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POPULATION GENETICS
POPULATION GENETICS
• The science of genetics can be broadly divided into four major subdisciplines
Each of these four areas focuses on a different aspect of heredity.
• Transmission genetic
genetic processes that occur within individuals and how genes are passed from
one individual to another.
• Molecular genetics
molecular nature of heredity: how genetic information is encoded within the
DNA and how biochemical processes of the cell translate into the phenotype.
• Population genetics
applies the principles of transmission genetics to large groups of individuals,
focusing on the transmission processes at one or a few genetic loci.
• Quantitative genetics
also considers the transmission of traits simultaneously determined by many
genes. Both population and quantitative genetics apply Mendelian principles,
and they are amenable to mathematical treatment.
POPULATION GENETICS:
 The study of the rules governing the
maintenance and transmission of genetic
variation in natural populations.
• In this discipline, our perspective shifts away
from the individual and the cell and focuses
instead on a large group of individuals, a
Mendelian population.
A Mendelian population
 is a group of interbreeding individuals who share a common set of genes.
 The genes shared by the individuals of a Mendelian population are called
the gene pool.
• Gene pool:
Collection of all genes /alleles/alternative forms of allele of all the
individuals in a population.
• Gene: segment of DNA controlling a particular trait. Occur in units
• Allele : Alternative forms of a particular gene. occurs in pairs or more
• 1) Diploid, autosomal locus with 2 alleles: A and a
PARENTS GAMETES ZYGOTES
(DIPLIOD) (HAPLOID) (DIPLOID)
• These parents produce a large gamete pool (Gene Pool) containing alleles
A and a.
A A a a A a
a a A A a a a
a A a a A A
A a A
Gamete (allele) Frequencies:
Freq(A) = p
Freq(a) = q
 p + q = 1
Genotype Frequencies of 3 Possible Zygotes:
AA Aa aa
Freq (AA) = pA x pA = pA
2
Freq (Aa) = (pA x qa) + (qa x pA) = 2pAqa
Freq (aa) = qa x qa = qa
2
 p2 + 2pq + q2 = 1
• By convention, if there are 2 alleles at a locus, p and q are used to
represent their frequencies
• The frequency of all alleles in a population will add up to 1
– For example, p + q = 1
General Rule for Estimating Allele Frequencies from
Genotype Frequencies:
Genotypes: AA Aa aa
Frequency: p2 2pq q2
 Frequency of the A allele:
p = p2 + ½ (2pq) ( AA + ½ Aa)
 Frequency of the a allele:
q = q2 + ½ (2pq) ( aa + 1/2Aa)
Sample Calculation: Allele Frequencies
Assume N = 200 indiv. in each of two populations 1 & 2
 Pop 1 : 90 AA 40 Aa 70 aa
 Pop 2 : 45 AA 130 Aa 25 aa
In Pop 1 :
 p = p2 + ½ (2pq) = 90/200 + ½ (40/200) = 0.45 + 0.10 = 0.55
 q = q2 + ½ (2pq) = 70/200 + ½ (40/200) = 0.35 + 0.10 = 0.45
In Pop 2 :
 p = p2 + ½ (2pq) = 45/200 + ½ (130/200) = 0.225 + 0.325 = 0.55
 q = q2 + ½ (2pq) = 25/200 + ½ (130/200) = 0.125 + 0.325 = 0.45
• For example, consider a population of wildflowers that is
incompletely dominant for color:
– 320 red flowers (CRCR)
– 160 pink flowers (CRCW)
– 20 white flowers (CWCW)
• Calculate the number of copies of each allele:
– CR  (320  2)  160  800
– CW  (20  2)  160  200
• To calculate the frequency of each allele:
– p  freq CR  800 / (800  200)  0.8
– q  freq CW  200 / (800  200)  0.2
• The sum of frequency alleles is always 1
– 0.8  0.2  1
Main Points:
 p + q = 1 (more generally, the sum of the allele frequencies equals one)
 p2 + 2pq +q2 = 1 (more generally, the sum of the genotype frequencies
equals one)
 Two populations with markedly different genotype frequencies can have
the same allele frequencies
Hardy-Weinberg Equilibrium
• The Hardy-Weinberg principle states that frequencies of alleles and
genotypes in a population remain constant from generation to generation
• In a given population where gametes contribute to the next generation
randomly, allele frequencies will not change
p2 + 2pq + q2 = 1
The Hardy-Weinberg principle describes a population that is
not evolving
If a population does not meet the criteria of the Hardy-
Weinberg principle, it can be concluded that the population is
evolving
Alleles in the population
Gametes produced
Each egg: Each sperm:
80%
chance
20%
chance
80%
chance
20%
chance
Frequencies of alleles
p = frequency of
q = frequency of
CW allele = 0.2
CR allele = 0.8
• Hardy-Weinberg equilibrium describes the constant frequency of
alleles in such a gene pool
• Consider, for example, the same population of 500 wildflowers and
1,000 alleles where
– p  freq CR  0.8
– q  freq CW  0.2
The frequency of genotypes can be calculated
CRCR  p2  (0.8)2  0.64
CRCW  2pq  2(0.8)(0.2) 0.32
CWCW  q2  (0.2)2  0.04
• If p and q represent the relative frequencies of the only two possible
alleles in a population at a particular locus, then
– p2  2pq  q2  1
– where p2 and q2 represent the frequencies of the homozygous
genotypes and 2pq represents the frequency of the heterozygous
genotype
Conditions for Hardy-Weinberg Equilibrium
• The Hardy-Weinberg theorem describes a hypothetical population that
is not evolving
• In real populations, allele and genotype frequencies do change over
time
It predicts both allele and genotype frequencies in populations (non-
evolving ones).
• The first condition that must be met for Hardy-Weinberg equilibrium is the
lack of mutations in a population.
• The second condition that must be met for Hardy-Weinberg equilibrium is
no gene flow in a population.
• The third condition that must be met is the population size must be
sufficient so that there is no genetic drift.
• The fourth condition that must be met is random mating within the
population.
• Finally, the fifth condition necessitates that natural selection must not
occur.
Applying the Hardy-Weinberg Principle
• We can assume the locus that causes phenylketonuria (PKU) is in Hardy-
Weinberg equilibrium given that:
 The PKU gene mutation rate is low
 Mate selection is random with respect to whether or not an individual is a
carrier for the PKU allele
 Natural selection can only act on rare homozygous individuals who do not
follow dietary restrictions
 The population is large
 Migration has no effect as many other populations have similar allele
frequencies
• The occurrence of PKU is 1 per 10,000 births
– q2  0.0001
– q  0.01
• The frequency of normal alleles is
– p  1 – q  1 – 0.01  0.99
• The frequency of carriers is
– 2pq  2  0.99  0.01  0.0198
– or approximately 2% of the population
Population genetics
Population genetics
Natural Selection
• Natural selection is the process through which populations of living
organisms adapt and change. Individuals in a population are naturally
variable, meaning that they are all different in some ways.
• Differential success in reproduction results in certain alleles being
passed to the next generation in greater proportions
• For example, an allele that confers resistance to DDT increased in
frequency after DDT was used widely in agriculture
• Directional Selection- one extreme trait is favored over
the others, causing the organism to be more fit and
have more offspring that survive.
• An example of this is running speed in rabbits. The
faster rabbits can outrun predators easier, so they are
less likely to get eaten, and more likely to survive and
produce offspring. Directional selection favors the trait
of fast running.
• Stabilizing Selection- the traits that are the most average are
selected for, and the extremes are selected against.
• One example of a trait that has experienced stabilizing
selection is birth weight. Babies that are very small are often
not healthy enough to survive, while babies that are too large
may get stuck in the birth canal, causing death of the baby
and frequently death of the mother as well.
• Disruptive Selection- the extreme traits are selected for,
and average traits are selected against.
• One example of this is beak sizes in birds. If the only
seeds available in an environment are small seeds and
large seeds, natural selection will favor birds with either
small or large beaks. The birds with medium sized
beaks will not be very effective at feeding, so medium
beaks will be selected against.
Natural selection is the only mechanism
that consistently causes adaptive
evolution
• Evolution by natural selection involves both chance and “sorting”
– New genetic variations arise by chance
– Beneficial alleles are “sorted” and favored by natural selection.
• Only natural selection consistently results in adaptive evolution
GENETIC DRIFT
• Genetic drift (allelic drift or the Sewall Wright effect)is the change in the
frequency of an existing gene variant (allele) in a population due to random
sampling of organisms.
• The alleles in the offspring are a sample of those in the parents, and chance has a
role in determining whether a given individual survives and reproduces.
• Genetic drift may cause gene variants to disappear completely and thereby
reduce genetic variation.
• It can also cause initially rare alleles to become much more frequent and even
fixed.
• When few copies of an allele exist, the effect of genetic drift is larger, and when
many copies exist, the effect is smaller.
• In 1968, population geneticist Motoo Kimura rekindled the debate with his neutral
theory of molecular evolution, which claims that most instances where a genetic
change spreads across a population are caused by genetic drift acting on
neutral mutations.
5
plants
leave
off-
spring
Generation 1
p (frequency of CR) = 0.7
q (frequency of CW) = 0.3
CRCR CRCR
CRCW
CWCW CRCR
CRCW
CRCR CRCW
CRCR CRCW
CRCR
CWCW
CRCW
CRCR CWCW
CRCW
CWCW
CRCR
CRCW CRCW
Generation 2
p = 0.5
q = 0.5
2
plants
leave
off-
spring
CRCR
CRCR CRCR
CRCR
CRCR
CRCR
CRCR
CRCR
CRCR
CRCR
Generation 3
p = 1.0
q = 0.0
The Founder Effect
• The founder effect occurs when a few individuals become
isolated from a larger population
• Allele frequencies in the small founder population can be
different from those in the larger parent population
The Bottleneck Effect
• The bottleneck effect is a sudden reduction in population size
due to a change in the environment
• The resulting gene pool may no longer be reflective of the
original population’s gene pool
• If the population remains small, it may be further affected by
genetic drift
Population genetics
Main points:
 Genetic drift is significant in small populations
 Genetic drift causes allele frequencies to change at random
 Genetic drift can lead to a loss of genetic variation within
populations
 Genetic drift can cause harmful alleles to become fixed
Gene Flow
• Gene flow consists of the
movement of alleles among
populations
• Alleles can be transferred
through the movement of fertile
individuals or gametes (for
example, pollen)
• Gene flow tends to reduce
variation among populations
over time
Gene flow can decrease the fitness of a population
• Consider, for example, the great tit (Parus major) on the Dutch island of
Vlieland
– Mating causes gene flow between the central and eastern populations
– Immigration from the mainland introduces alleles that decrease fitness
– Natural selection selects for alleles that increase fitness
– Birds in the central region with high immigration have a lower fitness;
birds in the east with low immigration have a higher fitness
Gene flow is an important agent of evolutionary change in human
populations
Population in which the
surviving females
eventually bred
Central
Eastern
Survival
rate
(%)
Females born
in central
population
Females born
in eastern
population
Parus major
60
50
40
30
20
10
0
Central
population
NORTH SEA Eastern
population
Vlieland,
the Netherlands
2 km
Natural selection is the only mechanism that
consistently causes adaptive evolution
• Evolution by natural selection involves both chance and
“sorting”
– New genetic variations arise by chance
– Beneficial alleles are “sorted” and favored by natural selection
• Only natural selection consistently results in adaptive evolution
Genetic Variation
• Describe the variation in the DNA sequence in each
of our genomes. Genetic variation is what makes us
all unique, whether in terms of hair colour, skin
colour or even the shape of our faces.
