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By G Dunn; Brian Everitt

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Them particularly attractive. 3) That is, the dissimilarity between i and j is independent of the direction in which it is measured, and must be positive provided the two OTUs are not coincident. 4) That is, dij will take some non-zero value if i and j are not the same OTU. 5) (d) Triangular inequality: Given three OTUs i, j and k, the dissimilarities between them satisfy the inequality ~~~+4 p~ The triangular inequality is also known as the metric inequality, and dissimilarity coefficients satisfying the above properties are known as metrics and generally referred to as distances rather than dissimilarities.

4) i= 1 If the first r. components explain a large amount of the total variance as indicated by Ii = 1 Ai/trace (S), then scores on each of these components for each OTU may be used in later analyses in place of the original characters. 5) where Xi is the vector of character scores for OTU i. 4 Examples not independent of the scale(s) of the original measurements. MUltiplying one of the variables by a 'constant (for example, by altering the scale from metres to centimetres) will change the covariance matrix and produce a different set of principal components.

The following example from Sokal & Sneath (1963) illustrates some of the difficulties over the appropriate way to deal with negative matches when estimating similarity. The absence of wings, when observed among a group of distantly related organisms (such as a camel, louse and nematode), would surely be an absurd indication of affinity. Yet a positive character such as the presence of wings (or flying organs defined without qualifications as to kind of wing) could mislead equally when considered for a similarly heterogeneous assemblage (for example, bat, heron and dragonfly).

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