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An important use for a bubble plot is in displaying the behaviour of a further measured variable, which has not been used in the multivariate analysis, across the sample positions on an ordination, e.g. in superimposing environmental or contaminant variables ...

Given the inadequacies of vector plots for displaying species contributions to ordinations, but the practical need to reduce the number of graphs which can be displayed in publications, PRIMER 7 introduces a segmented bubble plot, which attempts simultaneously...

The BC zooplankton density data sheet in C:\Examples v7\BC zooplankton was used in the last half of Section 6 to illustrate different clustering methods, and the workspace Bristol Channel ws may be available from that. If not, open the data, fourth-root transf...

Another new feature in PRIMER 7 is the ability to construct bubble plots in 3-d ordinations, where the same ‘3-d effect’ representation of bubbles is employed as was seen earlier in 2-d plots – only now, of course, (✓3D effect) is the default. These are reason...

For these data, a segmented bubble plot on a 2-d ordination provides a succinct summary of the relative balance of the main dietary components for these 7 fish species, when examined on data averaged over all replicate gut samples for each fish species (as in ...

It is worth repeating the point made at the start of these examples on bubble plots: if the routine cannot find one or more of the sample labels of the MDS points in the supplied secondary data sheet of bubble values, you will get a blank graph with the messa...

A significant new feature in PRIMER 7 is the construction of metric MDS ordinations (mMDS), together with variations such as threshold mMDS (tmMDS) and a specific combination of nMDS and mMDS; the rationale and details are fully covered towards the end of Chap...

Show this by running the matching nMDS to the above mMDS, this time setting (Minimum stress: 0.001). For the 2-d nMDS, identify the greatest contributions to the stress by clicking on outlying points in the Shepard diagram, which then lists the pairs of cities...

Another feature introduced in PRIMER 7 is more of a teaching tool than an analysis method per se, namely the ability to watch the steps of the MDS iterative process (for either nMDS or mMDS) in converging – or failing to converge! – to an optimal 2- or 3-d rep...

Close the World cities worksheet (it will not be needed again) and re-open workspace Morlaix ws, from earlier in this section. It contains the data sheet Morlaix macrofauna abundance, fourth-root transformed and with Bray-Curtis similarity matrix, Resem1, on w...

The mMDS Shepard diagram above strongly suggests a middle course between simple metric and non-metric MDS, which we shall term threshold metric MDS (tmMDS), in which the Shepard plot is fitted by a straight line but not through the origin. It will almost alway...

Though usually greatly inferior to nMDS for typical ordinations from community similarities (e.g. with coefficients from the Bray-Curtis family), purely metric MDS (mMDS) becomes a valuable tool for ordinations based on only a handful of samples, when the info...

The PRIMER 7 nMDS dialog box includes a new option to (✓Fix Collapse). This addresses the problem of indeterminacy in some nMDS plots, when two (or more) groups of samples have very different communities, such that all dissimilarities between the groups are la...

A variation of the above, and a final new PRIMER 7 feature to discuss in this section, is the option to mix, in equal measure, stress functions from two resemblance matrices, in a single nMDS. There are possible applications to data sets in which a single MDS ...

The series of ANOSIM (analysis of similarity) tests, accessed through Analyse>ANOSIM, operate on a resemblance matrix as the active sheet and carry out non-parametric tests for designs which broadly parallel univariate 1- and 2- way ANOVA (analysis of variance...

Return to the W Australian fish diet data, introduced at the start of Section 4 and last seen under the Higher-d & scree plots heading of Section 8, showing MDS plots of dietary categories found in 65 (pooled) gut samples from 7 fish species. If the workspace ...

The table ending the results window gives the pairwise comparisons. For each pair of groups (fish species), the first data column is of pairwise R statistics. These are again a difference of average rank dissimilarities between and within the two groups, scale...

Checking the (✓Pairwise tests to worksheet) box has also sent the above R values to a worksheet in triangular format, which could be a useful layout for tabulating ANOSIM results in a publication. More subtly, this can be regarded as a resemblance matrix (of d...

ANOSIM applies equally well to data on environmental, biomarker or morphometric variables, which might be transformable to approximate normality; it is then a robust alternative to classical multivariate (MANOVA) tests such as Wilks’ lambda. The inevitable sli...

However, for the Ekofisk oil-field study of the last section there is a postulated cause for benthic community change (the presence of an oilfield) and impacts, if any, are expected to result in a monotonic change with increasing distance from the drilling cen...