New samples can be added without affecting the ordination. PCoA maximizes the linear correlation between distance measures and distance in the ordination. In contrast, PCA, RA, and DCA assume that there are potentially many gradients, but of declining importance. PCoA can be expressed as an eigenanalysis. NMDS Maximizes rank-order correlation between distance measures and distance in ordination space.
Stress is a measure of the mismatch between the two kinds of distance.
What it assumes is that dissimilarity is monotonically related to ecological distance. The configuration will change as the number of axes change. To increase the likelihood of finding the correct solution, a DCA is often performed first. A recent variant of NMDS is Local NMDS, which only minimizes stress locally. Polar Ordination Beals, E. W. 1984.