This document discusses population genetics and the Hardy-Weinberg equilibrium. It begins by defining key terms like population, gene pool, and alleles. It then explains the Hardy-Weinberg equilibrium, which describes the relationship between allele and genotype frequencies in a population with random mating and no evolutionary forces. The document provides examples of how to calculate genotype and allele frequencies and discusses factors that can disrupt Hardy-Weinberg equilibrium like natural selection, migration, genetic drift, and nonrandom mating.

1. Lectures by Kathleen Fitzpatrick
Simon Fraser University
Copyright © 2012 Pearson Education Inc.
Mark F. Sanders John L. Bowman
G E N E T I C
A N I N T E G R A T E D A P P R O A C H
A N A LY S I S Chapter 22
Population Genetics and
Evolution

2. Alleles
• Punnet squares
will track alleles
to an individuals
• How about
populations?

3. Populations and Gene Pools
• A population is a group of
interbreeding organisms
• A gene pool is the
collection of genes and
alleles found in the
members of a population
• The pattern of mating
between individuals
determines how alleles
are dispersed into
genotypes, and their
frequencies in successive
generations
http://www.bjupress.com

4. The Hardy-Weinberg Equilibrium
Describes the Relationship of Allele and
Genotype Frequencies in Populations
• Godfrey Hardy showed that with random mating and the absence
of evolutionary change, allele frequencies result in a stable
equilibrium frequency
• Wilhelm Weinberg independently came to a similar conclusion; the
result is the Hardy-Weinberg (H-W) equilibrium, named after both
of them

5. 5

6. The Hardy-Weinberg Equilibrium
• The simplest predictions of H-W equilibrium involve two
alleles of an autosomal gene, A1 and A2
• The frequencies for these are given as f(A1) = p and f(A2) =
q, with equal frequencies in males and females
• Since there are only two alleles of the gene,
p + q = 1.0
• For the two alleles, there are three possible genotypes:
A1A1,A1A2,andA2A2

7. Genotype Frequencies
• The genotype frequencies can be computed using the
binomial expansion (p + q)2
• The two p + q terms represent male and female
contributions to mating
• The summation of the genotype frequencies is
p2
+ 2pq + q2
= 1.0, where
– p2
= frequency of A1A1
– 2pq = frequency of A1A2
– q2
= frequency of A2A2

9. What is the genotype probability?
• In a hypothetical population, the allele A1
occurs 40% of the time and the A2 allele
occurs 60% of the time. What is the
probability of each of the genotypes in the
first generation?
What is allele
frequency of the NEXT
generation following
the first?

10. Allele frequencies do not change
from one generation to the next!
Allele frequencies do not change
from one generation to the next!

11. The Hardy – Weinberg equilibrium for two autosomal alleles

12. Random Mating
• Random mating for one generation produces genotype
frequencies that can be predicted from allele frequencies
• For any frequency of p and q, an expected equilibrium
distribution of genotypes can be derived
• With random mating and no evolutionary change, these
frequencies will remain constant from one generation to
the next
http://disneynumber1fan.deviantart.com/art/Random-Mating-OPEN-350760430

13. If the genotypes are not the
same, we must x2 to account
for reciprocal matings

14. One generation of
random mating
will produce a
population in HW
equilibrium
One generation of
random mating
will produce a
population in HW
equilibrium

15. Determining Autosomal Allele
Frequencies in Populations
• Documentation of allele frequency
changes over time is a hallmark of
population evolution
• Three equally valid methods can be
used to determine allele
frequencies of autosomal genes in
populations
• The Genotype Proportion Method
• The Allele-Counting Method
• The Square Root Method

16. The Genotype Proportion Method
• Can be used to determine allele frequencies whether or not a
population is in equilibrium
• It requires that the genotypes of all members is known
• Major limitation
• Each homozygote frequency is added to half the heterozygote
frequency to determine p and q
• B1B1 = 0.64, B1B2 = 0.32, B2B2 = 0.04
• What is ƒ(B1)?

17. The Allele Counting Method
• The allele counting method can also be used whether or
not a population is in H-W equilibrium
• It requires that the genotypes of all members is
identifiable based on phenotype, and so is feasible in
cases where alleles are codominant
17
Blood group M MN N
Number 406 744 332 = 1482
What is the frequency of M and N?What is the frequency of M and N?

