How could you test with a statistical test if there is an association between Gcn4pupstream vs. ORF binding and gene expression?

1. T-test to see if mean fold-change upon amino acid starvation is different for genesbound upstream vs. in ORF by Gcn4p

2. Hypergeometric test to see if upstream-bound genes are enriched for ‘induced’ genes(would require pre-determining which genes are ‘induced’)

Genetic mapping: linking phenotype to genotype

Lab studies of gene knockouts, RNAi, and mutagenesis screens can reveal phenotypes

A major goal is to do the reverse: use natural phenotypic variation to identify causal variants

reveals phenotypic and genetic variation relevant in ‘the wild’

Goal: Identify QTL (Quantitative Trait Locus) or QTN (Quantitative Trait Nucleotide)that significantly correlate with (and there likely explain) the phenotype

Linkage Mapping

Mate two parents with oppositephenotypes and score progeny

Association Mapping (GWAS)

Score many individuals fromnatural (randomly mating) populations

Ability to identify QTL/QTLs requires recombination to mix and match the genomes.

Linkage mapping: generate recombination through crosses. Generally need many individuals(or many generations: increased recombination frequency = smaller regions)

Association mapping: uses historical recombination events between individuals. Generallyrequires fewer individuals for the same statistical power.

Two strategies for genetic mapping

4

Goals of QTL linkage mapping

Ades 2008, NHGRI

To identify the loci that contribute to phenotypic

variation

1. Cross two parents with extreme phenotypes

2. Phenotype all the progeny

3. Genotype the progeny at markers across the genome

4. Associate the observed phenotypic variation with the underlying genetic variation

5. Ultimate goal: identify causal polymorphisms that explain the phenotypic variation

5

Backcross

Broman and Sen 2009

Phenotype: Drug tolerance

80% 20% viability

Usually have at least 100 individuals

6

Intercross

Broman and Sen 2009

Phenotype: Drug tolerance

80% 20% viability

Can reveal AA, BB, and AB genotypes. Takes more individuals

to map, due to more intricate genotypes generated

7

Genetic map: specific markers spaced across the genome

Markers can be:

• SNPs at particular loci

• Variable-length repeatse.g. ALU repeats

• ALL polymorphisms (if have whole genomes)

Ideally, markers shouldbe spaced every 10-20 cM

and span the whole genome

8

Genotype data: Determine allele at all markers in each F2

Phenotype:e.g. drug

tolerance score

9

Statistical framework

Broman and Sen 2009

1. Missing Data ProblemUse marker data to infer intervening genotypes

2. Model Selection ProblemHow do the QTL across the genome combine with the

covariates to generate the phenotype?

10

Marker regression: simple T-test (or ANOVA) at each marker

Marker 1: no QTL Marker 2: significant QTL (population means are different)

11

Marker regression

• Simple test – standard T-test/ANOVA

• Covariates (e.g. Gender, Environment) are to incorporate

• No genetic map necessary, since test is done separately on each marker

Advantages:

Disadvantages:

• Any individuals with missing marker data must be omitted from analysis

• Does not effectively consider positions between markers

• Does not test for genetic interactions (e.g. epistasis)

• The effect size of the QTL (i.e. power to detect QTL) is reduced by incomplete linkage to the marker

• Difficult to pinpoint QTL position, since only the marker positions are considered

12

Interval mapping

• In addition to examining phenotype-genotype associations at markers, look for associations between makers by inferring the genotype

A A A A

Q

• The methods for calculating genotype probabilities between markers typically use hidden Markov models to account for additional factors, such as genotyping errors

• Lander and Botstein 1989

13

Interval mapping

• Takes account of missing genotype information – all individuals are included

• Can scan for QTL at locations in between markers

• QTL effects are better estimated

Advantages:

Disadvantages:

• More computation time required

• Still only a single-QTL model – cannot separate linked QTL or examine for interactions among QTL

14

LOD scores

• Measure of the strength of evidence for the presence of a QTL at each marker location

LOD(λ) = log10 likelihood ratio comparing the hypothesis of a QTL at position λ versus that of no QTL

Pr(y|QTL at λ, µAAλ, µABλ, σλ)Pr(y|no QTL, µ, σ) { }log10

Phe

noty

pe LOD 3 means that the TOP model is 103 times more likely than

the BOTTOM model

15

LOD curves

How do you know which peaks are really significant?

Chromosome

16

LOD threshold

Broman and Sen 2009

•Consider the null hypothesis that there are no QTLs genome-wide

one locationgenome-wide

1. Randomize the phenotype labels on the relative to the genotypes2. Conduct interval mapping and determine what the maximum LOD score is

genome-wide3. Repeat a large number of times (1000-10,000) to generate a null distribution

of maximum LOD scores

17

LOD threshold

• 1000 permutations10% False Discovery Rate = LOD 3.19

(means that at this LOD cutoff 10% of peaks could be random chance)

5% FDR = LOD 3.52

• Boundary of the peak is often taken as points that cross (Max LOD – 1.5) (or - 1.8 for an intercross)

Association Mapping

Relies on historic matings in “randomly mating” populations.

Most populations are not randomly mating – therefore need to consider population structure.

Haplotype blocks:linked alleles

segregating togethermeans that onlysubsets of SNPs

need to be genotyped.

0.0000 0.2000 0.4000

Stra

ins

TASSEL: Trait Analysis by aSSociation, Evolution and Linkage

Bradbury et al. (Buckler Lab)

Genotypes for 65 strains

Phenotypes for 65 strains

Population Structure

PhylogeneticRelatedness

RandomError

RandomError

Dana Wohlbach

Association Mapping-lo

g p-

valu

eFDR threshold set by permutation analysis or q value correction

Meta-analysis of 15 GWAS studies of IBD = 75,000 people.- Imputation-based GWAS: imputed SNPs where there was missing data

(using known haplotypes and human HapMap3 reference data)

- Identified 25,075 SNPs that were significantly associated with IBD (p < 0.01)… collapsed these into 163 IBD-associated loci

* 71 of these are new, due to increased statistical power* 163 loci is “far more” than associated with any other complex disease* More SNPs are linked to non-coding/regulatory variation than missense

- Significant overlap with SNPs linked to immunodeficiences & bacterial infection

- 13.6% of the phenotypic variance is explained by all these loci together

The challenge with human GWAS: missing heritability

PNAS 2011

They argue much of the “missing” heritability is not really missing: additive interactions(without considering epistasis) can only account for so much …

>1200 variants associated with ~165 complex human diseases.

In most cases, known loci account for only 20-30% of the heritable phenotypic variance.

Significant SNP (FDR 1%)Insignificant SNP

Investigating Epistasis: Genetic Interactions?

Linear model foreach pair of

significant SNPs

How much of ‘missing’heritability is explained

by epistasis?

Dana Wohlbach

Many significant interactions between SNPs

Significant SNP (FDR 1%)Insignificant SNP

Dana Wohlbach

0.1% FDR (82 pairs)1.0% FDR (413 pairs)Genetic or Physical (SGD)

Significant interaction at: