Read more about Ordination on Wikipedia.
This code relies on package vegan in R by Jari Oksanen.
First, import data and load required libraries:
require(MASS) require(vegan) data(varespec) # species data data(varechem) # environmental data
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
Displaying dissimilarity using NMDS
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 data
chem_pca <- rda(varechem, scale = TRUE) # Run PCA biplot(chem_pca, scaling = 2) # display biplot