• Individuals of a species have similar characteristics
but they are rarely identical, the difference between
them is called variation.
• Single nucleotide polymorphisms (SNPs, pronounced
‘snips’) are the most common type of genetic
variation amongst people.
• Each single nucleotide polymorphism represents a
difference in a single DNA base, A, C, G or T, in a
person’s DNA. On average they occur once in every
300 bases and are often found in the DNA
between genes.
• Genetic variation results in different forms,
or alleles, of genes.
• For example, if we look at eye colour, people with
blue eyes have one allele of the gene for eye
colour, whereas people with brown eyes will have
a different allele of the gene
• Genetic variation can also explain some
differences in disease susceptibility and how
people react to drugs.
• Genetic variation is important in evolution.
• Evolution relies on genetic variation that is
passed down from one generation to the next.
Favourable characteristics are ‘selected’ for,
survive and are passed on. This is known
as natural selection.
How Genetic Variation Is Maintained
Many factors are involved:
1. MUTATION
• One of these is mutation, which is in fact the
ultimate source of all variation. However,
mutations do not occur very frequently
• This rate is too slow to account for most of the
polymorphisms seen in natural populations.
• However, mutation probably does explain some
of the very rare phenotypes seen occasionally,
such as albinism in humans and other
mammals.
2. SELECTIVE NEUTRALITY
• A second factor contributing to genetic variation in natural populations is selective
neutrality.
• Selective neutrality describes situations in which alternate alleles for a gene differ
little in fitness. Because small fitness differences result in only weak natural
selection, selection may be overpowered by the random force of genetic drift.
• Alleles whose frequencies are governed by genetic drift rather than by natural
selection are said to be selectively neutral.
3. NATURAL SELECTION
• Finally, several forms of natural selection act to maintain genetic variation
rather than to eliminate it.
• These include balancing selection, frequency-dependent selection, and
changing patterns of natural selection over time and space.
3.1 Balancing selection occurs when there is heterozygote advantage at a locus,
a situation in which the heterozygous genotype has greater fitness than either
of the two homozygous genotypes
• Under heterozygote advantage, both alleles involved will be maintained in a
population.
• A classic example of heterozygote advantage concerns the allele for sickle-cell
anemia. Individuals who are homozygous for the sickle-cell allele have sickle-
cell anemia, which causes the red blood cells to become sickle-shaped when
they release oxygen.
• These sickle-shaped cells become caught in narrow blood vessels, blocking
blood flow.
• Prior to the development of modern treatments, the disease was associated
with very low fitness, since individuals usually died before reproductive age
• Heterozygotes, however, have normal, donut-
shaped blood cells and do not suffer from
sickle-cell anemia.
• In addition, they enjoy a benefit of the sickle-
cell allele, which offers protection from
malaria.
• Consequently, heterozygous individuals have
greater fitness than individuals who have two
copies of the normal allele.
• Heterozygote advantage in this system is
believed to have played a critical role in
allowing a disease as harmful as sickle-cell
anemia to persist in human populations.
• Evidence for this comes from an examination
of the distribution of the sickle-cell allele,
which is only found in places where malaria is
a danger.
3.2 Another form of natural selection that maintains genetic variation in
populations is frequency-dependent selection.
• Under frequency-dependent selection, the fitness of a genotype depends
on its relative frequency within the population, with less-common
genotypes being more fit than genotypes that occur at high frequency.
• Frequency-dependent selection is believed to be fairly common in natural
populations.
• For example, in situations where there is competition for resources,
individuals with rare preferences may enjoy greater fitness than those
who have more common preferences.
• Frequency-dependent selection may also play a role in predation: if
predators form a search image for more common prey types, focusing on
capturing those, less common phenotypes may enjoy better survival.
Population genetics
3.3 Finally, changing patterns of selection over time or space can help to
maintain genetic variation in a population.
Time
• If selection patterns fluctuate over time, different alleles or genotypes may
enjoy greater fitness at different times.
• The overall effect may be that both alleles persist in a population.
• Changing selection pressures over time are encountered by a species of
grasshopper characterized by two color morphs, a brown morph and a green
morph.
• Earlier in the year, when the habitat is more brown, the better-camouflaged
brown grasshoppers enjoy greater protection from predators.
• Later in the season, however, the environment is greener and the green
grasshoppers have higher fitness.
Space
• Another possibility is that selection patterns vary from one place to another as
a result of differences in habitat and environment.
• The prevalence of different genotypes in different habitats, combined with
gene flow between habitats, can result in the maintenance of multiple alleles
in a population.
• One example comes from the allele for resistance to copper toxicity in
species of grass.
• Copper-tolerant alleles are common in areas adjacent to copper mines,
where the soil is contaminated.
• They are not expected in un-contaminated areas, however, where they are
less fit than normal alleles.
• However, because grass species are wind pollinated, gametes can travel
considerable distances, and copper-tolerant alleles are often found in
areas where they are at a selective disadvantage.
Mutation selection
• Mutation–selection balance is an equilibrium in the
number of deleterious alleles in a population that occurs
when the rate at which deleterious alleles are created
by mutation equals the rate at which deleterious alleles
are eliminated by selection.
• The majority of genetic mutations are neutral or
deleterious; beneficial mutations are relatively rare.
• The resulting influx of deleterious mutations into a
population over time is counteracted by negative selection
which acts to purge deleterious mutations.
• Mutation–selection balance was originally proposed to
explain how genetic variation is maintained in populations
• Although several other ways for deleterious mutations to
persist are now recognized, notably balancing selection
• Nevertheless, the concept is still widely used in evolutionary genetics, e.g.
to explain the persistence of deleterious alleles as in the case of spinal
muscular atrophy or, in theoretical models, mutation-selection balance
can appear in a variety of ways and has even been applied to beneficial
mutations (i.e. balance between selective loss of variation and creation of
variation by beneficial mutations).
