By Clarke & Warwick
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For each species abundance, subtract the mean count and divide by the standard deviation over all samples fo r that species. This makes the variance of samples along all species axes the same (= 1) so all species are of potentially equal importance in determining the principal components. This normalised analysis is referred to as cOrTelation-based peA rather than the covariancebased peA obtained when the data is not normalised ' Chopt«4 page~ (the terminology comes from whether the algebraic extraction of eigenvalues and eigenvectors takes place on the correlation or covariance matrix between species).
The PRIMER program CLUSTER displays the dendrogram from hierarchical agglomerative clusterirlg, allowiug a choice from the three li,lkage possibilities described below and wriou5 otpioNS for axis labelling, orientation etc. 20 I 30 '" 40 E 50 .. '" OO 7C r C80 1 I t 1 L 90 100 GGGGEEEEDDDDCCBBCBBCAAAA Fig. 1. Frie:rfjord macrofauna counts {F} . 1. guished, and that A, E and G do not link to B, C and D until quite low levels of between-gToup similarities are reached. The mechanism by which Fig. 1 is extracted from the Similarity matrix, including the various options for defining what is meant by the similarity of two groups of samples, is best described for a simpler example.
Even the computationally simplest of techniques, PCA, could never be carried out manually in any realistic example. Nonetheless, PCA tends to take only seconds, rather than minutes or hours, of processing time on a personal computer. The constraints are mainly on the number of species handled, and large numbers of samples can usuall y be accommodated. This is in contrast to cluster and MDS analyses which tend to be more constrained by the number of samples they can handle; once the data is reduced to a similarity matrix between samples (the input form to both clustering and MOS) the number of species in the original matrix is irrelevant.