Table of Contents
Animation of ordinations
The videos below are using real-world datasets (small vegetation surveys) to visualize the process of ordination by animating individual steps.
Correspondance analysis (CA)
The process of “reciprocal averaging” (RA, the old and alternative name for CA) starts from random sample scores assigned to each sample; as the video below shows, no matter what is the initial position of individual samples (here originating from the Vltava valley dataset), after a series of reciprocal averaging both animations (done on the same dataset) will converge to exactly the same solution.
The simulation below is done on a rather heterogeneous vegetation dataset (pine forest samples, classified into several vegetation associations, shown by different colour/symbol). The result shows an obvious arch effect.
The same dataset as above, with additional visualization aids; the upper right panel connects samples within the same group by spiderplot, the bottom left panel does the same with envelopes, and the bottom-right panel shows the values of eigenvalues for the first and second ordination axis.
Detrended correspondence analysis (DCA)
For DCA, the animation shows the process of detrending, starting from the result of CA on the heterogeneous dataset (see above). Detrending includes two main steps: 1) separation of samples along the first ordination axis into segments and centering their scores along the second axis, and 2) rescaling the scores on the first axis. Note that the animation is more for an effect - in contrast to CA ordination above, it just “connects” the initial and final position of samples with animated movement of samples.
Nonmetric multidimensional scaling (NMDS)
The same heterogeneous dataset as above (pine forest) is used also for NMDS calculated on Bray-Curtis distances.
The same animation, but with additional panels: top-right and bottom-left panel connects samples from the same group by spiderplot or envelope, respectively. The bottom-right panel shows the development of the stress value calculated on the final NMDS configuration (it decreased as the algorithm finds the optimal position of samples in the ordination space).