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Population Genetics
Population Genetics
• Population genetics is concerned with the
question of whether a particular allele or
genotype will become more common or less
common over time in a population, and Why.
• Example:
– Given that the CCR5-D32 allele confers immunity to
HIV, will it become more frequent in the human
population over time?
Predicting Allele Frequencies
Populations in Hardy-Weinberg
equilibrium
Yule vs. Hardy
• What are the characteristics of a population that
is in equilibrium or another words, not evolving.
• Yule thought that allele frequencies had to be
0.5 and 0.5. for a population to be in equilibrium.
• Hardy proved him wrong by developing the
Hardy-Weinburg equation.
Punnett square
• 60 % of the eggs
carry allele A and
40% carry allele a
• 60% of sperm carry
allele A and 40%
carry allele a.
Sample problem
• In a population of 100 people, we know that
36% are AA , 48% are Aa, and 16% are aa.
• Determine how many alleles in the gene
pool are A or a.
– Each individual makes two gametes....
– How many A alleles are in this population’s
gene pool? _____
120 (36*(2)+48)
– How many a alleles? _____
80 (16*(2) +48)
What percent of the alleles are A or a ?
120 / 200 = .6 or 60% A ; or
.6 = frequency of allele A
80 / 200 = .4 or 40% a ; or
.4 = frequency of allele a
• Creating the HardyWienburg equation is
a matter of combining
probabilities found in
the Punnett square.
Combining Probabilities
• The combined probability of two
independent events will occur together is
equal to the product of their individual
probabilities.
– What is the probability of tossing a nickel and
a penny at the same time and having them
both come up heads?
•½ x ½ = ¼
Combining Probabilities
• The combined probability that either of two
mutually exclusive events will occur is the
sum of their individual probabilities. When
rolling a die we can get a one or a two
(among other possibilities), but we cannot
get both at once. Thus, the probability of
getting either a one or a two is
• 1/6 + 1/6 = 1/3
Calculating Genotype Frequencies
• We can predict the genotype frequencies by
multiplying probabilities.
Hardy-Weinburg equation
Genotype Frequencies
Zygotes
Allelic frequency
Genotype frequency
AA
(p)(p)
p2
Aa
(p)(q)
2pq
aA
(q)(p)
aa
(q)(q)
q2
Genotype frequencies described by
p2+2pq+q2=1.0
The relationship between allele
and genotype frequency
• Let original A frequency be represented by p
and original a frequency be represented by q
• Since there are only two alleles possible for this
gene locus, The frequencies of A and a must
equal 1.0
• Therefore, p + q =1.0
Sample: calculating genotype frequencies
from allele frequencies?
If a given population had the following allele frequencies:
allele frequency (p) for A of 0.8
allele frequency (q) for a of 0.2
Determine the genotype frequencies of this population?
AA
0.64
Aa
aa
0.32
0.04
AA = p2 ; Aa = 2pq ; and aa = q2 as follows…
We can also calculate the frequency of alleles from
the genotype frequencies.
When a population is in equilibrium the
genotype frequencies are represented as..
P2 + 2pq +q2
The allele frequency can therefore be calculated
as follows.
A = p2 + ½(2pq)
and
a = q2 + ½(2pq)
Examining our example again we see that if
we use the frequencies we calculated for
each genotype….
p2
2pq
q2
0.64 AA
.32 Aa
.04 aa
A = p2 + ½ (2pq)
A=.64 + ½ (.32)
A = 0.8
and since q = 1-p ; then a = 1-(0.8 ) a = 0.2
These rules hold as long as a
population is in equilibrium.
Hardy Weinberg Equilibrium describes
the conclusions and assumptions that
must be present to consider a
population in equilibrium.
Hardy Weinberg Conclusions
1.
The allele frequencies in a population will not change
from generation to generation.
You would need at least 2 generations of data to
demonstrate this.
2.
If the allele frequencies in a population are given by p
and q then the genotype frequencies will be equal to
p2; 2pq ; q2.
Therefore if
AA can not be predicted by p2
Aa cannot be predicted by 2pq and
aa cannot be predicted by q 2
then the population is not in equilibrium
There are 5 assumptions which must be met
in order to have a population in equilibrium
1. There is no selection. In other words there
is no survival for one genotype over another
2. There is no mutation. This means that none
of the alleles in a population will change over
time. No alleles get converted into other forms
already existing and no new alleles are
formed
3. There is no migration (gene flow)New
individuals may not enter or leave the
population. If movement into or out of the
population occurred in a way that certain
allele frequencies were changed then the
equilibrium would be lost
Exceptions to Hardy Weinberg cont.
4. There are no chance events (genetic drift)
This can only occur if the population is
sufficiently large to ensure that the chance of
an offspring getting one allele or the other is
purely random. When populations are small
the principle of genetic drift enters and the
equilibrium is not established or will be lost as
population size dwindles due to the effects of
some outside influence
5. There is no sexual selection or mate
choice Who mates with whom must be
totally random with no preferential selection
involved.
