GWAS --- 15 years and on

The very first GWAS was published in 2005 about age-related macular degeneration.

Klein, et al., 2005, Science

GWAS --- 15 years and on

• More than 4,300 papers have reported on 4,500 GWAS studies

• Over 55,000 unique loci for nearly 5,000 diseases and traits

User-friendly data portals to query GWAS results

• GWAS catalog: a searchable database of SNP-trait association

• PhenoScanner: a curated database holding publicly available GWAS results

• GTex (Genotype-Tissue Expression) eQTL Browser: is a resource to study human gene expression and regulation and its relationship to genetic variation

• ENCODE: Encyclopedia of DNA elements, including elements that act at the protein and RNA levels, and regulatory elements.

Loos, 2020, Nature Communications

The driving forces for GWAS

• The decreasing cost of genome-wide genotyping

  • Now >20 times less expensive than 15 years ago

• The number of variants tested has increased

  • In human study, from ~500k variants in the early days to nearly 10 million in the lastest GWAS

• More refined phenotypes

  • Such as imaging-derived traits and multi-Omics outcomes (i.e., gene expression as a trait for GWAS)

• Advanced statistical analyses and sophisticated modeling

  • Multivariate GWAS to identify loci that affect multiple traits simultaneously
  • Integrate intermediate Omics data to conduct causal inference

    Z. Yang et al., 2022

Validation of GWAS results

Identifying GWAS loci is only the first step of a long journey

Translation of genetic loci into new biological insights

• Integrate multi-Omcis data

• Targeted molecular experiments is critical to establish the role of the prioritized genes.

Implement the knowledge into breeding practice

• Marker assistant selection (using large effect markers only)

• Genomic selection (using all genome-wide markers)

Steps for conducting GWAS

Uffelmann et al., 2021

Testing for associations

A quantitative trait is sometimes controlled jointly by

• major QTLs with large effects
• minor QTLs with small effects

Prevent Shrinkage

If markers that correspond to the major QTLs are known

• Then these markers can be treated as having fixed effects

  • It will prevents shrinkage of their estimates

• The remaining markers can be treated as having random effects

  • Their effects can still be estimated through RR-BLUP or other approaches.

Linear Mixed Model (LMM)

$$\begin{align*} \mathbf{y} &= \mathbf{Xb} + \mathbf{Zm} + \mathbf{e} \\ \end{align*}$$

$$\begin{align*} V(\mathbf{m}) &= \mathbf{I}V_{M_i} \\ & = \mathbf{I}(V_{G}/n_M) \end{align*}$$

Fit a marker as a fixed effect

With some modification of the above LMM model, a mixed-model approach can be used for association mapping:

$$\begin{align*} \mathbf{y} &= \mathbf{Xb} + \mathbf{w_i}m_i + \mathbf{Zm^*} + \mathbf{e} \\ \end{align*}$$

• Where $\mathbf{m_i}$ is the fixed effect due to the $i$th SNP marker
• $\mathbf{w_i}$ is an incidence vector for the SNP marker

G Model

$$\begin{align*} \mathbf{y} &= \mathbf{Xb} + \mathbf{w_i}m_i + \mathbf{Zm^*} + \mathbf{e} \\ \end{align*}$$

• Where $\mathbf{m_i}$ is the fixed effect due to the $i$th SNP marker
• $\mathbf{w_i}$ is an incidence vector for the SNP marker

This G model utilizes marker effects to account for variation due to QTL found on the background chromosomes.

Bernardo, 2013

• Like the QTL composite interval mapping approach

• The disadvantage of this type of approach is the uncertainty in how many background markers should be included.

  • If too few, the background variation will be underestimated

  • If too many, overfitting the model.

K model for GWAS

$$\begin{align*} \mathbf{y} &= \mathbf{Xb} + \mathbf{w_i}m_i + \mathbf{Zu} + \mathbf{e} \\ \end{align*}$$

In this LMM, the covariance matrix of $\mathbf{u}$ becomes equal to $\mathbf{A}V_A'$

• Where $\mathbf{A}$ is the additive relationship matrix, or kinship ( $\mathbf{K}$ ) matrix

• And $V_A'$ is the portion of the additive variance that is not accounted for by $\mathbf{m_i}$

In practice, $V_A'$ will need to be estimated by an iteractive procedure.

Multiple marker model

With multiple SNP markers

• $\mathbf{w_i}$ => an incidence matrix $\mathbf{W}$

• $m_i$ => a vector of $\mathbf{m}$

Multiple marker GWAS model

$$\begin{align*} \mathbf{y} &= \mathbf{Xb} + \mathbf{Wm} + \mathbf{Zu} + \mathbf{e} \\ \end{align*}$$

A two-step approach

• First, a single marker is included at a time

  • The significance of individual marker effects is then tested by z-tests

• Second, the markers found significant in the single-marker analyses are included in a multiple-marker model.

  • A standard model-selection procedure, such as backward elimination, maybe used to determine which markers should be incorporated in the final multiple-marker model.

Multiple sub-populations

In breeding context, we define each germplasm group or heterotic pattern as a subpopulation of the larger pool of inbred, hybrids, or clones.

• In maize, dent (Iowa Stiff Stalk Synthetic, BSSS) and flint (non-BSSS)

• Barley inbreds comprise six-row and two-row types

Population structure

• Separate analysis: One-subpopulation-at-a-time approach

• Joint analysis to account for the differences between the subpopulations

QK model for multiple sub-populations

K model

$$\begin{align*} \mathbf{y} &= \mathbf{Xb} + \mathbf{w_i}m_i + \mathbf{Zu} + \mathbf{e} \\ \end{align*}$$

QK model

$$\begin{align*} \mathbf{y} &= \mathbf{Xb} + \mathbf{Qv} + \mathbf{w_i}m_i + \mathbf{Zu} + \mathbf{e} \\ \end{align*}$$

• In this model, the effects due to different sub-populations are captured by $\mathbf{Qv}$

• The relatedness among lines within each sub-population is specified by the covariance matrix of $\mathbf{u}$.

Use PCA method to construct Q matrix

Price et al., 2006

Proposed a method to use principal component analysis (PCA) of marker-allele frequencies and the use of PCA scores as the $\mathbf{Qv}$ matrix.

What is in the Q matrix:

1. The columns in Q correspond to different PCA axes

2. The rows in Q correspond to PCA scores of the lines in $\mathbf{y}$

How many PCs?

• The first PC captures the largest amount of variation, and the 2nd captures the second-largest amount of variation, and so on.

• No fixed rule, but knowing the number of germplasm groups will help.

GWAS methods summary

K model

Account for relatedness using either pedigree records or marker data.

• Mainly $\mathbf{A}$ matrix (only considering additive relationship)

• $\mathbf{AD}$ matrix might be better

QK model

Account for effects of subpopulations and the relatedness within each subpopulation

• K matrix estimated from marker better than from pedigres

  Stich et al., 2008; Yu et al., 2006

G model or QG model

Utilizes RR-BLUP marker effects to account for variation due to QTL found on the background chromosomes.