A introduction to mathematical taxonomy - download pdf or read online

By G Dunn; Brian Everitt

ISBN-10: 0486435873

ISBN-13: 9780486435879

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2). 2 Quantitative characters Perhaps the simplest way to construct a measure of distance between groups is to use their character mean values, and then use a Euclidean or city-block metric. For example, if the two groups had means Xl ,X 2, ... 19) However, it might be more appropriate to consider measures which incorporate, in one way or another, knowledge of intra-OTU variation. 20) where i and y are the vectors of means of the two groups ; that is, x' =(X 1 ,X 2, ... ,xp), y' ='

The most familiar metric is, of course, Euclidean; it is familiar because we live in a locally Euclidean universe and this tends to give it advantages in numerical taxonomy, where it is very widely used, because our daily experience gives us an intuitive grasp of Euclidean distances and thereby enables us to grasp their properties without difficulty. 1(a). e. axes at right angles to ,each other). However, in practice, because of the correlation of character states, this assumption will not be justified and the Euclidean distance will be a poor measure of the actual distance between OTUs i and j.

2. 40 Measurement of similarity (b) Qualitative characters with more,than two states. In this case Sijt = 1 if the two individuals i and j are the same for the kth character and zero if they differ. The number of states in the character is not taken into account, and for this type of data Gower's coefficient is equivalent to the simple matching coefficient discussed earlier. (c) Quantitative data. 15) where Xii: is the value for OTU i on character k, and Rtis the range of the character values obtained either from a knowledge of the total range of the character in the relevant population, or as observed in the sample of OTUs under investigation.

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A introduction to mathematical taxonomy by G Dunn; Brian Everitt

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