## OverviewEdit

This page provides basic code for creating a distance matrix and running and plotting a Non-metric Multidimensional Scaling (NMDS) ordination.

Read more about Ordination on Wikipedia.

This code relies on package vegan in R by Jari Oksanen.

## DataEdit

First, import data and load required libraries:

```
require(MASS)
require(vegan)
data(varespec) # species data
data(varechem) # environmental data
```

## Distance matrixEdit

```
bray <- vegdist(varespec, method = "bray") # calculate a distance matrix
# There are many distance measure options for 'dist',
# discoverable by running '?dist'. Common distance measures include:
# 'bray' = Bray-Curtis
# 'canb' = Canberra
# 'euclidean' = Euclidean
```

# Unconstrained OrdinationEdit

## Displaying dissimilarity using NMDSEdit

NMDS analysis and plotting:

```
nmds <- metaMDS(varespec, k = 2,
distance = 'bray', autotransform = FALSE) # semi-black box NMDS function
ordiplot(nmds, type = "text") # Plot NMDS ordination
fit <- envfit(nmds, varechem[ ,1:4]) # Calculates environmental vectors
fit # Lists vector endpoint coordinates and r-squared values
plot(fit) # adds environmental vectors
# a linear representation of environmental variables is not always appropiate
# we could also add a smooth surface of the variable to the plot
ordisurf(nmds, varechem$N, add = TRUE, col = "darkgreen")
nmds$stress # stress value
```

In the metaMDS function, k is user-defined and relates to how easily the projection fits the dataframe when contrained to k dimensions. Conventional wisdom seems to suggest that stress should not exceed 10-12%. Stress is reduced by increasing the number of dimensions. However, increasing dimensionality might decrease the "realism" of a 2-dimensional plot of the first two NMDS axes.

We can also run a nMDS with 3 dimensions, fit environmental vectors and create a dynamic graph:

```
nmds3d <- metaMDS(varespec, k = 3,
distance = 'bray', autotransform = FALSE) # run nmds with 3 dimensions
nmds3d$stress # stress drops
fit3d <- envfit(nmds3d, varechem[ ,1:4], choices = 1:3) # fit environmental vectors to 3d space
ordirgl(nmds3d, envfit = fit3d) # dynamic 3D graph
```

## Running a principle component analysis (PCA) on environmental dataEdit

```
chem_pca <- rda(varechem, scale = TRUE) # Run PCA
biplot(chem_pca, scaling = 2) # display biplot
```