By G. Dunn
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The exponentially expanding quantities of organic info besides related advances in computing energy are making attainable the development of quantitative, predictive organic structures versions. This improvement may perhaps revolutionize these biology-based fields of technology. to help this variation, the U.
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3 for an explanation of the characters 1- 19. 1. Note that the sum of squares of the coefficients in each component is unity and that the sum of the latent roots is equal to the sum of the diagonal elements in S. The ftrst principal component accounts for nearly all of the variance in the three characters. 31 (height) The size of the turtle shells could be characterized by this single variable with little loss of information since it alone accounts for some 98% of the variation of the three measurements length, width and height.
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. ) This problem can be overcome either by using oblique coordinate axes and a measure such as M ahalanobis' generalised distance (see later) or by transforming to principal component axes (see Chapter 4). 2. For quantitative characters, Euclidean distance calculated directly on the raw data may make little sense where the characters have different scales.
Jardine & Sibson (1971) remark that such a procedure is 'absurd'. It has often been suggested that the correlation coefficient will be a useful measure of similarity in those situations where absolute size alone is regarded as less important than shape. Thus, in classifying plants and animals, the absolute sizes of the organisms or their parts are often of less importance than their shapes, and in such cases the investigator requires a similarity coefficient which will take the value unity whenever the set of character-state values describing two OTUs are parallel, irrespective of how far apart they are; for example, the following sets of scores are parallel in this sense: OTUI OTU2 OTU3 10 15 30 5 10 25 15 20 35 3 8 23 20 25 40 The correlation coefficient meets this requirement (it takes the value unity for each pair of OTUs in the above example); unfortunately, the converse is not true since the correlation may take the value one even when the two sets of values are not parallel.
An Introduction to Mathematical Taxonomy by G. Dunn