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PowerPoint to accompany
Genetics: From Genes to
Genomes
Fourth Edition
Leland H. Hartwell, Leroy Hood,
Michael L. Goldberg, Ann E. Reynolds,
and Lee M. Silver
Prepared by Mary A. Bedell
University of Georgia
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Hartwell et al., 4th edition
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PART
VI
Beyond the Individual Gene and Genome
CHAPTER
Variation and Selection
in Populations
CHAPTER OUTLINE
 19.1 The Hardy-Weinberg Law: Predicting Genetic Variation in Populations
 19.2 Causes of Allele Frequency Changes
 19.3 Analyzing Quantitative Variation
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Three subfields of genetics based on the unit
object that is the focus of study
Molecular genetics – the unit entity is the gene
Formal genetics – the unit entity is the individual organism,
defined by genotype
Population genetics – the unit entity is a population of
interbreeding individuals
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Terms used to describe populations
Population – group of interbreeding individuals of the same
species that inhabit the same space at the same time
Gene pool – sum total of alleles carried by all members of a
population
• Changes can occur because of mutation, immigration
of new individuals into or out of the population, or
decreased fitness
Microevolution – changes in allele frequencies within a
population
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Terms used to describe populations (cont)
Phenotype frequency – proportion of individuals in a
population that have a particular phenotype
Genotype frequency – proportion of individuals in a
population that carry a particular genotype
Example: A gene with two alleles (A and B) in a population
of 20 individuals
12 are AA
4 are AB
4 are BB
Genotype frequencies: AA = 12/20 = 0.6
AB = 4/20 = 0.2
BB = 4/20 = 0.2
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Calculating allele frequencies
Allele frequency – proportion of gene copies in a population
that are of a given allele type
Example with genotype frequencies: AA = 12/20 = 0.6
AB = 4/20 = 0.2
BB = 4/20 = 0.2
Allele frequencies: in 20 people, there is a total of 40 alleles
12 AA individuals  24 A alleles
4 AB individuals  4 A alleles and 4 B alleles
4 BB individuals  8 B alleles
Frequency of A alleles = (24 + 4)/40 = 0.7
Frequency of B alleles = (8 + 4)/40 = 0.3
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From genotype frequencies to
allele frequencies
Fig 19.2
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The Hardy-Weinberg law correlates allele and
genotype frequencies
Developed independently in 1908 by G.H. Hardy and W.
Weinberg
Five simplifying assumptions:
• The population has an infinite number of individuals
• Individuals mate at random
• No new mutations appear
• No migration into or out of the population
• Genotypes have no effect on ability to survive and
transmit alleles to the next generation
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Predicting genotype frequencies in
the next generation
Sexually reproducing, diploid organisms
Two steps needed to relate genotype frequencies in one
generation to the next generation
• Allele frequencies should be the same in adults as in
gametes
• Allele frequencies in gametes can be used to calculate
expected genotype frequencies in zygotes of the next
generation
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The Hardy-Weinberg law is a binomial equation
Fig 19.3
In a large population of randomly breeding individuals with
no new mutations, no migration, and no differences in
fitness based on genotype:
p2 + 2pq + q2 = 1
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Hartwell et al., 4th edition, Chapter 19
(Equation 19.1)
10
Predicting the frequency of albinism:
A case study
In a population of 100,000 people:
100 aa albinos, 1800 Aa carriers, 98,100 AA individuals
Total A alleles = (2 x 98,100) + 1800 = 198,000
Total a alleles = (2 x 100) + 1800 = 2,000
Frequency of A allele = p = 198,000/200,000 = 0.99
Frequency of a allele = q = 2,000/200,000 = 0.01
p2 = (0.99)2 = 0.9801
q2 = (0.01)2 = 0.0001
2pq = 2(0.99)(0.01) = 0.0198
Predicted genotypes in the next generation of 100,000
individuals:
100,000 x 0.9801 = 98,010 AA individuals
100,000 x 0.0198 = 1980 Aa individuals
100,000Copyright
x 0.0001
=
10 aaInc.individuals
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The population genetics of blue-eye color
Blue-eye color in humans is recessive to brown eyes and
arose 6,000 – 10,000 years ago
Trait is very common in Europe but rare outside of Europe
Geographic differences in
proportions of European
populations expressing the
blue eyes phenotype
Fig 19.4a
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A SNP located in an enhancer of the OCA2
gene is associated with blue eye color
The SNP rs12913832 is located in an intron of the HERC2 gene
Fig
19.4b
Haplotype structure of SNP alleles at the OCA2-HERC2 region
Fig
19.4c
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Frequencies of the A and G alleles of the SNP
rs12913832 in different populations
p = rs12913832A
q = rs12913832G
Fig 19.4d
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Use of the Hardy-Weinberg equation with
mixed populations
Example: Blue-eye phenotype in a population derived from 100
people from northern Finland and 100 people from Yakuts of
eastern Siberia
p = frequency of rs12913832A
q = frequency of rs12913832G
In Finnish population of 100 people, q = 0.84
q2 = (0.84)2 = 0.71
2pq = 2 (0.16)(0.84) = 0.27
71 estimated to be GG (blue eyes)
27 estimated to be GA (brown-eyed carriers)
In Yakut population of 100 people, q = 0.10
q2 = (0.1)2 = 0.01
2pq = 2 (0.9)(0.1) = 0.18
1 estimated to be GG (blue eyes)
18 estimated to be GA (brown-eyed carriers)