18. The Square Root Method
• The square root method can only be used if a population is in H-W
equilibrium
• One allele must be recessive (a disease allele)
• q is calculated as the square root of the frequency of the
homozygous recessive class, and then p is simply calculated as 1.0 −
q
• In the US, cystic fibrosis occurs in 1
in 2,000 newborn infants. What is
the frequency of the disease allele?
How many people are
carriers?

19. The Hardy-Weinberg Equilibrium for
More Than Two Alleles
• H-W equilibrium values can be determined for more
than two alleles, e.g., in the case of three alleles,
such as the ABO blood type alleles
• The allele frequencies are p, q, and r
• In this case, p + q + r = 1.0 and the allele frequencies
are calculated by the trinomial expansion: (p + q + r)2
• The six possible genotypes are predicted by
p2
+ 2pq + q2
+ 2pr + r2
+ 2qr = 1.0

21. Testing the Hardy-Weinberg
Prediction
• The assumptions of H-W equilibrium are unattainable in
real populations
• How do we determine if observed genotype frequencies
in populations are significantly different from those
predicted by H-W equilibrium?
21

23. Practice Problems!
• Friendly Reminder! Even numbered problems
at the end of the Chapter have answers in the
back of the book
• Do problems 10, 18, 19, 20, 21
• Will get answers for 19 & 21 in review session

24. 24
ANIMATION: Population Genetics-1

25. 25
ANIMATION: Population Genetics-2

26. 26
ANIMATION: Population Genetics-3

27. 27
ANIMATION: Population Genetics-4

28. Calculating Genotype Frequencies for
X-Linked Genes Using the Hardy-
Weinberg Equilibrium
• The pattern of transmission of X-
linked genes differs from that of
autosomal genes because males
are hemizygous
• Males inherit their X chromsome
from the their mothers and
transmit their X chromosome
exclusively to their daughters.

29. Determining Frequencies for X-
Linked Alleles
• For X-linked genes with two alleles, A1 and A2, females
have three possible genotypes: A1A1, A1A2, and A2A2
• Males are hemizygous and so have only two possible
genotypes, A1Y or A2Y
• Therefore, p and q can be easily estimated as p = f(A1Y)
and q = f(A2Y)
• Female genotypes should be seen in the frequencies: p2
,
2pq, and q2

31. Example: Red-Green Color
Blindness
• Red-green color blindness is an X-linked recessive trait
that affects about 9 percent of human males
• What is the expected frequencies of homozygous
normal, heterozygous, and color-blind females?

32. 32

33. Hardy-Weinberg Equilibrium for
X-Linked Genes
• Allele frequencies in males and
females are stable as long as
random mating takes place.
• For X-linked genes, a single
generation of random mating does
not achieve equilibrium; several
generations are required
• Due to sex-dependent differences
in transmission of X-linked genes,
the male frequencies will be the
same as the female frequencies in
the previous generation Males transmit their X alleles
exclusively to their daughters!

35. Practice Problem
• Question 24

36. 22.3 Natural Selection Operates
Through Differential Reproductive
Fitness Within a Population
• H-W equilibrium is maintained when there is no evolutionary
change in a population
• However, allele frequencies do change when evolution occurs
• The evolutionary impact can be calculated as long as the effect on
allele frequency can be estimated

37. Differential Reproductive
Fitness and Relative Fitness
• Natural selection favors certain phenotypes
• Anatomical
• Physiological
• Behavioral traits
• Leads to increased reproductive success of individuals
with certain phenotypes: differential reproductive fitness
• Quantified using relative fitness (w), and organisms with
the highest reproductive success are assigned a value of
w = 1.0
• Individuals that reproduce less successfully have their
relative fitness decreased by a proportion called the
selection coefficient (s) w = 1 - s

38. Directional Natural Selection
• In directional natural selection, one phenotype has a
higher relative fitness than other phenotypes
• acts to increase the frequency of the favored allele over the
others

39. 1. What is the selection coefficient for the
heterozygotes?
2. How many survivors of each genotype in the
next generation?
3. What are the allele frequencies in the next
generation of survivors?
1. What is the selection coefficient for the
heterozygotes?
2. How many survivors of each genotype in the
next generation?
3. What are the allele frequencies in the next
generation of survivors?

