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 5 between genomic coordinates 360,294 and 600,294. This represents 100% of the chromosome. A total of 8669 variants genotyped in 505 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

External metadata for my specific SNPs can be broken down by the superpopulation which are based in different continents and the population which is based in different regions in the continents . The self-identified ethnicity of each person is indicated in the row names 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 2252 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 8675 SNPS and 505 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 2.6-2
# 3D scatter plot
library(scatterplot3d)

Loading data

Load the fully processed data:

NOTE: with ~2504 SNPs, this CSV is ~307 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.

## TODO: Change to your .csv file name

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

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

## TODO: Make sure that your 
##   introductory information above 
###  reflects the size of the data being load
dim(vcf_scaled)
## [1] 2504 8675

Principal Components Analysis

The data are scaled and ready for analysis. Only the first six columns contains 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 52.48624 -1.890401 -0.02826732 -0.05293623
## 2 HG00097 GBR       EUR female 52.48624 -1.890401 -0.02826732 -0.05293623
## 3 HG00099 GBR       EUR female 52.48624 -1.890401 -0.02826732 -0.05293623
## 4 HG00100 GBR       EUR female 52.48624 -1.890401 -0.02826732 -0.05293623
## 5 HG00101 GBR       EUR   male 52.48624 -1.890401 -0.02826732 -0.05293623
## 6 HG00102 GBR       EUR female 52.48624 -1.890401 -0.02826732 -0.05293623
##           X3          X4
## 1  1.1593241 -0.01998402
## 2  1.1593241 -0.01998402
## 3 -0.8622271 -0.01998402
## 4 -0.8622271 -0.01998402
## 5 -0.8622271 -0.01998402
## 6 -0.8622271 -0.01998402

PCA

Principal Components Analysis was run using prcomp().

# TODO: change the -1 to code that 
## 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, #TODO
                              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 16.495112       3.139              3.139
## PC2  2 12.474886       1.795              4.934
## PC3  3 11.251945       1.460              6.394
## PC4  4 10.511988       1.275              7.669
## PC5  5 10.292883       1.222              8.891
## PC6  6  9.601151       1.063              9.954
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 16.495112       3.139              3.139
## PC2  2 12.474886       1.795              4.934
## PC3  3 11.251945       1.460              6.394
## PC4  4 10.511988       1.275              7.669
## PC5  5 10.292883       1.222              8.891
## PC6  6  9.601151       1.063              9.954

PC1 explains 3.1% percent of the variation, PC2 explains. 1.8%, and PC3 explains 1.4%. In total, the first 3 PCs explain only ~6.3% of the variability in the data. The scree plot indicates that the first ~665 PCs are useful explain ~60% of the variation in the data. In further analysis such as GWAS the first 665 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 = "population",   # TODO
              shape = "population",   # TODO
              main = "PCA Scatterplot",
         ylab = "PC2 (1.8% of variation)",
         xlab = "PC1 (3.1% 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",   # todo
                  shape = "population",   # todo
                  main = "PCA Scatterplot",
          ylab = "PC3 (1.4% of variation)",
          xlab = "PC2 (1.8% 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",   # todo
            shape = "population",   # todo
            main = "PCA Scatterplot",
      ylab = "PC3 (1.4% of variation)",
      xlab = "PC1 (3.1% 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 (3.1%)",
              ylab = "PC2 (1.8%)",
              zlab = "PC3 (1.5%)")

#Conclusion Looking at the first PCA Scatterplot we can see that there is a mix of variation between the population groups. Most of the points are close together, however we cannot definitively conclude that there are significant groupings using the first 2 PCs. The 2nd PCA scatter plot however shows significant groups, mainly we see differences between the African population and the rest of the groups. The last scatterplot, we can see some variation in the groups comparing PC1 to PC3. THe most significant is among PC3 where the African groups seems to have more of a variance compared to the other groups. Overall there seems to be more a grouping with the African population compared to the rest of the population