Mendelian Genetics in
Populations – 1
Hardy-Weinberg Equilibrium,
Selection and Mutation
1
Hardy-Weinberg genotype frequencies (Fig. 5.5)
2
Hardy-Weinberg genotype frequencies – 2
• Given a locus with 2 alleles, A and a
• If the frequency of A is p, and the frequency of a is q
• And if there is random union of gametes (= random mating
of diploid genotypes)
• Then the genotype frequencies of zygotes will be p2 AA;
2pq Aa; q2 aa
• These genotype frequencies are known as the HardyWeinberg genotype frequencies or proportions
• In the example on the previous slide: p = 0.6 and q = 0.4,
so that p2 = 0.36, 2pq = 0.48, and q2 = 0.16
3
Hardy-Weinberg equilibrium: 1
Provided that there are no evolutionary
“forces” acting on a population, allele and
genotype frequencies will remain constant
from one generation to the next, and the
genotype frequencies will be the HardyWeinberg proportions: p2, 2pq, q2 (for a
locus with two alleles).
4
Hardy-Weinberg equilibrium – 2
Start here
Random union of gametes
Equal survivorship
of genotypes = no
natural selection
Equal fertility of adult
genotypes = no
natural selection
Equal survivorship of genotypes = no natural selection
5
Allele frequencies in gametes are the same as
in adults that make gametes (Fig. 5.6b)
6
Requirements for Hardy-Weinberg
equilibrium
• Random mating
• No natural selection (i.e, equal survivorship
and reproduction of genotypes)
• Infinite population size (i.e., no random
genetic drift)
• No mutation
• No migration
7
Why is Hardy-Weinberg important?
• It is a formal statement of the conditions under
which evolution will not occur
• Genotype frequencies at many loci in many
populations often agree quite closely with H-W
expectations (i.e., H-W is a useful tool)
• For example, H-W tells us that “rare” alleles will
almost always be found in heterozygotes: suppose
p(A) = 0.99 and q(a) = 0.01, then the frequency of
heterozygotes Aa is 2pq ≈ 0.02 and the frequency
of aa is q2 = 0.0001. In other words, for every a
allele that is in a homozygote, 100 more are in
heterozygotes
8
Natural selection by differential survivorship
Random union of gametes
Start here
Differential
survivorship =
natural selection
New frequency of B1
= [(36 x 2) + 36] / [(36 + 36 + 8) x 2]
= 108 / 160 = 0.675
Equal fertility of adult
genotypes = no
natural selection
Equal survivorship of genotypes = no natural selection
9
Allele and genotype frequency changes as a
result of natural selection
• In the previous slide, the frequency of allele B1 increased
from 0.6 to 0.675 as a result of one generation of selection,
and the frequency of B2 declined from 0.4 to 0.325
• If there is random mating, the frequency of B1B1 zygotes in
the next generation will be (0.675)2 = 0.456; the frequency
of B1B2 will be 2(0.675)(0.325) = 0.439; and the frequency
of B2B2 will be (0.325)2 = 0.106
• If similar directional selection continues for a large number
of generations, virtually all alleles in the population will be
B1 and virtually all individuals will be B1B1 homozygotes
(= “fixation” of B1)
10
Allele frequency change under persistent directional selection
(B1B1 most fit, heterozygote intermediate)
Think of B1 as a new favorable mutation
Note: Rate of increase in frequency of B1 is slow when B1 is rare because most copies of B1 are in
heterozygotes, which have lower fitness than B1B1 homozygotes
11
Laboratory natural selection on the alcohol
dehydrogenase (Adh) locus of D. melanogaster
Enzyme from AdhF homozygotes breaks down alcohol twice as fast as enzyme from AdhS homozygotes.
Higher fitness of AdhF allele in presence of ethanol could be due to higher survival or more reproduction
12
The CCR5-D32 allele revisited
• Individuals who are homozygous for the D32 allele are
resistant to infection by HIV (CCR5 is a protein on the surface of
host cells that is used as a co-receptor by the virus)
• This suggests that HIV may be a selective force to increase
the frequency of the D32 allele in human populations: is
this likely to happen?
• The frequency of the D32 allele varies among human
populations from > 0.20 to < 0.01
• The rate of increase in the frequency of the D32 allele
depends on (1) its current frequency in a population, and
(2) the prevalence of HIV infection (which determines the
strength of selection)
13
Predicted
changes in allele
frequencies at the
CCR5 locus due
to the AIDS
epidemic (Fig.
5.15)
(a) high initial D32 allele frequency
and high incidence of HIV (=
strong selection & rapid increase in
allele frequency)
(b) high initial D32 allele
frequency and low incidence of
HIV (= weak selection and little
change in allele frequency)
(c) low initial D32 allele frequency
and high incidence of HIV (=
strong selection but little change in
allele frequency)
14
Selection on
recessive and
dominant
alleles – a
recessive lethal
in the flour
beetle (Fig.
5.6)
15
Selection favoring dominant or recessive alleles (Box 5.7)
16
Selection favoring dominant or recessive
alleles - 2
• When a low-fitness recessive allele (e.g., a lethal
recessive) is rare, it is difficult for natural selection
to remove it from the population
• Similarly, when a high-fitness recessive allele is
rare, it is hard for natural selection to increase its
frequency
• In both cases, this is because most copies of the
recessive allele will be “hidden” in heterozygotes,
where they are shielded from natural selection
17
Selection for heterozygotes = overdominance
(Fig. 5.18)
18
Selection for heterozygotes – 2
• Overdominant selection results in a stable
equilibrium in which both alleles at a 2allele locus remain in the population
• Compare this to the previous models of
directional selection that push the most fit
allele toward fixation
19
Sickle-cell disease and malaria: overdominance and
genetic load – 1
• Sickle-cell disease is inherited as an autosomal recessive
disorder (a mutation of the b-globin gene) – people with
sickle-cell disease have greatly reduced life span
• In regions of the world where malaria is common,
heterozygotes have highest fitness because they are more
resistant to malaria than are normal homozygotes
• Estimated relative survivorships in regions with high
incidence of malaria are:
AA
AS
SS
(normal homozygote)
(heterozygote)
(sickle-cell disease)
0.89
1.0
0.20
20
Sickle-cell disease and malaria: overdominance and
genetic load – 2
• The cost of overdominance is the continual production of less fit
homozygotes (AA and SS) via sexual reproduction (Mendelian
segregation and recombination)
• Population geneticists refer to this cost as genetic load, or, in this case,
segregational load
• At equilibrium, the frequency (p) of A is about 0.88 and the frequency
(q) of S is about 0.12
• This means that about q2 = 0.0144: i.e., about 1.5% of births in these
populations have sickle-cell disease
• Although natural selection acts to maximize the mean fitness of the
population given the available genetic variation, it clearly is not
optimal.
• Wouldn’t it be “best” to have an allele that conferred resistance to
malaria but that didn’t cause a debilitating genetic disease when
homozygous?
21
Sickle-cell disease and malaria: limits to selection
• It turns out, there is such an allele, C, which gives the following
relative fitnesses:
AA
AS
CC
AC
SC
SS
0.89
1.0
1.31
0.89
0.70
0.20
• A population would be most fit if all individuals were CC homozygotes
• The problem, however, is that it is very difficult (maybe impossible) for
natural selection to increase the frequency of the C allele when it is rare
because virtually all copies of the C allele will be in AC and SC
heterozygotes, which don’t have high enough fitness (relative to AS and
AA)
• There is no guarantee that just because a “better” allele is available,
natural selection will cause it to increase in frequency
22