MSc in Genetics - UABbioinformatica.uab.es/base/documents/masterGP/Population...MSc in Genetics...

Antonio Barbadilla

Group Genomics, Bioinformatics & Evolution

Institut Biotecnologia I Biomedicina

Departament de Genètica i Microbiologia

UAB

Course 2012-13 1

Population Genomics: Theory

MSc in Genetics

MSc in Genetics Module Genomics & Proteomics

Antonio Barbadilla Population Genomics: Theory

2 Antonio Barbadilla

Outline

Population thinking: population genetics

The explanation of genetic variation: neutral theory and selection

Detecting natural selection at the nucleotide level: The MKT

Measures of nucleotide variation

Linkage disequilibrium

The golden age of population genetics

Cataloguing nucleotide variation at the genome scale

Exercices



3 3 Antonio Barbadilla Lesson 6. Genome variation: I. nucleotide variation



4 Antonio Barbadilla Lesson 6. Genome variation: I. nucleotide variation

Genetic variation is the

cornerstone of biological

evolution

R. C. Lewontin



5 Antonio Barbadilla

A G A G T T C T G C T C G A G G G T T C T G C G C G A G T G T T C T G C G C G

Origin and

substitution of genetic variants

within populations

Evolution



6

Population is the substrate where evolution occurs



Nothing in Biology Makes Sense Except in the Light of Evolution

Theodosious Dobzhansky

Nothing in Evolution Makes Sense Except in the Light of Population Genetics

Michael Lynch

Evolution and population genetics



8

Population is the substrate where evolution occurs

Mendelian population: a group of interbreeding individuals sharing a common gene pool



•Genetic variation or genetic polymophism: Existence in a population of two or more allelic forms in appreciable frequencies

•Gene or allelic frequency (population property, basic unit of evolution): f(A) proportion of an allele in the population

One gene, two alleles case A and a How does allelic frequency

change over time?

Hardy-Weinberg equilibrium law plays the role of the inertia principle in Dynamics: if not force is acting on the population, allelic and genotypic frequencies remains unchangable over time.

Sperm

Egg

AA p2

Aa pq

Aa pq

aa q2

A

p a

q

a q

A p

Allelic frequencies

Hardy-Weinberg law assumes that alleles of a infinite population unite at random to form genotypes of the next generation

9



The problematic of population genetics is the description and explanation of genetic variation within and between populations

Theodosious Dobzhansky

Population genetics



The theory of population genetics

Ronald Fisher J. B. S. Haldane Sewall Wright

Founders of Population Genetics

(1918-1932)

Genetic Drift

Natural Selection

Mutation

Migration

Factors changing gene frequencies in populations

Structure of population genetics

A theory of forces



1

3 2

The struggle for the measurement of genetic variation



13

The Great Obsession of population genetics (Gillespie 2004) What evolutionary forces led to the observed pattern of genetic variation?



H. J. Muller

Teorías de la variación en los 60

•Ausencia de variación

•Selección purificadora

•Genotipo salvaje es óptimo

•Muller (laboratorio)

•Eugenesia

•Variación ubicua

•Selección equilibradora

•No existe un genotipo salvaje

•Dobzhansky (naturalista)

•¡Viva la diversidad!, no interferencia

Teoría clásica Teoría equilibradora



60-70

•Electropheretic variation

The struggle for the measurement of genetic variation



16

Neutral theory of molecular evolution (1968)

Motoo Kimura

Mutations are mainly neutral or strongly deleterious

Tomoko Ohta

0 0

DGRP Freeze 1 Patterns polymorphism and divergence

along chromosome arms in D. melanogaster

PopDrowser -> http://popdrowser.uab.cat;

2L 2R 3L 3R X Tel Cen Cent Tel Cen Cen Cen Tel Tel Cen

Genome variation data

http://dgvbrowser.uab.cat/






20

Neutral theory of molecular evolution



21 21 Antonio Barbadilla Lesson 6. Genome variation: I. nucleotide variation

Schrödinger equation (general)

F = ma (Newton’s dynamics 2nd law)



Nature of genetic variation

Mutation

=

Individual

Substitution

=

Population



23



24



Allelic frequency

Time

1

0

gen.4Nt fix

Dynamics of neutral substitutions

Neutral theory of molecular evolution Assumption

New mutations are mainly neutral or strongly deleterious

µ

ln2 Ntlost

•Polymorphism •Heterozygosity in the equilibrium H = = 2N x 2N µ = 4N µ



26

µ N



Polymorphism and divergence are coupled

Species A Species B

Species B

Species A

Substitution Substitution => divergence

Time from separation




Polymorphism and divergence are coupled

Species A

• Divergence increases over time

D = 2Tµ

• Polymorphism reaches a dynamic equilibrium

H = = 4N µ


Species B



29



Allelic frequency

Time

1

0

The intellectual elegance of Neutral theory: Play the role of null hypothesis

The Myth of Sysiphus and molecular evolution



II: Mutaciones selectivamente ventajosas

gen. )2ln(2

Ns

t

1

0

4Ns

1

Dynamics of selective advantage mutations

Allelic frequency

Time



How to detect positive (adaptive) selection in a background of neutral mutations?



