Appendix A. Supplementary figures and tables showing potential sampling biases within the original PBDB data set, the distribution of pairwise distances and corresponding beta indices within each stage, diversity indices using the Chao-2 estimators of shared unsampled taxa, rates of overall genus-level origination and extinction over both pulses of O-S mass extinction, and additional range size/effect size plots (including data for individual brachiopod genera).

Supplementary figures and tables showing potential sampling biases within the original PBDB data set, the distribution of pairwise distances and corresponding beta indices within each stage, diversity indices using the Chao-2 estimators of shared unsampled taxa, rates of overall genus-level origination and extinction over both pulses of O-S mass extinction, and additional range size/effect size plots (including data for individual brachiopod genera)

Raw data

Excel file with raw data for all surfaces (univariate and multivariate). Measurements are retrodeformed, after mathematically removing tectonic bed-parallel shortening (see Clapham et al., 2003; Wood et al., 2003). Only complete measurements are used; measurements from incomplete/broken specimens are excluded

Ediacaran distributions in space and time_supplementary

Database tables of Ediacaran fossil occurrences, with additional tables describing the formatting of the database and a catalogue of geochronological data associated with fossiliferous Ediacaran strata. Also included are subsequent statistical analyses of the data-set using hierarchical cluster analysis and confidence intervals

Ordinary least squares regressions between ln body mass and ln skeletal element dimensions in a sample of 863 volant birds.

<p>Regression equations are shown in the format <i>y</i> = <i>mx</i> +<i>b</i>, and presented with their coefficient of determination (<i>R</i>²) in panels. 95% prediction intervals (red), and 95% confidence intervals (green) are also depicted. At this scale, 95% confidence intervals virtually overlap the OLS fit (pink) for the more precise regressions. Regression statistics are presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082000#pone-0082000-t002" target="_blank">Table 2</a>. </p

Barplots illustrating variance in slopes (gray) and intercepts (black) of regressions between body mass and our 13 skeletal measurements, among all treated avian orders.

<p>Barplots illustrating variance in slopes (gray) and intercepts (black) of regressions between body mass and our 13 skeletal measurements, among all treated avian orders.</p

Scatterplot illustrating close correspondence of SMA regressions between coracoid HAF and mean species body mass (a), and coracoid HAF and recorded individual body mass (b).

<p>Coefficient of determination and equations (in format <i>y</i> = <i>mx</i> +<i>b</i>) are given in panels. Statistics for comparison via SMA regression are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082000#pone-0082000-t002" target="_blank">Table 2</a>.</p

Skeletal Correlates for Body Mass Estimation in Modern and Fossil Flying Birds

<div><p>Scaling relationships between skeletal dimensions and body mass in extant birds are often used to estimate body mass in fossil crown-group birds, as well as in stem-group avialans. However, useful statistical measurements for constraining the precision and accuracy of fossil mass estimates are rarely provided, which prevents the quantification of robust upper and lower bound body mass estimates for fossils. Here, we generate thirteen body mass correlations and associated measures of statistical robustness using a sample of 863 extant flying birds. By providing robust body mass regressions with upper- and lower-bound prediction intervals for individual skeletal elements, we address the longstanding problem of body mass estimation for highly fragmentary fossil birds. We demonstrate that the most precise proxy for estimating body mass in the overall dataset, measured both as coefficient determination of ordinary least squares regression and percent prediction error, is the maximum diameter of the coracoid’s humeral articulation facet (the glenoid). We further demonstrate that this result is consistent among the majority of investigated avian orders (10 out of 18). As a result, we suggest that, in the majority of cases, this proxy may provide the most accurate estimates of body mass for volant fossil birds. Additionally, by presenting statistical measurements of body mass prediction error for thirteen different body mass regressions, this study provides a much-needed quantitative framework for the accurate estimation of body mass and associated ecological correlates in fossil birds. The application of these regressions will enhance the precision and robustness of many mass-based inferences in future paleornithological studies.</p> </div

Avian coracoid disparity, and measuring the maximum diameter of the humeral articulation facet.

<p>i: Right coracoids in dorsolateral view shown to scale for ten avian taxa with different glenoid geometries. Figured coracoids are a) <i>Cygnus olor</i> (Anseriformes: Anatidae), b) <i>Ardeotis kori</i> (Gruiformes: Otididae), c) <i>Balearica regulorum</i> (Gruiformes: Gruidae), d) <i>Buteo regalis</i> (Accipitriformes: Accipitridae), e) <i>Bubo scandiacus</i> (Strigiformes: Strigidae), f) <i>Amazona aestiva</i> (Psittaciformes: Psittacidae), g) <i>Puffinus griseus</i> (Procellariiformes: Procellariidae), h) <i>Leucophaeus atricilla</i> (Charadriiformes: Laridae), i) <i>Podiceps nigricollis</i> (Podicipediformes: Podicipedidae), and j) <i>Nucifraga columbiana</i> (Passeriformes: Corvidae). ii: Close-up of omal coracoid extremities for the taxa listed above (not to scale). Gray lines illustrate the maximum diameter of the HAF. ‘fl’ denotes an extended flange sternolateral to the main portion of the glenoid facet (present in some taxa such as certain anseriforms and gruiforms), which was not included in the HAF measurement. Similarly, ‘ac’ denotes an extended concavity along the acrocoracoid crest (present in some taxa such as certain accipitriforms and procellariiforms), which was not included in the HAF measurement. </p

Scatterplots illustrating the variance in OLS regression lines for 18 avian orders, comparing (left panel) body mass vs coracoid HAF, and (right panel) body mass vs femur length.

<p>Corresponding sample sizes and coefficients of determination are given in plots.</p

Comparison of the predictive power of several body mass proxies based on their mean percent prediction error (PPE).

<p>Mean PPE for each correlate is represented by a circle, with 95% confidence intervals in black. The least precise correlate as reckoned by PPE (tarsometatarsus length) is shown in red, while the most precise (coracoid HAF length) is shown in green.</p