Database construction and taxon sampling

863 skeletons of extant, volant birds, with masses spanning three orders of magnitude, were sampled from the Vertebrate Zoology collection of the Yale Peabody Museum (Table S1). To account for sexual dimorphism in body mass estimates, only specimens preserving sex identification data were used. For paired bones, the right side element was measured, unless absent. The following measurements were taken for each specimen: maximum femur length (FL), least femur shaft diameter in anterior view (FD), least femur shaft circumference (FC), maximum humerus length (HL), least humerus shaft circumference (HC), least humerus shaft diameter in anterior view (HD), maximum tibiotarsus length (TiL), maximum tarsometatarsus length (TaL), least tarsometatarsus diameter in anterior view (TaD), least tarsometatarsus shaft circumference (TaC), maximum coracoid lateral length (CLL), least coracoid shaft width (CSW), and maximum diameter of the coracoid’s humeral articulation facet (HAF) (Figure 1). Although tibiotarsus circumference has been demonstrated to scale closely with body mass in birds [23], we found that tibiotarsi were often broken, making any measurement other than maximum length difficult to make precisely. Therefore, this study does not recreate the tibiotarsus regressions presented in [23]. Digital calipers sensitive to 0.01 mm were used for measurements of bone length and diameter, and nylon string was used to measure bone circumference at the point of minimum shaft circumference. For the smallest specimens, circumference was calculated from orthogonal width and depth measurements, after [23].

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Figure 1. Avian coracoid disparity, and measuring the maximum diameter of the humeral articulation facet.

i: Right coracoids in dorsolateral view shown to scale for ten avian taxa with different glenoid geometries. Figured coracoids are a) Cygnus olor (Anseriformes: Anatidae), b) Ardeotis kori (Gruiformes: Otididae), c) Balearica regulorum (Gruiformes: Gruidae), d) Buteo regalis (Accipitriformes: Accipitridae), e) Bubo scandiacus (Strigiformes: Strigidae), f) Amazona aestiva (Psittaciformes: Psittacidae), g) Puffinus griseus (Procellariiformes: Procellariidae), h) Leucophaeus atricilla (Charadriiformes: Laridae), i) Podiceps nigricollis (Podicipediformes: Podicipedidae), and j) Nucifraga columbiana (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.

https://doi.org/10.1371/journal.pone.0082000.g001

The majority of these measurements have been used as body mass correlates by previous authors (e.g. 20-24,31). In contrast, coracoid HAF dimensions have only been investigated as a potential body mass correlate in one previous study [37], using a relatively small and taxonomically limited dataset. The HAF-bearing portion of the coracoid is amongst the most commonly preserved avian fossil elements in many fossil localities [37-40], underscoring the potential utility of a robust HAF-body mass relationship. Here, we formalized the measurement of avian HAF dimensions by measuring the maximum diameter of the glenoid (Figure 1). Only the main, sub-ovular portion of the glenoid was measured; in instances where a depression extended omal to the main portion of the glenoid onto the acrocoracoid crest (Fig. 1ii d, g), or sternomedial to the main portion of the glenoid as a narrow flange around the scapular cotyla (Figure 1ii a, b, e, j), these extensions were not included in the measurement. A visual depiction of how the measurement was taken for taxa with varying HAF geometries is provided in Figure 1.

Many previous attempts to estimate the original body masses of fossil taxa suffer due to limited taxonomic sampling of extant taxa, or by ignoring the existence of sexual dimorphism (e.g. 41). To avoid these pitfalls, this study only draws measurements from individuals identified to sex, and samples a greater number of individuals than any previously published avian body mass dataset (see Table S1).

Statistical Analyses

The strength of correlation between measured skeletal dimensions and body mass was determined using coefficient of determination (R²) values from ordinary least squares regression. Mean body mass estimates and corresponding sex information for each of the bird species were obtained from [42]. In order to investigate the differences between regressions for mean body mass and actual body mass, we compared regressions between the maximum diameter of the coracoid HAF, and both mean and recorded individual body mass for a subset of our total dataset. This subset, comprising the only specimens associated with recorded body mass in our dataset, represented 115 individuals, from 31 genera in 9 avian orders. Scaling relationships and strength of correlation were compared using standardized major axis (SMA) regression using the package Smatr in R [43]. For all analyses, we used the natural log (ln) of these data to mitigate the effects of extreme outliers on regression coefficients [30,34].

We subsequently used regression equations for each measured skeletal correlate to predict body mass, and calculated percent prediction error (PPE) by comparing predicted with observed body mass in the style of [30]. Because clade- and ecology-specific variations in gait and limb posture may subject the vertebrate skeleton to different stress regimes (e.g. 23,30), the strength of various skeletal measurements as body mass correlates might be expected to vary among taxonomic groups. We therefore repeated our analyses for the entire dataset broken down into individual avian orders. All analyses were performed using the statistical software R version 2.15.2 [43].

