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Population Genetics

Dr Pupak Derakhshandeh-Peykar, PhD

Ass Prof of Medical Science of Tehran University

Ref.: Population and Evolutionary Ref.: Population and Evolutionary Genetics: A primerGenetics: 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 diversityGenetic drift genetic diversity

Migration genetic diversity

Non-random genetic diversity

mating

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What's the most important factor in evolution?

SELECTIONSELECTION 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. Descent with Modification from Common Ancestor

2. Diversity is result of Differential Survival 3. and/or Differential Reproduction among

individuals4. 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 Evolutionby 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=

= هدفدار ن�ژاد اصالح

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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:Genes in Populations:

Hardy Weinberg Hardy Weinberg EquilibriumEquilibrium

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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 Types of measures of genetic variation (1)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 Types of measures of genetic variation (2)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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Properties of alleles in a population Allele frequencies Genotypes frequencies

Hardy-Weinberg equilibrium

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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 If there are n alternative alleles … … there will be n(n+1)/2 possible genotypes

Homozygotes 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 1908Hardy, 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 generationsAutosomal locusLarge populationRandom matingEqual 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:

p2(frequency of AA)

2pq(frequency of Aa)

q2(frequency of aa)

*p = allelic frequency of A*q = allelic frequency of a

*p2 + 2pq + q2 = 1

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population is at equilibrium

A(p)=0.5a(q)=0.5

A(p)=0.5AA(p2)0.5�x�0.5�=�0.25

Aa(pq)0.5�x�0.5�=�0.25

a(q)=0.5Aa(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

P2

2PH2PQ

H2

2QHQ2

P2

PHPH _

2PQ__

¼H2 ½H2 ¼H2

QH QH_

Q2_ _

_ _

Total 1 p2 2pq q2

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Conclusion

Genotype frequencies are function of allele frequencies

Equilibrium reached in one generationIndependent of initial genotype

frequenciesRandom 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=0.02Q=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 Hardy-

Weinberg equilibrium

Max. heterozygosityp = 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�

pqXAY�

p

Xa(q)XAXa�

qpXaXa�

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 genotypingUnexpected population structurePresence of homologous regions in the

genome

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TestingHardy 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