A universal scaling relationship between body mass and proximal limb bone dimensions in quadrupedal terrestrial tetrapods

Abstract

Background: Body size is intimately related to the physiology and ecology of an organism. Therefore, accurate and consistent body mass estimates are essential for inferring numerous aspects of paleobiology in extinct taxa, and investigating large-scale evolutionary and ecological patterns in the history of life. Scaling relationships between skeletal measurements and body mass in birds and mammals are commonly used to predict body mass in extinct members of these crown clades, but the applicability of these models for predicting mass in more distantly related stem taxa, such as non-avian dinosaurs and non-mammalian synapsids, has been criticized on biomechanical grounds. Here we test the major criticisms of scaling methods for estimating body mass using an extensive dataset of mammalian and non-avian reptilian species derived from individual skeletons with live weights.

Results: Significant differences in the limb scaling of mammals and reptiles are noted in comparisons of limb proportions and limb length to body mass. Remarkably, however, the relationship between proximal (stylopodial) limb bone circumference and body mass is highly conserved in extant terrestrial mammals and reptiles, in spite of their disparate limb postures, gaits, and phylogenetic histories. As a result, we are able to conclusively reject the main criticisms of scaling methods that question the applicability of a universal scaling equation for estimating body mass in distantly related taxa.

Conclusions: The conserved nature of the relationship between stylopodial circumference and body mass suggests that the minimum diaphyseal circumference of the major weight-bearing bones is only weakly influenced by the varied forces exerted on the limbs (that is, compression or torsion) and most strongly related to the mass of the animal. Our results, therefore, provide a much-needed, robust, phylogenetically corrected framework for accurate and consistent estimation of body mass in extinct terrestrial quadrupeds, which is important for a wide range of paleobiological studies (including growth rates, metabolism, and energetics) and meta-analyses of body size evolution.

Figure 1

Limb scaling patterns in mammalian clades. Lines are fitted based on the SMA results presented in Table 1. (A) Log femoral length and circumference plotted against log body mass. (B) Log humeral length and circumference against log body mass. (C) Log femoral length plotted against log humeral length. (D) The log of combined humeral and femoral circumference against log body mass. SMA, standardized major axis.

Figure 2

Limb scaling patterns in quadrupedal terrestrial tetrapods. Lines are fitted based on the SMA results presented in Table 1. Lissamphibians are plotted (green) but no line was fitted due to its small sample size and body mass range. (A) Log femoral length and circumference plotted against log body mass. (B) Log humeral length and circumference against log body mass. (C) Log femoral length plotted against log humeral length. (D) The log combined humeral and femoral circumference against log body mass. SMA, standardized major axis.

Figure 3

Limb scaling patterns in different mammalian size classes. Lines are fitted based on the SMA results presented in Table 4. All three comparisons plot the log total stylopodial circumference against log body mass in the mammalian sample of the dataset. Size class comparisons are based on previously studied thresholds discussed in the text [78,93,94]. Mammals above and below 20 kg (A), 50 kg (B), and 100 kg (C). SMA, standardized major axis.

Figure 4

Raw OLS regression for body mass estimation and percent prediction error of body mass proxies. (A) The least-squares regression of the raw data between the log total stylopodial circumference and log body mass in a sample of 245 (talpids removed) mammals and non-avian reptiles. Regression equation shown in the format y = mx + b, and is presented along with its coefficient of determination (R²), mean percent prediction error (PPE), standard error of the estimate (SEE), and Akaike Information Criterion (AIC). (B) Comparison of the predictive power of several body mass proxies based on their mean PPE. The mean PPE of each proxy is represented by the black circle along with their 95% confidence error bars. The plot is divided into two sections representing the results from the bivariate and multiple regression analyses. Variables regressed against body mass are labelled along the x-axis. Labels marked with an * represent the analyses in which the data was phylogenetically adjusted through the use of a phylogenetic generalized least squares bivariate or multiple regression. C_F, femoral circumference; C_H, humeral circumference; L_F, femoral length; L_H, humeral length; OLS, ordinary least squares.