MEASURING GENETIC VARIATION IN NATURAL
POPULATIONS
TWO COMMONLY USED MEASURES TO QUANTIFY GENETIC VARIATION ARE:
P – the proportion of polymorphic loci (those that have 2 or
more alleles)
H – the average heterozygosity = proportion of loci at which
a randomly chosen individual is heterozygous.
At protein level
• Electrophoresis works by separating proteins as they move through a gel matrix.
• Once they are separated, a specific stain is added to the gel to visualize the
proteinbands.
• In one common form of protein electrophoresis, proteins are separated on the
basis of a combination of charge, which varies depending on the amino acids, and
folding conformation of the protein.
• This procedure was soon used to examine genetic variation in hundreds of plant
and animal species
• A polymorphic locus is any locus that has more than one allele present
within a population.
• The proportion of polymorphic loci (P) is calculated by dividing the number
of polymorphic loci by the total number of loci examined.
• For example, suppose we found that of 33 loci in a population of green frogs,
18 were polymorphic. The proportion of polymorphic loci would be
18/33=0.55.
• It is important to realize that the proportion of polymorphic loci depends on
the technique used to identify polymorphism and on the sample size.
Gel electrophoresis:
AN ALLOZYME GEL
SS FS FF
SS FS
FS FF
FF FS SS
Monomorphic locus: all individuals fixed for same allele
Polymorphic locus: 2 alleles
 Frequency of F allele, p = 10 / 20 = 0.5
 Frequency of S allele, q = 10 / 20 = 0.5
 H = 4 /10 = 0.4
* * * *
DNA level
• To determine genetic variation at the DNA level ,to estimate heterozygosity, we
use an example where we assay nucleotide polymophism using restriction
enzymes
• Suppose that two individuals differ in one or more nucleotides at a particular
DNA sequence and that the differences occur at a site recognized by a restriction
enzyme.
• One individual has a DNA molecule with the restriction site, but the other
individual does not because the sequences of DNA nucleotides differ.
• If the DNA from these two individuals is mixed with the restriction enzyme and
the resulting fragments are separated on a gel, the two individuals produce
different patterns of fragments.
• The different patterns on the gel are called restriction fragment length
polymorphisms, or RFLPs.
• They indicate that the DNA sequences of the two individuals differ.
• RFLPs are the fragment patterns produced on a gel when the DNA is cut by
the restriction enzyme.
Neutral theory of molecular evolution
• The theory was introduced by the Japanese
biologist Motoo Kimura in 1968, and independently
by two American biologists Jack Lester King
and Thomas Hughes Jukes in 1969
• It holds that most evolutionary changes occur at the
molecular level, and most of the variation within and
between species, are due to random genetic drift
of mutant alleles that are selectively neutral.
• Mutations are either harmful or beneficial to the
population
• A neutral mutation is one that does not affect an
organism's ability to survive and reproduce. The
neutral theory assumes that most mutations that are
not deleterious are neutral rather than beneficial.
• The neutral theory instead proposed that the majority of molecular
changes, such as in DNA sequence, are caused by random processes acting
on selectively neutral mutants, meaning they inferred no advantage or
disadvantage.
• By using complex calculations, Kimura showed that the rate of evolution
cannot be explained by positive or negative selection because it is too high
and that many mutations must instead be neutral.
• Neutral mutations become widespread by a process called random
genetic drift, in which a mutation spreads throughout the population due
to chance alone.
Population genetics
• Neutral genetic variation is described as that which is unaffected by
natural selection.
• The neutral theory allows for the possibility that most mutations are
deleterious, but holds that because these are rapidly removed by natural
selection, they do not make significant contributions to variation within
and between species at the molecular level.
• the neutral theory of molecular evolution contends that at the molecular
level, most evolutionary changes and polymorphisms within species are
not caused by natural selection, but by random genetic drift.
• Example
include silent point mutations, which are neutral because they do not
change the amino acids in the proteins they encode.
Fishers Theorem
• Fisher's fundamental theorem of natural
selection
is an idea about genetic variance in population
genetics developed by the statistician
and evolutionary biologist Ronald Fisher
It states:
• "The rate of increase in fitness of
any organism at any time is equal to its
genetic variance in fitness at that time."Or
in more modern terminology:
• "The rate of increase in the mean fitness of
any organism, at any time, that is
ascribable to natural selection acting
through changes in gene frequencies, is
exactly equal to its genetic variance in
fitness at that time".
• The rate of increase in the average fitness of a population is equal to the
genetic variance of fitness of that population”.
• The “genetic variance” in the foregoing statements is the linear or additive
component of the fitness variance in current literature.
Linkage Disequilibrium
• Linkage disequilibrium — the non random association of alleles at
different loci
• is a sensitive indicator of the population genetic forces that structure a
genome.
• non-random association of alleles at different loci in a given
population.
• Linkage disequilibrium is influenced by many factors,
including selection, the rate of genetic recombination, mutation
rate, genetic drift the system of mating, population structure,
and genetic linkage.
• Mechanisms that restrict recombination, such as asexual reproduction,
promote the continuance of linkage disequilibrium, leading to the
domination of a limited number of alleles.
• Linkage disequilibrium is also maintained through chromosomal
translocations and inversions that reduce recombination.
• When natural selection favors linkage disequilibrium, chromosomal
rearrangements will also increase the linkage.
• The so-called supergenes are closely linked genes that affect one or
several related traits that have arisen through linkage disequilibrium
• When the frequency of genotypes at more than two loci can be expressed as
the cumulative product of the respective allele frequencies of each locus,
those genes are said to be at the state of "linkage equilibrium."
• Suppose that two different loci, A and B, each have two alleles, A1 and A2,
and B1 and B2, respectively. Let us denote frequencies of alleles A1 and A 2 at
locus A in a population as x1 and x2.
• Similarly, let us denote the allele frequencies at locus B as yl and y2.
