Introduction

The example is split into 2 Parts:

Part 1 must be completed first to create a file, SNPs_cleaned.csv, that has been completely prepared for analysis.

Now in Part 2, you will analyze the data with PCA. The steps here will be:

  1. Center the data (scale())
  2. Run a PCA analysis (prcomp())
  3. Evaluate the scree plot from the PCA (screeplot())
  4. Evaluate the amount of variation explained by the first 2 PCs.
  5. Extract the PCA scores for plotting (vegan::scores())
  6. Plot the data

Tasks

In the code below all code is provided. Your tasks will be to do 4 things:

  1. Give a meaningful title to all sections marked “TODO: TITLE”
  2. Write 1 to 2 sentences describing what is being done and why in all sections marked “TODO: EXPLAIN”
  3. Add titles and axes to plots in all sections marked “TODO: UPDATE PLOT”
  4. Write 1 or 2 sentences interpreting the output from R in all sections marked “TODO: INTERPRET”

Preliminaries

Load the vcfR package with library()

library(vcfR) # KEY
## Warning: package 'vcfR' was built under R version 4.2.2
## 
##    *****       ***   vcfR   ***       *****
##    This is vcfR 1.13.0 
##      browseVignettes('vcfR') # Documentation
##      citation('vcfR') # Citation
##    *****       *****      *****       *****
library(vegan)
## Loading required package: permute
## Loading required package: lattice
## This is vegan 2.6-2
library(ggplot2)
library(ggpubr)

Set the working directory

setwd("~/Pitt/Year 4/Fall2022/BIOSC1540")

Load the data

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

warning("If this didn't work, its may be because you didn't set your working directory.")
## Warning: If this didn't work, its may be because you didn't set your working
## directory.

Data analysis

TODO: Center and Scale Data

TODO: Use the Scale function to center and scale our data for each SNP to prepare for PCA.

SNPs_scaled <- scale(SNPs_cleaned)

TODO: Run PCA

TODO: Use the prcomp function to run PCA on our scaled data

pca_scaled <- prcomp(SNPs_scaled)

TODO: Generate Screeplot

TODO: Determine how many PCs are essential to interpret the data by visualizing their importance using a screeplot

TODO: UPDATE PLOT WITH TITLE

screeplot(pca_scaled, 
          ylab  = "Relative importance",
          main = "Principle Components")

TODO: INTERPRET SCREEPLOT

PC1 captures a wide amount of variation. PC1 and PC2 are the most important to consider, however, PC1 is the most important by far.

TODO: Determine Percent Variation

TODO: Determine how much percent of variation is captured by each PC by converting our PCA analysis to represent captured percent of variation.

summary_out_scaled <- summary(pca_scaled)
PCA_variation <- function(pca_summary, PCs = 2){
  var_explained <- pca_summary$importance[2,1:PCs]*100
  var_explained <- round(var_explained,1)
  return(var_explained)
}
var_out <- PCA_variation(summary_out_scaled,PCs = 10)
N_columns <- ncol(SNPs_scaled)
barplot(var_out,
        main = "Percent variation Scree plot",
        ylab = "Percent variation explained")
abline(h = 1/N_columns*100, col = 2, lwd = 2)

TODO: INTERPRET VARIANCE EXPLAINED

PC1 accounts for the largest percent of variation within the data set. If we wanted to account for ~99% of the variation, we would need to consider every PC that is above the red line.

TODO: Generate Biplot

TODO: Create a biplot using our PCA analysis to determine if any single feature is highly correlated to the PCs.

biplot(pca_scaled)

TODO: EXPLAIN WHY THIS IS A BAD IDEA It is ugly, there are too many SNPS and thus too many vectors. This results in this being to ugly to interpret anything.

TODO: Plot Labeled Data

TODO: Generate PCA scores to plot and determine if we can see any clusters forming for each individual point.

pca_scores <- vegan::scores(pca_scaled)

TODO: Add categorical labels back to data

pop_id <- c("Nel","Nel","Nel","Nel","Nel","Nel","Nel","Nel",
"Nel", "Nel", "Nel", "Nel", "Nel", "Nel", "Nel", "Alt",
"Alt", "Alt", "Alt", "Alt", "Alt", "Alt", "Alt", "Alt",
"Alt", "Alt", "Alt", "Alt", "Alt", "Alt", "Sub", "Sub",
"Sub", "Sub", "Sub", "Sub", "Sub", "Sub", "Sub", "Sub",
"Sub", "Cau", "Cau", "Cau", "Cau", "Cau", "Cau", "Cau",
"Cau", "Cau", "Cau", "Cau", "Cau", "Div", "Div", "Div",
"Div", "Div", "Div", "Div", "Div", "Div", "Div", "Div",
"Div", "Div", "Div", "Div")

TODO: Label PCA scores with population ID so we can then plot data on a scatter plot.

pca_scores2 <- data.frame(pop_id,
                              pca_scores)

TODO: Generate Scatter Plot

TODO: Visualize PCA results by plotting PCA scores and determine if we see any clusters forming that can be used to group based on population categories.

TODO: UPDATE PLOT WITH TITLE TODO: UPDATE X and Y AXES WITH AMOUNT OF VARIATION EXPLAINED

ggpubr::ggscatter(data = pca_scores2,
                  y = "PC2",
                  x = "PC1",
                  color = "pop_id",
                  shape = "pop_id",
                  xlab = "PC1 (19.9% variation)",
                  ylab = "PC2 (2.3% variation)",
                  main = "PCA of SNP Data")

TODO: INTERPRET PLOT

We have three distinct groups of Cau/Div, Alt/Nel, and Sub. We could run a clustering algorithm to determine if this is true clusters we see forming and how significant this would be.