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<br />DOUGLAS ET AL.-GlLA GEOMETRIC MORPHOMETRICS
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<br />videotaped following procedures outlined in
<br />Douglas (1993) and McElroy and Douglas
<br />(1995). Specimens were allocated to species
<br />based on overall appearance coupled with mor-
<br />phometric and meristic characters (Douglas et
<br />ai., 1989; Douglas, 1993). Allocations were done
<br />by consensus among several collaborating re-
<br />searchers (see Acknowledgments).
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<br />Data collection.-For each specimen, Cartesian
<br />coordinates of 15 landmarks (LMs) were digi-
<br />tized directly from a frozen video image using
<br />a VisionPlus-AT OFG frame-grabber board (Im-
<br />aging Technology) and Morphosys 1.20-0FG
<br />software (Meacham, 1993). An additional four
<br />"helping points" (points 10, 11, 13, 14; Book-
<br />stein, 1991) were similarly recorded. Positions
<br />of the remaining six helping points (points 20- .
<br />25) were computed geometrically from coordi-
<br />nates of digitized landmarks using Morphosys.
<br />Helping points were primarily derived to assist
<br />in quantifying shape of the nuchal hump (as
<br />per McElroy and Douglas, 1995). Eleven (of 15)
<br />LMs were used by McElroy and Douglas (1995)
<br />and are defined therein. The remaining four
<br />[i.e., LM4 (vertical of insertion of anal fin);
<br />LM15 (tip of snout); LM18 (posterior border of
<br />operculum); LM19 (ventral border of opercu-
<br />lum; Fig. 1)] are unique to this study. All LMs
<br />and points are illustrated in Figure 1.
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<br />Statistical analyses.-In common with Bookstein
<br />(1991) and others (e.g., Loy et ai., 1993; Car-
<br />penter, 1996), centroid-size is used as a measure
<br />of overall body size, whereas body shape is
<br />quantified using shape coordinates. Centroid
<br />size is defined as the square root of the
<br />summed, squared distance of all landmarks
<br />about their centr9id (the square root of the
<br />above formulation is inadvertently omitted by
<br />Bookstein, 1991). Centroid size exhibits all the
<br />desirable properties of a size variable, in partic-
<br />ular that of being uncorrelated with shape un-
<br />der a null hypothesis of no allometry (Mosi-
<br />mann, 1970; Bookstein, 1989a). In this study,
<br />centroid size was found to be positively corre-
<br />lated with standard length (r= 0.93; P< 0.00l).
<br />Shape coordinates allow the study of shape
<br />variation by considering triangles of landmarks.
<br />Two landmarks are chosen as baseline and are
<br />given coordinates [0,0] and [1,0], respectively.
<br />With a baseline AB (Le., with A = [0,0] and B
<br />= [1,0]), the coordinates of C are then trans-
<br />formed to [X' ,Y], following equations in Book-
<br />stein (I 989b ). This is repeated across the n-2
<br />non baseline landmarks. The new coordinates
<br />[X' ,V] are termed shape coordinates, the prop-
<br />erties of which are demonstrated by Bookstein
<br />
<br />(1991:125-186). Of particular importance is
<br />that they encompass all possible shape variables
<br />derivable from interlandmark distances (Le., ra-
<br />tios, angles, areas, etc.). As noted earlier, con-
<br />figurations of landmarks optimally superim-
<br />posed using a least-squares procedure based on
<br />Procustes-distances demonstrate greater statisti-
<br />cal power than shape coordinates when used to
<br />test equity of shape amongst populations
<br />(Rohlf, 2000).
<br />Shape coordinates in this study were derived
<br />using the baseline LM3-LMI5 (Fig. 1) and ap-
<br />plied in three subsequent analyses. The first ex-
<br />amined variation within the six samples of G.
<br />CYPha, whereas the second examined variation
<br />within the seven samples of G. robusta. Size var-
<br />iation in each of these analyses was first evalu-
<br />ated by using ANOVA to test for differences in
<br />centroid size among populations. Mean shapes
<br />were derived for populations of each species by
<br />first averaging then plotting shape coordinates.
<br />Shape differences were evaluated among pop-
<br />ulations of each species by using MANOVA in-
<br />dividually for each of the 23 nonbaseline coor-
<br />dinate pairs, then summarized using canonical
<br />variates analysis (CVA; Marcus, 1989). All mor-
<br />phological distances (Mahalanobis D2) values
<br />obtained from CVA were corrected for sample
<br />size using the formula in Marcus (1993). Clas-
<br />sification results from CVAs of the shape coor-
<br />dinates were compared with those of 100 ran-
<br />domized runs using the datasel. Congruence
<br />between truss and shape-coordinate analyses
<br />was then assessed using Mantel tests of Mahal-
<br />anobis distance matrices (as per Douglas and
<br />Endler, 1982).
<br />The third analysis examined variation among
<br />all 13 populations (i.e., both species together)
<br />using relative warp analysis (RWA; Bookstein,
<br />1991; Rohlf, 1993). To understand relative warp
<br />analysis, one must first understand the concept
<br />of a thin-plate spline (Bookstein, 1989b). Given
<br />two forms, one can use an interpolation func-
<br />tion (Le., the thin-plate spline) to map land-
<br />marks from one form [the "tangent configura-
<br />tion" (as per Rohlf et ai., 1996)] onto corre-
<br />sponding landmarks of the second. In this
<br />sense, thin-plate splines are analogous to defor-
<br />mation grids of Thompson (Thompson, 1917).
<br />A shape-space ("bending energy") metric ex-
<br />presses the level of deformation required to
<br />map the image to its target form. Put simply,
<br />RWA consists of fitting a thin-plate spline for the
<br />transformation of each specimen in the sample
<br />to a single tangent configuration. Variation
<br />among specimens is described in terms of the
<br />variance in the parameters of the spline func-
<br />tion and are expressed relative to the bending
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