• The genotypic frequency, X1, of A1 B1 (allele A1 at locus A and allele B1 at
locus B) can be expressed as X1 = x1y1 when those genes are at linkage
equilibrium. When this relationship does not hold for some reason, those
genes are said to be in a state of "linkage disequilibrium.“
• Therefore, the linkage disequilibrium, D, can be measured by D (X1 – x1y1.
When D = 0, linkage equilibrium exists
Population genetics
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Population genetics

  • 2. • The science of genetics can be broadly divided into four major subdisciplines Each of these four areas focuses on a different aspect of heredity. • Transmission genetic genetic processes that occur within individuals and how genes are passed from one individual to another. • Molecular genetics molecular nature of heredity: how genetic information is encoded within the DNA and how biochemical processes of the cell translate into the phenotype. • Population genetics applies the principles of transmission genetics to large groups of individuals, focusing on the transmission processes at one or a few genetic loci. • Quantitative genetics also considers the transmission of traits simultaneously determined by many genes. Both population and quantitative genetics apply Mendelian principles, and they are amenable to mathematical treatment.
  • 3. POPULATION GENETICS:  The study of the rules governing the maintenance and transmission of genetic variation in natural populations. • In this discipline, our perspective shifts away from the individual and the cell and focuses instead on a large group of individuals, a Mendelian population.
  • 4. A Mendelian population  is a group of interbreeding individuals who share a common set of genes.  The genes shared by the individuals of a Mendelian population are called the gene pool.
  • 5. • Gene pool: Collection of all genes /alleles/alternative forms of allele of all the individuals in a population.
  • 6. • Gene: segment of DNA controlling a particular trait. Occur in units • Allele : Alternative forms of a particular gene. occurs in pairs or more
  • 7. • 1) Diploid, autosomal locus with 2 alleles: A and a PARENTS GAMETES ZYGOTES (DIPLIOD) (HAPLOID) (DIPLOID) • These parents produce a large gamete pool (Gene Pool) containing alleles A and a. A A a a A a a a A A a a a a A a a A A A a A
  • 8. Gamete (allele) Frequencies: Freq(A) = p Freq(a) = q  p + q = 1 Genotype Frequencies of 3 Possible Zygotes: AA Aa aa Freq (AA) = pA x pA = pA 2 Freq (Aa) = (pA x qa) + (qa x pA) = 2pAqa Freq (aa) = qa x qa = qa 2  p2 + 2pq + q2 = 1
  • 9. • By convention, if there are 2 alleles at a locus, p and q are used to represent their frequencies • The frequency of all alleles in a population will add up to 1 – For example, p + q = 1
  • 10. General Rule for Estimating Allele Frequencies from Genotype Frequencies: Genotypes: AA Aa aa Frequency: p2 2pq q2  Frequency of the A allele: p = p2 + ½ (2pq) ( AA + ½ Aa)  Frequency of the a allele: q = q2 + ½ (2pq) ( aa + 1/2Aa)
  • 11. Sample Calculation: Allele Frequencies Assume N = 200 indiv. in each of two populations 1 & 2  Pop 1 : 90 AA 40 Aa 70 aa  Pop 2 : 45 AA 130 Aa 25 aa In Pop 1 :  p = p2 + ½ (2pq) = 90/200 + ½ (40/200) = 0.45 + 0.10 = 0.55  q = q2 + ½ (2pq) = 70/200 + ½ (40/200) = 0.35 + 0.10 = 0.45 In Pop 2 :  p = p2 + ½ (2pq) = 45/200 + ½ (130/200) = 0.225 + 0.325 = 0.55  q = q2 + ½ (2pq) = 25/200 + ½ (130/200) = 0.125 + 0.325 = 0.45
  • 12. • For example, consider a population of wildflowers that is incompletely dominant for color: – 320 red flowers (CRCR) – 160 pink flowers (CRCW) – 20 white flowers (CWCW) • Calculate the number of copies of each allele: – CR  (320  2)  160  800 – CW  (20  2)  160  200
  • 13. • To calculate the frequency of each allele: – p  freq CR  800 / (800  200)  0.8 – q  freq CW  200 / (800  200)  0.2 • The sum of frequency alleles is always 1 – 0.8  0.2  1
  • 14. Main Points:  p + q = 1 (more generally, the sum of the allele frequencies equals one)  p2 + 2pq +q2 = 1 (more generally, the sum of the genotype frequencies equals one)  Two populations with markedly different genotype frequencies can have the same allele frequencies
  • 15. Hardy-Weinberg Equilibrium • The Hardy-Weinberg principle states that frequencies of alleles and genotypes in a population remain constant from generation to generation • In a given population where gametes contribute to the next generation randomly, allele frequencies will not change p2 + 2pq + q2 = 1 The Hardy-Weinberg principle describes a population that is not evolving If a population does not meet the criteria of the Hardy- Weinberg principle, it can be concluded that the population is evolving
  • 16. Alleles in the population Gametes produced Each egg: Each sperm: 80% chance 20% chance 80% chance 20% chance Frequencies of alleles p = frequency of q = frequency of CW allele = 0.2 CR allele = 0.8
  • 17. • Hardy-Weinberg equilibrium describes the constant frequency of alleles in such a gene pool • Consider, for example, the same population of 500 wildflowers and 1,000 alleles where – p  freq CR  0.8 – q  freq CW  0.2 The frequency of genotypes can be calculated CRCR  p2  (0.8)2  0.64 CRCW  2pq  2(0.8)(0.2) 0.32 CWCW  q2  (0.2)2  0.04
  • 18. • If p and q represent the relative frequencies of the only two possible alleles in a population at a particular locus, then – p2  2pq  q2  1 – where p2 and q2 represent the frequencies of the homozygous genotypes and 2pq represents the frequency of the heterozygous genotype
  • 19. Conditions for Hardy-Weinberg Equilibrium • The Hardy-Weinberg theorem describes a hypothetical population that is not evolving • In real populations, allele and genotype frequencies do change over time
  • 20. It predicts both allele and genotype frequencies in populations (non- evolving ones). • The first condition that must be met for Hardy-Weinberg equilibrium is the lack of mutations in a population. • The second condition that must be met for Hardy-Weinberg equilibrium is no gene flow in a population. • The third condition that must be met is the population size must be sufficient so that there is no genetic drift. • The fourth condition that must be met is random mating within the population. • Finally, the fifth condition necessitates that natural selection must not occur.
