The Weighted Separation Index: A Multivariate Technique for Separating Members of Closely-Related Species Using Qualitative Differences

Abstract

Vogt, W. G., and D. G. McPherson (School of Biological Sciences and School of Agriculture, University of Sydney, Sydney, Australia: Present addresses Division of Entomology, C.S.I.R.O. Canberra and Mathematics Department, University of Tasmania, Hobart, Australia) 1972. The weighted separation index: a mtultivariate techniqtue for separating members of closely-related species tusing qualitative differences. Syst. Zool. 21:187-198.An index (the weighted separation index) is described which uses qualitative variables to provide a measure of likeness to two known groups of individuals (D. tryoni and D. neohumeralis). An identification rule is presented by which this index may be employed to discriminate between the members of two populations. Where separation of two species is associated with a low probability of misidentification, the weighted separation index is also suited to the separation of a third or hybrid group whose members are intermediate with respect to the two known groups. [Discrimination; qualitative techniques.] The separation of morphologically similar species sometimes requires the use of characters that are not subject to precise measurement. Differences in colour and pattern, for example, are difficult to measure and are usually treated as qualitative variables. The weighted separation index makes it possible to employ two or more qualitative variables as discriminators. The main advantage of this technique is that the values assumed by the index are largely independent of the scales used to measure variation in the different characters. This index was initially developed to separate the two species of Tephlitid flies, Dacus tryoni and D. neohiumeralis. THE SELECTION OF A SEPARATE INDEX In the biological sense, a separation index is a discriminatory device used to separate individuals of closely related groups; an index value is a measure of an individual's likeness to the members of either of two or more groups. The concept of likeness is frequently difficult to apply to organisms, because of the variability that is encountered within each group or species. However, the use of a statistical index enables the biologist to state in precise terms the criteria which he uses to estimate likeness. If likeness can be defined by the use of a single character, then the criterion may be simple and there may be little disagreement in deciding upon it. Unfortunately, biological variation is usually too great to permit the use of a simple index based on one character and it is then necessary to employ many characters, each of which contributes to the measure of likeness. Thus separation of the individuals of closely related groups often necessitates multivariate analysis and, since thinking in many dimensions at the same time is not easy, the multivariate data that need to be analysed are first reduced to one dimension by combining the variables concerned into a single equation. By far the most widely used technique which adopts this approach is Fisher's discriminant analysis in which a linear combination of the variables is obtained. If each variable has a continuous distribution and, furthermore, if each variable has a normal distribution, then Fisher's technique possesses a certain optimum property, namely that of ensuring the smallest probability of misidentification (on average). In such problems it is common however