By G Dunn; Brian Everitt
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Extra info for A introduction to mathematical taxonomy
0 calculated by dividing each column of values by the standard deviation of the three character values. 12) The shape coefficient, Ci, looks formidable but is essentially nothing more than the variance of the differences in the character states of the OTUs being compared. It is likely to be large when considerable discrepancy in the magnitude of the differences occurs, including a mixture of positive, negative and negligible terms. The size coefficient, C~, will be large when the character states of the two OTUs are quite different in magnitude, and the differences are largely in one direction.
Sneath & Sokal (1973) are also critical of the usual definition of homology and prefer to use the term operational homology which implies resemblance between parts with respect to some set of properties. This leads to the idea of the classification of characters, or primary classification, as opposed to the classification of organisms, which may be called secondary classification (Jardine, 1967). One decides that two characters are homologous on the basis of resemblance measured according to some predetermined set of rules.
1, and clearly the pairs of measurements are highly correlated. H one wished to express the variation in these two characters on a single axis or dimension, what would be the 'best' axis to choose? One intuitively sensible answer to this question would be to choose the axis which maximizes the variance of the projections of the four points onto itself, since this will provide the maximum discrimination between the four buttercups. It is easy to show that such an axis is given by the line of best fit, in the least-squares sense, to the points; that is, the line that minimizes the sum of squares of the distances between the points and itself.