40. 40
1. Survivors of each genotype:
B1B1 = (1.0)(360) = 360
B1B2 = (0.80)(480) = 384
B2B2 = (0.40)(160) = 64
2. Allele frequencies next generation:
f(B1) = [(2)(360) + (384)]/1616 = 0.683
f(B2) = [(2)(64) + (384)]/1616 = 0.317
808 of the original
1,000 organisms
remain after
natural selection!
808 of the original
1,000 organisms
remain after
natural selection!

41. Directional Natural Selection Over Time
• Directional natural selection will increase the frequency of certain
alleles with variable intensity, depending on the strength of
selection
• Greater selection strength the greater the difference in relative fitness
frequencies
• Progression toward fixation, i.e., where f(B1) = 1.0 is more rapid
with strong selection and very slow when selection is weaker
• The strongest selection occurs when one genotype has w = 0.0
• What does this mean?

42. Start
ƒ(B1)= 0.01
ƒ(B2)= .99
Start
ƒ(B1)= 0.01
ƒ(B2)= .99
Natural selection is
strongest when the
natural selection
differences between
the genotypes is
larger!
Natural selection is
strongest when the
natural selection
differences between
the genotypes is
larger!
Allele frequency
change is slow when
allele frequencies are
low and faster when
alleles numbers are
higher
Allele frequency
change is slow when
allele frequencies are
low and faster when
alleles numbers are
higher

43. Directional Natural Selection;
Progression to Fixation
• Directional natural selection against organisms with the
recessive phenotype will cause the frequency of the
dominant allele to increase and the recessive to decrease
• Eventually the recessive allele may be completely
eliminated
• However, this can be a slow process, as heterozygous
individuals will still carry the recessive allele

44. 25% of the population
will be removed this
generation!
25% of the population
will be removed this
generation!
Population starts with
50% B and 50% b
Big change in allele
frequencies
Still going to make bb!

45. Laboratory Experiment on
Directional Selection
• Cavener and Clegg examined four subpopulations of Drosophila for
50 generations to test the effects of directional selection in
increasing the frequency of the allele AdhF
(Adh–alcohol
dehydrogenase)
• The original population had AdhF
allele frequency of 0.38
• Two subpopulations were reared on ethanol-rich food, and two on food without
ethanol

47. Natural Selection Favoring
Heterozygotes
• Balanced polymorphism: allele frequencies are
maintained by selection against either homozygote
• E.g., individuals who are heterozygous for the sickle cell anemia
allele, βA
βS
, resistant to malaria, such that heterozygotes in regions
where malaria is prevalent are favored over either homozygote
Malaria:
Plasmodium that
infects RBCs

48. Example: Model for Natural
Selection Favoring Heterozygotes
• Malaria Example:
• Suppose relative fitness of Cc individuals is 1.0, of CC is
0.80, and of cc is 0.20
• In generation 0, the allele frequencies are both 0.50
• What are the allele frequencies after a single
generation?
• What will the genotype frequencies be after
reproduction?

49. The recessive allele will
decrease in frequency
relative to the dominant, but
will not be eliminated
Total: 0.75

50. 50
ANIMATION: Population Genetics-5

51. 22.5 Migration
• Migration refers to the movement of organisms between
populations and thus genes flowing between populations
• Migration is also known as gene flow and the new
population is called an admixed population

52. Effects of Gene Flow
• Gene flow has two principal effects on population:
• In the short run, gene flow can change allele frequencies in the
admixed population
• In the long run, gene flow acts to equalize frequencies of alleles
between populations that remain in genetic contact
• Can slow genetic divergence and block speciation

53. Island Model of
Migration
• The admixed
population has an
immediate
evolutionary change in
allele frequencies, but
will not be in H-W
equilibrium at first; this
requires one
generation of random
mating
Immediate effect
Single generation mating brings
alleles into HW equilibrium

54. 22.6 Genetic Drift Causes Allele
Frequency Change by Sampling
Error
• Genetic drift refers to chance fluctuations of allele
frequencies that result due to sampling error
• Genetic drift occurs in all populations but is especially
prominent in small populations
http://evolution.berkeley.edu/evosite/evo101/IIID1Samplingerror.shtm
50/50 start50/50 start Draw
6:4
Draw
7:3
Draw
4:6
Population
random
fluctuating
around
tan/green