  • 21. Applying the Hardy-Weinberg Principle • We can assume the locus that causes phenylketonuria (PKU) is in Hardy- Weinberg equilibrium given that:  The PKU gene mutation rate is low  Mate selection is random with respect to whether or not an individual is a carrier for the PKU allele  Natural selection can only act on rare homozygous individuals who do not follow dietary restrictions  The population is large  Migration has no effect as many other populations have similar allele frequencies
  • 22. • The occurrence of PKU is 1 per 10,000 births – q2  0.0001 – q  0.01 • The frequency of normal alleles is – p  1 – q  1 – 0.01  0.99 • The frequency of carriers is – 2pq  2  0.99  0.01  0.0198 – or approximately 2% of the population
  • 25. Natural Selection • Natural selection is the process through which populations of living organisms adapt and change. Individuals in a population are naturally variable, meaning that they are all different in some ways. • Differential success in reproduction results in certain alleles being passed to the next generation in greater proportions • For example, an allele that confers resistance to DDT increased in frequency after DDT was used widely in agriculture
  • 26. • Directional Selection- one extreme trait is favored over the others, causing the organism to be more fit and have more offspring that survive. • An example of this is running speed in rabbits. The faster rabbits can outrun predators easier, so they are less likely to get eaten, and more likely to survive and produce offspring. Directional selection favors the trait of fast running.
  • 27. • Stabilizing Selection- the traits that are the most average are selected for, and the extremes are selected against. • One example of a trait that has experienced stabilizing selection is birth weight. Babies that are very small are often not healthy enough to survive, while babies that are too large may get stuck in the birth canal, causing death of the baby and frequently death of the mother as well.
  • 28. • Disruptive Selection- the extreme traits are selected for, and average traits are selected against. • One example of this is beak sizes in birds. If the only seeds available in an environment are small seeds and large seeds, natural selection will favor birds with either small or large beaks. The birds with medium sized beaks will not be very effective at feeding, so medium beaks will be selected against.
  • 29. Natural selection is the only mechanism that consistently causes adaptive evolution • Evolution by natural selection involves both chance and “sorting” – New genetic variations arise by chance – Beneficial alleles are “sorted” and favored by natural selection. • Only natural selection consistently results in adaptive evolution
  • 30. GENETIC DRIFT • Genetic drift (allelic drift or the Sewall Wright effect)is the change in the frequency of an existing gene variant (allele) in a population due to random sampling of organisms. • The alleles in the offspring are a sample of those in the parents, and chance has a role in determining whether a given individual survives and reproduces. • Genetic drift may cause gene variants to disappear completely and thereby reduce genetic variation. • It can also cause initially rare alleles to become much more frequent and even fixed. • When few copies of an allele exist, the effect of genetic drift is larger, and when many copies exist, the effect is smaller. • In 1968, population geneticist Motoo Kimura rekindled the debate with his neutral theory of molecular evolution, which claims that most instances where a genetic change spreads across a population are caused by genetic drift acting on neutral mutations.
  • 31. 5 plants leave off- spring Generation 1 p (frequency of CR) = 0.7 q (frequency of CW) = 0.3 CRCR CRCR CRCW CWCW CRCR CRCW CRCR CRCW CRCR CRCW CRCR CWCW CRCW CRCR CWCW CRCW CWCW CRCR CRCW CRCW Generation 2 p = 0.5 q = 0.5 2 plants leave off- spring CRCR CRCR CRCR CRCR CRCR CRCR CRCR CRCR CRCR CRCR Generation 3 p = 1.0 q = 0.0
  • 32. The Founder Effect • The founder effect occurs when a few individuals become isolated from a larger population • Allele frequencies in the small founder population can be different from those in the larger parent population
  • 33. The Bottleneck Effect • The bottleneck effect is a sudden reduction in population size due to a change in the environment • The resulting gene pool may no longer be reflective of the original population’s gene pool • If the population remains small, it may be further affected by genetic drift
  • 35. Main points:  Genetic drift is significant in small populations  Genetic drift causes allele frequencies to change at random  Genetic drift can lead to a loss of genetic variation within populations  Genetic drift can cause harmful alleles to become fixed
  • 36. Gene Flow • Gene flow consists of the movement of alleles among populations • Alleles can be transferred through the movement of fertile individuals or gametes (for example, pollen) • Gene flow tends to reduce variation among populations over time
  • 37. Gene flow can decrease the fitness of a population • Consider, for example, the great tit (Parus major) on the Dutch island of Vlieland – Mating causes gene flow between the central and eastern populations – Immigration from the mainland introduces alleles that decrease fitness – Natural selection selects for alleles that increase fitness – Birds in the central region with high immigration have a lower fitness; birds in the east with low immigration have a higher fitness Gene flow is an important agent of evolutionary change in human populations
  • 38. Population in which the surviving females eventually bred Central Eastern Survival rate (%) Females born in central population Females born in eastern population Parus major 60 50 40 30 20 10 0 Central population NORTH SEA Eastern population Vlieland, the Netherlands 2 km
  • 39. Natural selection is the only mechanism that consistently causes adaptive evolution • Evolution by natural selection involves both chance and “sorting” – New genetic variations arise by chance – Beneficial alleles are “sorted” and favored by natural selection • Only natural selection consistently results in adaptive evolution
  • 40. Genetic Variation • Describe the variation in the DNA sequence in each of our genomes. Genetic variation is what makes us all unique, whether in terms of hair colour, skin colour or even the shape of our faces. • Individuals of a species have similar characteristics but they are rarely identical, the difference between them is called variation. • Single nucleotide polymorphisms (SNPs, pronounced ‘snips’) are the most common type of genetic variation amongst people. • Each single nucleotide polymorphism represents a difference in a single DNA base, A, C, G or T, in a person’s DNA. On average they occur once in every 300 bases and are often found in the DNA between genes.
