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PRIMER therefore includes a number of S extrapolators – attempts to predict the true total number of species that would be observed as the number of samples tends to infinity (the asymptote of the species accumulation curve), assuming that a closed community i...

For this final section, we consider only cases in which the samples form a 1-way layout, i.e. there is a single (a priori defined) factor whose levels divide the data into groups, the samples in a group being considered replicates of that factor level. This fa...

Ordination means plots are therefore a vital tool for interpretation but, in relation to their univariate counterparts, they lack one useful feature – the ability to get an approximate feel for the uncertainty in our knowledge of position of each mean point on...

The construction of approximate regions is approached through bootstrap averages. We only have one observed mean from n replicates for a particular group – leaving aside how that is calculated for the moment. What we need, for a plausible region estimate, is e...

These averages can then be used to generate a bootstrap region for each of the g groups – at its simplest by displaying the full set of b$\times$g averages in a 2-d (or 3-d) ordination. Here is the first obvious approximation therefore, namely that a 2- or 3-d...

The Analyse>Bootstrap Averages routine allows both metric and non-metric options for the MDS ordination of the bootstrap average regions. However, mMDS is the recommended choice, and the default. The motivation for constructing a region plot for the group mean...

Though hopefully the above gives the motivation and an idea of the way the region estimates are constructed, the most important instruction of this Section is to read Chapter 18 of CiMC! The detailed reasoning and information it gives will not be repeated here...

These b bootstrap averages for each of the g groups are then displayed in a low-d mMDS space and you have control of whether to display any or all of: the b$\times$g bootstraps (✓Bootstrap averages); the overall averages for each group (✓Group averages); the s...

The diet study for 7 species of W Australian fish, with a variable number of dietary samples from each, has been seen several times now. In Section 3 we selected a subset of just the 3 congeneric species, Sillago schomburgkii (10 samples), S. bassensis (14) an...

None of the above is necessary in order to create the means plot with regions based on bootstrap averages – it was included purely to note the initial steps the routine takes, under the automatic m option, in order to determine the mMDS dimensionality in which...

The above study was not an example given in Chapter 18 of CiMC and was therefore discussed in detail, but bootstrap average regions are given and interpreted for three other data sets there, and we shall end just by showing a region plot from one of those, for...

A final example of bootstrap regions which do strongly overlap, and for which the hypothesis tests (such as ANOSIM) give no indication at all that the groups differ, is shown in Fig. 18.7 of CiMC. It can be reproduced here by opening the Fal macrofauna counts ...