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Blue eyes vs. brown eyes in a mixed
population (cont)
Total population = 100 Finns + 100 Yakuts = 200
Total GG (blue eyes) = 71 Finns + 1 Yakut = 72
Total GA (carriers) = 27 Finns + 18 Yakuts = 45
Total number of G alleles = (2 x 72) + 45 = 189
Frequency of G alleles = q = 189/400 = 0.47
Expected frequency of offspring with blue eyes (GG) from
these 100 Finns and 100 Yakuts:
q2 = (0.47)2 = 0.22
If 200 offspring, then 0.22 x 200 = 44 with blue eyes
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Properties of populations described by
Hardy-Weinberg equilibrium
Conservation of allele proportions
• Even though the genotype frequencies can change in
the second generation, there will be no change in allele
frequencies
A stratified population formed from two (or more) distinct
populations will become balanced in a single generation
• At Hardy-Weinberg equilibrium, genotype frequencies
will be p2, 2pq, and q2
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Hardy-Weinberg provides a starting point for
modeling population deviations
Natural populations rarely meet the simplified assumptions
of Hardy-Weinberg
• New mutations at each locus arise occasionally
• No population is infinitely large
• Migrations of small groups of individuals does occur
• Mating is not random
• There are genotype-specific differences in fitness
Hardy-Weinberg equation is useful for estimating
population changes through a few generations
• Not as useful for predicting long-term changes, but
does provide a foundation for modeling
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Using Monte Carlo simulations to model
long-term changes in allele frequencies
Monte Carlo simulations use a computer program to model
possible outcomes of randomly chosen matings over a
designated number of generations
• Starting population has a defined number of
individuals that are homozygous and heterozygous
• Mating pairs are chosen through a random-number
generating program
• Genotypes of offspring at each generation are based
on probabilities
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Using Monte Carlo simulations to model
long-term changes in allele frequencies (cont)
At each generation in the simulation:
• Total offspring number and parental population size are
equal
• Parental generation is discarded and offspring serve as
parents of next generation
Multiple, independent simulations are performed
Each simulation represents a possible pathway of genetic
drift
• Change in allele frequencies as a consequence of
random inheritance from one generation to the next
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Modeling genetic drift in populations
of different sizes
Six Monte Carlo simulations run with two initial populations
of heterozygous individuals
• In these simulations, there was no selection
(a) Initial population has 10 individuals
(b) Initial population has 500 individuals
Fig 19.5
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Population size and time to fixation
Fixation – when only one allele in a population has survived
and all individuals are homozygous for that allele
• No further changes can occur (in the absence of migration or
mutation)
At each generation, changes in allele frequencies are
relatively small
Over many generations, there can be large changes in allele
frequency
In populations with 2 alleles present at equal frequencies,
median number of generations to fixation is roughly equal
to the total number of gene copies in breeding individuals
• e.g. Population of 10, median fixation time is 20 generations
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Founder effects and population bottlenecks
Founder effects – occur when a few individuals separate
from a larger populations and establish a new population
• Founder allele frequencies can be different from
original population
Population bottlenecks – large proportion of individuals die
(e.g. from environmental disturbances)
• Survivors are equivalent to a founder population
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Natural selection acts on differences in fitness
to alter allele frequencies
Fitness – individual's relative ability to survive and transmit
its genes to the next generation (a statistical measurement)
• Cannot be measured in individuals in a population
• But, can be measured in all individuals of the same genotype
in a population
• Two basic components: viability and reproductive success
Natural selection – the process that progressively
eliminates individuals whose fitness is lower
• Individuals whose fitness is higher become the parents of
the next generation
• Occurs in all natural populations
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Natural selection often acts through
environmental conditions
Natural selection in giraffes on the savannah
• During long droughts, longer necks are needed to
reach tree leaves
Giraffes with longer necks
had higher fitness than
giraffes with short necks
Fig 19.6
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Modifications to Hardy-Weinberg
In populations undergoing selection, each genotype has a
relative fitness
e.g. Population with two allele (R and r)
Relative fitness (ω) of each genotype (RR, Rr, and rr):
ωRR
ωRr
ωrr
Relative frequencies of each genotype at adulthood:
p2ωRR
2pqωRr
q2ωrr
Individual fitness for each genotype is arbitrary
Average fitness of the population:
2
2
ω = p ωRR + 2pqωRr + q ωrr
(Equation 19.4a)
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Changes in allele
frequencies caused
by selection
Fig 19.7
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Calculating the changes in allele frequencies
due to selection
p' and q' represent allele frequencies after one generation of
selection
q (q rr  p Rr )
q 2 rr  (2pq Rr ) / 2
q' 



