Introduction

This report summarizes the analysis workflow and results of an analysis of SNPs from the 1000 Genomes Project.

Data preparation

Obtaining and loading data

Single Nucleotide Polymorphism (SNPs) data in VCF format were obtained from the 1000 Genomes Project.

SNPs were downloaded using the Ensembl Data Slicer from chromosome 18 between genomic coordinates 31,462,906 and 31,702,906. A total of 6988 variants genotyped in 2504 individuals were downloaded.

The VCF file was loaded into R using the vcfR package (function read.vcfR) and converted to counts of the minor allele using the function vcfR::extract.gt().

Meta-data and sample information

Meta Data for this project if from the 1000genomes project. Each individual has been anonymized behind a sample ID. However for each ID we have information on their local population (country), super population (region), sex, longitude and latitude. This allows for us to analyze differences/similarities in population groups

These SNPs were then screened for any SNPs that were invariant (fixed), resulting in removal of 1721 SNPs (features). This was done using the invar_omit() function by Nathan Brouwer. There were no NA’s found in any SNP column, thus no imputation had to occur on this data set.

The data was then centered and scaled using R’s scale() function. (Alternatively a SNP-specific centering technique common in other studies could have been applied).

The data were then saved in .csv format using write.csv() for PCA analysis.

After final processing the data contained 5267 SNPS and 2504 samples (people).

Data Analysis

The code below carries out a PCA on the data and presents the results. The key steps are:

  1. Load the data with read.csv().
  2. Process the data with prcomp().
  3. Extract PCA scores.
  4. Carry out PCA diagnostics, including construction of a scree plot.
  5. Plot PCs 1 through 3 as scatterplots as pairwise scatterplot.
  6. Plots PCS 1 through 3 as a 3D scatterplot.

Packages

The following packages were used in this analysis:

# plotting:
library(ggplot2)
library(ggpubr)

# scores() function
library(vegan)
## Loading required package: permute
## Loading required package: lattice
## This is vegan 2.6-4
# 3D scatter plot
library(scatterplot3d)

Loading data

Load the fully processed data:

NOTE: with ~6,000 SNPs, this CSV is ~250 megabytes. There are more specialized packages for doing PCA with datasets this big. I do not recommend working with more than 10,000 SNPs with basic R functions as we have done in class.

vcf_scaled <- read.csv(file = "ity1_clean_data.csv")

Check the dimensions of the data to confirm this is the correct data:

# 2504 Samples
# 5267 SNPS + 6 columns of metadata = 5273
dim(vcf_scaled)
## [1] 2504 5273

Principal Components Analysis

The data are scaled and ready for analysis. Only the first 6 columns contains character data and needs to be omitted.

head(vcf_scaled[,1:10])
##    sample pop super_pop    sex      lat       lng          X5          X6
## 1 HG00096 GBR       EUR   male 52.48624 -1.890401 -0.06641229 -0.03999201
## 2 HG00097 GBR       EUR female 52.48624 -1.890401 -0.06641229 -0.03999201
## 3 HG00099 GBR       EUR female 52.48624 -1.890401 -0.06641229 -0.03999201
## 4 HG00100 GBR       EUR female 52.48624 -1.890401 -0.06641229 -0.03999201
## 5 HG00101 GBR       EUR   male 52.48624 -1.890401 -0.06641229 -0.03999201
## 6 HG00102 GBR       EUR female 52.48624 -1.890401 -0.06641229 -0.03999201
##            X7          X8
## 1 -0.01998402 -0.01998402
## 2 -0.01998402 -0.01998402
## 3 -0.01998402 -0.01998402
## 4 -0.01998402 -0.01998402
## 5 -0.01998402 -0.01998402
## 6 -0.01998402 -0.01998402

PCA

Principal Components Analysis was run using prcomp().

# NOTE: This takes ~3min to run
## omits the proper number of columns
vcf_pca <- prcomp(vcf_scaled[,-c(1:6)])

Get the PCA scores, which will be plotted.:

vcf_pca_scores  <- vegan::scores(vcf_pca)

Combine the scores with the sample information into a dataframe.

# call data.frame()
vcf_pca_scores2 <- data.frame(population = vcf_scaled$super_pop,
                              vcf_pca_scores)

# set as a factor
vcf_pca_scores2$population <- factor(vcf_pca_scores2$population)

PCA diagnostics

The following steps help us understand the PCA output and determine how many PCs should be plotted and/or used in further analyses such as scans for natural selection, cluster analysis, and GWAS.

