tomatoes were crossed with green stemmed plants. The f1 were
all purple stemmed. When the F1 plants were allowed to self pollinate the resulting F2 produced
310 purple stemmed plants and 120 green stemmed plants
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Which is the dominant allele and give a symbol for this
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Give the symbol for the recessive allele
Draw a genetic diagram to show the F1 and F2 cross
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Unit 4 Populations and environment
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In the F2 offspring 310 were purple stemmed (210 heterozygous)and 120 green
stemmed – what is the actual allele frequency of the recessive allele?
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Use the answer to the question above and Hardy-Weinberg equation to work out the
number of plants that would be expected to be homozygous recessive
Q 1 If you observe a population and find that 16% show the recessive trait, you know the
frequency of the aa genotype. This means you know q2. What is q for this population
1. If the frequency of two alleles in a gene pool is 90% A and 10% a, what is the frequency of
individuals in the population with the genotype Aa?
0.81, 0.09, 0.18, 0.01, 0.198
Complete questions 1 to 4 page 127
Other questions to practice
1. A single gene with two alleles controls variation in haemoglobin type in sheep. There are three
different phenotypes corresponding to genotypes SASA, SASB, SBSB.
In a flock of 175 sheep the frequency of the allele SA was found to be 0.6 and SB was 0.4.
a) If the animals mated randomly what frequencies of allele SA and allele SB would be expected
in the next generation? (1)
b) Using the hardy-Weinberg equation calculate the number of sheep with each phenotype in the
flock. Show your working
3. A population of Capaea nemorali (land snail) lived in a field. In a survey there were 1400 pink
shelled snails and 600 were yellow. There were two alleles for shell colour.
Y = pink shell (dominant), y = yellow shell (recessive)
a) What is the frequency of each allele?
b) How many of the snails were heterozygous.
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Unit 4 Populations and environment
4. a) List the criteria which must be satisfied before applying the Hardy Weinberg principle
b) In a population of 160 small mammals, some had dark brown coat and the others had light
brown coat Dark brown (B) is dominant. In the population 48 were light brown. Using the HardyWeinberg equations calculate
The frequency of homozygous dominant and heterozygous individuals in the population
How many of each of the genotypes (BB, Bb, bb) would there be in a future population of 10 000
individuals.
Selection and Speciation
The Hardy Weinberg equation predicts that allele frequencies will remain unchanged from
generation to generation. The principle will not hold true if different genotypes have different
fertilities.
Natural selection
Sometimes the allele frequency within a population changes. This can happen when the allele
codes for a characteristic that affects the chances of an organism surviving.
- Causes a change in the allele frequency of a gene in a population
- Arises because of individuals have different fertilities. A phenotype which confers the highest
fertility rate is said to be fit (remember concept survival of the fittest – those best adapted will
survive and pass on their genes).
What is a gene pool?
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Unit 4 Populations and environment
Types of Selection
Natural selection can change allele frequency in two ways – directional selection and stabilising
selection
1. Directional Selection
Selection may favour individuals in one direction from the mean of the population. An
environmental change that favours phenotypes on one side of the mean. This means that these
individuals are more likely to survive and breed passing on their alleles. Over time the mean will
shift in that direction.
The fittest phenotypes are at one end of the range resulting in a new modal value – it shifts in one
direction
Example – bacterial resistant to an antibiotic and the evolution of the giraffe
(make any additional notes if required)
2 Stabilising Selection
Selection may favour average individuals due to the environment being stable. The individuals
with the phenotype nearest the mean are favoured and the extremes are less likely to pass on
their alleles
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Unit 4 Populations and environment
The fittest phenotype is in the middle of the range – individuals at either end are less fit so die or
have less offspring
After selection the modal value is less
Example – babies born with low or high birth masses are less likely to survive and reproduce
(make any additional notes) Read and answer Q 1 and 2 page 131
Problem : A group of early giraffes lives in a lush forest with many trees and shrubs of
different heights to feed on. These giraffes have necks of various lengths, with most
giraffes having a medium length neck. Then a blight passed through the area, killing off all
of the low growing plants, leaving only tall trees whose leaves are far off the ground.
Giraffes with shorter necks now have a hard time getting food, while those with longer
necks can feed on the high-growing leaves. After several generations, the giraffes in this
area all have longer necks than those before the blight.
