Population Genetics lecture note by ZY.pptx

Population Genetics
BIOG. 512
School of Biological Sciences and Biotechnology
Haramaya University
1
Zekeria Yusuf (PhD)

Topics to be Covered
1. Introduction
2. Qualitative and quantitative traits
3. Quantitative genetic parameters: genetic variability parameters, variance &
covariance components
4. Genotype frequencies and HW-principle
5. Genetic and Phenotypic variation
6. Organization of Population Genetics
Darwinian Selection
Genetic drift and effective population size,
Population structure and gene flow,
7. Molecular population genetics
8. Association mapping and QTL mapping
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Zekeria Yusuf (PhD)

1. Introduction….
• Population Genetics: the study of the rules governing the
maintenance and transmission of genetic variation in natural
populations.
• The study of the change of allele frequencies, genotype
frequencies, and phenotype frequencies,
• Population genetics involves the understanding of how genes and
alleles are distributed & maintained at particular frequencies in
populations.
• Evolution can be defined as a change in gene frequencies through time.
• Population genetics tracks the fate, across generations, of Mendelian
genes in populations.
• Population genetics is concerned with whether a particular allele or
genotype will become more or less common over time, and WHY?
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Zekeria Yusuf (PhD)

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• Population genetics = application of genetic principles
to entire populations of organisms
• Population = group of organisms of the same species
living in the same geographical area
• Subpopulation = any of the breeding groups within a
population among which migration is restricted
• Local population = subpopulation within which most
individuals find their mates
Population Genetics

1. Introduction
• Population: a group of the same species living in an area
• Gene Pool: the sum total of genetic information present in a population
at any given point in time.
• Phenotype: a morphological, physiological, biochemical, or behavioral
characteristic of an individual organism.
• Genotype: the genetic constitution of an individual organism.
• Locus: a site on a chromosome, or the gene that occupies the site.
• Gene: a nucleic acid sequence that encodes a product with a distinct
function in the organism.
• Alleles: alternate forms of a gene.
• Gene (Allele) Frequency: the relative proportion of a particular allele at
a single locus in a population (a number between 0 and 1).
• Genotype Frequency: the relative proportion of a particular genotype
in a population (a number between 0 and 1).
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Zekeria Yusuf (PhD)

1. Introduction….
• Members of a species can interbreed & produce fertile offspring
• Species have a shared gene pool
• Gene pool – all of the alleles of all individuals in a population
• Different species do NOT exchange genes by interbreeding
• Different species that interbreed often produce sterile or less
viable offspring e.g. Mule
• No two individuals are exactly alike (variations)
• More Fit individuals survive & pass on their traits
Speciation: Formation of new species
• One species may split into 2 or more species
• A species may evolve into a new species
• Requires very long periods of time
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Zekeria Yusuf (PhD)

The Gene Pool
• Members of a species can
interbreed & produce fertile
offspring
• Species have a shared gene pool
• Gene pool – all of the alleles of all
individuals in a population
• Different species do NOT
exchange genes by interbreeding
• Different species that interbreed
often produce sterile or less viable
offspring e.g. Mule
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Zekeria Yusuf (PhD)

Genetic Variability
What is variability??
• Presence of differences among
the individuals of plant
population
• Due to differences in genetic
constitution
• Due to differences in
environment
• Essential for resistance to biotic
and abiotic factors &
adaptability
Zekeria Yusuf (PhD) 11

Sources of variability
• Spontaneous mutations
• Natural outcrossing
• Recombination
Measures of conservation
• Global gene pool (introducing genotypes from
other localities)
• Deliberate use of heterogeneous populations
• Use of multiline varieties

Features of polygenic traits
• Continuous variation
• Small and undetectable effect of individual gene
• Several genes involved
• No possibility of grouping into distinct classes
• High effect of environment
• Analyzed based on mean, variance & covariance
• Possibility of metric measurements
• Low stability

Types of polygenic variation
1. Phenotypic variation:
Observable; Genotypic + environmental;
Measured as phenotypic variance
2. Genotypic variation:
Inherent; Unaltered by environment;
Measured as genotypic variance
3. Environmental variation: non heritable; uncontrolled;
measured as error mean variance
Assessment of polygenic variation
• Requires metric measurements,
• Observes several individuals and mean values are used in
studies,
• Uses mean, variance, covariance etc. from replications

Multiple genes
• polygenic trait is one whose phenotype is influenced by
more than one gene
• Polygene – any group of non-allelic genes, each having
a small quantitative effect, that together produce a
wide range of phenotypic variation;
• - also called multiple factor, quantitative gene.
• There are several but not an unlimited number of
genes involved in the expression of a polygenic trait.
• The loci act in concert in an additive fashion.
• The phenotype is a result of the interaction of the
genotype and the environment.
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Zekeria Yusuf (PhD)

VARIANCES AND COVARIANCES
• The variability present in a population is of polygenic
nature and this polygenic variation is of three types
• 1) Phenotypic
• 2) Genotypic
• 3) Environmental
• The statistical procedure which separates (or) splits the
total variation into different components is called
analysis of variance (or) ANOVA.
• ANOVA is useful in estimating the different
components of variance. It provides basis for the test of
significance and it is carried out only with replicated
data obtained from standard statistical experimental
results.
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F (calculated) is compared with F(Table) value by looking at the F table for
replication df(r-1) and error df values(r-1)(t-1).If the calculated F value is
greater than F(Table value) then it is significant.
Genotypic variance: It is the inherent variation which remains unaltered by the
environment. It is the variation due to genotypes. It is denoted by VG and is
calculated using the formula:
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GCV>PCV : little influence of environment,
selection will be rewarding
PCV>GCV : apparent influence of environment,
selection may be misleading
ECV>PCV&GCV : significant influence of
environment, selection will be ineffective

Heritability and genetic advance are important selection parameters and
heritability estimate along with genetic advance are interpreted as
follows
1) High heritability accompanied with high genetic advance indicates
heritability is due to additive (or) fixable variation and selection may
be effective.
2) High heritability accompanied with low genetic advance indicates non
additive gene action and selection for such characters may not be
rewarding.
3) Low heritability accompanied with high genetic advance reveals that
characters are governed by fixable gene effects and low heritability is
due to high environmental influence and selection may be effective.
4) Low heritability accompanied with low genetic advance indicates that
character is highly influenced by environment and selection is
ineffective.
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A heritable trait is not necessarily adaptive.
Every gene must express itself in an environment, and all environments must act
on the genotype an individual gets.
Finding no heritability for the trait is not a demonstration that genes are
irrelevant; rather, it demonstrates that, in the particular population studied, there
is no genetic variation at the relevant loci or that the environments in which the
population developed were such that different genotypes had the same
phenotype.
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Zekeria Yusuf (PhD)
A high heritability does not mean that a trait is unaffected by its environment.
In general, the heritability of a trait is different in each population and in each set of
environments; it cannot be extrapolated from one population and set of environments
to another.

Twin studies
• Theoretically, any phenotypic differences between identical twins are
environmental.
• Phenotypic differences between fraternal twins can be due to both
environmental and genetic differences.
If the heritability is high,
•identical twins will normally be very similar for a trait
•fraternal twins will be less similar
If the heritability is low,
•identical twins may not be much more similar than fraternal twins.
If variation for a trait is completely heritable,
•identical twins should be have a correlation near 1
• fraternal twins should have a correlation near 0.5
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Zekeria Yusuf (PhD)

Questions that can be answered in in accordance
with the laws of population genetics
• Why a dominant trait does not increase in a population at the
expense of a recessive one?
• How can the carrier frequency be determined when knowing the
disease incidence?
• Why a particular genetic disorder can be more common in one
population or community than in another?
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Zekeria Yusuf (PhD)

What can allele frequencies tell us about a population?
1. Whether the gene pool is stable or undergoing change
2. We can estimate the rate of change
3. If we know the rate of change we can make predictions about
likely future trends
4. This has important applications in conservation of wild
populations and in captive breeding programmes
• Is there any rule which defines how gene pools behave from
generation to generation?
Yes: the Hardy-Weinberg Theorem or Equation
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Zekeria Yusuf (PhD)

HW-principle
• Hardy-Weinberg law: Independently discovered by Godfrey H. Hardy
(1877-1947) and Wilhelm Weinberg (1862-1937): states that
population of organisms considered to have a stable equilibrium (no
change in gene and allele frequencies) iff the following conditions
meet.
1. Population is infinitely large, to avoid effects of genetic drift (=change in
genetic frequency due to chance or sampling error).
2. Within the population mating occurs at random.
3. There is no selective advantage for any genotype i.e. all gametes are
equally viable and fertile.
4. There is no mutation/migration/gene flow
• These parameters describe a non-evolving/ideal population
5. diploid organism, sexual reproduction, nonoverlapping generations
The driving forces of evolution are the reverse of HWP
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Zekeria Yusuf (PhD)

Some facts about assumptions of the Hardy-Weinberg law:
1. Population is infinitely large:
• Assumption is unrealistic.
• Large populations are mathematically similar to infinitely large populations.
• Finite populations with rare mutations, rare migrants, and weak selection generally fit Hardy-Weinberg
proportions.
2. Mating is random:
• Few organisms mate randomly for all traits or loci.
• Hardy-Weinberg applies to any locus for which mating occurs randomly, even if mating is non-random
for other loci.
• This works because different loci assort independently due to recombination.
3. No natural selection, No mutation, and No migration
Gene pool must be closed to the addition/subtraction of new alleles.
Selection can subtract alleles or cause some alleles to increase in frequency.
Mutation always adds to variation (generates novel alleles).
Effects of mutation can be accommodated with a model (e.g., infinite alleles model).
Migration can either add or subtract variation depending on which alleles migrants carry and
whether they immigrate or emigrate.
Like random mating, condition applies only to the locus under study.
Genes are unlinked because alleles sort independently on different chromosomes due to
recombination.
HW explains how Mendelian segregation influences allelic and genotypic frequencies in a
population.

