# interpreting NMDS ordinations that show both samples and species

I am using the vegan package in R to plot non-metric multidimensional scaling (NMDS) ordinations. I am using this package because of its compatibility with common ecological distance measures. When you plot the metaMDS() ordination, it plots both the samples (as black dots) and the species (as red dots). My question is: How do you interpret this simultaneous view of species and sample points?

My understanding of NMDS:

• The algorithm places your points in fewer dimensional (say 2D) space
• The algorithm moves your points around in 2D space so that the distances between points in 2D space go in the same order (rank) as the distances between points in multi-D space.

BUT there are 2 possible distance matrices you can make with your rows=samples cols=species data:

1. distances between samples based on species composition (i.e. distances in species space)
2. distances between species based on co-occurrence in samples (i.e. distances in sample space)

Is metaMDS() calculating BOTH possible distance matrices automatically?

Is the ordination plot an overlay of two sets of arbitrary axes from separate ordinations?

How do you interpret co-localization of species and samples in the ordination plot?

note: I did not include example data because you can see the plots I'm talking about in the package documentation example.

• I don't know the package. But I can suppose it is multidimensional unfolding (MDU) - a technique closely related to MDS but for rectangular matrices. – ttnphns Apr 2 '15 at 17:38
• It's true the data matrix is rectangular, but the distance matrix should be square. I'll look up MDU though, thanks. – rrr Apr 3 '15 at 21:54

The NMDS vegan performs is of the common or garden form of NMDS. If metaMDS() is passed the original data, then we can position the species points (shown in the plot) at the weighted average of site scores (sample points in the plot) for the NMDS dimensions retained/drawn. The weights are given by the abundances of the species.
You'll notice that if you supply a dissimilarity matrix to metaMDS() will not draw the species points, because it does not have access to the species abundances (to use as weights).
• If the species points are at the weighted average of site scores, why are species points often completely outside the cloud of site points? For instance plot(metaMDS(dune), type="t"), species Airaprae, Empenigr and Hyporadi are all placed much higher on NMDS2 than the highest site scores. – emudrak Apr 16 '18 at 1:38
• @emudrak the WA scores are expanded to have the same variance as the site scores (see argument expand in ?wascores). Argument shrink in scores.metaMDS method allows you to undo this expansion. – Gavin Simpson Apr 16 '18 at 15:41