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Many community data sets possess some a priori defined structure within the set of samples, for example there may be replicates from a number of different sites (and/or times). A pre-requisite to interpreting community differences between sites should be a de...

Fig.6.3 displays the MDS based only on the 12 samples (4 replicates per site) from the B, C and D sites of the Frierfjord macrofauna data. The null hypothesis (H$_o$) is that there are no differences in community composition at these 3 sites. In order to exam...

The rank similarities underlying Fig. 6.3 are shown in Table 6.2 (note that these are the similarities involving only sites B, C and D, extracted from the matrix for all sites and re-ranked). Averaging across the 3 diagonal sub-matrices (within groups B, C and...

examined data from 10 replicate transects across a single coral-reef site in S. Tikus Island, Thousand Islands, Indonesia, for each of the six years 1981, 1983, 1984, 1985, 1987 and 1988. The community data are in the form of % cover of a transect by each of...

Three types of field and laboratory designs are considered here: a) the 2-way nested case can arise where two levels of spatial replication are involved, e.g. sites are grouped a priori to be representative of two ‘treatment’ categories (control and polluted, ...

analysed meiobenthic communities from three putatively polluted (P) areas of the Firth of Clyde and three control (C) sites, taking three replicate samples at each site (with one exception). The resulting MDS, based on fourth-root transformed abundances of th...

An example of a two-way crossed design is given in and is introduced more fully here in Chapter 12. This is a so-called natural experiment, studying disturbance effects on meiobenthic communities by the continual reworking of sediment by soldier crabs. Two ...

Although the above test may still function if a few random cells in the 2-way layout have only a single replicate, its success depends on reasonable levels of replication overall to generate sufficient permutations. A commonly arising situation in practice, h...

A final example demonstrates a positive outcome to such a test, in a common case of a 2-way layout of sites and times with the additional feature that samples are missing altogether from a small number of cells. Fig. 6.11 shows again the MDS, from Chapter 5, ...

Generalised ANOSIM statistic for the 1-way case Now return to the simple one-way case of page 6.2, with multivariate data from a number of pre-specified groups (A, B, C, …, e.g. sites, times or treatments) and with replicate samples from each group. It is well...

studied the soft-sediment macrobenthos at 39 sites at different distances (100m to 8km) and different directions away from the Ekofisk oil platform in the N Sea {E}, to examine evidence for changes in the assemblage with distance from the oil-rig. The sites w...

Under the non-parametric framework adopted in this manual (and in the PRIMER package) three forms of 2-way ANOSIM tests were presented on page 6.5: 2-factor nested, B within A (denoted by B(A)); 2-factor crossed (denoted A$\times$B); and a special case of A$...

These data are discussed more fully in Chapters 15 and 16; sampling of coral assemblages took place over a number of years between 1983 and 2000, see , along three permanent transects. Transect A, considered here, was sampled on each occasion by twelve ‘10m pl...

Table 6.4 details all viable combinations of 3 factors, A, B, C, in crossed/nested form, ordered/unordered, and with/without replication at the lowest level. Fully crossed designs are denoted A$\times$B$\times$C, e.g. locations (A) each examined at the same s...

We begin the 3-factor examples with a fully crossed design A$\times$B$\times$C of the composition by volume of the taxa found in the foreguts of King Wrasse fish from two regions of the western Australian coast, just part of the data on labrid diets studied by...

We now consider the fully nested design, C(B(A)). In north-eastern New Zealand, examined assemblages of invertebrates colonising kelp holdfasts at three spatial scales: 4 locations (A), with 2 sites (B) per location, sampling 2 areas (C) at each site and with...

The final example in this chapter is of a mixed nested and crossed design B$\times$C(A), for a total of 192 macrobenthic samples (282 species) from: A: four sub-tidal Areas of Tees Bay (Fig. 6.18, top left), with C: two Sites from each area, the same sites bei...

For typical species abundance matrices, it is much preferable to use a non-parametric ANOSIM-type permutation test rather than classical MANOVA; the latter will almost always be totally invalid. A realistic alternative is the semi-parametric PERMANOVA tests ...

Chapter 2 (page 2.4) describes how the original data matrix can be used to define similarities between every pair of species; two species are positively associated (i.e. ‘similar’) if their numbers or biomass or cover etc tend to fluctuate in proportion across...

describe in full detail a range of useful SIMPROF tests, which they classify as Types 1, 2 and 3. Type 1 SIMPROF has already been seen in Chapter 3 (page 3.5) and is concerned with testing hypotheses, in subsets of the samples, about whether the similarities ...