33

•Divergence • K = µ

•Polymorphism • Neutral heterozygosity = 4N µ



34

Synonymous and non-synonymous sites

C T T C T A

C T T C C T

non-synonymous site

synonymous site

Leu

Leu Pro

Leu

http://www.google.es/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=kfld1wclhgdMDM&tbnid=-_lDNSFmTwzXpM:&ved=0CAUQjRw&url=http://www.chemguide.co.uk/organicprops/aminoacids/dna4.html&ei=BQCdUaa8PKO50QXAy4DACg&bvm=bv.46751780,d.ZGU&psig=AFQjCNFk7C5lzT_cFQMXYC6t8Ya96MCWXw&ust=1369330036556345



How to detect adaptive fixation in a class of sites? •Neutral hypothesis: Correlation polymorphism and divergence •Adaptive hypothesis: adaptive fixation uncouples divergence and polymorphism

McDonald, J. H. Y M. Kreitman. 1991. Adaptive protein evolution at the Adh locus in Drosophila. Nature 351: 652-654.

McDonald and Kreitman Test (MKT)

Fixation by positive (adaptive) selection

Fixation by neutral process

Neutral sites (synonymous sites)

Putative positive selected sites (non-synonymous sites)



McDonald-Kreitman test (MKT)

K Kneut μneut

Ratio divergence = ω =

i 4Nμneut_i neut 4Nμneut

Ratio polymorphism =

= 4Nμ k = μ

Neutral expectance

i = non-synonymous or putative selected sites

=

Only neutral fixation

= μneut_i

= μ neut_i

μneut



Extended McDonald-Kreitman test (ext MKT)

i neut

= ki kneut

Only neutral fixation

+ Adaptive fixation i neut

< ki kneut



Fixed Polymorphic Synonymous Ds Ps Non-synonymous Dn Pn

•Null hypothesis: the proportion of fixed versus polymorphic mutations is the same for synonymous and non-synonymous mutations.

•G or 2 test: variants are classified as (1) fixed or polymorphic; or (2) synonymous or non-synonymous

MKT Chi-square table. Observed (Expected) segregating sites

Relative excess suggests directional selection

Dn Relative excess suggests directional selection or purifying selection

Pn



Structure of gene Adh (256 codons)

Exon 1 Exon 2 Exon 3 Exon 4

3’ 5’

Adh Gene of Drosophila melanogaster Kreitman, M. 1983. Nucleotide polymorphism at the alcohol dehydrogenase locus of Drosophila melanogaster. Nature 304: 412-417.

•13 synonymous polymorphism

•1 non-synonymous polymorphism



Fixed Polymorphic Non-synonymous 7 (3,2) 2 (5,8) Synonymous 17 (20,8) 42 (38,2)

G = 7,43 or X2

= 8,1 **

Polymorphism and divergence in locus Adh for closely related species of Drosophila melanogaster, D. simulans and D. yakuba

•Null hypothesis: the proportion of fixed versus polymorphic mutations is the same for synonymous and non-synonymous mutations.

•G or 2 test: variants are classified as (1) fixed or polymorphic; or (2) synonymous or non-synonymous

MKT Chi-square table. Observed (Expected) segregating sites



41

Exercise 1: Go to the Web page Standard & Generalized MacDonald-Kreitman test (http://mkt.uab.cat). Test the examples and try to understand the difference between the standard and generalized MKT. Which is the parameter alpha whose value is given in the results of the test. How do you would estimate it?

