Transcript What is Population Genetics?

Population Genetics
Dr Pupak Derakhshandeh-Peykar, PhD
Ass Prof of Medical Science of Tehran
University
Ref.: Population and Evolutionary
Genetics: A primer
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What is Population Genetics?

The genetical study of the process of
evolution

(The study of the change of allele
frequencies, genotype frequencies, and
phenotype frequencies)
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Population genetics:

One of the oldest and richest
examples of success of mathematical
theory in biology

Mendelian genetics and Darwinian
natural selection in the first part of
the 20th century 
“modern synthesis”
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Population Genetics is…

About microevolution (evolution within
species)

Strongly dependent on mathematical models

A relatively young science (most important
discoveries are from after 1930)
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Factors causing genotype
frequency changes
Selection
 Mutation
 Random Drift
 Migration
 Recombination
 Non-random Mating

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What forces are responsible for
divergence among populations?

Mutation
genetic diversity

Selection
 genetic diversity

Genetic drift
 genetic diversity

Migration
 genetic diversity

Non-random
mating
 genetic diversity
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What's the most important
factor in evolution?
SELECTION

Natural selection causes evolution:
 There is variation in fitness (selection(

That variation can be passed from one
generation to the next (inheritance(

This is the central insight of Darwin
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THEORIES of EVOLUTION
and the
DARWINIAN REVOLUTION
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Darwin's Theory of Evolution
Four Basic Themes:
1.
2.
3.
4.
Descent with Modification from Common
Ancestor
Diversity is result of Differential Survival
and/or Differential Reproduction among
individuals
with different Heritable characteristics
= Process of Natural Selection
Law of Evolution by Natural Selection
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Charles Darwin (1809-1882)
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Theory of Evolution by Natural
Selection (1859)
Charles Darwin (1809-1882)
Inherited Variation among individuals
↓
Differential survival and/or reproduction
(“hard” inheritance)
↓
Change in genetic composition of population
↓↓↓↓
Evolution
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Jean Baptiste Lamarck (1744-1829)
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Theory of Evolution
by Inheritance of Acquired Characteristics
(1809)
Jean Baptiste Lamarck (1744-1829)
Environmental change
↓
Change in organismal form
↓
Inheritance of acquired characteristics
(“soft inheritance”)
↓
Change in composition of population
↓↓↓
Evolution
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Lamarck’s vs. Darwin’s Theories
=‫انقراض‬
=‫اصالح نژاد هدفدار‬
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Dates, Contributors to Evolutionary
Thinking - 1
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Dates, Contributors to Evolutionary
Thinking - 2
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Genes in Populations:
Hardy Weinberg
Equilibrium
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Alleles

Alternative forms of a particular
sequence

Each allele has a frequency
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Alleles
 Yeast:
12 Mb ; 6,340 genes
 Nematode
elegance: 97 Mb;
19,100 genes
 Human:
3,700 Mb; 75,000 genes!
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Methods used to measure genetic
variation:

Genetic variation contains information
about an organism’s ancestry

determines an organism’s potential for
evolutionary change, adaptation, and
survival

1960s-1970s: genetic variation was first
measured by protein electrophoresis (e.g.,
allozymes)
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1980s-2008s: genetic variation
measured directly at the DNA level (1):





Restriction Fragement Length
Polymorphisms (RFLPs)
Minisatellites (VNTRs)
DNA sequence
DNA length polymorphisms
Single-stranded Conformation
Polymorphism (SSCP)
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1980s-2008s: genetic variation
measured directly at the DNA level (2):
 Microsatellites
(STRs)
 Random Amplified Polymorphic
DNAs (RAPDs)
 Amplified Fragment Length
Polymorphisms (AFLPs)
 Single Nucleotide Polymorphisms
(SNPs)
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Types of measures of genetic
variation (1):

Polymorphism = % of loci or nucleotide
positions showing more than one allele
or base pair.

Heterozygosity (H) = % of individuals
that are heterozygotes

Allele/haplotype diversity = measure of
diversity and different alleles/haplotypes
within a population.
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Types of measures of genetic
variation (2):

Nucleotide diversity = measure of number and
diversity of variable nucleotide positions
within sequences of a population.

Genetic distance = measure of number of base
pair differences between two homologous
sequences.

Synonomous/nonsynonomous substitutions =
% of nucleotide substitutions that do not/do
result in amino acid replacement.
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Hardy-Weinberg
equilibrium



Properties of alleles in a population
Allele frequencies
Genotypes frequencies
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Allele Frequency


For two alleles
 Usually labeled p and q = 1 – p
For more than 2 alleles
 Usually labeled pA, pB, pC ...
 … subscripts A, B and C
indicate allele name
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Genotype

The pair of alleles carried by an individual



Homozygotes


If there are n alternative alleles …
… there will be n(n+1)/2 possible genotypes
The two alleles are in the same state
Heterozygotes

The two alleles are different
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The simple part …
Genotype frequencies lead to allele
frequencies…
 For example, for two alleles:
 pA = pAA + ½ pAB (> p=P+1/2 H*)
 pB = pBB + ½ pAB (> q=Q+1/2 H)
 However, the reverse is also
possible!