Hardy-Weinberg Equilibrium
• Null Model = population is in HW Equilibrium
– Useful
– Often predicts genotype frequencies well
The possible range for an allele or genotype frequencies
therefore lies between ( 0 – 1): with 0 meaning complete absence
of that allele or genotype from the population (no individual in the
population carries that allele or genotype);1means
complete fixation of the allele or genotype (fixation means that
every individual in the population is homozygous for the allele --
i.e., has the same genotype at that locus).

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Zekeria Yusuf (PhD)
 Genes do not change from one allelic state to another (no mutation).
 All individuals have equal probabilities of survival and reproduction (no selection).

The gene pool of NON-
EVOLVING population
remains CONSTANT over
multiple generations (allele
frequency doesn’t change)
The Hardy-Weinberg Equation:
P + q= 1 allele frequencies
p2 + 2pq + q2=1 gene
frequencies
Where:
p2 = frequency of AA genotype
2pq = frequency of Aa
q2 = frequency of aa genotype

Hardy-Weinberg Equilibrium
• Consider a single locus with two alleles (A, a), the
possible genotypes are (AA, Aa, aa)
• Question: How the genotype frequencies
propagate through the generation?
genotype freq.
W
2V
U
....
....
W
2V
U
W
2V
U
aa
Aa
AA
n
n
n
1
1
1
0
0
0











P0 = P(A) = U0+V0
Q0 = P(a) = W0+V0 = 1- P0

H.W. Equilibrium
2
0
n
0
0
n
2
0
n
0
0
1
2
1
2
2
0
2
0
0
2
0
2
1
1
2
0
0
1
2
0
1
2
0
2
0
0
2
0
0
0
2
0
1
Q
W
Q
2P
V
2
,
P
U
.........
Q
2P
V
2
Q
W
,
P
)
Q
P
P
(
)
V
(U
U
......
......
Q
2P
V
2
Q
W
symmerty
By
P
)
V
(U
4
1
)
V
2
(
2
1
)
V
2
U
(
2
U
U
mating
random
Assume























GENOTYPE VERSUS GENE FREQUENCIES
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Zekeria Yusuf (PhD)

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Zekeria Yusuf (PhD)
Mendelian genetics implies that genetic variability can persist indefinitely,
unless other evolutionary forces act to remove it.

• If an autosomal recessive disorder is in Hardy-Weinberg
equilibrium the carrier frequency can be estimated by
doubling the square root of the disease incidence (2pq, p very
close to 1).
• Otherwise rare single-gene disorders can show a high
incidence in a small population because of a founder effect
coupled with genetic isolation.
• When a serious autosomal recessive disorder has a relatively
high incidence in a large population this is likely to be due to
heterozygote advantage.
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Zekeria Yusuf (PhD)

Allelic frequency
Allelic frequency = Number of
copies of a given allele divided
by sum of counts of all alleles
BB appears 452 times
Bb appears 43 times
bb appears 2 times
492 moths
994 alleles
Frequencies
B (904 + 43) ÷ 994 = 0.953
b (43 + 4) ÷ 994 = 0.047
Total 1.000
BB
Bb
Bb
bb

Can also calculate it from the genotypic frequencies
BB was 0.909
Bb was 0.087
bb was 0.004
Therefore frequency of B = Frequency of BB + ½
frequency of Bb
f(B) = .909 + ½ 0.087 = .909 + .0435 = .9525
F(b) = 0.004 + ½ 0.087 = 0.004 + 0.0435 = 0.047
What about multiple alleles?

HW Equilibrium for X-linked loci
• Assume at generation n
– gene frequency for female
– gene frequency for male
=>
n
r
0 0
2 1
lim
3 3
n
n
q q r q r
 

   
n
q

• Proof : Under the similar conditions,
we have
=> 1 1
1 1
2
1
( (1 ) )
2
1 1
( )
2 2 1
1
2 1
2 0 2, 1
n n n n
n n n n
q r a r a q
a a
q r q r
a
a
a
a a a
 
 
     

  

 

     
1
1 1
1
( )
2
n n
n n n
r q
q r q

 




 



• a = 2
• a = -1
1 1 0 0
0 0
1 1 1
2 2 2
2
lim
3
n n n n
n
n
q r q r q r
q r
q q
 


     

  
1 1
1
( ) lim( ) 0
2
n n n n n n
n
q r q r q r
  
      

Allelic frequencies at X linked locus
same principle
However remember for humans that males only have one X
So that
F(one allele = 2 X the homzygous genotype) + the number of
heterozygotes + the males with the phenotype all divided by the
number of alleles in the population (2 X females) plus males.

Genotype Number
A1A1 4
A1A2 41
A2A2 84
A1A3 25
A2A3 88
A3A3 32
Total 274
f(A1) = Total number of A1 in population divided by
total number of alleles

Genotype Number Number of A1
A1A1 4 2 X 4
A1A2 41 41
A2A2 84
A1A3 25 25
A2A3 88
A3A3 32
Total 274
f(A1) = ((2 X 4) + 41 + 25) ÷ (2 X 274)
= (8 +41 + 25) ÷ 548
= 74 ÷ 548
= 0.135

THE EXTENSION OF H-W TO LOCI WITH MANY ALLELES
 Regardless of the number of alleles per locus, the H-W principle still applies as long as
the organisms are diploid.
 Assume that you have a locus with n alleles (A1, A2, … , An), and the allele frequencies
are given by p1, p2, p3, … , pn.
 The expected frequency of any homozygote is just the square of the allele frequency.
F (A1A1) = p1
2, F (A6A6) = p6
2, etc.
 The expected frequency of any heterozygote is 2 times the product of the respective
allele frequencies.
F (A1A3) = 2p1p3, F (A3A5) = 2p3p5, etc.
 Expected heterozygosity is 1 – Σ(pi
2).

If there are only two alleles, the frequency of the more frequent allele is
indicated by p, while the frequency of the less frequent allele is indicated by q.
P + q = 1
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Zekeria Yusuf (PhD)

Gene and Allele frequencies
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Zekeria Yusuf (PhD)

However, it can be shown that in a large randomly mating population, in which
there is no disturbance by outside influences, dominant traits do not increase at the
expense of recessive ones.
In fact, in such a population, the relative proportions of the different genotypes
(and phenotypes) remain constant from one generation to another.
This is known as the Hardy-Weinberg principle which is one of the most
important fundamental principles in human genetics.
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Zekeria Yusuf (PhD)

Deviation from HWE
• A non-evolving population is the exception rather than the rule
• If a population is evolving, then allele frequencies will change
over time i.e. the composition of the gene pool will change from
one generation to the next,
• Because changes in a population’s gene pool is evolution on a
small scale, we refer to it as microevolution
• Microevolution (evolution within a species) occurs even if the
frequency of alleles are changing for only a single locus
• If we track allele and genotype frequencies in a population over
many generations, some loci will show a Hardy-Weinberg
equilibrium but alleles at other loci will be changing.
Deviation from HW principles brings about evolution
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Zekeria Yusuf (PhD)

Causes of deviations from Hardy-Weinberg (HW) equilibrium
‣ inbreeding
‣ assortative and disassortative mating
‣ fragmented populations

The impact of complete positive genotypic assortative mating (like
genotypes mate) or self-fertilization on genotype frequencies

The impact of complete positive genotypic assortative mating (like genotypes mate) or
self-fertilization on genotype frequencies…
• The initial genotype frequencies are represented by D, H, and R.
When either of the homozygotes mates with an individual with the
same genotype, all progeny bear their parent’s homozygous
genotype.
• When two heterozygote individuals mate, the expected genotype
frequencies among the progeny are one half heterozygous genotypes
and one quarter of each homozygous genotype.
• Every generation the frequency of the heterozygotes declines by one-
half while one-quarter of the heterozygote frequency is added to the
frequencies of each homozygote (diagonal arrows).
• Eventually, the population will lose all heterozygosity although allele
frequencies will remain constant.
• Therefore, assortative mating or self-fertilization changes the packing
of alleles in genotypes but not the allele frequencies themselves.

