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Meiosis and variation
Lesson 10
Population genetics
Learning objectives
You should be able to:
Use the Hardy–Weinberg principle to
calculate allele frequencies in
populations
Write a definition of the
terms population and gene
pool
A population is a group of individuals of
the same species that can interbreed
A gene pool is the set of genetic
information carried by a population
What is population
genetics?
Population genetics is the study of the entire
pool of genetic diversity within a population.
This is greater than the genetic diversity
shown by one individual
In population genetics, scientists measure and
predict changes in allele and genotype
frequency from generation to generation
Studying it allows us to answer questions such
as ‘how many children born in the UK in the
next 10 years, are likely to develop cystic
fibrosis?’
The birth of population
genetics
As we discussed in the last lesson, Mendel’s ideas about
how inheritance operated did not catch on because
noone knew of a mechanism by which they could
work i.e. genes.
Even Charles Darwin didn’t know a mechanism by which
his inheritance of desirable characteristics could occur.
As work in the late nineteenth and early twentieth
century showed Mendel’s ideas to have been correct,
scientists realised that it was important to consider the
genetic diversity of the entire population when
studying evolution
Scientists in the early twentieth century, such as Godfrey
Harvey and Wilhelm Weinberg (of whom more later)
thus developed the study of population genetics
How does population
genetics work?
One of the main challenges in population
genetics is to work out the frequency of an
allele within the population
This is easy enough if the allele we want to
know about is codominant but a bit harder if
it is recessive or dominant
In order to measure the frequency of an allele
within a population we therefore need to
know how the trait that it confers is
inherited, in other words if it is dominant,
codominant or recessive
Working out the frequency
of a codominant allele
within a population
Imagine a population of aliens in which skin colour is conferred
by one gene locus
The alleles that may be found at this locus are SR coding for red
pigment and SY coding for yellow pigment, in other words they
are codominant.
If an allele is present then the pigment that it codes for is always
produced in the alien’s skin cells. If both alleles are present
then both of the pigments that they code for are present
The possible genotypes for this locus are
SR SR Red pigment only – the aliens have red skin
SR SY Both red and yellow pigments – the aliens have orange skin
SY SY
Yellow pigment only – the aliens have yellow skin
Working out the allele frequency
In a population of 100 aliens:
41 have red skin
genotyope
46 have orange skin
genotype
13 have yellow skin
genotype
=
=
=
SR SR
SR SY
SY SY
The 41 red aliens represent 82 SR alleles (41 x 2)
The 46 orange aliens represent another 46 SR alleles
So of the 200 alleles for this trait within the population, 128 are SR
The frequency of SR within the population is therefore 128/200 = 0.64
The frequency of SR + SY = 1
So the frequency of the SY allele = 1 - 0.64 = 0.36
But what if the alleles we
are looking at are dominant
or recessive?
Imagine that the allele for red pigment was dominant
so that any alien with it had red skin
We could not therefore tell if a red alien was
homozygous or heterozygous
This makes calculating the frequency of either allele
more problematic
We have to use something called the Hardy-Weinberg
equation
Godfrey Hardy
A British
mathematician
Wilhelm Weinberg
A German doctor
These two scientists developed the
Hardy-Weinberg principle
This states that the allele frequency in a population is
distributed according to a mathematical model
known as the Hardy-Weinberg equation
The following assumptions are made for this to be
correct:
• The population is very large
• Mating is random
• No selective advantage exists for a particular
genotype
• There is no mutation, migration or genetic drift
The Hardy-Weinberg
equation
p2 + 2pq + q2 = 1
p and q represent the frequency of two alleles
in a population
p2 = the frequency of individuals with two p
alleles
2pq = the frequency of individuals who are
heterozygous
q2 = the frequency of individuals homozygous
for the q allele
An example
Lets take cystic fibrosis as an example
Remember, this is conferred by as recessive allele
Possible genotypes are:
CFCF where the person is entirely healthy
CF cf where the person carries the allele but does not
develop the disease
cfcf where the person develops cystic fibrosis
We know if someone has cystic fibrosis because they need
medical treatment but how could we tell how many
symptomless carriers there were in a population of 2000
in which only one person had cystic fibrosis?
Calculating the frequency of
heterozygotes
Lets say:
p represents the frequency of the dominant allele CF
q represents the frequency of the recessive allele cf
Therefore:
p2 = frequency of genotype CFCF
q2 = frequency of genotype cfcf
2pq = frequency of CFcf
We know that p2 + 2pq + q2 = 1
We also know that q2 = 1/2000 = 0.0005
The maths bit (it’s not hard)
If q2 = 0.0005 then q is the square route of this
So q = 0.022
We know that p + q must = 1
Therefore p = 1 – 0.022 = 0.978
The frequency of carriers = 2pq
2pq = 2 x 0.978 x 0.022 = 0.043
This means that 4.3% of the population are carriers
Our population was 2000
4.3% of 2000 = 0.043 2000 = 86