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By G Dunn; Brian Everitt
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All that is required for perfect correlation is that one set of scores be linearly related to the second set (see Fleiss & Zubin, 1969, for an example). Because of these points, and others made by Eades (1965) and Minkoff (1965), the correlation coefficient used as a measure of similarity must be regarded as unsatisfactory. Measures of dissimilarity and distance As mentioned in the introduction of this chapter, similarity and dissimilarity are mutually dependent terms. Given any similarity measure, s, the corresponding dissimilarity might simply be defined as 1 - s, so that identical OTUs would have similarity unity and dissimilarity zero.
5 Homology of characters When one makes a decision to compare the character states of different organisms or groups of organisms, one has to decide whether it is valid to compare a particular feature of organism A with a similar feature of organism B; that is, whether the two features 22 Taxonomic characters or characters are homologous. Simpson (1961) has defined homology to be 'resemblance due to inheritance' from a common ancestry'. One would not, for example, consider the leg of a cat and the leg of a beetle to be homologous, and the same would apply to the wing of a bat and the'wing of a butterfly.
1 which represents four OTUs scored on each of five binary characters. By calculating a particular coefficient for each pair of OTUs shown in this table we arrive at the similarity matrix for the set of OTUs. Each entry in such a matrix shows the similarity between one pair of OTUs. 2. (Two points to note about these similarity matrices are, first, that self-similarities are unity, and secondly, that the matrices are symmetric since the similarity between OTUs i and j is the same as the similarity between j and i).
A introduction to mathematical taxonomy by G Dunn; Brian Everitt