Genetic Distance: Definitions
• Allele: Different forms of a gene.
• Genotype: The specific allele in an individual.
• Phenotype: The expression of a genotype.
Allele
Homozygote
Phenotype
Heterozygote
Genotype
Homozygote
Genetic Distance: Definitions
• Microsatellite: Short consecutive repeats:
• Single nucleotide polymorphism (SNP): Variation
in a single nucleotide of a genome between two
individuals.
Genetic Distance: Definitions
• Linkage disequilibrium (LD): Correlation
between alleles at two different position.
• Haplotype: Combination of alleles at multiple
linked loci which are transmitted together.
Evolution
• Evolutionary forces:
-
Natural selection: Probability of survival and
reproduction
- Genetic drift: Change in allele frequencies
entirely by chance.
Selection vs Drift
The two forces that determine the fate of alleles
in a population
• Drift
– Change in allele frequencies due to sampling
– a ‘stochastic’ process
– Neutral variation is subject to drift
• Selection
– Change in allele frequencies due to function
– ‘deterministic’
– Functional variation may be subject to selection (more later)
Genetic Drift 1
Genetic Drift 2: Population Size Matters
4 populations
2 at N=25
2 at N=250
Effective population size Ne
• Sewall Wright (1931, 1938)
• “The number of breeding individuals in an idealized population that would
show the same amount of dispersion of allele frequencies under random
genetic drift or the same amount of inbreeding as the population under
consideration".
• Usually, Ne < N (absolute population size)
• Ne != N can be due to:
–
–
–
–
fluctuations in population size
unequal numbers of males/females
skewed distributions in family size
age structure in population
Selection vs Drift 1: |s| and Pop Size
If |s| < 1/Ne,
then selection is ineffective and the alleles are solely
subject to drift: the alleles are “effectively neutral”
What is the probability of fixation?
If |s| < 1/Ne, then P(fix) =
If |s| > 1/Ne, then P(fix) =
q
1 - e-4 Ne sq
1 - e-4 Ne s
Ne = effective pop size
s = selection coefficient
q = allele frequency
Source: A. Sidow, BIOSCI 203
-
Mutation: Change in
nucleotide sequence of
genes caused by copying
error or exposure to
radiation, chemical
substance, viruses,...
- Migration
• Fixation Index (Fst):
Measure of population
differentiation.
• ΠBetween(ΠWithin):
Average number of
pairwise difference
between two
individuals sampled
from different (the
same) population.
ΠBetween
ΠWithin
NON-RANDOM MATING
 Inbreeding: mating between close relatives leads to
deviations from H-W equilibrium by causing a deficit of
heterozygotes.
 In the extreme case of self-fertilization:
Generation
AA
Aa
aa
0
p2
1
p2 + (pq/2) pq
2
p2 + (3pq/4)pq/2
2pq
q2
q2 + (pq/2)
q2 + (3pq/4)
HOW CAN WE QUANTIFY THE AMOUNT OF
INBREEDING IN A POPULATION?
 The inbreeding coefficient,
F
 The probability that a randomly chosen individual
caries two copies of an allele that are identical by
descent from a recent ancestor.
 The probability that an individual is autozygous
 Consider two pedigrees:
Full-sib mating
IBD
A1*A2
A1A2
A1*A2
A1*A2
A1*A1*
Backcross
A1*A2
A1A2
A1*A1
IBD
A1*A1*
AVERAGE F FROM EACH MATING IS 0.25
LOSS OF HETEROZYGOSITY IN LINE OF SELFERS
 Population Size (N) = 1
Heterozygosity after one generation, H1 = (1/2) x H0
Heterozygosity after two generations, H2 = (1/2)2 x H0
After t generations of selfing, Ht = (1/2)t x H0
 Example: After t = 10 generations of selfing, only 0.098%
of the loci that were heterozygous in the original
individual will still be so. The inbred line is then
essentially completely homozygous.
DECLINE IN HETEROZYGOSITY DUE TO INBREEDING
HETEROZYGOSITY IN A POPULATION THAT IS PARTIALLY INBRED
 In an inbred population the frequencies of homozygous
individuals are higher than expected under HWE. Thus,
the observed heterozygosity will be lower that expected
under HWE.
Hobs = 2pq(1-F) = Hexp(1-F).
 F ranges from 0 (no inbreeding) to 1 (completely inbred
population)
F CALCULATED FROM HETEROZYGOTE DEFICIT
F = (Hexp – Hobs) / H exp
Where,
Hexp = frequency of heterozygotes if all matings were random
INBREEDING COEFFICIENT, F
 As the inbreeding coefficient
(F) increases, fitness often
decreases.