What type of selection has occurred in this giraffe population?
Problem : A population of arboreal rodents lives in one species of pine tree. These pine
trees have very evenly spaced branches of uniform thickness. Rodents that are too small
cannot reach between the branches to move around in the tree. Rodents that are too big
and heavy break through the branches and fall out of the trees. The rodent population
contains adults of very uniform size.
What type of selection has created this uniform size distribution in these rodents?
You will need to be able to interpret data relating to the effect of selection. For example if the
allele frequency is changing what factors are causing that change in frequency?
Complete Q 1 to 4 on the cuckoo
Speciation
Speciation is the evolution of new species from existing species
What is a species
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If two populations become separated in some way, the flow of alleles between them ceases. The
environmental factors that each group faces may differ and selection may differ resulting in the
type and frequency of the alleles changing.
Over time the two populations gene pools may change so that even when reunited they cannot
breed and produce fertile offspring – they have become separate species.
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Unit 4 Populations and environment
Speciation can occur due to geographical isolation (allopatric speciation)
Read page 132 and 133
The population becomes divided by a physical barrier
such as water, mountains, desert, or just a large
distance.
If the two environments (abiotic or biotic) are different,
then the two populations will experience different
selection pressures and will evolve separately. Even if
the environments are similar, the populations may
change by random genetic drift, especially if the
population is small.
Even if the barrier is removed and the two populations meet
again, they are now so different that they can no longer
interbreed.
They are therefore reproductively isolated and are two distinct
species. They may both be different from the original species, if
it still exists elsewhere.
Exam Questions
The two-spot ladybird is a small beetle. It has a red form and a black form. These two forms
are shown in the diagram.
Colour is controlled by a single gene with two alleles. The allele for black, B, is dominant to
the allele for red, b.
Scientists working in Germany compared the number of red and black ladybirds over a
ten-year period. They collected random samples of ladybirds from birch trees.
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Unit 4 Populations and environment
(a) (i) It was important that ladybirds in the samples were collected at random. Explain
why.
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(1 mark)
(ii) Suggest one method by which the scientists could collect a random sample of
ladybirds from the trees.
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(1 mark)
Some of the results from the investigation are shown in the table.
(b) Use the Hardy-Weinberg expression to estimate the percentages of red ladybirds and
black lady birds in the Autumn 1933 ladybird population.
Show your working.
Answer .................................................. red ladybirds
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(2 marks)
(c) (i) The evidence from the table shows that the black ladybirds were at a disadvantage
and survived less well over winter. Explain this evidence.
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Unit 4 Populations and environment
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(2 marks)
(ii) The scientists found that black ladybirds heated up more quickly and became
active at lower temperatures than red ladybirds. How might this explain the
poorer survival of black ladybirds over winter?
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(2 marks)Spec paper
Lake Malawi in East Africa contains around 400 different species of cichlids which are
small, brightly coloured fish. All these species have evolved from a common ancestor.
(a) Describe one way in which scientists could find out whether cichlids from two
different populations belong to the same species.
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(2 marks)
(b) During the last 700 000 years there have been long periods when the water level was
much lower and Lake Malawi split up into many smaller lakes. Explain how
speciation of the cichlids may have occurred following the formation of separate,
smaller lakes.
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(4 marks)
(c) Many species of cichlids are similar in size and, apart from their colour, in appearance.
Suggest how the variety of colour patterns displayed by these cichlids may help to maintain the
fish as separate species.
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Unit 4 Populations and environment
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(2 marks)
2 Sickle cell anaemia is an inherited condition. The condition is determined by the allele Hbs.
This allele causes one amino acid in the haemoglobin molecule to be replaced with a
different amino acid. The allele HbA causes the production of normal haemoglobin.
(b) The table shows the frequency of the Hbs allele in five populations.
(b) (i) Populations R and U are found in regions where malaria is common. Explain
how the table provides evidence for this statement.
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(2 marks)
(b) (ii) Use the Hardy–Weinberg equation to predict the frequency of babies homozygous for the
HbA allele in the next generation of population R. Show your working.
Frequency of babies in the next generation homozygous for HbA ..........................
(2 marks)
June 08 Mod 5
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