Default scree plot

A default R scree plot was created with screeplot(). This plot does not provide extra information for assessing the importance of the PCs.

screeplot(vcf_pca, 
          xlab = "Principal Components")

Advanced scree plot

The original workflow and function for making a more advanced scree plot lacked flexibility (Brouwer, personal communication). The following function and workflow simplifies things

  1. Run PC (done above)
  2. Call function PCA_variation() (below) on PCA output.
  3. (Do NOT call summary() on PCA output)
  4. Call function screeplot_snps() on the output of PCA_variation() to make an advanced scree plot
  5. Call function PCA_cumulative_var_plot() to show the cumulative variation explained as more PCs are considered
NEW Functions
PCA_variation() function

This function extacts information needed to make a more advanced, annotated scree plot.

# This is a NEW function
PCA_variation <- function(pca){
  
  # get summary information from PCA
  pca_summary <- summary(pca)
  
  # extract information from summary
  ## raw variance for each PC
  variance <- pca_summary$importance[1,]
  
  ## % variance explained by each PC
  var_explained <- pca_summary$importance[2,]*100
  var_explained <- round(var_explained,3)
  
  ## cumulative % variance  
  var_cumulative <- pca_summary$importance[3,]*100
  var_cumulative <- round(var_cumulative,3)
  
  # prepare output
  N.PCs <- length(var_explained)
  var_df <- data.frame(PC = 1:N.PCs,
            var_raw  = variance,
            var_percent = var_explained, 
            cumulative_percent = var_cumulative)
  
  # return output
  return(var_df)   
}
screeplot_snps() function

This functions makes a more advanced scree plot better suited for PCS on for SNPs.

# This is a NEW function
screeplot_snps <- function(var_df){
total_var <- sum(var_df$var_raw)
N <- length(var_df$var_raw)
var_cutoff <- total_var/N
var_cut_percent <- var_cutoff/total_var*100
var_cut_percent_rnd <- round(var_cut_percent,2)
i_above_cut <- which(var_df$var_percent > var_cut_percent)
i_cut <- max(i_above_cut) 
ti <- paste0("Cutoff = ",
            var_cut_percent_rnd,
            "%\n","Useful PCs = ",i_cut)
plot(var_df$var_percent,
        main =ti, type = "l",
     xlab = "PC",
     ylab = "Percent variation",
     col = 0)

segments(x0 = var_df$PC,
         x1 = var_df$PC,
         y0 = 0, 
         y1 = var_df$var_percent,
         col = 1)


segments(x0 = 0,
         x1 = N,
         y0 = var_cut_percent, 
         y1 = var_cut_percent,
         col = 2)

}
PCA_cumulative_var_plot() function

This makes a plot complementary to a scree plot. A scree plot plots the amount of variation explained by each PC. This plot plots a curve of cumulative amount of variation explained by the PCs.

# This is a NEW function
PCA_cumulative_var_plot <- function(var_df){
  plot(cumulative_percent ~ PC, 
       data = var_out,
       main = "Cumulative percent variation\n explained by PCs",
       xlab = "PC",
       ylab = "Cumulative %",
       type = "l")
  
  total_var <- sum(var_df$var_raw)
N <- length(var_df$var_raw)
var_cutoff <- total_var/N
var_cut_percent <- var_cutoff/total_var*100
var_cut_percent_rnd <- round(var_cut_percent,2)
i_above_cut <- which(var_df$var_percent > var_cut_percent)
i_cut <- max(i_above_cut) 

percent_cut_i <- which(var_out$PC == i_cut )
percent_cut <- var_out$cumulative_percent[percent_cut_i]
segments(x0 = i_cut,
         x1 = i_cut,
         y0 = 0, 
         y1 = 100,
         col = 2)

segments(x0 = -10,
         x1 = N,
         y0 = percent_cut, 
         y1 = percent_cut,
         col = 2)

}
Advanced screeplot analysis
Extract information

Extract information on the variance explained by each PC.

var_out <- PCA_variation(vcf_pca)

Look at the output of PCA_variation()

head(var_out)
##     PC   var_raw var_percent cumulative_percent
## PC1  1 10.824956       2.225              2.225
## PC2  2  8.070153       1.237              3.461
## PC3  3  7.954962       1.201              4.663
## PC4  4  7.533291       1.077              5.740
## PC5  5  6.984999       0.926              6.667
## PC6  6  6.881898       0.899              7.566
Advanced screeplot

This advanced scree plot shows the amount of variation explained by all PCs. It marks with a horizontal line what the cutoff is for the amount of Percent variation explained that is useful, and a vertical line for where that line interacts the curve of the scree plot. The title indicates the percentage value of the cutoff and which PC is the last PC below that value. Though only the first few PCs can be plotted, PCs below the cut off value (“useful PCs) should probably used for further machine learning algorithms.