55. By chance an allele
can be fixed or
eliminated
The number of
generations is takes
to do this can vary
Genetic Drift

56. The Founder Effect
• Establishment of a new
population by a small
number of founding
organisms can produce
a difference in allele
frequencies, and is
called the founder
effect
• The allele frequencies
of the new population
may differ from the
original population as a
result of sampling error

58. The Founder Effect and
Genetic Disorders
• 1700s: the Old Order Amish in
Pennsylvania were established by
a founding population of about
200
• They exhibit high frequencies of
autosomal and X-linked recessive
disorders that are rare in the
populations of origin (European)
and the nearby non-Amish
populations
• Ex. Ellis-van Crevald Syndrome:
• Autosomal reccessive
• Short stature, short forearms, extra
digits on hands and feet

59. Genetic Bottlenecks
• In genetic bottlenecks, a
relatively large population is
reduced to a very small
number by a catastrophic
event unrelated to natural
selection
• Survivors of the bottleneck
likely have a low level of
genetic diversity and usually
carry alleles in very different
frequency than the original
population

61. 61

62. 22.7 Nonrandom Mating Alters
Genotype Frequencies
• Nonrandom mating upsets H-W equilibrium
• Nonrandom mating patterns:
• Inbreeding, mating between related individuals
• positive assortative and negative assortative mating with
respect to specific phenotypes mating together

63. Inbreeding
• Inbreeding, also called consanguinous
mating, is mating between gentically
related individuals
• Consanguinous = ‘with blood’
• Mates will share a greater proportion of
alleles with one another than random
members of a population
• Consequence of inbreeding:
• an increase in the frequency of homozygous
genotypes
• decrease in the frequency of heterozygous
genotypes

64. Self-Fertilization
• Inbreeding, for self-fertilizing plants and some self-fertilizing
animals, is a normal reproductive process
• Assuming that the starting parent is heterozygous, subsequent
self-fertilization leads to a decrease in heterozygous frequency by
one-half in each generation
• The allele frequencies remain the same; but genotype frequencies
change each generation
http://facstaff.uww.edu/tipperyn/reprodbio/index.htm

65. Allele frequencies remain at ƒ(A1) = ƒ(A2) = 0.50

66. Inbreeding in Mammalian
Populations
• First-cousin mating is relatively
common in some human societies
and is common in mammals in
general (10% worldwide)
• Uncommon in US
• First cousin matings results in in
infants with homozygous recessive
conditions at a higher frequency than
expected in the general population
• If a recessive allele is more frequent
in a population, chances of a
recessive homozygote in a first-
cousin mating is only a few times
more likely than in random mating
Charles Darwin Emma Darwin

67. Inbreeding Depression
• The genetic consequences of
inbreeding for populations is an
increase in the frequency of
homozygous genotypes
• Inbreeding depression is the
reduction of fitness of inbred
organisms due to the reduced
level of heterozygosity
• Among plants that reproduce by
self-fertilization, inbreeding
depression is low, whereas
among mammals, it can be
severe

68. Assortative Mating
• When mates of similar phenotype
choose one another, it is known as
positive assortative mating; mates
of dissimilar phenotype undergo
negative assortative mating
• Positive assortative mating differs
from inbreeding in being focused
on phenotype rather than
“relatedness”
• In both cases, the effect is limited
to the genes that influence the
phenotype and its impact on the
overall population is limited by the
mating that is otherwise random

69. Assortative Mating in Humans
• Positive Assortative Mating:
• Height
• Skin color
• IQ
• Dwarfism
– Negative Assortative
Mating:
• Redheads

70. 22.8 Species and Higher Taxonomic
Groups Evolve by the Interplay of
Evolutionary Processes
• Evolutionary change at the
species level and above is driven
by reproductive isolation that
can result from any conditions
that prevent one population
from mating with others
• Morphological
• Behavioral
• Geographical
– Isolated populations adapt to
their particular circumstances,
leading to divergence and
speciation
Ex. Fruit flies & food preference?
http://evolution.berkeley.edu/evolibrary/article/evo_44

71. Speciation
• Charles Darwin (1859, On
the Origin of Species by
Means of Natural Selection)
laid out two guiding
principles of speciation:
• Hereditary variation exists in
all species and controls
phenotypic variability, passed
from parent to offspring
• Natural selection allows for
increased survival and
reproduction in individuals
with favored phenotypic
attributes

72. Processes of Speciation
• What speciation is NOT:
• Simple, straight line of descent
• Organized plan to evolve to
the ‘most advanced species’
• Evolutionary history
resembles a multibranched
bush
NO:
YES! 