Ecology and clade-dependence of body mass regressions

Our data illustrate several important aspects of allometric scaling relationships among 18 orders of extant, volant birds: the strength of our 13 measured body mass correlates differ significantly overall, and the relative precision of different elements as body mass predictors sometimes varies significantly among broad taxonomic groups, likely reflecting adaptive ecological overprinting in clades exhibiting widely disparate ecologies [44]. However, the high precision of many of the correlations presented here indicates that, regardless of potentially confounding factors such as phylogenetic position, ecology, and flight style, these regressions can be used to infer relatively narrow upper and lower bound prediction intervals on body mass estimates across Aves, as well as for fossil flying birds (Figure 2). These findings are consistent with several previous studies that have investigated the dimensions of avian skeletal elements as potential body mass correlates [20-24]. However, we demonstrate that among the skeletal elements examined here, the maximum diameter of the coracoid HAF is generally the most accurate predictor of avian body mass, and that the slopes and intercepts of this regression among all studied avian orders show the least variance. These findings suggest low ecological overprinting of HAF dimensions in extant flying birds, and illustrate this measurement’s potential utility for the accurate estimation of body mass in fossil flying birds. In addition, these analyses show that the coracoid HAF serves as an equally good predictor of body mass when either mean species body mass, or recorded individual body mass is considered. We therefore suggest that in instances where close correspondence between mean species and true body masses can be demonstrated (Figure 4), using mean species body masses in allometric studies will enable more specimens, and a correspondingly broader taxonomic sample to be investigated.

We also acknowledge two additional factors affecting our data and analyses that may have an effect on the final regression parameters: 1) these data are not strictly independent, as the 863 studied specimens exhibit varying degrees of common ancestry, which may spuriously increase or decrease the strength of allometric scaling relationships. In addition, 2) our use of multiple individuals belonging the same species in the dataset may also skew our calculated regression parameters. Although 1) can be addressed by employing generalized least squares models (e.g. 45), the low interordinal variance exhibited by many of the regressions presented here (Figure 5, Table 4) indicates relatively little phylogenetic dependence in this dataset. Previous allometric studies have demonstrated largely insignificant phylogenetic dependence of limb scaling patterns in terrestrial quadrupeds [30], and inappropriate application of phylogenetic regression can result in poor statistical performance [46]. Further, our broad taxonomic sampling across Aves complicates the acquisition of a robust phylogeny with a specified set of branch lengths incorporating every taxon in this analysis, which would be beyond the scope of this study. For these reasons, and for ease of comparison with previously published avian allometric studies [30], we have elected to present OLS results instead of phylogenetic regressions. Future work may delve into the question of phylogenetic correlation in avian allometric data.

We attempted to address 2) by re-running analyses on two restricted datasets where multiple specimens of any single species were omitted by random deletion. We then compared the relative ordering of skeletal measurements as body mass correlates, both as coefficient of determination and PPE, with those of our original analyses. Sample sizes for these single-individual analyses were 317 (the number of individual species in our dataset). Regression parameters and coefficients of determination resulting from analysis of these restricted datasets were extremely similar to those of the total dataset (Table S8), and the re-analysis resulted in minimal re-ordering of skeletal measurements in terms of their strength as body mass predictors (Figure S2).

The varying strengths of our skeletal measurements as body mass correlates, both within the entire dataset, and among different avian orders, probably reflect the influence of ecological and biomechanical constraints on element dimensions. Although the ecological and phylogenetic importance of many of these data will be discussed elsewhere, we highlight some of the broader patterns concerning the strength of the coracoid HAF as a morphological correlate for body mass, in a comparative context with other frequently applied skeletal measurements. In particular, the strength of the observed correlation between coracoid HAF dimensions and body mass likely has its basis in flight biomechanics; failure of the shoulder joint in a wild flying bird would probably be fatal, and larger birds appear to exhibit larger shoulder articulations to provide adequate safety factors for stress dissipation during the active flight stroke. Additionally, the circumferences of hindlimb elements scale closely with body mass, as these bones are subject to numerous biomechanical and energetic trade-offs, and as such have narrow tolerance limits (see 21,23,47-50).