Figure 1

http://mkt.uab.cat/

http://mkt.uab.cat/

http://mkt.uab.cat/

http://mkt.uab.cat/

http://mkt.uab.cat/

http://mkt.uab.cat/

http://mkt.uab.cat/



42



43



G

C

Single nucleotide polymorphism (SNP)

44



Nature and classification of Single Nucleotide Polymorphism (SNP)

•A nucleotide change •Transversion-Transition | Indel

•Changes of two o few nucleotides or indels – >

Simple Nucleotide Polymorhism

•Coding SNP •Synonymous •Non synonymous or replacement

•Non-coding SNP: CNS, 5’ and 3’UTR, intron, 5’ and 3’ intergenic

Classification

45



Description levels of genetic variation

SNPs BRCA2

Individual 1 acgtagcatcgtatgcgttagacgggggggtagcaccagtacag



Individual 4 acgtagcatcgtttgcgttagacgggggggtagcaccagtacag

Individual 5 acgtagcatcgtttgcgttagacgggggggtagcaccagtacag

Individual 6 acgtagcatcgtttgcgttagacggcatggcaccggcagtacag




one-dimensional: SNP to SNP

multi-dimensional: Haplotype

46



SNPs per 10000 bases along the human chromosome 6 (2001 Nature 409: 928-941)

HLA

47



Functional genome regions

48



49

• Number of segregating sites per nucleotide (Watterson 1975):

S/m • Watterson Ѳ estimator (1975):

Ѳw = (S/m) / 1/𝑖𝑛−1𝑖=1

• , nucleotide diversity o expected nucleotide

heterozygosity (Tajima 1983): average number of differences by site among pair of randomly samples sequences

= 1𝑛2𝑚 𝑘𝑖𝑗

𝑛𝑗=𝑖+1

𝑛−1𝑖=1

S = number segregating sites m = number of nucleotides analyzed n = sample size (number of sequences)

𝑘𝑖𝑗 is the number of differences between sequence i and j



50

Site frequency spectrum



Nucleotide variation in gen Rhodopsin 3 of Drosophila simulans

Data summary: Sample n = 5 sequences. Size m = 500 nucleotides

•Number of segregating sites per nucleotide: 16/500 = 0.0320

•Watterson Ѳ estimator = Ѳw = (16/500)/(1+1/2+1/3+1/4) = 0.0154

•Diversidad nucleotídica: = 79/(500 x 10) = 0.0158

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 T C T A C C T C C T C G G T T A

2 T C C T A C C T C C T G G T T T

3 C T C C C C C T C T T T G C T A

4 C T C C C C C T T C T G A C T T

5 C T C C C T C T T T T G G C C A

6 6 4 7 4 4 4 4 6 6 4 4 4 6 4 6



52

Exercise 2: Given the data set of DNA sequences of Figure 1 and 2 below: • Estimate the most common measures or summary statistics of nucleotide variation (S/m, Ѳw , and the site frequency spectrum)

Sequence 1 … A … G … C … G …

Sequence 2 … A … G … T … G …

Sequence 3 … A … A … T … T …

Sequence 4 … T … G … T … T …


Figure 1

Figure 2



53

Exercise 1: Given the data set of DNA sequences of Figure below: • Estimate the most common summary statistics of nucleotide variation (S/m, Ѳw , and the site frequency spectrum)

Sequence 1 … A … G … C … G …

Sequence 2 … A … G … T … G …

Sequence 3 … A … A … T … T …



0

0,5

1

1,5

2

2,5

0.2 0.4

Site frequency spectrum

Number of SNPs

Minor allele frequency

S/m = 4/m Ѳw = (4/m) / [1 + (1 / 2) + (1 / 3) + (1 / 4) = (4/m) / 2.083] = (6+4+4+6)/(m x 10)=2/m

Responses



54

Software for estimation of nucleotide variation DnaSP — DNA Sequence Polymorphism, is a software package for the analysis of nucleotide polymorphism from aligned DNA sequence data. Variscan is a software package for the analysis of DNA sequence polymorphisms at the whole genome scale. MEGA, Molecular Evolutionary Genetics Analysis, is a software package used for estimating rates of molecular evolution, as well as generating phylogenetic trees, and aligning DNA sequences. Available for Windows, Linux and Mac OSX (since ver. 5.x). Arlequin3 software can be used for calculations of nucleotide diversity and a variety of other statistical tests for intra-population and inter-population analyses. Available for Windows.

http://www.ub.es/dnasp/

http://www.ub.edu/softevol/variscan/

http://www.megasoftware.net/

http://cmpg.unibe.ch/software/arlequin3/



First estimates of nucleotide diversity in the Drosophila genus

Species Number of

genes

No coding region

Coding region Total Synonymous



First estimates of nucleotide diversity in the human genome

Nucleotide diversity (π) Density SNP number Chromosome

Autosomes 1-22



57



Multidimensional structure of genetic variability

A G A G T T C T G C T C G

A G G G T T C T G C G C G A G G G T T A T G C G C G

A G A G T T C T G C T C G A G A G T T C T G C T C G

A G A G T T C T G C T C G

A G A G T T C T G C T C G A G A G T T C T G C T C G

A G G G T T A T G C G C G A G G G T T A T G C G C G A G G G T T A T G C G C G

A G G G T T A T G C G C G

A G G G T T A T G C G C G

58



Linkage disequilibrium (D’ Lewontin)

