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 22 between genomic coordinates 21299928 and 21539928. This represents 100% of the chromosome. A total of 1911 variants genotyped in 2504 individuals were downloaded in the raw data.

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().

Data subsetting

Because of the large size of the data file 10000 random SNPs were selected using R’s sample() function. This allowed the data to be analyzed much more efficiently while representing key features of the data. A full analysis will require use of all of the SNPs.

Meta-data and sample information

1000 Genomes Population Meta data was available for use for these populations. This meta data of the population contained 4 columns of character data. The population and super population of each individual is idicated on each row of the dataframe. This information was extracted, cleaned with regular expressions and added as a column to the dataframe.

Data cleaning

These SNPs were then screened for any SNPs that were invariant (fixed), resulting in removal of 375 SNPs (features). This was done using the invar_omit() function by Nathan Brouwer.

NOTE: The original workflow code for removing invariant SNPs contained and error that resulted in no columns actually being removed (Brouwer, personal communication). The code was updated and a reduction in the size of the dataframe after omitting invariant columns confirmed by checking the dimensions of the dataframes before and after this process using dim().

The data were then screened for rows (people) with >50% NAs. There were no NAs in the data, so no rows were removed due to the presence of excessive NAs. Similarly, because no NAs were present no imputation was required.

The data were 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 1917 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 1917 SNPs, this CSV is ~39.3 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 = "vcf_for_PCA.csv")

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

dim(vcf_scaled)
## [1] 2504 1917

Principal Components Analysis

The data are scaled and ready for analysis. Only the first 4 columns contain character data and needs to be omitted.

head(vcf_scaled[,1:10])
##    sample pop super_pop    sex      lat        lng         X1         X2
## 1 HG00096 GBR       EUR   male 1.419725 -0.1190525 -0.0600481 -0.1367733
## 2 HG00097 GBR       EUR female 1.419725 -0.1190525 -0.0600481 -0.1367733
## 3 HG00099 GBR       EUR female 1.419725 -0.1190525 -0.0600481 -0.1367733
## 4 HG00100 GBR       EUR female 1.419725 -0.1190525 -0.0600481 -0.1367733
## 5 HG00101 GBR       EUR   male 1.419725 -0.1190525 -0.0600481 -0.1367733
## 6 HG00102 GBR       EUR female 1.419725 -0.1190525 -0.0600481 -0.1367733
##            X3          X4
## 1 -0.04899962 -0.01998402
## 2 -0.04899962 -0.01998402
## 3 -0.04899962 -0.01998402
## 4 -0.04899962 -0.01998402
## 5 -0.04899962 -0.01998402
## 6 -0.04899962 -0.01998402

PCA

Principal Components Analysis was run using prcomp().

vcf_pca <- prcomp(vcf_scaled[,-c(1:4)])

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(super_pop = vcf_scaled$super_pop, 
                              vcf_pca_scores)

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

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. PC1, PC2, and PC3 seem to have relative importance and will be plotted later in the report.

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 7.251458       2.749              2.749
## PC2  2 6.000955       1.882              4.631
## PC3  3 5.456191       1.556              6.187
## PC4  4 4.781130       1.195              7.382
## PC5  5 4.624231       1.118              8.500
## PC6  6 4.427505       1.025              9.525
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 7.251458       2.749              2.749
## PC2  2 6.000955       1.882              4.631
## PC3  3 5.456191       1.556              6.187
## PC4  4 4.781130       1.195              7.382
## PC5  5 4.624231       1.118              8.500
## PC6  6 4.427505       1.025              9.525

PC 1 explains 2.749% percent of the variation, PC2 explains. 1.882%, and PC3 explains 1.556%. In total, the first 3 PCs explain ~6.2% of the variability in the data. The scree plot indicate that the first ~595 PCs are useful explain ~85% of the variation in the data. In further analysis such as GWAS the first 595 PCs should therefore be used.

Plot PC1 versus PC2

Plot the scores, with super-population color-coded

# make color and shape = "super_pop"
ggpubr::ggscatter(data = vcf_pca_scores2,
                  y = "PC2",
                  x = "PC1",
              color = "super_pop",   
              shape = "super_pop",   
              main = "PCA Scatterplot",
         ylab = "PC2 (1.882% of variation)",
         xlab = "PC1 (2.749% 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 = "super_pop",  
                  shape = "super_pop",  
                  main = "PCA Scatterplot",
          ylab = "PC3 (1.556% of variation)",
          xlab = "PC2 (1.882% 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

ggpubr::ggscatter(data = vcf_pca_scores2,
                  y = "PC3",
                  x = "PC1",
                  ellipse = T,
            color = "super_pop",   
            shape = "super_pop",   
            main = "PCA Scatterplot",
      ylab = "PC3 (1.556% of variation)",
      xlab = "PC1 (2.749% 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$super_pop)
scatterplot3d(x = vcf_pca_scores2$PC1,
              y = vcf_pca_scores2$PC2,
              z = vcf_pca_scores2$PC3,
  color = colors_use,
              xlab = "PC1 (2.749%)",
              ylab = "PC2 (1.882%)",
              zlab = "PC3 (1.556%)")

It does not seem like any of the superpopulations are apparent as groups in the scatterplots.