Genetic Variation
• Genetic variation is the raw material of evolutionary change:
how do we measure it?
• What are the forces that cause genetic changes within
populations? That is, what mechanisms cause evolutionary
change?
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Zekeria Yusuf (PhD)

Population structure/ differentiation
• Population structure is one of the most studied and least understood
aspects of population genetics.
• Broadly speaking, structure refers to any deviation from random-mating,
and includes phenomena such as inbreeding, associative mating (where
reproduction is stratified among genotypes), and geographical subdivision.
Geographical structure has received the most attention for two reasons:
• First, geographical structure is an inescapable fact of biology. Populations
may be separated by oceans, mountains or deserts. Even when there are no
barriers to gene flow, organisms do not disperse randomly across the
species range – rather, they tend to remain close to where they were born.
Under these circumstances, genetic and phenotypic differences can
accumulate between populations.
• The second reason is that differentiation between local populations must
represent the early stages of speciation.
• Geographical structure is the non-random mating of individuals with
respect to location.

Population structure
Geographic Variations:
• Variation in a species due to climate or another geographical condition
• Populations live in different locations. Example: Finches of Galapagos
Islands & South America,
Heterozygote Advantage:
• Favors heterozygotes (Aa)
• Maintains both alleles (A,a) instead of removing less successful alleles
from a population e.g. Sickle cell anemia:
Homozygotes exhibit severe anemia, have abnormal blood cell shape,
and usually die before reproductive age.
Heterozygotes are less susceptible to malaria
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Zekeria Yusuf (PhD)

Nonrandom Mating
• HWE assumes that mating is random in the population
• Most natural populations deviate in some way from
random mating
• There are various ways in which a species might
deviate from random mating,
• The two most common departures from random
mating:
inbreeding
population subdivision or substructure

Nonrandom mating: assortative matings
• Positive assortative mating: describes the case when
individuals with like genotypes or phenotypes tend to mate.
• Negative assortative mating occurs when individuals with
unlike genotypes or phenotypes tend to mate (also called
disassortative mating).
• Both of these general types of non-random mating will impact
expected genotype frequencies in a population.

Nonrandom mating: assortative matings
• Mating among related individuals, termed consanguineous mating or
biparental inbreeding, increases the probability that the resulting
progeny are homozygous compared to random mating.
• This occurs since relatives, by definition, are more likely than two
random individuals to share one or two alleles that were inherited
from ancestors they share in common (this makes mating among
relatives a form of assortative mating)
• Therefore, when related individuals mate their progeny have a higher
chance of receiving the same allele from both parents, giving them a
greater chance of having a homozygous genotype.
• Sexual autogamy or self-fertilization is an extreme example of
consanguineous mating where an individual can mate with itself by
virtue of possessing reproductive organs of both sexes.

Fixation and Fitness
Fixation of an allele: an allele must increase in frequency and
ultimately become fixed in the population (all individuals have the
same allele).
• The fixation index (F) measures deviation from Hardy–Weinberg
expected heterozygote frequencies.
• Fixation index (F): the proportion by which heterozygosity is
reduced or increased relative to the heterozygosity in a randomly
mating population with the same allele frequencies.
Fitness: of a genotype, a measure of individual’s ability to survive
and reproduce (it is rather relative with respect to other
individuals).

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Fitness and Its Measurement
• Fitness: A phenotype with greater fitness usually increases in
frequency
– Most fit is given a value of 1
• Fitness is a combination of:
– Survival: how long does an organism live
– Mating success: how often it mates
– Number of offspring per mating that survive

Fitness
Derivation: w in general means “relative fitness”: a measurement of the relative
ability of individuals with a certain genotype to reproduce successfully.
W11, for instance, means the relative ability of individuals with the A1A1
genotype to reproduce successfully. w is always a number between 0 and 1.
Adding fitness (w) to the Hardy-Weinberg equation as shown above allows you to
predict the effect of selection on gene and allele frequencies in the next
generation.
Take the Hardy-Weinberg equation and multiply each term (the frequency of each
genotype) by the fitness of that genotype. Add those up and you get the mean
fitness, 𝑤 (“w-bar”) . Divide through by 𝑤 and you get the second equation.
Here, each term of the equation is multiplied by the fitness of a genotype divided
by the mean fitness. If a genotype is fitter than average, this quotient is greater
than 1, and that genotype will increase in frequency in the next generation. If a
genotype is less fit than average, the quotient is less than 1, and that genotype
will decrease in frequency in the next generation.

Selection coefficient (s)
A related term to fitness (w) that you may run across is the
selection coefficient, s.
The selection coefficient compares two phenotypes and provides
a measure of the proportional amount that the phenotype under
consideration is less fit.
With no selection against a phenotype s=0 and if a phenotype is
completely lethal s=1.
The relation ship between relative fitness (w) and the selection
coefficient (s) is s = 1-w.

Fixation Indices
The fixation index as a measure of deviation from expected levels
of heterozygosity is a critical concept that will appear in several
places later in this text,
The fixation index plays a conceptual role in understanding the
effects of population size on heterozygosity & also serves as an
estimator of the impact of population structure on the
distribution of genetic variation.

Population differentiation
• high fragmentation of habitats
‣ instead of one continuous habitat (panmixia) ➡
separated populations without or with limited
migration between them,
• genetic differentiation between populations
‣ due to genetic drift, stochasticity, selection etc...
• measuring population fragmentation: using F-statistics
(Wright, 1969).

Genetic Structure
• Genetic structure exists whenever there are non-random
associations between genotypes and other factors.
• geographical structure; subpopulations; isolation-by-
distance
• habitat-based structure: microenvironments; host races
• sex-based structure: sex chromosomes; maternal and
paternal mtDNA in mussels
• allele-based structure: balancing selection; inversions
Such associations can arise through purely neutral
processes (e.g. limited dispersal between subpopulations)
or because of selection (e.g., local adaptation).

Detecting and describing genetic structure
• The most commonly used methods of summarising structure within
genetic variability are the F statistics developed by Sewall Wright
(1951).
• F statistics partition genetic variability as measured by levels of
• heterozygosity into components of within population & between
population variation.
• Forexa. suppose you have collected data on genetic variability
within your favourite species, from samples spread across the
country. Although the population may actually be continuous across
the country, it is natural to divide your sample into different
populations, and to ask how much variation there is within each
level of structure relative to other levels.
• The most cited statistic is the proportion of total heterozygosity
(HT) that is explained by within population heterozygosity (HS).
Where the line over HS indicates that it is the average heterozygosity within
populations.

Detecting and describing genetic structure….
• Other F statistics may measure the proportion of heterozygosity
within populations that is explained by within individual
heterozygosity (FIS: a measure of inbreeding) or the proportion of
variation explained by successively higher levels of population
classification (e.g. sample site < region < country < continent).
• F statistics describe the partitioning of variability within the sampled
data. In themselves they do not tell us whether there is any significant
structure within the data. Significance levels are best estimated by
permutation.
• The null distribution of the statistic of interest (e.g. FST) under the
hypothesis of no significant structure is obtained empirically by
randomising alleles or genotypes with respect to location.
• If the observed level of structure is greater than expected by chance,
there is evidence for genetic differentiation.

Detecting and describing genetic structure….
• Before looking at some estimates of FST from natural populations, it is
worth mentioning a couple of things about F statistics.
1. because it is a ratio, the statistic contains no information about absolute
levels of genetic variability.
• In many ways this is good because we want to know about
differentiation relative to other processes (e.g. inbreeding, mutation
rate), but it also throws away much information, and is liable to have
high sampling variance when levels of heterozygosity are low.
2. some F statistics can actually be negative. For example, suppose there is
a tendency for individuals to actively avoid breeding with relatives.
Levels of heterozygosity within individuals will therefore tend to be
higher than levels of heterozygosity in the local population, and the
statistic FIS will be negative.

