Interpreting the results
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When a Canonical Correspondence Analysis is undertaken a range of tabbed sheets of output will be produced. In this section we will use the Dune Meadow data to take you through the output.
Having undertaken a CCA from the drop-down:
we first examine the Variance tab. The multiple correlation species/environment scores indicate how much of the variation in species composition is explicable from the environmental variables. The figure of 0.9579 for the first axis indicates that we can account for most of the variation in species composition by taking account of the environmental variables. The maximum and minimum values for this coefficient are 1.0 and 0, and a value close to 1 indicates that the environmental variables are having an appreciable effect. This correlation should be viewed with great caution and can be highly misleading - see Problems with Species-Environment Correlation. Note also that the first canonical axis explains about 21% of the total variability. This is quite a large amount but may not be significant. A Monte Carlo test must be used to test for significance.
The results of the Monte Carlo test with 1000 replicates are shown below. This indicates that the amount of variability explained by the environmental variables is significant for both the first and second canonical axes ( Probability < 0.05 - less than a 5% chance that the observed relationship could occur by chance).
The sample and species scores that will be plotted are presented in grids in the Sample Score and Species Score tabs. Generally you will be far more interested in the plot of the results which is viewed from the Ordination Plot tab is shown below. This is a plot of the 1st and 2nd canonical axes, which we have shown above are the only statistically significant axes. Thus, there is not much point in examining the other axes.
The lengths and positions of the arrows provide information about the relationship between the environmental variables and the derived axes. Arrows that are parallel to an axis (e.g. moisture and axis 1) indicate a correlation, the length of the arrow tells us about the strength of that correlation. Thus, pasture is related to axis 1 but not as strongly as moisture. Neither of these is related to axis 2.
The above plot is rather confusing and cluttered because we have plotted the environmental vectors or centroids, the site (sample) scores and the species (dependent variable) scores all on the same graph. Further, all the labels have been included. The graph plotting options allow many variations to be plotted to make the output clearer.
The position of the sites indicates their status with respect to the environmental variables. Thus site 19 has a negative score on axis 2 and axis 2 has a high manure component. This indicates that we would predict there has been little manuring on site 19.
In similar fashion the positions of the species indicates their response to particular environmental variables. For example Potpal, Elepal and Ranfla are associated with moist sites.
We can see the inferred relationship between the species and the different environmental variables far more clearly using the Rank Plot tab as shown for moisture below.
The position of the species Potpal, Elepal and Ranfla at the extreme high moisture content end of the distribution is now quite clear.