73. Evolution of the
genus Equus
The lineage of
horses and their
relatives the zebras
and donkeys can
be traced from the
early Eocene (54
million years ago)
to present, but
there are
numerous
branches of the
lineage that did
not produce
modern-day
organisms

74. Construction of Evolutionary Trees
• Equus tree reconstructed using
fossil evidence
• Genetic reconstruction:
• DNA isolated from Neandertal
bones in E. Europe.
– Fragmentary, but provided a
nearly complete sequence
determination of a Neandertal
genome
– At present, 6 genomes have been
found
– 2012: Neandertal DNA
sequences present in genomes of
human indigenous to Europe and
Asia, but not Africa (not present)
– 2-4% of modern human DNA has
Neaderthal origin
Reconstruction of the head of the
Shanidar 1 fossil, a Neanderthal male
who lived c. 70,000 years ago (
John Gurche 2010

75. Patterns of Speciation
• The evolutionary tree of
Equus illustrates two
patterns of speciation:
• Anagenesis is the process
by which an original
species is transformed
into a different species
over many generations
• Cladogenesis is a pattern
of branching in which an
ancestral species gives
rise to two or more new
species
http://biology-forums.com/index.php?action=gallery;sa=view;id=710

76. Evolution of the
genus Equus
The lineage of
horses and their
relatives the zebras
and donkeys can
be traced from the
early Eocene (54
million years ago)
to present, but
there are
numerous
branches of the
lineage that did
not produce
modern-day
organisms

77. Reproductive Barriers and
Speciation
• Anagenesis and cladogenesis
share features:
• Inherited genetic variation
controlling phenotype
• Adaptation through natural
selection
• Reproductive isolation
• Reproductive barriers that
prevent exchange of genes
between populations may be
prezygotic or postzygotic
http://evolution.berkeley.edu/evosite/evo101/VSpeciation.shtml

78. Reproductive Barriers
• Prezygotic mechanisms of
reproductive isolation prevent
mating between members of
different species or the
formation of a zygote following
interspecies mating
• Postzygotic mechanisms result
in failure of a fertilized zygote
to survive, or survival of but
sterility of the individual
produced Male donkey + female horse = Mule
63 chromosomes (62 donkey, 64 horse)
STERILE

79. 79

80. Allopatric Speciation
• Allopatric speciation occurs when populations are
separated by a physical barrier and thus develop in
separate geographic locations or environments
• Physical barrier between two segments of a population (glacier,
mountain range, canyon)
• colonization of a new territory by some members of a
population
jobspapa.com

82. Diversification of Drosophila
Species on Hawaiian Islands
• Hundreds of species of
Drosophila inhabit the
Hawaiian Islands, which
were formed volcanically
• The most closely related
species are found on
adjacent islands, and the
phylogenetic pattern of
species origin corresponds
to the emergence of islands http://evolution.berkeley.edu/evosite/evo101/VBDefiningSpeciation.shtml

83. 83

84. Sympatric Speciation
• In sympatric speciation, population
genetics or postzygotic mechanisms
prevent gene flow between the two
populations, that are not physically
separated
• Genetic mechanisms or postyzygotic
mechanisms that prevent successful
interbreeding
• Some prezygotic mechanimsism:
behavioral, seasonal, or other processes
that limit opportunities for interbreeding
• For example, animals that develop
nocturnal or diurnal patterns of
activity are most likely to mate with
others with the same pattern
Ex.: Male frog call no
longer attracts the
female

85. Sympatric Speciation; Polyploidy
• A clear example of sympatric speciation occurs in plant species that diverge
through the development of polyploidy
• Mating between a polyploid species and a nonpolyploid one can result in reduced
fertility of hybrid offspring

87. Questions?