# Are NMDS Axis the same calculated for one or more dimensions?

I used NMDS axes of an ecological community as proxys for the community similarity in the different samples. I would like to "quantify" the importance of the different NMDS axis according to the stressreduction. Now my question is: If I calculate an NMDS with one dimension would the NMDS axis of that be the same as the first axis of a NMDS calculated with two dimensions? Of course, I tried that myself using the metaMDS function in vegan and the axis are not exactly same but correlate with a coefficient >0.9. How can that be explained?

• NMDS is an iterative fitting procedure ( stats.stackexchange.com/a/14017) which results (coordinates) depend on the number of dimensions requested - unlike that in PCA. So, the first axis might be different in 2dim and 1dim analysis. If happens it is strongly correlated that is due to the peculiarities of the data analyzed. – ttnphns Mar 23 '18 at 16:11

• Assuming the dimensions are relatively independent That is unclear. What dimensions? Could you elaborate and support your statement, please? – ttnphns Mar 23 '18 at 16:15