FST in natural populations
• In the early days of molecular population genetics, calculating F statistics from
patterns of allozyme variation was a growth industry. Naturally, the greatest
interest was in the differentiation of human populations, and studies of the
major races of humans (Caucasians, Africans, Chinese) put FST in the region of
0.07. In other words, 93% of all allozyme variation is within populations and
only 7% is between.
• Remarkably, similar levels of differentiation can be observed at much finer
scales. For example, about 8% of the variation among Yanomama American
Indians is between villages and 92% is within (though the total level of
heterozygosity among the villages is much less than the worldwide level).
• Is this a lot or a little differentiation? The answer is really only meaningful in
relation to other species. Human commensals, such as house mice and
Drosophila melanogaster show similar levels of differentiation (perhaps not
surprisingly), though D. melanogaster is less differentiated.
• Certainly humans are on the low end of the spectrum for levels of
differentiation. Some organisms, for example the Jumping Rodent have an FST
of over 0.5, suggesting strong racial differentiation, and maybe even the
presence of reproductively isolated sub-species.

FST in natural populations
• More recently, in the era of DNA sequencing studies, the habit of
calculating FST has gone out of fashion, but it is of interest to
compare the results of allozyme and nucleotide studies. Using the
data from recent surveys of nucleotide diversity from SNPs in
humans and D. melanogaster the levels of differentiation for DNA
sequences seem very similar to those from allozymes.
• F statistics can be used to describe genetic differentiation between
any groups of organisms,
• whether they are spatially separated or not. Forex, a study of the
tapeworm Ascaris in Guatemala found strong differentiation
between samples from humans and samples from pigs kept in the
same villages (Anderson et al. 1993). Host preference, or low
migration rates between the two populations might explain why
populations differentiate even when in sympatry (without
geographic separation).

FST -approaches
FST 
sA
2
pA (1  pA )
Nm
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10
FST
Wright (1951) [The genetical structure of
populations. Ann. Eugen. 15:323-354.]
noted the following relationship holds
when populations reach an equilibrium
between genetic drift and migration:
where N is the variance effective
population size of the
average population, and
m is the average proportion of
immigrants in each population
Problem: Useful parameter space is for
FST values between 0.1 and 0.4
F
ST 
1
4Nm 1 Nm is a virtual number

The inbreeding effect of population structure
• F statistics provide a way of summarising information on
geographical structure to genetic variability, but what is it they
are actually measuring?
• If we just consider a single locus, genetic differentiation
between populations means nothing more than differences in
allele frequency between populations (with the extreme of
different alleles being fixed in different populations).
• Suppose we have just two populations in which just two alleles
are segregating, but at different frequencies (p1 and p2
respectively). If each population is in Hardy-Weinberg
equilibrium, the expected homozygosity in each population is
given by

The inbreeding effect of population structure…
• Where q = 1- p. However, suppose we did not know that we were actually
sampling from different populations. In this case, the expected frequency
of homozygotes is
• With a bit of algebraic rearrangement, it follows that the observed
frequency of homozygotes in the combined populations is inflated relative
to that expected by the variance in allele frequency over populations
Consequently, a naive analysis that did not account for population structure
would find an excess of homozygotes – exactly the same result as would occur
if individuals within a single population have a tend to mate with relatives
(inbreed).
Deviations from Hardy-Weinberg equilibrium in the direction of an excess of
homozyogotes may be indicative of unaccounted for levels of local population
structure.

The inbreeding effect of population structure…
• What is the relationship between the inbreeding effect of structure and
population differentiation as measured by F statistcs?
• From the relationship H = 1 – F (heterozygosity = 1 –homozygosity) it follows
that we can write FST in terms of the inflation of levels of homozygosity.
In other words, the degree of population differentiation as measured by Wright’s FST
statistic is directly proportional to the variance in allele frequency over populations. This
relationship generalises in the case of multiple alleles at many loci
Where the summation is over alleles i at loci j.

The Wahlund effect
Population structure creates effective inbreeding, because local fluctuations in
allele frequency tend to inflate the frequency of homozyogotes.
The opposite side of the coin is that if two differentiated populations are
brought into contact and allowed to mate, the frequency of heterozygotes will
increase relative to their frequency in the individual populations.
The Wahlund effect, as this process is known, has an important medical
implication.
Due to genetic drift and founder effects, the frequency of recessive diseases,
or abnormal phenotypes varies considerably between populations. For
example, the combined frequency of mutations that cause cystic fibrosis is
about 0.07 in Caucasian populations but is considerably lower in other races
(e.g. Arab and African populations).
Other recessive disorders at high frequency in particular populations include
albinism in the South American Indian Hopi tribe and Tay Sachs disease in
Ashkenazi Jews. Consequently, offspring where one parent is from a different
race will tend to have a lower risk of inheriting a disease-causing mutation.

Wahlund Effect and F Statistics -- The Interaction of Drift and Gene Flow…

• Hence the subdivision of the population into genetically distinct demes causes
deviations from Hardy-Weinberg that are identical in form to those caused by an
inbreeding system of mating within demes.
• This “inbreeding coefficient” is called Fst because it refers to the deviation from
Hardy-Weinberg caused by allele frequency deviations in the subdivided demes
from the total population allele frequency. This Fst is simply a standarized
variance of allele frequencies across demes.
• In general, the more important drift is relative to gene flow, the larger the value
of Fst.
• For example, the Yanomama Indians are very war-like, and new villages are
frequently formed from a group of related individuals that leave an old village
due to a dispute. This "lineal fissioning" of villages accentuates founder effects
(because the founding individuals are related). Fst among the Yanomama
villages is 0.073.
• The nearby Xavante Indians are more peaceful and do not have lineal fissioning,
and their Fst is 0.0091. On a world wide scale, the Fst for the 3 major human
races is about 0.15, only about twice as much differentiation as seen among
Yanomama villages. Zekeria Yusuf (PhD) 163

Other species show much more subdivision than humans. E.g., kangaroo rats have an Fst
of 0.676 throughout their range, and the Fst between blocks on the same street for the
snail Rumina (which has mixed random-mating and selfing as well as limited dispersal
capabilities) is 0.538.

Finally, Fst can be measured from genetic survey data. In contrast, measuring gene
flow directly dispersal studies is very difficult and unreliable.
The genetic theory shows that even very little exchange between populations can
result in much effective gene flow. Hence, “rare” dispersal events have great
evolutionary importance but are difficult to study.
Moreover, even when you detect dispersal, it doesn’t mean the migrants you see
will successfully mate in their new population.
In addition, such direct observation nearly always misses the occasional or rare long
distance dispersal events which we have shown are quite effective in keeping
populations from diverging from one another.
Overall, direct measurement of gene flow is tedious, ineffective and tends to
underestimate the true values.
On the other hand, estimation of gene flow via Fst gives an “evolutionary” picture
which automatically takes into account all these various possibilities. However, Fst is
an effective measure of gene flow over evolutionary time if your underlying model
of subdivision is accurate.

Unusual patterns of FST
Summaries of patterns of genetic variability at many loci paint an
overall picture of genetic differentiation within a species.
Yet some of the most interesting aspects of differentiation can only
be seen by looking at a finer scale.
The general picture for humans and D. melanogaster is that patterns
of allozyme and DNA variability tell the same story about levels of
genetic differentiation.
However, this is not always the case. In the American Oytser
(Crssostrea virginica) allozyme variation shows no differentiation
between Atlantic populations and those from the Gulf of Mexico.
However, looking at DNA variation, there is a sharp discontinuity in
allele frequencies between the two populations, which is particularly
pronounced for mtDNA. Very similar sharp discontinuities are also
seen in mtDNA from a diverse array of organisms including Sea Bass
and the Seaside Sparrow.
The difference between DNA and allozyme studies suggests the
influence of natural selection on protein variability, but there is no
clear understanding of how selection might be acting.

Unusual patterns of FST
Variation between loci in levels of differentiation also provides a fascinating
window into the processes creating genetic differentiation.
A study of eight allozyme loci in the Checkerspot butterfly (Euphydrya editha:
McKenchie et al. 1975) found similar, low levels of differentiation for seven of
them, but one locus, hexokinase has a much higher FST. One possibility is that
ecological differences between the population studies have driven local
adaptation at this gene in different directions in different populations.
However, testing this hypothesis is not a straightforward process.
Finally, it is worth reiterating some of the problems with using F statistics as a
measure of population differentiation.
First, delineating populations, or geographic levels over which to test is
arbitrary, and has the potential to be influenced by the data in such a manner
that testing by permutation is not appropriate.
Second, F statistics have large sampling variance, particularly when
polymorphism is low.
Finally, and perhaps most importantly, by focusing on a single summary
statistic, a huge amount of information is thrown away.

