BIOMETRIC ANALYSIS OF GEOGRAPHIC VARIATION AND RACIAL AFFINITIES
Authors: THORPE By R. S. 
Published: January 2008

Summary1. The study of geographic variation and the racial affinities between populations is of central importance to systematics and evolutionary theory. When using phenotypic variation to measure the similarity between the populations of a species one should analyse the variation in several characters simultaneously. This is a statistical procedure and is known as multivariate analysis. Multivariate analysis of phenotypic variation, unlike some other methods, has the advantage of not being dependent on living specimens.2. To obtain an adequate sample at each locality, and an adequate distribution of localities within a given geographic area, can be a major problem. The pooling of data from adjacent localities is discussed.3. There are several sources of phenotypic variation within a species, e.g. sexual and ontogenetic variation. Failure to eliminate the non‐geographic sources of variation can confuse the assessment of the similarity between populations.4. Correlation between characters can reflect similar genetic control and/or similar patterns of geographic variation, the biological interpretation being influenced by whether the data come from one locality or many.5. The influences of environmental induction and genetic control cannot easily be separated. Also, some characters may not be entirely homologous throughout the range of the species.6. Most studies rely on far too few characters of a too restricted type to give an ‘overall’ assessment of the phenotypic similarity. This is one of the most neglected aspects of the study of geographic variation.7. The various forms of clinal and categorical variation, the precise nature and position of sharp transition (hybrid) zones, the relationship between non‐adjacent as well as adjacent populations and the phenotypic divergence between island populations, etc., all come under the heading of geographic variation. The ideal technique should be able to elucidate all types of geographic variation but some techniques can only be used effectively with a few of them. Moreover, techniques may be limited in their application because they require the data to conform to certain models, e.g. normal distribution.8. The degree of phenotypic similarity between populations can be measured by a wide range of similarity coefficients. Comparison between even a small series of populations produces a large set (or matrix) of similarity coefficients that is difficult to interpret. However, the relationships between populations can be summarized in several ways and these may be loosely grouped into four categories; (i) network diagrams, (ii) contours and isometric plots, (iii) hierarchical clusters, and (iv) ordination methods. These methods are explained and their advantages and limitations discussed.9. The hierarchical (dendritic) model of cluster analysis is unsuitable for analysing all but a few types of geographic variation.10. There are several types of ordination technique. They all aim to summarize the variation of many characters in a reduced number of axes. One can either emphasize the biological interpretation of each separate axis, or treat the analysis as a classifying technique and assess the grouping of the populations in the space defined by the axes. Considerable care is needed in interpreting the results of both of these approaches.If correctly applied, ordination techniques generally can be used to analyse all the forms of geographical variation and are therefore recommended. Contrary to current practice they can be used with a large number of characters. The advantages and limitations of the various ordination techniques are discussed.11. Contours and their three‐dimensional isometric plots can be used to portray geographic variations in the information obtained from a multivariate analysis. However, contours and isometric plots are limited in their applicability and the amount of information they can convey.12. The sophistication of some multivariate methods should not be allowed to cloak the scientific inadequacies of a study. The use of more than one technique and variety in the choice of pertinent parameters may be of value in indicating the reliability of the results.