Understanding GWAS

Example

• At a given locus, there are three genotpyes (AA, AB, BB).
• They correspond to different trait values.
• Two possibilities - discrete/binary trait or continuous.
• Continuous:
  • The higher "B" allele, the higher the trait value (in this case, body size)
  • We can solve this with linear regression
• For a binary trait (e.g. color in two morphs), we just have the probability which is determined by the genotype
• This process is repeated across the genome for each SNP and the p-values are collected - then you determine how the different loci across the genome effect the trait and determine significance

Significance vs effect size

• After collecting all these p-values and determining which genes are most significantly correlated, we need to remember that this is different from the size of the effect
  • You could have a very strong correlation/significance between a certain allele and life expectancy, but the allele only changes life expectancy by 20 minutes.

One thing we haven't accounted for

!GenomicAnalysis_3_Cristofari, p.11
In this GWAS chart of a certain disease, you can see the significant loci are organized in these peakson different chromosomes. This is because of genetic linkage - these sites on separate chromosomes are close to each other and get mixed up during meiosis (recombination).

Genetic Linkage

• A happens as a single event in one chromosome in one cell.
• Most mutations happen in somatic cells, this is what can lead to cancer
• To be transmitted, the mutation needs to happen in a germline cell
  • In animals these are separate types of cell (gametes)
  • In plants, somatic cells can give rise to germline cells, so many more mutations can be transmitted.
• Meiotic recombination makes it so mutations in one haplotype can make the same mutation be "cut-and-pasted" into another haplotype and the linked location.
• Ones that are close together are very likely to be swapped in recombination, but ones that are futher away are more likely to be mixed in recombination.
  • When they are far enough away, we can consider them as independent from each other. This is linkage decay
• There is almost no recombination in the centromeres (center of the chromosome), or at the telomeres (edge of the chromosomes).
  • It mostly happens at "recombination hotspots" in between the centromeres or telomeres
  • We can calculate the "linkage distance" (probability of two alleles being reshuffled in the next generation)- 1 Morgan (M) means they will always be reshuffled (two different chromosomes)
  • Apparently this concept is seen as a bit outdated now and isn't in the literature much anymore

Marey maps

• These plots show the genetic distance in centimorgans vs physical distance in base pairs. It shows which part of the chromosomes have the most recombination

Conclusion

• Genetic linkage is a consequence of the fact that alleles exist on physical molecules of DNA
• The closer the alleles are physically, the more tightly they are linked (the same combination will be in many haplotypes/individuals)
• When they are further, they are more often separated in recombination
• If they are on separate chromosomes they are not linked at all

Linkage Disequilibrium

• When Natural Selection is happening on a new mutation, then surrounding linked loci are also propagated through the genome
  • These (usually neutral) alleles "hitch-hike" along with the beneficial mutation
• The target of selection is the new mutation, but the other neutral alleles come along with it because of linkage

Given this data, how do you determine which is the selected mutation?

• In the past we would just check which proteins are being coded for and see how this is affected
• However, now we know that the amount of available transfer RNA varies according to codon, so sometimes even if there is a protein being coded, it's not happening "fast enough".
• So the only real test is to do gene editing and measure effects in a wet lab.

After many generations

• Over time, due to linkage decay, the association between these alleles will break down.
  • At first, in the initial spread of mutation, there is a pretty wide area around the beneficial allele called the "LD block"
  • After millions of generations, the block begins to erode due to other recombination events so that only the beneficial mutation and its immediate neighbors are still associated with each other
    !GenomicAnalysis_3_Cristofari, p.30
    In the above chart, if we were plotting population allelic richness instead of linkage correlation, we would see the inverse of the chart but it would tell the same story.

Other effects on LD

• If we mix samples from different populations, association between different
• For example, if we have two populations that differ on one trait we are interested in. However due to drift the rest of the genome is also different.
  • So, when we look at the genetics, there appear to be a lot of other genes correlated with the trait. But in reality this is just due to drift since these are separate populations.
  • As ecologists this is a common problem when trying to find genetic basis for a trait between populations.

LD and GWAS

Two main effects

• A useful effect: We use LD to increase statistical power (QTL)
• A problematic effect: LD can cause "pseudoreplication" and mess up your whole analysis

Quantitative Trait Locus mapping (QTL)

• In this approach, we are searching for specific loci that affect a trait
• If we take two very inbred lines (fully homozygous) and cross them, we have a full heterozygote hybrid generation (F1)
• We should be able to predict the trait of the F1
• When we do a backcross, one chromosome must be exactly identical to the one from the parent line

Significance

• Let's saw we've done a GWAS and found that there are 10 SNPs that were significant. However, all of these SNPs are not independent to each other - they are linked. Therefore, these are not ten independent tests
• What's a p-value?
  • The chance of observing that strong of a test statistic (e.g. correlation coefficient) by chance if the null hypothesis is true.

First step: LD Pruning

• Pick one SNP and taking all the neighboring 50
• building a correlation matrix between them
• Remove any highly-correlated pairs of SNPs from your analysis
• Repeat for the next block of 50 SNPs until you've done the whole genome
  • This will leave only the "independent" SNPs

False Discovery Rate Correction

• After this, we can apply more statistical rigor by looking to see if there are false positives in our data
• If we run a simulation based on our null hypothesis, this will give us our expected significance at each p-value.
• The definition of a p-value = 0.05 tells us that 5% of sites will have a value at least that extreme. p=0.1 tells us 10% of sites will have this value.
• This is a uniform distribution - so if we plot the expected p-values (from a simulation) vs observed p-values on a Quantile-quantile (QQ) plot

QQ plot with true associations (2)

• If the QQ plot looks like this (note that the axis are $-{\log }_{10}(p)$):
  !GenomicAnalysis_3_Cristofari, p.42
  In this plot, around expected p-value is 0.01 ($-{\log }_{10}(p)=2$), this means that we have more highly significant sites compared with what is expected. We can highlight these values that differ strongly from the null line, this accounts for false positives/multiple testing.

Pathological QQ plot (p-value inflation)

!GenomicAnalysis_3_Cristofari, p.44
In this plot, the observed p-values are higher than expected by a constant amount, every site is more significant than expected. This probably means there is population structure in your data, for example if there are subpopulations, or you are sampling individuals from completely different populations.

Main Points (for the quiz)

• Linkage disequilibrium is either caused by:
  • Selection on a mutation - recombination means its nearby alleles are associated with it
  • Population structure (different subpopulations have different alleles due to genetic drift, these are associated with certain traits)
• p-values inflation occurs when there is population structure, this can be caused by a "hybrid zone" if you are sampling two different populations and treating them as one
  • So in the question where they ask about the causes of p-value inflation, you can pick both population structure AND hybrid zones
• If there is no heritability, there is no genetic component to the trait - therefore zero heritability will mean no linkage disequilibrium.
• I'm not sure, but I think that LD should be inversely proportional to both effective population size $N_e$ and recombination rate $r$:

- This would mean that to get the same LD with $2N_e$, we would need $0.5r$.
- This one was a bonus question anyways