Population genetic models of structure
• The aim of population genetics is to understand the forces that shape
patterns of genetic variability within and between species. To understand
how different evolutionary forces can create genetic differentiation
between populations it is natural to analyse simple models that extract the
key elements of the process we are interested in.
• However, the Fisher Wright model assumes random-mating between all
individuals. How can we introduce population structure?
• There are two simple models that are widely used as caricatures of
population structure.
1. The island model was first introduced by Haldane and considers a single
island that receives a constant proportion of migrants, m each generation
from an infinitely large mainland population. There is no migration from
the island back to the mainland.
• A subtle variant of this model is the n-island model, in which n identical
populations exchange migrants each generation such that each population
receives a proportion m/n of migrants from every other population.
• As the number of islands gets very large, the properties of the n-island
model become very similar to those of the island model.

Dispersal models
Continuous populations
• Isolation-by-distance
Discrete populations
• Stepping-stone
• Island model

Galapagos
Rift
N
S
E
W
2°
13
°
11
°
9°
East
Pacific
Rise
Fst.
Migration
rate
Guaymas
21°
DISTANCE (Km)
1000 10,000
20
10
5
100
Reject expectations of "island model"
Consistent with stepping-stone model
Inference: a species with more limited dispersal abilities
Black et al. 1994 Gene flow among vestimentiferan tube worm
(Riftia pachyptila) populations from hydrothermal vents of the Eastern Pacific. Marine Biology 120: 33-39.
The giant tubeworm, Riftia pachyptila

Identity by descent (ibd) in the island model
• As with the standard Fisher-Wright model, the natural place to start analyzing
the properties of the island model is to consider identity-by-descent (ibd) for
alleles sampled from within a population (symbolized by f).
• That is, we wish to look at the build up of ibd within the island, starting from
the current time and looking back to previous generations.
• Suppose we choose two chromosomes at random from within the island
population. Looking backwards in time, there are three possible events that
might have occurred in the previous generation.
1. As in the standard model, both chromosomes may have come from the
same parent, with probability 1/2Ne in a diploid population (where Ne is the
effective population size of the island). If so, the alleles are identical by
descent.
2. Another possibility is that the chromosomes are derived from different
parents, both of which were on the island. In this case, the identity-by-
descent is ft-1
3. Finally, we have the possibility that one parent was an immigrant from the
mainland population. For each chromosome this has probability m, so
ignoring the possibility that both parents were immigrants, the probability of
migration is 2m.

• What is the identity-by-descent in this case? What we are
really interested in is the build up of identity within the
population due to the local structure. So the ibd for
chromosomes in this configuration is zero. Putting this
together

• What does this mean? There are two important points raised by this
result.
1. The critical value for determining the build up of ibd within the island
population relative to the mainland population is the product of the
island effective population size and the migration rate.
• As mutation, selection & recombination typically influence genetic
diversity only through their product with the effective population size.
This is because the effects of deterministic forces are only important
relative to genetic drift (which occurs at the rate of 1/2Ne).
2. remarkably little migration is required to prevent the build up of ibd
within the island population. The product 2Ne x m is the (effective)
number of migrants (assumed to be diploids) that appear in the island
population each generation.
• So even a handful of migrants per generation are sufficient to prevent
extensive ibd from accumulating within the island.

The relationship between the population migration rate and FST
We can use the result concerning ibd to tell us about the relationship between the
migration rate and the level of genetic differentiation as measure by FST.
A heuristic approach is to say that ibd is closely related to identity in state if the
mutation rate is low relative to the migration rate and mainland population size.
Under these circumstances the build up of identity in state within the island
population relative to the mainland population is almost equivalent to the build up of
ibd. In other words:

The relationship between the population migration rate and FST
For example, if we take FST in humans to be 0.067, Nem is
estimated to be 3.5. What should we make of this number? In
truth, not much.
First, as I have said before, FST has large sampling variance, so
the estimate of Nem will also have large variance.
Second, if we plot the relationship between FST and Nem, it is
clear that for FST values less than 0.1 (the usual situation) there
is very little power to accurately estimate Nem.
In short, do not trust moment estimates of Nem from FST.

Wright’s diffusion model for allele frequency differentiation
The relationship between identity-by-descent and fST is just one
of many possible ways of looking at the effects of population
structure on genetic differentiation.
Wright (1931, 1951) took a different approach, by extending his
diffusion theory method for looking at the effects of mutation
and selection on the distribution of allele frequencies within
populations.
Consider the island model in which migrants from the mainland
population replace a fraction m of the population each
generation.
Wright wanted to ask how genetic drift within the island
population may lead the frequency of an allele on the island to vary
relative to the mainland.
If the mainland population is very large relative to the island, the frequency of
an allele among migrants, xI will be constant over time.

Using the usual diffusion theory notation, we can describe the mean and
variance in change in allele frequency within the island, x, over a single
generation

• While this analysis uses much more of the information in the
genetic data, it suffers from two very serious limitations.
1. the island model is clearly inappropriate for the data, but
there is no coherent theory for allele frequency distributions
in non-equilibrium models.
2. diffusion theory is not tractable for more than one locus.
There is simply no way of incorporating information about
linkage disequilibrium to give greater power.
Fortunately, both these problems are relatively easy to deal
with under a coalescent model.
• The one situation concerning population structure where
diffusion theory is currently more powerful than coalescent
theory is in the case of continuous population models – as
opposed to the discrete populations imposed here.

The coalescent in structured populations
The coalescent is a statistical description of the
genealogical history of a sample taken from a population.
Looking backwards in time, we can trace the line of
ancestry from a chromosome in the current sample until
the point where it coalesces with the ancestral lineage
leading to another chromosome in the sample.
The coalescent process can be related to standard Fisher-
Wright population models, & can be adapted to
incorporate recombination, population growth, and even
types of natural selection.
The coalescent can be adapted to describe ancestral
processes under population structure.

Pairwise coalescence time in the structured coalescent
There is one analytical result of importance that arises directly
from the structured coalescent.
Consider the history of a pair of chromosomes sampled at
random from within one population. What is the expected time
to coalescence for this pair of chromosomes?
Looking backwards in time, the waiting time until the first event
is exponentially distributed with rate
And the probability that the first event is a coalescent is

In other words, when sampling within a population, the expected time
to coalescence (hence also the expected pairwise differences in the
infinite sites model) for a pair of chromosomes is equivalent to that
expected if the entire ensemble of populations were a single panmictic
unit.
In contrast, the expected pairwise differences for a pair of
chromosomes sampled from between populations can be much greater.
However, for M >> 1, the effect of subdivision on total diversity will be
small.
While subdivision does not affect the expected value pairwise
differences, it greatly affects the distribution.
When migration between populations is low, most chromosome pairs
will coalesce rapidly within the population, while a few will have much
longer coalescence times as chromosomes.
Consequently, by looking at the distribution of pairwise differences for
chromosomes sampled within a population, it should be clear whether
there is overdispersion relative to the single population expectation.

Coalescent FST. Also by analogue of Wright’s Fstatistics, Slatkin (1991) related FST with
the time to most recent common ancestor (i.e. the coalescence time) for a pair of alleles
chosen within the same subpopulation and drawn randomly from the total population.

The effect of population structure on allele frequency
• The coalescent within a structured population can almost be divided up into
two separate phases that operate on different time scales.
• When migration rates are low, for chromosomes sampled from a single
population we expect a rapid phase during which there are multiple coalescent
events, but during which some lineages ‘migrate’ to other populations.
• When there is only a single ancestral lineage remaining in the sampled
population, the second phase begins, during which ancestral lineages in
different populations slowly migrate around the species range, with occasional
coalescent events.
• Because the second phase occurs on a much longer time-scale than the first
phase, most mutations segregating in a sample will have occurred during this
phase.
• Because of the rapid coalescence during the first phase, this is much more
likely in the structured coalescent than in the standard coalescent in a
panmictic population.
• Can we use standard techniques for detecting departures from neutrality to
detect this effect? In general, the answer is no.

Linkage disequilibrium in structured populations
• So far we have only considered how structure affects patterns
of variability at a single locus.
• One of the most interesting, and underdeveloped areas of
population genetics is how population structure affects
patterns of association between alleles at different loci –
linkage disequilibrium.
• The classical definition of linkage disequilibrium for a pair of
alleles (A and B) at two loci is

Linkage disequilibrium (LD) is generated by the random processes of
mutation and sampling in a finite population, and is broken down by
recombination.
Population structure affects patterns of LD in two ways.
1. for chromosomes sampled from the same population, structure tends to
increase LD relative to the case of no structure.
This is because the rapid coalescence within a population generates high
frequency derived mutations that are in complete association with each
other – leading to an excess of variants in near total association.
2. The second effect of structure on LD occurs when chromosomes from
different populations are compared.

• Suppose we have two isolated populations, both of
which are in complete linkage equilibrium, but there
are differences in allele frequency between the
populations.
• If we did not know that the populations were
separate, a naive analysis would detect linkage
disequilibrium between alleles, even at unlinked
loci.
• The magnitude of LD caused by this process is
proportional to the difference in allele frequency
between the populations. For a pair of populations,
if we write

• In this analysis we are pretending that there are two populations that are in
fact separate, but that we are unaware of the distinction.
• The term admixture is used to describe the combination of two (or more)
previously separate populations.
• Admixture is very common in humans, and probably also in human
commensals, because of large-scale changes in migration patterns over
human history.
• For example, interbreeding between American Indians and Europeans,
between Africans and other races in South Africa, between the settlers of
north and south Japan, brought together genetic material from previously
differentiated peoples.
• Consequently, differences in allele frequency between these groups will
tend to generate apparent LD between even unlinked loci.
• Recombination in subsequent generations will slowly erode LD over time,
but significant levels of LD can persist for many generations following
secondary contact.
• Admixture is a particularly important problem in applying population
genetic methods to disease mapping.

Selection in structured populations
• Coalescent theory provides a powerful way of predicting
patterns of genetic variability in structured populations for
neutral mutations.
• Furthermore, the coalescent can be adapted to include
features such as time-varying migration rates and changes in
population size, which are common elements of biological
reality.
• However, for many people, the goal of evolutionary biology is
to understand how natural selection shapes variation, both
within and between species.

How structure affects the fixation probability of beneficial mutations,
and hence the rate of adaptive evolution?
• Suppose a new mutation appears that is beneficial to all individuals in all
environments, and has a fitness advantage of s relative to the wild-type.
• Maruyama (1970) used a branching-process argument to show that for the
n-island model, the fixation probability of such unconditionally beneficial
mutations is essentially unaffected by population structure.
• That is, the fixation probability is given by Haldane’s original approximation
of 2s.
It should be noted that while the fixation probability is unaffected by structure,
elements of the fixation process such as the time to fixation and the allele
frequency distribution enroute to fixation are considerably affected by
structure.
• The second type of problem we may want to address is what happens when
different genotypes are favoured in different places. That is, there is
environmental heterogeneity across a species range and this creates
different selection pressures in different places.
• Can spatially varying selection pressures maintain polymorphism within the
population?

• Levene (1953) showed that under certain circumstances,
environmental heterogeneity can, in fact, maintain polymorphism
within a species.
• Suppose there are just two types of habitat, scattered across a
species range, and just two types of genotype. One genotype is
favoured in one habitat; the other genotype is favoured in the
other habitat.
• If environmental heterogeneity is fine-grained, such that
individuals experience both habitats during their lifetime, then the
genotype with the highest mean (geometric) fitness will spread to
fixation.
• However, if heterogeneity is coarse-grained, and individuals
experience only a single habitat during their life, then
polymorphism can be maintained, even if offspring disperse
evenly over the species range.

Levene’s result is of considerable importance, but its generality has been questioned.
A number of authors have pointed out that the conditions under which
polymorphism is maintained in the Levene model are very narrow – selection
has to be strong and finely balanced against habitat frequency.
Modifications to the model, such as habitat choice and assortative mating make
the conditions less restrictive, but it is clear that the Levene model is not a
general explanation for genetic polymorphism.
Perhaps the single most unrealistic assumption in the model is that offspring
disperse evenly over the entire species range. In most species, dispersal is
localized.
This creates correlations in the environment experienced by parents and their
offspring, and creates the potential for local adaptation.
Local adaptation can occur when migration (offspring dispersal) occurs on a
shorter scale than heterogeneity in the environment.

Indirect evidence for local adaptation: clines
• When one allele is favoured in one place and another in a different place, local
adaptation can occur if migration rates are low. But migration, however slow,
will ensure that genotypes from one place end up in the other. Consequently,
local adaptation will result in relatively smooth gradients in allele frequency at
selected loci over the scale of environmental heterogeneity. Such gradients in
allele frequency are known as clines.
• And the detection of clines is one way of indirectly detecting local adaptation.
• One of the most famous clines in population genetics is the gradient in the
frequency of the fast and slow (electrophoretic) alleles of the enzyme Alcohol
dehydrogenase (Adh) in Drosophila melanogaster. Adh breaks down alcohol
(present in the flies’ diet as they eat fruit), and the fast allele has a two-fold
higher level of activity than the slow variant. The fast allele is at high frequency
in northern Europe and the north of the USA, and the slow variant is at high
frequency in southern Europe and Africa and in the southern USA.
• However, they also found another polymorphism, an insertion-deletion
polymorphism called Ñ1, which shows a more pronounced cline (frequency
changes from 0.05 to 0.6) and is almost complete linkage disequilibrium with
the fast/slow variant.
• It seems likely that in fact this polymorphism is the target of selection, and
that the gradient in the fast/slow polymorphism is an indirect consequence of
linkage disequilibrium (and may also be epistatic selection).

That markers closely linked to sites experiencing selection (local adaptation) may show
similar patterns of geographic variation as the selected mutations themselves provides a
potential way of detecting local adaptation without full characterization of all genetic
variation.
The most extreme example of this situation occurs when two partially reproductively
isolated species are brought into secondary contact.
Admixture between previously isolated populations creates strong linkage
disequilibrium even between unlinked markers, simply due to allele frequency
differences between populations.
If the offspring of matings between the two species/populations suffer a strong fitness
disadvantage due to incompatibilities at many loci across the genome, indirect selection
on neutral markers due to linkage disequilibrium with the selected loci creates an
effective barrier to gene flow across the entire genome.
Regions where previously isolated species come into contact are called hybrid zones.
Within hybrid zones, there are steep, concordant clines in allele frequency at neutral
markers across the genome, and also in phenotypic traits.
The few instances where genetic variants from one population have introgressed (spread
into) the other population may be indicative of the spread of unconditionally beneficial
mutations.
Indirect evidence for local adaptation: clines

Local selective sweeps
• Another way of using linkage between neutral
markers and selected loci is to look for the traces
of local selective sweeps.
• Local selective sweeps occur when a new mutation
that is locally advantageous arises in a population
and sweeps to a high local frequency, removing
variation at linked, neutral loci.
• Locally reduced variability at a marker that is
consistently variable in other populations may be
indicative of local adaptation.

Sewall Wright’s shifting-balance theory ( r/nship drift and selection )
• Finally, it is worth discussing one of the most important and
contentious theories relating to population structure.
• Sewall Wright’s overwhelming passion was population structure –
much of theory in this lecture is due to him – and his great ambition
was to combine his work on drift and selection in subdivided
population into a single, general theory of evolution. This theory has
become known as the shifting-balance theory.
• The shifting-balance argues that the majority of adaptation in species
occurs not through the mass selection principles expounded by Fisher
and Haldane, but in a manner that can only work in subdivided
populations.
• The key feature of the shifting-balance theory is that alleles at
different loci in a genome interact such that there is no simple
relationship between genotype and fitness. This is element, called
epistasis, formally states that the fitness effects of alleles at different
loci are not multiplicative.

• For example, suppose we have two loci, and two alleles at each. Suppose
the fitnesses of different genotypes are
If the population is initially fixed for alleles A and B, then while the genotype
aabb is fitter than the genotype AABB, in order to reach the state aabb the
population has to decrease in fitness.

• Epistasis between alleles creates a complex surface of
population fitness (a function of allele frequency) that is
known as the adaptive landscape.
• Earlier Wright had shown that the expected change in allele
frequency due to selection is
• Where x is allele frequency and w with a line above is the
mean population fitness. So an allele will only increase in
fitness by selection if it increases mean population fitness.
• Consequently, under the mass-selection rules of Fisher and
Haldane, the population will never go from AABB to aabb.

However, things are different in a subdivided population. Actually, the
important thing is the subdivided populations consist of multiple finite
populations.
when the population is small, genetic drift can lead to deleterious mutations
reaching high frequency.
Consequently, in a small, finite population, there is some chance that the
population will drift down the adaptive landscape to a point of lower fitness,
before going up the other side (through selection) and reaching the higher
peak.
In the language of the shifting-balance, the population can cross the
adaptive valley.
Partially isolated populations can therefore be thought of as natural
experiments, allowing a species to try out different regions of the adaptive
landscape.

Furthermore, there is considerable evidence for epistasis in natural
populations.
F2 hybrid breakdown (the low fitness of second generation hybrids) can be
explained by the breakdown of coadapted gene complexes (Fenster et al.
1997), and some coadapted gene complexes are well known (e.g. genes
controlling mimicry in the butterfly Heliconius).
However, there is a good theoretical reason to suppose that the shifting
balance is not the general explanation of adaptation that Wright wished for.
The main problem is the last phase of the process. Once a subpopulation has
reached the new, higher peak, this genotype then has to spread throughout
the rest of the species (see Coyne et al. 1997).
The problem is that aabb genotypes spreading throughout the rest of the
species will tend to mate with AABB genotypes and consequently will
produce offspring with low fitness (for exactly the same reasons we get
F2breakdown). Adaptation will tend to be restricted to the local population.