Make the scree plot with screeplot_snps()

screeplot_snps(var_out)

Cumulative variation plot

The cumulative variation plot shows how much variation in the data explained in total as more and more PCs are considered. The vertical red line shows the cutoff value from the scree plot (above). The horizontal line indicates what the total percentage of variation explained by these useful PCs is.

Make cumulative variation plot with PCA_cumulative_var_plot()

PCA_cumulative_var_plot(var_out)

PCA Scatterplots

The object created above var_out indicates how much variation is explained by each of the Principal components. This information is often added to the axes of scatterplots of PCA output.

head(var_out)
##     PC   var_raw var_percent cumulative_percent
## PC1  1 10.824956       2.225              2.225
## PC2  2  8.070153       1.237              3.461
## PC3  3  7.954962       1.201              4.663
## PC4  4  7.533291       1.077              5.740
## PC5  5  6.984999       0.926              6.667
## PC6  6  6.881898       0.899              7.566

PC 1 explains 2.225% percent of the variation, PC2 explains. 1.237%, and PC3 explains 1.201%. In total, the first 3 PCs explain only ~5% of the variability in the data. The scree plot indicate that the first 651 PCs are useful explain ~75% of the variation in the data. In further analysis such as GWAS the first 651 PCs should therefore be used.

Plot PC1 versus PC2

Plot the scores, with super-population color-coded

# NOTE: population = super_pop because of how df was constructed above
ggpubr::ggscatter(data = vcf_pca_scores2,
                  y = "PC2",
                  x = "PC1",
              color = "population",
              shape = "population",   
              main = "PCA Scatterplot",
         ylab = "PC2 (1.237% of variation)",
         xlab = "PC1 (2.225% of variation")

Note how in the plot the amount of variation explained by each PC is shown in the axis labels.

Plot PC2 versus PC3

Plot the scores, with super population color-coded

# make color and shape = "super_pop"
ggpubr::ggscatter(data = vcf_pca_scores2,
                  y = "PC3",
                  x = "PC2",
                  color = "population",   
                  shape = "population",   
                  main = "PCA Scatterplot",
          ylab = "PC3 (1.201% of variation)",
          xlab = "PC2 (1.237% of variation)")

Note how in the plot the amount of variation explained by each PC is shown in the axis labels.

Plot PC1 versus PC3

Plot the scores, with super population color-coded

# make color and shape = "population"
ggpubr::ggscatter(data = vcf_pca_scores2,
                  y = "PC3",
                  x = "PC1",
                  ellipse = T,
            color = "population",   
            shape = "population",   
            main = "PCA Scatterplot",
      ylab = "PC3 (1.201% of variation)",
      xlab = "PC1 (2.225% of variation)")

Note how in the plot the amount of variation explained by each PC is shown in the axis labels.

3D scatterplot

The first 3 principal components can be presented as a 3D scatterplot.

colors_use <- as.numeric(vcf_pca_scores2$population)
scatterplot3d(x = vcf_pca_scores2$PC1,
              y = vcf_pca_scores2$PC2,
              z = vcf_pca_scores2$PC3,
  color = colors_use,
              xlab = "PC1 (2.225%)",
              ylab = "PC2 (1.237%)",
              zlab = "PC3 (1.201%)")

Conclusion

The plot of PC1 vs PC3 shows the most prominent clustering for this data. Overall, it appears that the African super-population is heavily grouped together while all the others are spread fairly evenly. What’s interesting is that this spread is only seen in PC1. All the populations are clustered in a very small range when looking at PC2 or 3. Even though these explain less variation than PC1, when looking at both of them combined they would explain about the same. However, unlike PC1, no super-populations are distinct, meaning we can not make any reasonable conclusions about the uniqueness of each population with this data set.