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638 COPEIA, 1995, NO. 3 TABLE 1. NUMBER OF INDIVIDUALS OF Gala robusea AND G. cypha SAMPLED FROM EACH OF EIGHT LOCAL- ITIES IN THE UPPER COLORADO RIVER BASIN. Population Label- G. mbusta G. gpha Total Black Rocks B 19 25 44 Cataract Canyon C 6 11 17 Desolation Canyon D 24 22 46 Debeque Canyon Q 20 0 20 Grand Canyon G 0 28 28 Rifle R 25 0 25 Westwater Canyon W 56 57 113 Yampa River Y 65 5 70 Totals 215 148 363 ' Labels refer to symbols on Figure I Data collection.-For each specimen, the (X,Y) coordinates of 20 anatomical landmarks (Strauss and Bookstein, 1982; Fig. 2; Appendix) were digitized directly from frozen videotape images using a VisionPlus-AT OFG frame grabber board and Morphosys morphometric analysis software, Version 1.29 OFG (Meacham, 1993). In addition, coordinates of five of 12 "helping points" (points 4, 10, 11, 13, 14; Bookstein et al., 1985) and the ends of the scale bar were similarly recorded; positions of the remaining seven helping points (points 26-32) were com- puted geometrically from coordinates of digi- tized landmarks using Morphosys. Helping points were configured primarily to quantify shape of the nuchal hump, which is highly vari- able in these fishes but for which few anatomical landmarks can be identified (Douglas, 1993). A modified box truss (Bookstein et al., 1985; Douglas, 1993; Fig. 2) consisting of 56 individ- ual distances between pairs of landmarks was constructed for each specimen using Morpho- sys. All measurements were expressed relative to the scale bar (i.e., in absolute mm). These data formed the basis for all statistical analyses and are available upon request from the au- thors. Statistical methods.-All measurements were loge transformed and subjected to principal com- ponents analysis (PGA) of the variance-covari- ance (VCV) matrix using NTSYS-pc (Rohlf, 1992). In all cases, the resulting first principal axis (PC I) explained a large proportion of the total variance (> 78%), and character loadings on this vector were of the same order of mag- nitude and uniform in sign. Given these pat- terns and the broad (> 2 x) range of size dif- ferences among specimens, PC I was interpret- ed as a general size factor (Jolicoeur and Mos- imann, 1960; Jolicoeur, 1963; Rising and Somers, 1989). To minimize effects of general size on subsequent procedures, transformed data were projected onto the space orthogonal to the first principal axis using the algorithm of Rohlf (1992), corresponding to Burnaby's (1966) method for size correction. Although this tech- nique generates a data set of "general-size-al- lometry-free shape" variables (Bookstein, 1989), it is important to remember that "shape" in this context is statistically uncorrelated with our measure of general size (PCI) but is likely cor- related biologically with physical size (Sund- berg, 1989; Bookstein, 1989). As such, we refer to these data as size corrected rather than size free. Size-corrected data matrices were examined for the presence of significant among-group morphological differences through canonical variates analysis (CVA) and multiple discrimi- nant function analysis (DFA) using Statistical Analysis Systems (SAS Institute, 1985). Signif- icance of univariate tests was assessed based on Bonferroni-adjusted probabilities. Within-group VCV matrices derived from size-corrected data were tested for homogeneity using a likelihood ratio test (Morrison, 1976). Predicted group membership was then estimated a posteriori for all specimens, based on their generalized- squared Mahalanobis distance from the cen- troid of each source group. Because within- group variances were homogeneous in all cases, this classification criterion was based on pooled VCV matrices. Although error rates derived from internal classification are unreliable as a measure of the efficacy of discriminant func- tions to assign unknown specimens, they pro- vide a maximum bound on the classification power one might expect and allow distinctive- ness of groups used in discrimination to be as- sessed. Hierarchical relationships of groups in dis- criminant space was visualized using NTSYS-pc through cluster analysis of generalized pairwise distances among group means. Because any clustering technique produces clusters regard- less of the actual structure of the data, we em- ployed single and complete linkage clustering methods (Sneath and Sokal, 1973) as well as UPGMA. The robustness of resulting clusters was evaluated qualitatively by producing a strict consensus of all trees derived from these meth- ods. Clusters resolved in the consensus topology are likely to be well supported (Rohlf, 1992). For intraspecific analyses (see below), the matrix correlation between canonical distances among group means and geographic proximity (in river miles) among sampling localities was examined