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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...

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...