*H=2pq
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Hardy-Weinberg Equilibrium




Relationship described in 1908
 Hardy, British mathematician
 Weinberg, German physician
Random union of games
Shows n allele frequencies determine
n(n+1)/2 genotype frequencies
 Large populations
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Hardy-Weinberg Equilibrium
Explains how Mendelian
segregation influences allelic and
genotypic frequencies in a
population
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Required Assumptions in
Hardy-Weinberg law (1):

Diploid, sexual organism (Parthenogenetic)

Non-overlapping generations
Autosomal locus
 Large population
 Random mating
 Equal genotype frequencies among
sexes

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Required Assumptions in
Hardy-Weinberg law (2):




Absence of natural selection
Population is infinitely large, to avoid
effects of genetic drift
No mutation
No migration
< If assumptions are met, population will be in
genetic equilibrium
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Two expected predictions:

Allele frequencies do not change over generations

After one generation of random mating, genotypic
frequencies will remain in the following
proportions:
(frequency of AA)
p2
(frequency of Aa)
2pq
(frequency of aa)
q2
*p = allelic frequency of A
*q = allelic frequency of a
*p2 + 2pq + q2 = 1
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population is at equilibrium
A(p)=0.5
a(q)=0.5
A(p)=0.5
AA(p2)
0.5 x 0.5 = 0.25
Aa(pq)
0.5 x 0.5 = 0.25
a(q)=0.5
Aa(pq)
0.5 x 0.5 = 0.25
aa(q2)
0.5 x 0.5 = 0.25
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Random Mating:
Mating Type Frequencies
P2
2PH
2PQ
H2
2QH
Q2
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Mendelian Segregation:
Offspring Genotype Frequencies
Total
P2
P2
2PH
2PQ
H2
2QH
Q2
PH
1
_
¼ H2
_
_
p2
_
PH
2PQ
½ H2
QH
_
2pq
_
_
_
¼ H2
QH
Q2
q2
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Conclusion

Genotype frequencies are function of
allele frequencies
Equilibrium reached in one generation
 Independent of initial genotype
frequencies
 Random mating, etc. required


Conform to binomial expansion
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Simple HWE Exercise

If the defective alleles of the cystic
fibrosis (CFTR) gene have cumulative
frequency of 1/50 what is:

The proportion of carriers in the
population? p=P+1/2H H=2pq=2(p-P)=0.04
p=0.98

P=0.96
q=0.02
Q=0.0004
The proportion of affected children at
birth?
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Frequencies of genotypes AA, Aa, and aa relative to the
frequencies of alleles A and a in populations at HardyWeinberg equilibrium
Max. heterozygosity
p = q = 0.5
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Hardy-Weinberg for loci with more
than two alleles:

For three alleles (A, B, and C) with frequencies p, q, and r:

Binomial expansion 

(p + q + r)2 = p2(AA) + 2pq(AB) + q2(BB) + 2pr(AC) +
2qr(BC) + r2(CC)

For four alleles (A, B, C, and D) with frequencies p, q, r,
and s:

(p + q + r + s) 2 = p2(AA) + 2pq(AB) + q2(BB) + 2pr(AC) +
2qr(BC) + r2(CC) + 2ps(AD) + 2qs(BD) + 2rs(CD) + s2(DD)
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Hardy-Weinberg for X-linked
alleles (1):
e.g., Humans and Drosophila (XX = female, XY =
male)
XA(p)
Xa(q)
Y
XA(p)
XAXA
p2
XAXa
pq
XAY
p
Xa(q)
XAXa
qp
XaXa
q2
XaY
q
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Hardy-Weinberg for X-linked
alleles (2):







Females
Hardy-Weinberg frequencies are the same for
any other locus:
p2 + 2pq + q2 = 1
Males
Genotype frequencies are the same as allele
frequencies:
p+q=1
Recessive X-linked traits are more common
among males.
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Checking Hardy-Weinberg
Equilibrium


A common first step in any genetic study is to
verify that the data conforms to Hardy-Weinberg
equilibrium
Deviations can occur due to:
 Systematic errors in genotyping
 Unexpected population structure
 Presence of homologous regions in the
genome
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Testing
Hardy Weinberg Equilibrium

Consider a sample of 2N alleles

nA alleles of type A
nB alleles of type B




nAA genotypes of type AA
nAB genotypes of type AB
nBB genotypes of type BB
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nA= nAA + ½ nAB / N
nB= nBB + ½ nAB / N
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Simple Approach

Calculate allele frequencies (o) and
expected counts (e)

Construct chi-squared test statistic

Convenient, but can be inaccurate:

especially when one allele is rare
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