THE SIGNATURES OF PATCHES AND GRADIENTS IN ECOLOGICAL ORDINATIONS

When multivariate ordination techniques are applied to marine ecological data sets, the first ordination axis commonly correlates with lithologic indicators of water depth. Stratigraphic plots of axis 1 scores typically display long-term trends, superimposed with high-frequency variation that may be comparable in scale to the long-term trend and that has been attributed to faunal patchiness. Here, I explore through numerical models calibrated with field data how patchiness and faunal gradients are expressed in ordinations, specifically detrended correspondence analysis (DCA). The simulations use DCA results for the Upper Ordovician Kope Formation of the Cincinnati, Ohio area, from which values of Preferred Depth, Depth Tolerance, and Peak Abundance were calculated relative to DCA Axis 1 scores. These values were combined with the DCA Axis 1 scores for each bed to construct simulated Kope faunal samples. The first of three simulations did not include faunal patchiness. DCA Axis 1 sample scores produced from this first simulation match almost exactly the smoothed DCA scores used as input, confirming the utility of DCA in extracting simple faunal gradients. In the second simulation, faunal patchiness was included and produced the long-term DCA Axis 1 sample score pattern that was input, but also included high-frequency variation as seen in the original Kope DCA analysis, suggesting that patchiness is indeed the source of this high-frequency signal. In the third solution, peak abundances of all species were set to equally large values, which dampened the high-frequency variation, indicating that the large amplitude of the high-frequency signal results from the dominance of a handful of taxa. The results of these simulations suggest that DCA Axis 1 sample scores do not directly reflect water depth. To produce a measure of water depth, some signal averaging, such as a moving average, is needed to remove high-frequency variations produced by faunal patchiness.