Although Wright’s theory may not be a general explanation for
adaptation within species, it seems quite plausible that it is an
important feature of local adaptation.
Or at least that local adaptation can create epistatic interactions
between alleles that are then exposed when populations are brought
into secondary contact.
For example, Haldane’s rule of unisexual sterility and inviability in
species crosses is probably explained by epistasis. Haldane’s rule states
that when only one sex of hybrids between two species is sterile, it is
heterogametic sex (the XY sex or equivalent).
In mammals the heterogametic sex is male, but in birds and butterflies,
it is the female. Sterility and inviability in these cases seems to be
caused by a breakdown of recessive epistatic interactions between
alleles at loci on the X chromosome (Z in birds) and autosomes.
Epistasis is probably an important feature of evolution, but not in the
way Wright supposed.

Fixation index

Fixation index…
• The individual, subpopulation, and total population
heterozygosities are identical in populations after
compensating for the degree to which observed and
expected heterozygosities are not met at different levels of
population organization.
• The average observed heterozygosity is greater or less than
the average expected heterozygosity for subpopulations:
HI = HS(1 − FIS )
• to the extent that there is non-random mating (FIS ≠0).
Similarly, the average expected heterozygosity for
subpopulations is less than the expected heterozygosity of
the total population under panmixia: HS = HT(1 − FST )
• to the extent that subpopulations have diverged allele
frequencies (FST > 0).

Fixation index…
• The total deviation from expected heterozygosity within and
among subpopulations is then HI = HT(1 − FIT)
• Although these equations, represent a different way to
articulate and think of the biological impacts of allele frequency
divergence among subpopulations and non-random mating
within subpopulations.
• Each fixation index expresses the degree to which random
mating expectations for the frequency of heterozygous
genotypes are not met. Using these equations it is also possible
to show how the total reduction in heterozygosity relates to the
combined fixation due to non-random mating and
subpopulation divergence: 1 − FIT = (1 − FST)(1 − FIS)

FST-like Statistics
• A number of related indices of genetic differentiation have been
subsequently derived in link with the natures of the diagnostic genetic
markers, such as GST (Nei 1973), ΦST (Excoffier et al., 1992), QST (Prout
and Barker, 1993; Spitze, 1993), RST (Slatkin, 1995). These are referred to
as FST-like statistics for convenience.
GST. In practice, the most widely applied statistic for measuring population
genetic differentiation is Nei’s GST (1973), an extension of FST for loci with
multiple states of alleles.
It analyzes allele frequency variation among subpopulations in terms of
heterozygosity or gene diversity as defined by Nei (1973).
Given a diploid population with K subpopulations and I allelic states at a
locus. Denote the frequency of the ith allele in the population as pi, and
the corresponding frequency in subpopulation k as pki.
Let HT = 1-JT be the total heterozygosity, i.e. the probability of genotypes
with the union of two different states of alleles, of the total population,
where
is the homozygosity (i.e. the probability of genotypes with the union of
two identical states of alleles).

GST….
• Nei (1973) referred to HT and JT as gene diversity and gene identity of the
total population, respectively.
• Extended from the definition of pairwise diversity of two populations, he
defined DST as the average gene diversity between subpopulations.
• The total gene diversity is then linearly decomposed as HT = HS + DST,
where HS is defined as the (average) gene diversity within subpopulations,
which can also be written in form of average gene identity within
subpopulation as HS = 1- JS.
• Nei regarded DST as a measure of absolute magnitude of gene
differentiation. The differentiation relative to the total population, named by
Nei the coefficient of gene differentiation is given by
GST = DST / HT = (HT - HS) / HT.

• For a neutral locus with only two types of allele, it can be shown that GST is identical
to Wright’s FST.
• For multiple allelic situations, GST is equal to the median of FST for all alleles,
especially by definition expressed in equation (2).
• Note that for definition of FST in equation (1), FIS and FIT can be negative as they
are similar to correlation coefficient; however, quantities used for defining GST are
all nonnegative.
GST….

Θ, correlations of gene frequencies
• Θ, By analogue of Wright’s F-statistics, Weir and Cockerham
(1984) derived a set of parameters f, ϴ & F to describe
correlations of gene frequencies, by the variance of the allele
frequencies between populations (σw), the variance of the
allele frequencies between individuals within populations (σb),
and the variance of the allele frequencies between gametes
within individuals (σa).

: as an estimator of ϴ
• and used as an estimator of ϴ (the equivalent of Wright's FST).
θ can be regarded as co-ancestry coefficient (or relatedness) for
alleles within a subpopulation relative to the total population.
• A unique point is that their estimator also accounted for
sampling variance of population and samples which are drawn
from the population.
• can be approximated by the sample mean and variance of
allele frequency as,

ΦST, based on AMOVA
• ΦST. Another FST analogous statistic, ΦST, was developed by Excoffier (1992). It
is based on the idea of analysis of variance (ANOVA) and was termed "analysis
of molecular variance (AMOVA)".
• They extended the work of Cockerham (1973) and Weir and Cockerham (1984),
which partitioned the overall variance into within and among populations
components, to a comparable analysis of haplotypic diversity.
• A matrix of squared distances of each pair of haplotypes was constructed and
used to calculate sum of squared deviations of different subdivisions.
• The distance metric can be customarily specified to any meaningful
evolutionary or genetic distance according to the research question.
• If a binary distance between haplotypes is used, one for identical haplotype and
zero for different haplotypes, then ΦST is the same as ϴ or FST. To test the
significance of each component of variances, a permutation procedure was
conducted.
• The null distribution of component of variance was calculated from a large
number of replicate data sets by reallocating each individual to a randomly
chosen population.

RST, mutational process of microsatellite loci
• RST, which is also a FST-like statistic, specifically accounting for the
mutational process of microsatellite loci, was introduced by Slatkin (1995).
• RST is the fraction of total variance of allele size from between populations
(Slatkin, 1995).
• Allele size is measured as the number of repeat units in the short microsatellite
DNA sequences.
• Slatkin showed that, for microsatellite loci following generalized stepwise
mutation model, RST has very similar property as that of FST under a K-alleles
mutation model.
• The FST analogues such as GST, ϴ and ΦST, in particular GST, have been
criticized to be constrained by within subpopulation heterozygosity HS
(Edelaar and Bjorklund, 2011).

Conservation genetics
How genetic analyses can help threatened species:
some examples...
‣ measure inbreeding/ outbreeding depression
‣ loss of genetic diversity
‣ fragmentation of population and reduction of gene
flow
‣ genetic drift
‣ define management unit
‣ understand aspects of species biology important for
their conservation

Other Sources of Variation
1. Mutations:
- In stable environments, mutations often result in little or
no benefit to an organism, or are often harmful
- Mutations are more beneficial (rare) in changing
environments (Example: HIV resistance to antiviral drugs)
2. Genetic Recombination:
- source of most genetic differences between individuals in
a population
3. Co-evolution:
-Often occurs between parasite & host and flowers & their
pollinators
4. Sexual reproduction: the union of gametes during
fertilization is a process dependent on chance.
244
Zekeria Yusuf (PhD)

Factors influencing the genetic diversity within a
gene pool include
population size,
mutation,
genetic drift,
natural selection,
environmental diversity,
migration and
non-random mating patterns.

Human genetic variation
• Patterns of human genetic variation
– Among populations
– Among individuals
– How evolutionary factors influence variation
• “Race” and its biomedical implications
• Linkage disequilibrium, evolution, and disease-gene
identification
The “four major factors of evolution”
1. Mutation: the author of variation
2. Natural selection: the editor
3. Genetic drift: the randomizer
4. Gene flow: the homogenizer
246
Zekeria Yusuf (PhD)

Neighbour joining method
265
Zekeria Yusuf (PhD)

Why genetic diversity is important in populations...
1. genetic diversity required to evolve or to adapt to new environment or
environmental modifications.
2. genetic diversity reflects evolutionary potential
Loss of genetic diversity often associated with inbreeding, reduction of
reproductive fitness and extinction risk
• example 1 - habitat selection: peppered moth (Biston betularia) in UK
• - dark and light forms
• - night: active / day: resting on trees
• ➡ camouflage critical for survival
• - light form: camouflaged on lichen-covered tree trunks
• - Industrialisation: kill lichen by sulphur pollution
• ➡ light form: visible / dark form: camouflaged

Linkage Equilibrium
alleles
frequency
: haplotype frequency of in the
generation
: recombination frequency(= ),
i j
AB
{ }
i
A { }
j
B
{ }
i
p { }
j
q
( )
n i j
P AB
A B
th
n

1
0
2

 
1
( )
2
m f
 


Linkage Equilibrium
if
1
( ) (1 ) ( )
n i j n i j i j
P AB P AB p q
 

  
1
( ) (1 )[ ( ) ]
n i j i j n i j i j
P AB p q P AB p q
 
   
0
(1 ) [ ( ) ] 0
n
i j i j
P AB pq

    0
 

Methods used to measure genetic variation at molecular level:

Genetic Markers
A genetic marker is a gene or DNA sequence with a known
location on a chromosome and associated with a particular
gene or trait.
It can be described as a variation, which may arise due to
mutation or alteration in the genomic loci, that can be
observed.
A genetic marker may be a short DNA sequence, such as a
sequence surrounding a single base-pair change (single
nucleotide polymorphism, SNP), or a long one, like
minisatellites.