Conversely, the dimensions of some avian skeletal elements can be more heavily influenced by ecological, as opposed to biomechanical factors, such as wading and prey handling [51]. Such elements are consequently expected to make poor body mass correlates. We suggest that the relatively weak correlation found between tarsus length and body mass reflects one such example of ecological overprinting; certain ecological groups (i.e., waders) exhibit disproportionately long tarsometatarsi, while others (i.e., raptors and owls) tend to have disproportionately short tarsometatarsi—a specialization related to prey handling efficiency [51,52]. In support of this, the variance in regression parameters for tarsometatarsus length among the 18 avian orders sampled here vastly exceeds that of any other regression parameter (Figure 4; Table 4). These analyses demonstrate that skeletal measurements exhibiting high interordinal variance would likely comprise poor predictors of body mass in fossil birds, unless the fossil in question could be confidently diagnosed to the crown-group of an order represented in our sample.

Coracoid dimensions have been used to estimate body mass for fossil birds previously (e.g. 31,37,53). In particular, Elzanowski et al. (2012) [31] generated several highly precise coracoid-based allometries for mass estimation of fossil Procellariiformes. Two of these correlates (minimum coracoid shaft width and maximum lateral length of the coracoid) are examined in the present study. Although the correlation coefficients reported by Elzanowski et al. (2012) [31] are higher than those reported here, in our dataset Procellariiformes show the highest overall body mass correlation of all studied orders (mean correlation coefficient of all allometries, see Table 3), indicating that a wide variety of skeletal measurements may provide accurate body mass estimates in this clade. Although the regressions for minimum coracoid shaft width and maximum lateral coracoid length exhibit relatively low interordinal variance overall (Figure 5), they are surpassed by other correlates as preferable predictors of avian body mass (Figure 2).

One of the most frequently used skeletal measurements for estimating body mass in fossil crown- and stem-birds is femur length (e.g. 13,14,54); here we show that the interordinal variance in slope and intercepts of regression between femur length and body mass is substantially higher than in the length of the coracoid HAF (Figure 6). The much tighter clustering in OLS regression lines indicates greater reliability in using coracoid HAF rather than femur length when estimating body mass across a variety of taxonomic groups. As such, we suggest that a variety of other body mass correlates, including maximum HAF diameter and maximum coracoid lateral length be used in lieu of femur length for estimating body mass in fossil volant birds, when these elements are preserved (Figure 2).

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Figure 6. 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.

Corresponding sample sizes and coefficients of determination are given in plots.

https://doi.org/10.1371/journal.pone.0082000.g006

Scaling relationships and allometry are widely accepted as a useful means to estimate body mass for fossil crown-group taxa [14,30,55]. However, the applicability of such methods for estimating body mass in more distantly related stem-group taxa, especially those that fall outside the body size range observed in extant clade representatives, is less well understood ([30], references therein). As a result, we cannot presently justify applying these extant avian body mass regressions to distantly related stem taxa (for example to basal theropods); however, crown group scaling relationships such as the ones described here are currently the most robust method for estimating mass in crownward stem taxa falling within the range of body masses in the extant dataset (such as Ichthyornis) [30]. Estimation of body mass with associated prediction intervals in these presumably volant stem-group taxa will provide a level of robustness to body mass-dependent paleobiological studies that has been elusive up to this point.

Paleobiological implications

Addressing many of the fundamental biological and ecological questions surrounding the early evolution of modern birds requires fully articulated (and thus exceptional) fossils. However, the lightweight, buoyant, and relatively fragile nature of bird skeletal remains conspires against their articulated preservation in many depositional settings [56-60]. As such, complete bird fossils are rare, and often make up a disproportionately small percentage of vertebrate remains from otherwise well sampled, fossiliferous localities [61]. However, elements comprising the avian pectoral girdle, in particular the omal extremity of the coracoid, are represented in many assemblages disproportionately often, with humeri, tarsometatarsi, and tibiotarsi also being commonly preserved (e.g. 37,38,57). A scientific premium is therefore placed on discovering new physiological and ecological correlates (such as those afforded by the allometric scaling relationships described here) that can extract additional information from this largely fragmentary and depauperate fossil record.

In addition, although isolated, fragmentary fossil bird bones are often of limited taxonomic use, several recent studies have revealed that the omal extremity of the coracoid can be phylogenetically informative. In fact, the avian coracoid is amongst the richest sources of characters for cladistic analyses of fossil birds [37,62]. The phylogenetic utility of omal coracoid extremities was illustrated by Longrich et al. (2011) [37], who discovered definitive evidence for avian mass extinction at the K-Pg boundary solely on the basis of coracoid morphotypes present above and below the boundary. As such, establishing coracoid measurements as robust body mass proxies holds valuable paleobiological implications: a single, isolated omal coracoid fragment can theoretically be used to diagnose taxonomic affinity, body mass, and by extension, estimates of a host of additional macroecological and biomechanical attributes such as a species’ energetic demands, maximum population density, and aspects of locomotory mechanics [5,7,8,63].