A New Statistical Approach to Geographic Variation Analysis

The authors discuss the problems of describing geographic variation data and develop statistical methods for categorizing sets of populations sampled from different localities. The general approach of the simultaneous test procedures, available with a variety of statistical tests and for continuous as well as for categorical data, is employed with these techniques. Geographical regions are defined as sets of connected localities, with connectedness being defined geometrically. Maximal acceptahle connected sets of localities (defined as regions) or coarsest acceptable connected partitions of the entire set of localities are found by these procedures. These are illustrated with several examples. I. AIMS AND PURPOSES The primary aim of geographic variation anialysis in biological systematics is the description and summarization of patterns of variation and covariation of characteristics of organisms that are distributed over an area. Such analyses are generally applied to species populations to study the variation of diverse characters. The most frequently studied characters are morphological, but recently there have also been such studies of biochemical, physiological, behavioral, cytological, immunological, as well as genetic characters. The basis for studies in geographic variation rests on the existence of populations of comparable organisms at a number of localities in the area under study. Comparisons of these populations are made in terms of one or more observable characters and the analyses relate these comparisons to differences in location. Data for studies in geographic variation consist of samples taken from the populations at a given number of localities, with a set of characteristics observed for each organism sampled. Summary statistics may be computed for each sample, as, for example, means and standard deviations for single measurable characteristics, correlations for pairs of such variables, etc. A summary of the data would then consist of a list of localities, each accompanied by its set of summary statistics for observed characteristics. In most cases, the infornation in such a list would be difficult to grasp and much would be gained by plotting the statistics on a map (or several maps) according to their location. Such graphic representation often reveals a good deal about the geographic variation pattern involved. A step beyond mere description of the pattern of variation of the characteristics of organisms is categorization. Usually, one prefers to group together localities that are geographically adjacent and whose populations are similar in their characteristics. This may be desired merely for purposes of simplification and summarization, or for the formal or semi-formal recognition of a population or series of populations in terms of the Linnean system. The study of patterns of geographic variation will often lead to causal ana:lysis. One may attempt to interpret the variational and correlational patterns of a species as adaptations to variation in known environmental factors, such as climatic, topographic, or edaphic variables. Other possible causes of variation may be differences in associated species populations, such as host plants, parasites, predators, etc. Marked and abrupt changes in characters between close localities may be related to abrupt changes in the above factors, to strong barriers to dispersal of the organisms or to secondary zones of intergradation between allopatrically differentiated populations. Unusual patterns of