Multiple-Discriminant Analysis of Geographical Variation in the Aquatic Beetle, Rhantus Gutticollis (Say) (Dytiscidae)

Zimmerman, James R., and John A. Ludwig (Department of Biology, New Mexico State University, Las Cruces, New Mexico 88003) 1974. Multiple discriminant analysis of geographical variation in the aquatic beetle Rhantus gutticollis (Say) (Dytiscidae). Syst. Zool. 24:63-71.-Multiple-discriminant analysis with aid of the Mahalanobis D2 statistic is a useful way of.-analyzing geographical variation in Rhantus gutticollis (Say). A moderate number of mensural characters (14) and rather small sample sizes (N 25 or 30) give results which permit discrimination to a fine degree among apparently very similar populations. The approach reveals more features of geographical variation than would probably be seen in the usual one-character comparisons. It is a widespread species with considerable regional differentiation and with well-marked boundaries between different population groups. In spite of those differences, the situation does not readily lend itself to conventional subspecific fractionation. The results from MDA are interpreted as reflections of gene flow rather than differentiation of local populations. [multiple-discriminant analysis, geographic variation, Dytiscidae, gene flow.] The problem of analyzing geographical variation within species continues to receive attention by taxonomists. For the traditional taxonomist, recognition of geographical and ecological races, clines, chromosomal differences, and polymorphs has probably been the principal means of illustrating regional variations in species. Some character differences between populations have traditionally been compared using univariate statistical procedures. Increasingly more multivariate statistical studies have been used to examine geographical variation (see the review of Gould & Johnston 1972, and Genoways & Choate 1972, Rohwer 1972, Jackson 1973, Johnston 1973, Niles 1973). Among the techniques is multiple-discriminant analysis (MDA) which includes both discriminant functions and generalized distance, or the D2 statistic. Discriminant function is a linear function that will best discriminate between two sample populations based on multiple characteristics. Generalized distance is a measure of a statistical distance between two sample populations. D2 is easily calculated using a discriminant function (Rao 1952). We wish to examine geographic variation in the aquatic beetle Rhantus gutticollis (Say) using the D2 statistic. R. gutticollis is a medium-sized species of predacious diving beetle ranging from British Columbia to Costa Rica, and from the Pacific Coast to the western edge of the Great Plains (Fig. 1). Zimmerman and Smith (In press) document the species limits and synonymy used for this paper. R. gutticollis, described by Say in 1834 from Mexico, was long unknown and usually confused with R. binotatus (Harris). Wallis (1933) recognized gutticollis and considered it as distinct from a Pacific Northwest population which he described as hoppingi. Leech and Chandler (1956) confirmed that the two forms were separable and noted the occurrence of gutticollis and hoppingi in California. Another nominal species, R. mexicanus (Aube'), has proven to be a dark polymorphic form of gutticollis which occurs throughout the southern part of the range. It differs only in its mostly black rather than the irrorated (color applied as grains of sand) elytral pattern which is found in the more common morph. The mexicanus morph is indistinguishable from the common form in the 14 characters used in this study. Intergrades (with the penis and male protarsal claws as diagnostic characters) be-