  • 41. • Genetic variation results in different forms, or alleles, of genes. • For example, if we look at eye colour, people with blue eyes have one allele of the gene for eye colour, whereas people with brown eyes will have a different allele of the gene • Genetic variation can also explain some differences in disease susceptibility and how people react to drugs. • Genetic variation is important in evolution. • Evolution relies on genetic variation that is passed down from one generation to the next. Favourable characteristics are ‘selected’ for, survive and are passed on. This is known as natural selection.
  • 42. How Genetic Variation Is Maintained Many factors are involved: 1. MUTATION • One of these is mutation, which is in fact the ultimate source of all variation. However, mutations do not occur very frequently • This rate is too slow to account for most of the polymorphisms seen in natural populations. • However, mutation probably does explain some of the very rare phenotypes seen occasionally, such as albinism in humans and other mammals.
  • 43. 2. SELECTIVE NEUTRALITY • A second factor contributing to genetic variation in natural populations is selective neutrality. • Selective neutrality describes situations in which alternate alleles for a gene differ little in fitness. Because small fitness differences result in only weak natural selection, selection may be overpowered by the random force of genetic drift. • Alleles whose frequencies are governed by genetic drift rather than by natural selection are said to be selectively neutral.
  • 44. 3. NATURAL SELECTION • Finally, several forms of natural selection act to maintain genetic variation rather than to eliminate it. • These include balancing selection, frequency-dependent selection, and changing patterns of natural selection over time and space. 3.1 Balancing selection occurs when there is heterozygote advantage at a locus, a situation in which the heterozygous genotype has greater fitness than either of the two homozygous genotypes • Under heterozygote advantage, both alleles involved will be maintained in a population. • A classic example of heterozygote advantage concerns the allele for sickle-cell anemia. Individuals who are homozygous for the sickle-cell allele have sickle- cell anemia, which causes the red blood cells to become sickle-shaped when they release oxygen. • These sickle-shaped cells become caught in narrow blood vessels, blocking blood flow. • Prior to the development of modern treatments, the disease was associated with very low fitness, since individuals usually died before reproductive age
  • 45. • Heterozygotes, however, have normal, donut- shaped blood cells and do not suffer from sickle-cell anemia. • In addition, they enjoy a benefit of the sickle- cell allele, which offers protection from malaria. • Consequently, heterozygous individuals have greater fitness than individuals who have two copies of the normal allele. • Heterozygote advantage in this system is believed to have played a critical role in allowing a disease as harmful as sickle-cell anemia to persist in human populations. • Evidence for this comes from an examination of the distribution of the sickle-cell allele, which is only found in places where malaria is a danger.
  • 46. 3.2 Another form of natural selection that maintains genetic variation in populations is frequency-dependent selection. • Under frequency-dependent selection, the fitness of a genotype depends on its relative frequency within the population, with less-common genotypes being more fit than genotypes that occur at high frequency. • Frequency-dependent selection is believed to be fairly common in natural populations. • For example, in situations where there is competition for resources, individuals with rare preferences may enjoy greater fitness than those who have more common preferences. • Frequency-dependent selection may also play a role in predation: if predators form a search image for more common prey types, focusing on capturing those, less common phenotypes may enjoy better survival.
  • 48. 3.3 Finally, changing patterns of selection over time or space can help to maintain genetic variation in a population. Time • If selection patterns fluctuate over time, different alleles or genotypes may enjoy greater fitness at different times. • The overall effect may be that both alleles persist in a population. • Changing selection pressures over time are encountered by a species of grasshopper characterized by two color morphs, a brown morph and a green morph. • Earlier in the year, when the habitat is more brown, the better-camouflaged brown grasshoppers enjoy greater protection from predators. • Later in the season, however, the environment is greener and the green grasshoppers have higher fitness. Space • Another possibility is that selection patterns vary from one place to another as a result of differences in habitat and environment. • The prevalence of different genotypes in different habitats, combined with gene flow between habitats, can result in the maintenance of multiple alleles in a population.
  • 49. • One example comes from the allele for resistance to copper toxicity in species of grass. • Copper-tolerant alleles are common in areas adjacent to copper mines, where the soil is contaminated. • They are not expected in un-contaminated areas, however, where they are less fit than normal alleles. • However, because grass species are wind pollinated, gametes can travel considerable distances, and copper-tolerant alleles are often found in areas where they are at a selective disadvantage.
  • 50. Mutation selection • Mutation–selection balance is an equilibrium in the number of deleterious alleles in a population that occurs when the rate at which deleterious alleles are created by mutation equals the rate at which deleterious alleles are eliminated by selection. • The majority of genetic mutations are neutral or deleterious; beneficial mutations are relatively rare. • The resulting influx of deleterious mutations into a population over time is counteracted by negative selection which acts to purge deleterious mutations. • Mutation–selection balance was originally proposed to explain how genetic variation is maintained in populations • Although several other ways for deleterious mutations to persist are now recognized, notably balancing selection
  • 51. • Nevertheless, the concept is still widely used in evolutionary genetics, e.g. to explain the persistence of deleterious alleles as in the case of spinal muscular atrophy or, in theoretical models, mutation-selection balance can appear in a variety of ways and has even been applied to beneficial mutations (i.e. balance between selective loss of variation and creation of variation by beneficial mutations).
