Fig 1.
Simplified dinosaur cladogram plotted with approximate ages.
Phylogenetic tree data from Grady et al. [13] are supplemented with approximate ages. Lineage metabolism is colored according to the legend. Inset graphs at the top schematically show several hypotheses about dinosaur metabolism.
Fig 2.
Geometric effect of the shear transformation between log-log transformed Gmax and kC.
Panel (A) shows regions in the (M, kC) plane; (B) shows the same regions when transformed to (M, MkC). The scale is log-log transformed, so the transformation is (log(M), log(k) + log(C)) → (log(M), log(M) + log(k) + log(C); see Eq (9).
Fig 3.
Regression using Gmax or kC, kD as the dependent variable for several extant groups.
Using Gmax instead of kC or kD reduces the scatter on the graph and greatly increases R2, while leaving the slope b and its 95% confidence interval (in square brackets) unchanged. [w]: Werner and Griebeler [12], [g]: Grady et al. [13]. Red lines delineate the convex hulls encompassing the data points. Shaded regions bounded by dashed lines delineate 95% confidence bands on the regressions.
Fig 4.
Dinosaur growth-rate allometry.
[g]: data from Grady et al. [13]; [w]: data from Werner and Griebeler [12]. Plots on the left are the original data. Plots on the right, labeled *, are the corrected data sets with Archaeopteryx removed. Red lines delineate the convex hulls encompassing the data points. Shaded regions bounded by dashed lines delineate 95% confidence bands on the regressions. Note that for the [w] plots, N is not the number of taxa because there are multiple data sets for some taxa; the regressions are weighed to account for this. The original data set (upper right) includes 13 taxa; the corrected data set comprises 12 taxa (Archaeopteryx is excluded).
Fig 5.
Confidence and predictions bands versus convex hull.
Plot (A) shows the results of regression on Gmax for data sets from Grady et al. [13]. Shaded regions are the 95% confidence bands for the regressions. Plots (B) shows the range of variation within each group as a shaded convex hull polygons containing the data from each of the two studies, respectively. Dinosaurs are shown as a black outline; the dashed black outline represents dinosaurs excluding Archaeopteryx. Plot (C) shows the single prediction bands for regression of kC versus M for each group. Plot (D) shows the convex hull polygons for mass and BMR data from [13].
Table 1.
Data points that lie inside the convex hull polygon of each group.
The data points from Grady et al. [13] arranged vertically and the convex hull associated with each group horizontally. Because there is substantial overlap among the convex hulls, a data point may belong to more than one convex hull.
Table 2.
Data points that lie inside the convex hull polygon of each group.
The data points from Werner and Griebeler [12] arranged vertically and the convex hull associated with each group horizontally. Because there is substantial overlap among the convex hulls, a data point may belong to more than one convex hull.
Fig 6.
Fixed-slope regression residuals.
Each plot shows the histogram of growth rates adjusted to a mass of 1 g, assuming a fixed slope of b = 0.75 for data sets from (A) Grady et al. [13] and (B) Werner and Griebeler [12]. Histograms for endothermic groups are shaded light red; those for ectotherms are shaded light blue. The shaded band shows the growth rates that overlap among extant endotherms, ectotherms and dinosaurs (yellow). Plots (C) and (D) show the equivalent fixed-slope regressions for BMR data from [13].
Table 3.
The difference between the corrected Akaike information criterion (ΔAICc) was calculated for models fit to log-log transformed kC versus M data (from Grady et al.) or kD versus BMatMG data (from Werner and Griebeler), on a group-by-group basis. The models having ΔAICc = 0 (unshaded cells) are the best fit. Models having ΔAICc < 2 (bold numbers) have strong statistical support. The results show that substantial curvature effects exist for many groups. Models are defined in S2 Table. Best fits are plotted in S18 and S19 Figs.
Fig 7.
Correlations among BMR, kC, and M are not transitive.
(A) shows pairwise correlations between BMR and kC, BMR and M, and kC and M (see also S20 Fig). (B) through (D) show how three-dimensional (BMR,kC,M) points map to each of these pairwise correlations. Even though both BMR and kC have correlations to M, they are essentially not correlated to each other (R2 = 0.03).