Morphometric analysis of humerus and femur shape in Morrison sauropods: implications for functional morphology and paleobiology

Paleobiology, Summer 2004 by Bonnan, Matthew F

Differences in the coordinate distances of the reference form's landmarks and those of each specimen warp or bend the thin-plate spline into shapes that are visualized qualitatively, while generating quantitative variables called partial and relative warps (Bookstein 1991). Partial warps are a series of variables that describe uniform and nonuniform shape changes in an element. A single uniform, component (reported as an x-y coordinate pair) is generated that describes parallel changes in element shape, whereas several non-uniform partial warps (also reported in x-y coordinate pairs) are generated in order of most localized shape changes to more general, overall changes in form. As partial warps are correlated, normalized variables that collectively describe shape change, a MANOVA was used to detect the group mean differences reported here (as per Bookstein 1996). However, the biological significance of partial warps is problematic and complex (Rohlf 1998; Zelditch et al. 1998) and has led to controversy over their implementation and interpretation in morphometric studies (e.g., Zelditch et al. 1995, 1998; Rohlf 1998). Instead, relative warps are examined to extract biologically meaningful patterns of total shape change (Rohlf 1993; Bookstein 1996; Birch 1997).

Relative warps are principal components of shape change derived from the covariance matrix of partial warp scores. They are uncorrelated (orthogonal) and contain almost all of the variability within a given sample (Bookstein 1996; Birch 1997; Rohlf 1997b). As with PCA, relative warp (RW) 1 describes most of the cumulative sample variation, RW 2 describes most of the remaining cumulative sample variation, and so on. The major departure from PCA is that relative warps are principal coordinates of shape variation that are derived ultimately through Procrustes super-imposition methods (Bookstein 1996; Birch 1997; Rohlf 1997b). Therefore, the sample variation accounted for by the RWs is related to shape differences instead of linear dimensional measurements. Relative warps can be analyzed in several ways including various methods of data shearing, weighting, and the exclusion of uniform shape change components (see Rohlf 1993 and Bookstein 1996 for overviews). Here, relative warps were computed within the so-called total shape space (Bookstein's [alpha] = 0) to simplify the analysis and to examine global, local, uniform, and non-uniform changes in bone shape simultaneously (see Bookstein 1991, 1996 for more details). Shape changes reported by the relative warps were compared with the MANOVA results of the uniform and partial warp scores. An extensive literature exists on the application of thin-plate splines, and the reader is referred to Bookstein 1991, 1996 (and references therein) and Birch 1997 (provides a comparative example of the method) for more detailed procedural and statistical information.

Results

Traditional Morphometric Results

Forty-two humeri and 40 femora were measured for traditional morphometric analysis (humerus/femur: Apatosaurus [n = 15/12]; Diplodocus [n = 9/11]; Camarasaurus [n = 18/ 17]). Shapiro-Wilk results indicate that most humerus variables have a non-normal distribution (Table 1), whereas most femoral variables show normal distribution (Table 2). In both PCAs, four principal components were extracted. The overwhelming proportion of sample variation accounted for by PC 1 (humerus = 92%; femur = 85%) and the high positive loadings of all variables on this factor in both analyses suggest it is a size component (Tables 1, 2). Such results were expected and support previous analyses that suggest most limb variation in sauropods is accounted for by size differences. Interpreting the other components in both analyses was difficult, and few discernible patterns appear in the plots of the components or variables (see below). Refer to Figure 4 for plots of the humerus and Figure 5 for plots of the femur. Variable abbreviations (see Appendix 2) are included next to the variable names in the text to facilitate comparison with table data.