  • 52. MEASURING GENETIC VARIATION IN NATURAL POPULATIONS TWO COMMONLY USED MEASURES TO QUANTIFY GENETIC VARIATION ARE: P – the proportion of polymorphic loci (those that have 2 or more alleles) H – the average heterozygosity = proportion of loci at which a randomly chosen individual is heterozygous.
  • 53. At protein level • Electrophoresis works by separating proteins as they move through a gel matrix. • Once they are separated, a specific stain is added to the gel to visualize the proteinbands. • In one common form of protein electrophoresis, proteins are separated on the basis of a combination of charge, which varies depending on the amino acids, and folding conformation of the protein. • This procedure was soon used to examine genetic variation in hundreds of plant and animal species
  • 54. • A polymorphic locus is any locus that has more than one allele present within a population. • The proportion of polymorphic loci (P) is calculated by dividing the number of polymorphic loci by the total number of loci examined. • For example, suppose we found that of 33 loci in a population of green frogs, 18 were polymorphic. The proportion of polymorphic loci would be 18/33=0.55. • It is important to realize that the proportion of polymorphic loci depends on the technique used to identify polymorphism and on the sample size.
  • 57. SS FS FF SS FS FS FF FF FS SS Monomorphic locus: all individuals fixed for same allele Polymorphic locus: 2 alleles  Frequency of F allele, p = 10 / 20 = 0.5  Frequency of S allele, q = 10 / 20 = 0.5  H = 4 /10 = 0.4 * * * *
  • 58. DNA level • To determine genetic variation at the DNA level ,to estimate heterozygosity, we use an example where we assay nucleotide polymophism using restriction enzymes • Suppose that two individuals differ in one or more nucleotides at a particular DNA sequence and that the differences occur at a site recognized by a restriction enzyme. • One individual has a DNA molecule with the restriction site, but the other individual does not because the sequences of DNA nucleotides differ. • If the DNA from these two individuals is mixed with the restriction enzyme and the resulting fragments are separated on a gel, the two individuals produce different patterns of fragments.
  • 59. • The different patterns on the gel are called restriction fragment length polymorphisms, or RFLPs. • They indicate that the DNA sequences of the two individuals differ. • RFLPs are the fragment patterns produced on a gel when the DNA is cut by the restriction enzyme.
  • 60. Neutral theory of molecular evolution • The theory was introduced by the Japanese biologist Motoo Kimura in 1968, and independently by two American biologists Jack Lester King and Thomas Hughes Jukes in 1969 • It holds that most evolutionary changes occur at the molecular level, and most of the variation within and between species, are due to random genetic drift of mutant alleles that are selectively neutral. • Mutations are either harmful or beneficial to the population • A neutral mutation is one that does not affect an organism's ability to survive and reproduce. The neutral theory assumes that most mutations that are not deleterious are neutral rather than beneficial.
  • 61. • The neutral theory instead proposed that the majority of molecular changes, such as in DNA sequence, are caused by random processes acting on selectively neutral mutants, meaning they inferred no advantage or disadvantage. • By using complex calculations, Kimura showed that the rate of evolution cannot be explained by positive or negative selection because it is too high and that many mutations must instead be neutral. • Neutral mutations become widespread by a process called random genetic drift, in which a mutation spreads throughout the population due to chance alone.
  • 63. • Neutral genetic variation is described as that which is unaffected by natural selection. • The neutral theory allows for the possibility that most mutations are deleterious, but holds that because these are rapidly removed by natural selection, they do not make significant contributions to variation within and between species at the molecular level. • the neutral theory of molecular evolution contends that at the molecular level, most evolutionary changes and polymorphisms within species are not caused by natural selection, but by random genetic drift. • Example include silent point mutations, which are neutral because they do not change the amino acids in the proteins they encode.
  • 64. Fishers Theorem • Fisher's fundamental theorem of natural selection is an idea about genetic variance in population genetics developed by the statistician and evolutionary biologist Ronald Fisher It states: • "The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time."Or in more modern terminology: • "The rate of increase in the mean fitness of any organism, at any time, that is ascribable to natural selection acting through changes in gene frequencies, is exactly equal to its genetic variance in fitness at that time".
  • 65. • The rate of increase in the average fitness of a population is equal to the genetic variance of fitness of that population”. • The “genetic variance” in the foregoing statements is the linear or additive component of the fitness variance in current literature.
  • 66. Linkage Disequilibrium • Linkage disequilibrium — the non random association of alleles at different loci • is a sensitive indicator of the population genetic forces that structure a genome. • non-random association of alleles at different loci in a given population. • Linkage disequilibrium is influenced by many factors, including selection, the rate of genetic recombination, mutation rate, genetic drift the system of mating, population structure, and genetic linkage.
  • 67. • Mechanisms that restrict recombination, such as asexual reproduction, promote the continuance of linkage disequilibrium, leading to the domination of a limited number of alleles. • Linkage disequilibrium is also maintained through chromosomal translocations and inversions that reduce recombination. • When natural selection favors linkage disequilibrium, chromosomal rearrangements will also increase the linkage. • The so-called supergenes are closely linked genes that affect one or several related traits that have arisen through linkage disequilibrium
  • 68. • When the frequency of genotypes at more than two loci can be expressed as the cumulative product of the respective allele frequencies of each locus, those genes are said to be at the state of "linkage equilibrium." • Suppose that two different loci, A and B, each have two alleles, A1 and A2, and B1 and B2, respectively. Let us denote frequencies of alleles A1 and A 2 at locus A in a population as x1 and x2. • Similarly, let us denote the allele frequencies at locus B as yl and y2. • The genotypic frequency, X1, of A1 B1 (allele A1 at locus A and allele B1 at locus B) can be expressed as X1 = x1y1 when those genes are at linkage equilibrium. When this relationship does not hold for some reason, those genes are said to be in a state of "linkage disequilibrium.“ • Therefore, the linkage disequilibrium, D, can be measured by D (X1 – x1y1. When D = 0, linkage equilibrium exists