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The second way in which a cluster analysis can be displayed on a 2-d MDS plot, to aid assessment of the level of agreement, is to draw smoothed envelopes around each of the cluster groups, either for one or more slices at arbitrarily chosen similarity levels (...

Rather than creating a small number of (arbitrary) slices through a dendrogram, superimposed on a 2-d MDS, a further new feature in PRIMER 7 is the ability to draw the dendrogram as the third dimension in a 3-d plot of the 2-d MDS (or any ordination). As with ...

As we have seen for the nMDS run on the Exe nematode data, in the first graphic of this Section, a default MDS run produces both 2-d and 3-d configuration plots, and their associated Shepard diagrams, placed into a multi-plot (Multiplot1). A different plot win...

The 3-d Exe nematode nMDS plot should be in the current workspace as Graph5 under Multiplot1 (if necessary create it again, with default options, by Analyse>MDS>Non-metric MDS (nMDS) on the Bray-Curtis resemblance matrix for a square-root transform of the data...

Whilst it is relatively easy to visualise a 3-d plot by rotation of the axes – and PRIMER 7 is now able to output digital video of such rotations (as *.mp4, see below) – it is much harder to produce a convincing 3-d plot for static reproduction in 2-d, e.g. fo...

Re-open the workspace WA fish ws from C:\Examples v7\WA fish diets, which will provide an example where a 3-d MDS is necessary to get a reliable feel for the multivariate structure. The workspace WA fish ws should contain a data sheet Data2 of the dietary asse...

Run nMDS at a wider range of dimensionalities than the default and ask for a scree plot: Analyse> MDS>Non-metric MDS (mMDS)>(Min. dimension: 2) & (Max. dimension: 8) & (✓Scree plot), taking the other defaults (i.e. including Shepard plots). On the resulting mu...

The 3-d MDS plot box can be made to rotate horizontally, automatically (from whatever vertical perspective view it is manually set to), by Graph>Spin. This adds a top line of controls for the animation: to the left is a slider control w...

Some data sets have a natural sequence to their samples, usually a time series (though this can be a single spatial gradient), and it is usually a good idea to join the points on an ordination plot in that order – then referred to as trajectory plots. This is ...

A trajectory joining points on an ordination is simply added using Graph>Special>Overlays and taking the (✓Overlay trajectory) option and supplying a factor name for the trajectory sequence, which of course needs to have purely numeric entries. These do not ne...

The time pattern above is evident from simple addition of the trajectory but there are occasions when a confused MDS plot results from a longer sequence of points, especially if the multivariate structure tracks back on itself, repeating earlier states. Viewin...

In fact, if the animation is repeated with trajectories running across months, separately drawn for each year, using the option discussed earlier to split the trajectories, then the scale of the seasonal cycle can be made visually apparent in a dynamic way. Fi...

A clearer, static, example of the benefits of split trajectories on ordination plots is provided by macrofauna data from Tees Bay, collected and analysed by the Brixham Laboratory, SW England, in (amongst other locations) four sub-tidal areas, 1 to 4, spannin...

The final two sections of the Graph>Special dialog concern overlaying vectors and ‘bubbles’ of numeric values, rather than factors, either of the variables (e.g. species) from which the ordination has been created, or taken from an independent worksheet (e.g. ...

The above MDS draws on all 174 species (with more abundant species given greater weight) but only some species will be responsible for creating the observed gradient – others will be largely ‘noise’. The behaviour of a single species over the sites can best be...

A new feature in PRIMER 7 is that these bubbles will be plotted in different colours – or in mono hatching patterns if the General>(✓Monochrome) option is selected – according to levels of the Symbol factor, in this case the four distance groups from the oilfi...

The key to the left of the plot, which gives the root-transformed scale for Abra prismatica counts, has been defined automatically and may not therefore be optimal – the values, and even the number of categories, are now (in PRIMER 7) user-selectable. The smal...

A further new option on this Key dialog is to replace single-coloured circles with a (rectangular) supplied image plotted at different sizes. To illustrate this, within the C:\Examples v7\Ekofisk macrofauna directory there is a photo image of a single valve o...

Abra prismatica appears to be a species which can tolerate the contaminant or disturbance effects found relatively close to the oilfield since the plot shows that it is present in consistent numbers from sites 8km distant to those >250m – remember mentally to ...

One tempting alternative, commonly found in the literature, is to plot (species) variables as vectors on the MDS plot (see below). They are directional lines emanating from a common origin, pointing in the directions in which those species numbers increase, an...