spq 2
Δq = q' – q =


(Equation 19.5)
(Equation 19.7)
s = selection coefficient

Varies from 0 (no selection) to 1 (complete selection)

If s = 0, Δq is always negative
Rate of decrease depends on the allele frequencies
As q approaches 0, rate of decrease gets slower (Fig 19.8)
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Predicted and observed decrease in the
frequency of a lethal recessive allele over time
Fig 19.8
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An example of Monte Carlo modeling
of natural selection
Population with 500 individuals (1 Rr, 499 rr)
ωRR = 1.00
ωRr = 0.98
ωrr = 0.98
Six simulations:
In three simulations, R
allele goes extinct in
<100 generations
In three simulations, R
allele moves to fixation
Fig 19.9
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The fitness of alternative genotypes
in different environments
H. sapiens migrated out of Africa 70,000 years ago
Exposure to ultraviolet rays from sun decreases with
increasing distance from equator
• Affects vitamin D production and skin cancer incidence
• Close to equator, dark skin protects against skin cancer
• Farther from equator, lighter skin allows more UV for
sufficient vitamin D production
Skin pigmentation is a complex quantitative trait and is
determined by alleles at many genes
Alleles of several genes show strong associations with
different populations around the world (Fig 19.10)
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Geographic distribution of allele frequencies at
two skin pigmentation loci
Distribution of KITLG alleles
Distribution of SLC24A5 alleles
Fig 19.10a
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Fig 19.10b
32
Genetic response to cultural innovations
Lactase gene (LCT) required to digest milk
• In pre-agricultural societies, lactase isn't required after
weaning
• LCT expression is turned off after weaning
After cattle domestication (Turkey, ~8,000 years ago), ability
to digest milk conferred a survival advantage
~ 5,000 years ago, a DNA alteration in an LCT regulatory
sequence occurred
• Allows LCT expression at high level throughout life
• Different modern populations around the world vary in LCT
allele frequencies (Fig 19.10d)
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Frequency of the
sickle-cell allele
across Africa where
malaria is prevalent
Sickle-cell anemia is a
recessive trait caused by
mutations in the β-globin
locus
Heterozygous advantage
– individuals that are
carriers of sickle-cell are
resistant to malaria
Fig 19.11
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Balancing selection maintains deleterious
alleles in a population
For the β-globin locus, B1 is the normal allele and B2 is a
recessive disease allele
Relative fitness for B1B2 = 1
Selection coefficient for B1B1 = 1 – s1
Selection coefficient for B2B2 = 1 – s2
Changes in allele frequency resulting from selection
Δq = pq (s1 p  s 2 q )

