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Third edition The third edition of this unified framework for non-parametric analysis of multivariate data, underlying the PRIMER software package, has the same form and similar chapter headings to its predecessor (with an additional chapter). However, the tex...

Any initiative spanning quite as long a period as the PRIMER software represents (the first recognisable elements were committed to paper over 30 years ago) is certain to have benefited from the contributions of a vast number of individuals: colleagues, studen...

The purpose of this opening chapter is twofold: a) to introduce some of the data sets which are used extensively, as illustrations of techniques, throughout the manual; b) to outline a framework for the various possible stages in a community analysis¶. Example...

For diversity indices and other single-variable extractions from the data matrix, standard statistical methods are usually applicable and the reader is referred to one of the many excellent general statistics texts (e.g. ). The requisite techniques for each s...

The first example is from the IOC/GEEP practical workshop on biological effects of pollutants (), held at the University of Oslo, August 1986. This attempted to contrast a range of biochemical, cellular, physiological and community analyses, applied to field ...

Table 1.3. Distributional techniques. Summary of analyses for the four stages. A less condensed form of diversity summary for each sample is offered by distributional/graphical methods, outlined for the four stages in Table 1.3. Representation is by curves ...

Table 1.4. Loch Linnhe macrofauna {L}. Abundance/biomass matrix (part only); one (pooled) set of values per year (1963–1973). Fig. 1.3. Loch Linnhe and Loch Eil, Scotland {L}. Map of site 34 (Linnhe) and site 2 (Eil), sampled annually over 1963–1973. de...

describe the sampling of a transect of 12 sites across the sewage-sludge disposal ground at Garroch Head in the Firth of Clyde, SW Scotland ({G}, Fig. 1.5). The samples considered here were taken during 1983 and consisted of abundance and biomass values of 8...

Table 1.5 summarises some multivariate methods for the four stages, starting with three descriptive tools: hierarchical clustering (agglomerative or divisive), multi-dimensional scaling (MDS, usually non-metric) and principal components analysis (PCA). Table 1...

Table 1.7. Nutrient enrichment experiment, Solbergstrand mesocosm, Norway {N}. Meiofaunal abundances (shown for copepods only) from four replicate boxes for each of three treatments (Control, Low and High levels of added nutrients). Fig. 1.12. Nutrient en...

A framework has been outlined of three categories of technique (univariate, graphical/distributional and multivariate) and four analysis stages (representing communities, discriminating sites/conditions, determining levels of stress and linking to environmenta...

Data matrix The available biological data is assumed to consist of an array of p rows (species) and n columns (samples), whose entries are counts or densities of each species for each sample, or the total biomass of all individuals, or their percentage cover, ...

A trivial example, used in this and the following chapter to illustrate simple manual computation of similarities and hierarchical clusters, is provided by extracting six species and four years from the Loch Linnhe macrofauna data {L} of , seen already in Fig....

As discussed at the beginning of this chapter, quantitative uncertainty may make it desirable to reduce the data simply to presence or absence of each species in each sample, or this may be the only feasible or cost-effective option for data collection in the ...

Starting with the original data matrix of abundances (or biomass, area cover etc), the similarity between any pair of species can be defined in an analogous way to that for samples, but this time involving comparison of the ith and lth row (species) across all...

The converse concept to similarity is that of dissimilarity, the degree to which two samples are unlike each other. As previously stated, similarities (S) can be turned into dissimilarities ($\delta$), simply by: $$ \delta = 100 -S \tag{2.11} $$ which of cou...

On the grounds that it is better to walk before you try running, discussion of comparisons between specific similarity, dissimilarity and distance coefficients, that the PRIMER software refers to generally by the term resemblance measures, is left until after ...

The previous chapter has shown how to replace the original data matrix with pairwise similarities, chosen to reflect the particular aspect of community similarity of interest for that study (similarity in counts of abundant species, similarity in location of r...

The most commonly used clustering techniques are the hierarchical agglomerative methods. These usually take a similarity matrix as their starting point and successively fuse the samples into groups and the groups into larger clusters, starting with the highes...

perform hierarchical cluster analyses of zooplankton samples, collected by double oblique net hauls at 57 sites in the Bristol Channel UK, for three different seasons in 1974 {B}. This was not a pollution study but a baseline survey carried out by the Plymo...