Genetic Markers
Genetic markers are the biological features that are determined
by allelic forms of genes or genetic loci and can be transmitted
from one generation to another, and thus they can be used as
experimental probes or tags to keep track of an individual, a
tissue, a cell, a nucleus, a chromosome or a gene.
Genetic markers used in genetics and plant breeding can be
classified into two categories: classical markers and DNA
markers.
Classical markers include morphological markers, cytological
markers and biochemical markers.
DNA markers have developed into many systems based on
different polymorphism-detecting techniques or methods
(southern blotting–nuclear acid hybridization, PCR–polymerase
chain reaction, & DNA sequencing) such as RFLP, AFLP,
RAPD, SSR, SNP, etc. 276
Zekeria Yusuf (PhD)

Morphological markers
• During the early history of plant breeding, the markers
used mainly included visible traits, such as leaf shape,
flower color, pubescence color, pod color, seed color, seed
shape, hilum color, awn type & length, fruit shape, rind
(exocarp) color and stripe, flesh color, stem length, etc.
• These morphological markers generally represent genetic
polymorphisms which are easily identified & manipulated.
Therefore, they are usually used in construction of linkage
maps by classical two- and/or three point tests.
• Some of these markers are linked with other agronomic
traits and thus can be used as indirect selection criteria in
practical breeding.
277
Zekeria Yusuf (PhD)

Cytological markers
In cytology, the structural features of chromosomes can be shown
by chromosome karyotype and bands.
The banding patterns, displayed in color, width, order and
position, reveal the difference in distributions of euchromatin and
heterochromatin. For instance, Q bands are produced by
quinacrine hydrochloride, G bands are produced by Giemsa stain,
and R bands are the reversed G bands.
These chromosome landmarks are used not only for
characterization of normal chromosomes and detection of
chromosome mutation, but also widely used in physical mapping
and linkage group identification.
The physical maps based on morphological and cytological
markers lay a foundation for genetic linkage mapping with the aid
of molecular techniques.
278
Zekeria Yusuf (PhD)

Biochemical/protein markers- Allozymes (Isozyme)
• Biochemical/protein markers: Protein markers may also be
categorized into molecular markers.
• Isozymes are alternative forms or structural variants of an
enzyme that have different molecular weights and
electrophoretic mobility but have the same catalytic activity or
function.
• Isozymes reflect the products of different alleles rather than
different genes because the difference in electrophoretic
mobility is caused by point mutation as a result of amino acid
substitution. Therefore, iso‐zyme markers can be genetically
mapped onto chromosomes and then used as genetic markers to
map other genes.
• They are also used in seed purity test and occasionally in plant
breeding. There are only a small number of isozymes in most
crop species and some of them can be identified only with a
specific stain. Therefore, the use of enzyme markers is limited.
• Another example of biochemical markers used in plant
breeding is high molecular weight glutenin subunit (HMW-GS)
279
Zekeria Yusuf (PhD)

Biochemical Marker - Allozymes (Isozyme)….
• Allozymes are allelic variants of enzymes encoded by structural
genes.
• Because of changes in electric charge and conformation can affect
the migration rate of proteins in an electric field, allelic variation
can be detected by gel electrophoresis and subsequent enzyme-
specific stains that contain substrate for the enzyme, cofactors and
an oxidized salt (e.g. nitro-blue tetrazolium).
• Usually two, or sometimes even more loci can be distinguished for
an enzyme and these are termed isoloci. Therefore, allozyme
variation is often also referred to as isozyme variation .
• Although protein markers circumvent the effects of environment,
they have the drawbacks of a limitation in the number of
detectable isozymes as well as tissue and development stage
specificity.
280
Zekeria Yusuf (PhD)

Advantages:
The strength of allozymes is simplicity.
Because allozyme analysis does not require DNA extraction or
the availability of sequence information, primers or probes, they
are quick and easy to use.
Simple analytical procedures, allow some allozymes to be applied
at relatively low costs, depending on the enzyme staining reagents
used.
Allozymes are codominant markers that have high reproducibility.
Zymograms (the banding pattern of isozymes) can be readily
interpreted in terms of loci and alleles, or they may require
segregation analysis of progeny of known parental crosses for
interpretation.
Sometimes, however, zymograms present complex banding
profiles arising from polyploidy or duplicated genes and the
formation of intergenic heterodimers, which may complicate
interpretation.
281
Zekeria Yusuf (PhD)

• Disadvantages:
• relatively low abundance and low level of polymorphism.
• Moreover, proteins with identical electrophoretic mobility (co-
migration) may not be homologous for distantly related germplasm. In
addition, their selective neutrality may be in question.
• Lastly, often allozymes are considered molecular markers since they
represent enzyme variants, and enzymes are molecules. However,
allozymes are in fact phenotypic markers, and as such they may be
affected by environmental conditions.
• For example, the banding profile obtained for a particular allozyme
marker may change depending on the type of tissue used for the
analysis (e.g. root vs. leaf). This is because a gene that is being
expressed in one tissue might not be expressed in other tissues.
• On the contrary, molecular markers, because they are based on
differences in the DNA sequence, are not environmentally influenced,
which means that the same banding profiles can be expected at all times
for the same genotype.
282
Zekeria Yusuf (PhD)

DNA Makers/ Molecular markers
• DNA markers are defined as a fragment of DNA revealing
mutations/variations, which can be used to detect polymorphism between
different genotypes or alleles of a gene for a particular sequence of DNA in a
population or gene pool.
• A molecular marker is segment of DNA whose characteristics can be
measured and make inference to the ecology and evolution of individuals,
populations, and species
There are three methods to detect the polymorphism:
1. Southern blotting, a nuclear acid hybridization technique (Southern 1975),
2. PCR, a polymerase chain reaction technique (Mullis, 1990), as well as
3. microarray chip techniques use DNA hybridization combined with labeled
nucleotides, and new sequencing techniques detect polymorphism by
sequencing.
• Using PCR and/or molecular hybridization followed by electrophoresis (e.g.
PAGE –polyacrylamide gel electrophoresis, AGE – agarose gel
electrophoresis, CE – capillary electrophoresis), the variation in DNA samples
or polymorphism for a specific region of DNA sequence can be identified
based on the product features, such as band size and mobility. In addition to
Sothern blotting and PCR, more detection systems have been also developed.
283
Zekeria Yusuf (PhD)

Advantages of molecular markers
• DNA marker systems, which were introduced to genetic
analysis in the 1980s, have many advantages over the
traditional morphological & protein markers that are used in
genetic & ecological analyses of plant populations:
1. an unlimited number of DNA markers can be generated;
2. DNA marker profiles are not affected by the environment, &
3. DNA markers, unlike isozyme markers, are not constrained by
tissue or developmental stage specificity.
284
Zekeria Yusuf (PhD)

Properties of ideal molecular markers
An ideal molecular marker must have some desirable properties which are enlisted as follows:
1. Highly polymorphic/hypervariable nature: It must be polymorphic as it is
polymorphism that is measured for genetic diversity studies.
2. Codominant inheritance: discrimination of homozygous and heterozygous states
of diploid organisms.
3. Frequent occurrence in genome: a marker should be evenly and frequently
distributed throughout the genome.
4. Selective neutral behaviours: the DNA sequences of any organism are neutral to
environmental conditions or management practices.
4. High reproducibility: giving same result across labs.
5. Even distribution across the whole genome (not clustered in certain regions)
6. Clear distinct allelic features (so that the different alleles can be easily
identified)
7. Low cost to use (or cost-efficient marker development and genotyping)
8. Easy assay/detection & automation
9. High availability (un-restricted use) and suitability to be duplicated/multiplexed
(so that the data can be accumulated and shared between laboratories)
10. Single copy & Genome-specific in nature (especially with polyploids)
11. No detrimental effect on phenotype
285
Zekeria Yusuf (PhD)

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