(Equation 19.8)
Equilibrium frequency of B2 (qe) is reached when:
 qe =
s1
s1  s 2
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(Equation 19.9)
35
A comprehensive example: Human behavior
can affect evolution of pathogens and pests
Evolution of drug resistance in bacterial pathogens
• e.g. Tuberculosis and evolution of multi-drug resistant
strains of TB
Factors contributing to rapid evolution of resistance
• Short generation time and rapid reproduction
• Large population densities
• Strong selection imposed by antibiotics
• Gene transfer between bacteria
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The evolution of
resistance in TB bacteria
Repeated cycles of antibiotic
treatment coupled with premature
cessation of treatment
• At beginning of treatment,
occasional mutations in
bacteria can occur that confer
resistance
• If antibiotic treatment is
prematurely terminated, the
drug-resistant bacteria can
proliferate
Fig 19.12
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Evolution of pesticide resistance
Large-scale use of DDT and other synthetic insecticides
began in 1940s
• DDT is a nerve toxin in insects
• Dominant mutations in a single gene confer resistance
through detoxification of DDT
• With insecticide application, strong selection favors
heterozygotes
By 1984, there were >450 species of mites and insects that
had become resistant
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Changes in genotype frequencies in
mosquitoes in response to DDT
Use of DDT in Bangkok to control A. aegytpi mosquitoes began in 1964 and discontinued in 1967
R is dominant, resistance allele; S is susceptibility allele
RR genotype confers
a fitness cost:
In the absence of the
insecticide, resistance
is subject to negative
selection
Fig 19.14b
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Analyzing quantitative trait variation
Factors causing continuous variation of quantitative traits
• Number of genes that determine the trait
• Genetic and environmental factors that affect
penetrance and expressivity of the genes
One of the goals of quantitative analysis is to separate the
genetics effects from the environmental effects
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Studies of dandelions can help sort out the
effects of genes versus the environment
Most dandelion seeds arise from mitotic divisions – all
seeds from a single plant are genetically identical
Goal is to compare influence of genes and environment on
the length of the stem at flowering
Fig 19.15a
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Finding the mean and variance of
stem length in dandelions
Genetically identical plants grown on hillside:
• Variation in stem length should be a consequence of
environmental interactions (VE)
Fig 19.15b
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Genetically identical dandelions grown
in two environments
VE for growth in greenhouse < VE for growth on hillside
This difference in VE is a measure of the impact of the more
diverse environmental conditions on the hillside
Fig 19.15c
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Growth of genetically identical and genetically
diverse dandelions in a greenhouse
Difference in variance between genetically diverse and
identical plants is VG, the genetic variance
Fig 19.15d
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Growth of genetically identical and genetically
diverse dandelions on a hillside
Total phenotype variance (VP) = VE + VG
Fig 19.15e
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Heritability is the proportion of phenotypic
variance due to genetic variance
Heritability of a trait is always defined for a specific
population in a specific set of environmental conditions
Amounts of genetic, environmental, and phenotypic
variation may differ among traits
VG
VG
h 

VG VE VP
2
(Equation 19.11)
Heritability is measured in studies of groups with defined
genetic differences

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Measuring the heritability of bill depth in
populations of Darwin’s finches
Geospiza fortis on Daphne
Major in the Galápagos
Islands
Correlation between beak size
of offspring and the average of
the parents' beak sizes (slope
of line is 0.82)
Fig 19.16a, b
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Results if finch populations had no
environmental or no genetic effects
Approximately 82% of variation
in bill depth in Darwin's finches
is due to genetic variation
among individuals (Fig 19.16b,
slope of line is 0.82)
• If the environment had no
effect, then heritability would
be 1.0
• If there was not genetic
contribution, then heritability
would be 0
Fig 19.16c, d
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Heritability of polygenic traits in humans
can be studied using twins
Fig 19.17a
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Concordance of a trait in two children
raised in the same family
If the heritability is 0.0, no differences would be observed
between monozygotic (MZ), dizygotic (DZ), or unrelated by
adoption (UR)
Fig 19.17b
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Concordance of a trait in two children
raised in the same family (cont)
If the heritability is 1.0, differences would be observed in
comparing monozygotic (MZ), dizygotic (DZ), or unrelated
by adoption (UR)
The extent of difference varies with the trait frequency
Fig 19.17b
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A trait's heritability determines its
potential for evolution
Heritability quantifies the potential for selection
• A trait with high heritability has a large potential for
evolution
• Selection differential = S
 Difference between value for this trait in the parents and
value for this trait in the entire population (breeding and
non-breeding)
• Response to selection = R
 The amount of change in the mean value of a trait that
results from selection
R = h2S
(Equation 19.12)
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Bristle number in parents and offspring in a lab
population of D. melanogaster
This trait has a high heritability:
• Parents with high bristle numbers have offspring with
high bristle numbers
• Parents with low bristle numbers have offspring with
low bristle numbers
Fig 19.18
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Evolution of abdominal bristle number in
response to artificial selection in Drosophila
Artificial selection can be imposed on this trait –
• Flies with high bristle number bred together
• Flies with low bristle number bred together
Fig 19.19
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