Interpretation of species vectors in nMDS

[friendly]

I posed this question on SO, Interpretation of species vectors in nMDS, but have had no answers, so I'm raising it here.

I'm trying to compare results I get from a PCA biplot with what I can get from MASS:isoMDS() and vegan::metaMDS() particularly using vectors representing the variables to help interpret the MDS dimensions.

My question is essentially how I can understand what is returned by the $species component of metaMDS(). How is it calculated and what do the values represent?

The plots I make for PCA and isoMDS() are consistent with the interpretation that the variable vectors reflect correlations of the observed variables with the dimensions. The plot for metaMDS() is inconsistent for on of the variables (relwt) which points in the opposite direction.

Here is the plot from ggbiplot::ggbiplot()

https://i.stack.imgur.com/4jD0N.png

Here is what I get from metaMDS()

https://i.stack.imgur.com/8n99m.png

[jarioksa]

This is what help(metaMDS) says:

       6. Species scores: Function adds the species scores to the final
          solution as weighted averages using function ‘wascores’ with
          given value of parameter ‘expand’.

So they are not vectors but weighted averages.

If you want to get vectors, try envfit / vectorfit.