The Use of Ratio Variables in Systematics

Summary Eight ratio variables measured on 85 OTUs from Raoulia subg. Raoulia were studied to explore their distributional properties and discriminating abilities. The ratios are shown to be generally less normal than their constituents, a property that can (to varying degrees) be alleviated by the choice of the numerator as the constituent with the largest coefficient of variation. The discriminating properties of the ratios are shown to be as good as their constituents individually, implying that the ratios are potentially useful variables with unique properties. The problem of redundant variability as a product of including a ratio variable and its two constituents in a data set is also addressed. Given that the deletion of one of these variables is a solution to this, it is shown that removing the ratio does not necessarily optimise the amount of retained variability. Thus, the use of ratio variables is seen to be an empirical a posteriori decision that can be made on the basis of objective criteria.