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390 COPEIA, 2001, NO.2 Sile Codes Gila cypha Gila mlnula Black Rocks Cn, UT BR 25 19 Cataract Cn, UT CC 11 6 Desolation Cn, UT DC 22 24 Little CO River, AZ LC 28 Fig. l. Landmarks used in the current study. Def- Westwater Cn, UT WW 57 56 initions are given in text or in McElroy and Douglas Yampa River, CO YR 5 65 (1995). DeBeque Cn, CO DB 20 Rifle Cn, CO RI 25 morphological landmarks on. images of biolog- ical specimens (as in Douglas, 1993). Land- marks are (most often) homologous from im- age to image, thus permitting a detailed analysis of how the former shift relative to one another as shapes are contrasted. Bookstein (1991:55- 87) discusses types of landmarks, their configu- rations, and limitations. Once coordinates are obtained, geometric relationships are clarified by fitting the former to a function (such as a thin-plate spline, see below). The parameters of a thin-plate spline transformation can them- selves be used as variables in conventional mul- tivariate analyses (as done herein). Interestingly enough, changes in form resulting from size and uniform shape alterations (i.e., affine trans- formation) can now be easily separated from those resulting from nonhomogeneous changes (i.e., nonaffine or local deformations). This is also demonstrated herein. Nonaffine transfor- mations can be further split into partial warps or geometrically orthogonal components that correspond to deformations at different scales. It has been suggested that the relative contri- butions of these orthogonal components to overall shape change can, in turn, be employed as taxonomic characters (Zelditch et aI., 1992, 1995). However, this point is disputed (Book- stein, 1994; Naylor, 1996a; Rohlf, 1998). Other methods (such as Procrustes or finite element scaling analyses; Cheverud and Richtsmeier, 1986; Rohlf and Slice, 1990) can also be used to fit differences in landmark positions among organisms. Although there are differences among the methods noted above, all will usually lead to similar results particularly given the levels of shape variation normally found in biological data (Rohlf, 1999:212). However, to test this hy- pothesis, Rohlf (2000) used simulations to com- pare these (and other) methods in terms of type I error rates and their power for distin- guishing among shape differences. He found Procrustes-based analyses superior to other pro- cedures, and these in turn are now favored by most researchers today. However, Bookstein shape coordinates did almost as well as Pro- TABLE l. MATERIAL EXAMINED. crustes-based methods, as long as ~hape varia- tion was small and the baseline reasonable. The latter aspect is judged most crucial, in that base- lines defined by closely set landmarks displayed quite low power. An important aspect of a geometric morpho- metric analysis is that results can be displayed visually in terms of the 2-D or 3-D space of the organism. These are easier to interpret on a comparative basis because they are configured as shapes within a coordinate system (see be- low). AI; such, they provide an analytical and graphical means to decompose phenotypic var- iation at different spatial scales (i.e., highly lo- calized subregions vs globally diffuse forms: Naylor, 1996b). In this investigation, a geometric morpholog- ical analysis is conducted on two species of west- ern North American cyprinid fishes (Gila cypha and Gila robusta) rich in phenotypic shape (Fig. 1). The practicality of this endeavor is para- mount in that the former is endangered, where- as the latter is considered a "species of con- cern." Results from these analyses are then compared to a more traditional analysis of the same individuals employing distance measures extracted from a truss (McElroy and Douglas, 1995). The efficacy of the geometric approach is then evaluated relative to the truss analysis and conclusions from the two studies com- pared. The hypothesis under test is that signif- icant differences exist between results of the two types of analyses. 1:-. ... MATERIALS AND METHODS Video images.-The database consists of video im- ages of adul t G. robusta (n. = 215) and G. cypha (n = 148) collected from eight localities in the upper Colorado River basin during a 17-month span (May 1991 to October 1992). The two spe- cies were sympatric at five of these locations; G. TObusta was absent at one additional site, where- as G. cypha was missing at two others (Table 1). Saggital views (left side) of each individual were