Geometric class plots
These are essentially multiple frequency polygons, plotted on a single graph, for each sample in the active sheet, which needs to be a taxon (species) by samples array of genuine counts. If you wish to plot a single curve for each of a number of groups of samples then you should first pool replicates in each group with Tools>Sum – or, to pool all the samples in an array into a single sample, you can use Analyse>Summary Stats>(For•Variables)>(✓Sum). Then Plots>Geometric Class Plot gives several line plots (or just one) on a single (x,y) graph in which the y axis is the number of species that fall into a set of geometric ($\times$ 2) abundance classes (x axis). That is, each line on the plot gives the number (or %) of species represented in the sample by a single individual (class 1), 2-3 individuals (class 2), 4-7 individuals (class 3), 8-15 individuals etc. Statistical ecologists call these SAD curves (Species Abundance Distribution), and there is much early literature on fitting by distributions such as the truncated log-normal, proposed on (unconvincing) theoretical grounds. Fisher RA et al 1943, J Anim Ecol 12 was the first (as in so much else, statistically!) to model such data, fitting it to the single-parameter log series distribution – this parameter ($\alpha$) is the Fisher index calculated by Analyse>DIVERSE, see the previous section. It has been suggested that impact on assemblages changes the characteristic form of the SAD curve, lengthen¬ing the right tail because some species become very abundant and other, rarer, species (singletons) disappear.
Close the existing workspace (it is not needed again), and re-open the Clyde dumpground study, workspace Clyde ws2 analysed at the start of the last section, or just open the abundance matrix Clyde macrofauna counts from C:\Examples v7\ Clyde macrofauna. The plot would be cluttered with all 12 transect samples displayed, so contrast just two sets of pooled samples – the outer (1, 2, 11, 12) and inner (5, 6, 7, 8) sites – the pools need to be the same size for unbiased comparison. For Clyde macrofauna counts create a factor Pool, with two levels corresponding to these groups, using Edit>Factors>Add (leaving entries for other sites blank), and run Tools>Sum on the counts sheet, giving factor Pool. On the resulting matrix, Plots>Geometric Class Plot clearly shows the right shift in the abundance distribution at the inner sites. Close the workspace; it is not needed again.
