# Comparative functional analysis with R¶

Having this table one can use different statistical and visualisation software to analyse the results. One option would be to import a simpler version of the table into the program Fantom, a graphical user interface program developed for comparative analysis of metagenome data. You can try this in the end of the day if you have time.

But here we will use the statistical programming language R to do some simple analysis. cd to the directory where you have the cog-sum-mean-cov.tsv file. Then start R:

```
cd ~/metagenomics/cfa
R
```

and import the data:

```
tab_cog <- read.delim("cog-sum-mean-cov/cog-sum-mean-cov.tsv")
```

Assign the different columns with descriptors to vectors of logical names:

```
cogf <- tab_cog[,1] # cog family
cogfd <- tab_cog[,2] # cog family descriptor
cogc <- tab_cog[,3] # cog class
cogcd <- tab_cog[,4] # cog class descriptor
```

Make a matrix with the coverages of the cog families:

```
cogf_cov <- as.matrix(tab_cog[,5:ncol(tab_cog)]) # coverage in the different samples
```

And why not put sample names into a vector as well:

```
sample <- colnames(cogf_cov)
sample
```

Let’s clean the sample names a bit:

```
for (i in 1:length(sample)) {
sample[i] <- matrix(unlist(strsplit(sample[i],"_")), 1)[1,4]
}
```

Since the coverages will differ depending on how many reads per sample we have we can normalise by dividing the coverages by the total coverage for the sample (only considering cog-annotated genes though):

```
for (i in 1:ncol(cogf_cov)) {
cogf_cov[,i] <- cogf_cov[,i]/sum(cogf_cov[,i])
}
```

The cogf_cov gives coverage per cog family. Let’s summarise within cog classes and make a separate matrix for that:

```
unique_cogc <- levels(cogc)
cogc_cov <- matrix(ncol = length(sample), nrow = length(unique_cogc))
colnames(cogc_cov) <- sample
rownames(cogc_cov) <- unique_cogc
for (i in 1:length(unique_cogc)) {
these <- grep(paste("^", unique_cogc[i],"$", sep = ""), cogc)
for (j in 1:ncol(cogf_cov)) {
cogc_cov[i,j] <- sum(cogf_cov[these,j])
}
}
```

OK, now let’s start playing with the data. We can for example do a pairwise plot of coverage of cog classes in sample1 vs. sample2:

```
plot(cogc_cov[,1], cogc_cov[,2])
```

or make a stacked barplot showing the different classes in the different samples:

```
barplot(cogf_cov, col = rainbow(100), border=NA)
barplot(cogc_cov, col = rainbow(10), border=NA)
```

The vegan package contains many nice functions for doing (microbial) ecology analysis. Load vegan:

```
install.packages("vegan") # not necessary if already installed
library(vegan)
```

If installing doesn’t work for you have a look here http://www.stat.osu.edu/computer-support/mathstatistics-packages/installing-r-libraries-locally-your-home-directory

We can calculate pairwise distances between the samples based on their functional composition. In ecology pairwise distance between samples is referred to as beta-diversity, although typically based on taxonomic composition rather than functional:

```
cogf_dist <- as.matrix(vegdist(t(cogf_cov), method="bray", binary=FALSE, diag=TRUE, upper=TRUE, na.rm = FALSE))
cogc_dist <- as.matrix(vegdist(t(cogc_cov), method="bray", binary=FALSE, diag=TRUE, upper=TRUE, na.rm = FALSE))
```

You can visualise the distance matrices as a heatmaps:

```
image(cogf_dist)
image(cogc_dist)
```

Are the distances calculated on the different functional levels correlated?:

```
plot(cogc_dist, cogf_dist)
```

Now let’s cluster the samples based on the distances with hierarchical clustering. We use the function “agnes” in the “cluster” library and apply average linkage clustering:

```
install.packages("cluster") # not necessary if already installed
library(cluster)
cluster <- agnes(cogf_dist, diss = TRUE, method = "average")
plot(cluster, which.plots = 2, hang = -1, label = sample, main = "", axes = FALSE, xlab = "", ylab = "", sub = "")
```

Alternatively you can use the function heatmap, that calculates distances both between samples and between features and clusters in two dimensions:

```
heatmap(cogf_dist, scale = "none")
heatmap(cogc_dist, scale = "none")
```

And let’s ordinate the data in two dimensions. This can be done e.g. by PCA based on the actual coverage values or by e.g. PcOA or NMDS (non-metrical dimensional scaling). Let’s do NMDS:

```
mds <- metaMDS(cogf_dist)
plot(mds$points[,1], mds$points[,2], pch = 20, xlab = "NMDS1", ylab = "NMDS2", cex = 2)
```

We can color the samples according to date (provided your samples are ordered according to date). There are some nice color scales to choose from here http://colorbrewer2.org/:

```
install.packages("RColorBrewer") # not necessary if already installed
library(RColorBrewer)
color = brewer.pal(length(sample), "Reds") # or select another color scale!
mds <- metaMDS(cogf_dist)
plot(mds$points[,1], mds$points[,2], pch = 20, xlab = "NMDS1", ylab = "NMDS2", cex = 5, col = color)
```

Let’s compare with how it looks if we base the clustering on COG class coverage instead:

```
mds <- metaMDS(cogc_dist)
plot(mds$points[,1], mds$points[,2], pch = 20, xlab = "NMDS1", ylab = "NMDS2", cex = 5, col = color)
```

In addition to these examples there are of course infinite ways to analyse the results in R. One could for instance find COGs that significantly differ in abundance between samples, do different types of correlations between metadata (nutrients, temperature, etc) and functions, etc. Leave your R window open, since we will compare these results with taxonomic data in a bit.