B1 B2 Total

A1 p11 = p1q1 + D p12 = p1q2 - D p1

A2 p21 = p2q1 - D p22 = p2q2 + D p2

Total q1 q2 1

2. D’ = D / Dmax

1. DAB = pAB - pApB

3. r2AB = D2/ [pA(1-pA) qB(1-qB)]

(Lewontin & Kojima 1960)

(Lewontin 1964)

(Hill & Robertson 1968)




D = 0.5625 – 0.625 x 0.6875 = 0.1328

p1 ^ = n1. /2n = 10 / 16 = 0.625

q1 = n.1 /2n = 11 / 16 = 0.6875 ^

Χ2 = 5.606 > 3.84 *

B1 B2 Total

A1 9 1 10

A2 2 4 6

Total 11 5 16




D’ = 0.1328 / 0.1953 = 0.68

p1 q2

p2 q1

= 10/16 x 5/16

= 6/16 x 11/16

r212 = D2/ [p1 p2 q1 q2)] = 0.3502

B1 B2 Total

A1 9 1 10

A2 2 4 6

Total 11 5 16



c

c

c

c

Recombinaton and

linkage disequilibrium

DAB (t + 1) = (1 – c) DAB (t )

62

c = recombination rate




Linkage blocks

&

Tag SNPs

Linkage disequilibrium distribution along the human lipase lipoprotein gene (LPL). 66

SNPs around 10 kb of 142 chromosomes 63



64



65

The golden age of the study of genetic variation



Description and explanation of patterns of nucleotide variation at a large scale

• Patterns of polymorphism and divergence

• Neutral vs Selection variation (adaptive evolution)

Explanation of the genome complexity from first population

genetic principles (sensu M. Lynch)




Comparative and Functional Genomics

• Role of conserved and fast-evolution non-coding regions

Catalogue of human genetic variation and association studies genotype -> phenotype

• HapMap, Biobanks, GWAS

• Personalized Genomics




68

Exercise 2: Estimate manually the most common measures or summary statistics of nucleotide variation (S/m, Ѳw , p and the site frequency spectrum) and the three measures of linkage disequilibrium (D, D' and r2) for the 8 aligned sequences given below. m, the analyzed sequence length, is 100. Only variable sites are shown.

Sequence 1 … A … G … C … G … Sequence 2 … A … G … T … G … Sequence 3 … A … A … T … G … Sequence 4 … T … G … T … T … Sequence 5 … T … G … T … T … Sequence 6 … T … G … C … T … Sequence 7 … T … G … T … T … Sequence 8 … T … G … T … T …

Exercise 1: Go to the Web page Standard & Generalized MacDonald-Kreitman test (http://mkt.uab.cat). Test the examples and try to understand the difference within the standard and generalized MKT. Which is the parameter alpha whose value is given in the results of the test. How do you would estimate it?

Exercices

http://mkt.uab.cat/



69

> ki kneut

i neut <

=

+ Adaptive fixation +Weakly negative

selection

Exercices

Exercise 3: Consider that adaptive and weakly deleterious selection are acting in a DNA sequence. If you want to perform a MKT, search for a statistical approach to take into account the weakly negative selection to detect adaptive selection.



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• Population genomics in Drosophila: T.F.C. Mackay*, S. Richards*, E.A. Stone*, A. Barbadilla*, M. Barrón, D. Castellano, P. Librado, M. Ràmia, J. Rozas et al. 2012. The Drosophila melanogaster Genetic Reference Panel: A Community Resource for Analysis of Population Genomics and Quantitative Traits. Nature 482: 173-178.

• 1000 genome project: The 1000 Genomes Project Consortium. 2012. An integrated

map of genetic variation from 1,092 human genomes. Nature 491: 56-65.

Readings

http://www.nature.com/nature/journal/v482/n7384/full/nature10811.html




ftp://ftp.1000genomes.ebi.ac.uk/vol1/ftp/phase1/analysis_results/paper/1000genomes_phase1_nature11632.pdf



MSc in Genetics - UABbioinformatica.uab.es/base/documents/masterGP/Population...MSc in Genetics...

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