 INBREEDING
DEPRESSION
INBREEDING DEPRESSION IN HUMAN POPULATIONS
INBREEDING VERSUS RANDOM GENETIC DRIFT
 Inbreeding is caused by non-random mating and
leads to changes in genotype frequencies but not
allele frequencies.
 Random genetic drift occurs in finite populations,
even with completely random mating, and leads to
changes in both genotype and allele frequencies.
 Both processes cause a decline in heterozygosity.
 Why does inbreeding cause a decrease in
fitness?
 What genetic mechanisms, or type of
gene action are responsible?
Smith et al.
QUANTIFYING POPULATION SUBDIVISION
Vs.
 Random Mating Population Panmictic
 Subdivided Population Random mating within but
not among populations
HOW DO WE MEASURE MIGRATION (GENE FLOW)?
 Direct Methods – e.g., mark-recapture studies in natural
populations. For many organisms this is not a realistic
option.
 Indirect Methods – e.g., molecular marker variation.
SS
FS
SS
FF
FS
FS
FF
FF
FS
SS
CONSIDER TWO COMPLETELY ISOLATED POPULATIONS
 Due to random genetic drift, the allele frequencies in the populations
diverge.
 In an extreme case, they can be fixed for alternate alleles:
A1A1
A1A2
A2A2
Population 1
1.0
0
0
Population 2
0
0
1.0
Overall HWE
0.25
0.50
0.25
 Individuals in population 1 are clearly more closely related to one
another than they are to individuals in population 2.
 In this context, the inbreeding coefficient (F) represents the
probability that two gene copies within a population are the
same, relative to gene copies taken at random from all
populations lumped together.
QUANTIFYING POPULATION SUBDIVISION WITH FST
 Fst measures variation in allele frequencies among
populations.
Ranges from 0 to 1
 Fst compares the average expected heterozygosity of
individual subpopulations (S) to the total expected
heterozygosity if the subpopulations are combined (T).
 HS
( HT  H S )
FST 
 1  
HT
 HT



FST AND POPULATION SUBDIVISION
 At Panmixis, FST = 0
 All subpopulations
have the same allele
frequencies.
 Complete Isolation, FST = 1
 All subpopulations are
fixed for different alleles.
 Example:
 Consider three subpopulations with 2 alleles at
frequencies p and q,
p q HS=2pq
 Subpop 1:
0.7 0.3 0.42
 Subpop 2:
0.5 0.5 0.50
 Subpop 3:
0.3 0.7 0.42
Average HS = 0.446
 The total expected heterozygosity across all subpopulations is calculated
from the average allele frequency,
p
q
Subpop 1:
0.7 0.3
Subpop 2:
0.5 0.5
Subpop 3:
0.3 0.7
HT= 2pq = 0.5
p = 0.5 q = 0.5
Remember that,
 HS
( HT  H S )
FST 
 1  
HT
 HT



FST = (0.50 - 0.466) / (0.50) = 0.11
WRIGHT’S ISLAND MODEL:
 Consider n subpopulations that are
diverging by drift alone, not by natural
selection, and with an equal exchange of
migrants between populations each
generation at rate m……
m
m
m
m
 What is the
equilibrium level of
population
subdivision (FST)?
RELATIONSHIP BETWEEN FST AND Nm IN THE ISLAND MODEL
 Nm is the absolute number of migrant organisms that
enter each subpopulation per generation.
 At equilibrium:
 And:
Fˆ  Ft  Ft 1
1
FST 
1  4 Nm
 When Nm = 0, FST = 1
Nm = 0.25 (1 migrant every 4th generation), Fst = 0.50
Nm = 0.50 (1 migrant every 2nd generation), Fst = 0.33
Nm = 1.00 (1 migrant every generation), Fst = 0.20
Nm = 2.00 (2 migrants every generation), Fst = 0.11
ROLE OF DRIFT IN POPULATION DIVERGENCE
1
FST 
1  4 Nm
If Nm >> 1, little divergence by drift;
If Nm << 1, drift is very important
• Find Genes which are candidates to have
been under selection:
Very low and very high Fst distance.
Compare expected and observed values of Fst.
Detection of Selection in Humans with SNPs
Large-scale SNP-survey looked at:
106 Genes in an average of 57 human individuals
60,410 base pairs of noncoding sequence (UTRs, introns, some promoters)
135,823 base pairs of coding sequence
Some salient points:
• Because survey is snapshot of current frequencies,
evidence for selection or drift is indirect
• This is about bulk properties, not about individual genes
-
Fst matrix analysis:
Phylogenetic tree
Based on
SNP of 120
genes in
1,915
individuals
Principal Component Analysis
Based on
783
microsatellite
s in 1,027
individuals
• Mitochondrial DNA (mtDNA):
In mitochondria (out of nucleus)
– transmitted along only female lineages.
– No recombination.
High mutation rate:
• Abundance of polymorphic
Difficult genealogy reconstruction