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However, as was seen in the preceding section, the taxonomist using numerical methods needs to be aware that different approaches to coding character states, and the use of a particular similarity or distance measure (see Chapter 3), often imply subtle differences in character weighting. The real problem with a priori weighting is perhaps not that it is logically invalid, but that it is often very difficult to decide how to weight the characters in practice. After a classification has been arrived at, one may wish to be able to identify new individuals using a diagnostic key or some form of discriminant function analysis (see Chapter 7).

Here some characters will almost certainly be more useful than others, and so one uses a posteriori weighting of characters in the construction of such keys. This, however, is the last stage of the procedure, and should not influence the formation of the taxa concerned. 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.

This would be relatively unimportant if the coefficients were jointly monotonic, in the sense that if all OTU pairs for one of the coefficients were ordered so that their similarity values formed a monotonic series (that is, a series that either increases or decreases over the whole of its length), then those for the other coefficient also formed such a series. ) However, joint monotonicity is the exception rather than the rule for similarity coefficients and this can be illustrated with the similarities calculated above.

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