Final project Analysis: Analysis of 1000 Genomes Data with PCA
2022-12-12
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 17 between genomic coordinates 45622108 and 45862108. This represents 0.29% of the chromosome. A total of 7320 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
Merged the data by merge() which use with the population meta data are from the 1000 genomes_people_info2.csv file. Information about the population codes, super population, sample, sex, latitude and longitude are included.
Data cleaning
These SNPs were then screened for any SNPs that were invariant (fixed), resulting in removal of 1725 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. Even though no NAs were present, mean imputation was still performed to ensure no missing data could slip through.
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 7320 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:
Load the data with read.csv(). Process the data with prcomp(). Extract PCA scores. Carry out PCA diagnostics, including construction of a scree plot. Plot PCs 1 through 3 as scatterplots as pairwise scatterplot. Plots PCS 1 through 3 as a 3D scatterplot.
Packages
# 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)Load the data
vcf_scaled <- read.csv(file = "scaled_data_for_PCA.csv")Check the dimensions of the data to confirm this is the correct data:
dim(vcf_scaled)## [1] 2504 7326Principal 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 X1 X2
## 1 HG00096 GBR EUR male 52.48624 -1.890401 -0.01998402 -0.03462717
## 2 HG00097 GBR EUR female 52.48624 -1.890401 -0.01998402 -0.03462717
## 3 HG00099 GBR EUR female 52.48624 -1.890401 -0.01998402 -0.03462717
## 4 HG00100 GBR EUR female 52.48624 -1.890401 -0.01998402 -0.03462717
## 5 HG00101 GBR EUR male 52.48624 -1.890401 -0.01998402 -0.03462717
## 6 HG00102 GBR EUR female 52.48624 -1.890401 -0.01998402 -0.03462717
## X3 X4
## 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 -0.01998402PCA
Principal Components Analysis was run using prcomp().
## omits the first 6 columns contains character data
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.
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$population)PCA diagnostics
Examine the default screeplot
screeplot(vcf_pca,
xlab = "Principal Components")
Advanced scree plot
The original workflow and function for making a more advanced scree plot lacked flexibility (Brouwer, personal communication). The following function and workflow simplifies things
Run PC (done above)
Call function PCA_variation() (below) on PCA output. (Do NOT call summary() on PCA output) Call function screeplot_snps() on the output of PCA_variation() to make an advanced scree plot Call function PCA_cumulative_var_plot() to show the cumulative variation explained as more PCs are considered
NEW Functions
PCA_variation() function This function extracts information needed to make a more advanced, annotated scree plot.
# This is a NEW function
PCA_variation <- function(pca){
# get summary information from PCA
pca_summary <- summary(pca)
# extract information from summary
## raw variance for each PC
variance <- pca_summary$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 35.830422 17.539 17.539
## PC2 2 10.789610 1.590 19.129
## PC3 3 8.214336 0.922 20.051
## PC4 4 7.676077 0.805 20.856
## PC5 5 7.591127 0.787 21.643
## PC6 6 7.465309 0.761 22.404Advanced 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 35.830422 17.539 17.539
## PC2 2 10.789610 1.590 19.129
## PC3 3 8.214336 0.922 20.051
## PC4 4 7.676077 0.805 20.856
## PC5 5 7.591127 0.787 21.643
## PC6 6 7.465309 0.761 22.404PC 1 explains 17.53% percent of the variation, PC2 explains 1.59%, and PC3 explains 0.92%. In total, the first 3 PCs explain only ~20.05% of the variability in the data. The scree plot indicate that the first ~608 PCs are useful explain ~80% of the variation in the data. In further analysis such as GWAS the first 608 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",
shape = "population",
main = "PCA Scatterplot",
ylab = "PC2 (1,590% of variation)",
xlab = "PC1 (17.539% 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 (0.922% of variation)",
xlab = "PC2 (1.590% 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 (0.922% of variation)",
xlab = "PC1 (17.539% 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 (17,539%)",
ylab = "PC2 (1,590%)",
zlab = "PC3 (0.922%)")
Conclusion
It does not seem like any of the superpopulations that are in the seperate group in the scatterplots, and there are several outliers