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. 2022 Nov 15;242(3):436–446. doi: 10.1111/joa.13788

Coracoid strength as an indicator of wing‐beat propulsion in birds

Takumi Akeda 1,✉, Shin‐ichi Fujiwara 2
PMCID: PMC9919476  PMID: 36380603

Abstract

Birds generate a propulsive force by flapping their wings. They use this propulsive force for various locomotion styles, such as aerodynamic flight, wing‐paddle swimming and wing‐assisted incline running. It is therefore important to reveal the origin of flapping ability in the evolution from theropod dinosaurs to birds. However, there are no quantitative indices to reconstruct the flapping abilities of extinct forms based on their skeletal morphology. This study compares the section modulus of the coracoid relative to body mass among various extant birds to test whether the index is correlated with flapping ability. According to a survey of 220 historical bird specimens representing 209 species, 180 genera, 83 families and 30 orders, the section modulus of the coracoid relative to body mass in non‐flapping birds was significantly smaller than that of flapping birds. This indicates that coracoid strength in non‐flapping birds is deemphasised, whereas in flapping birds the strength is emphasised to withstand the contractile force produced by powerful flapping muscles, such as the m. pectoralis and m. supracoracoideus. Therefore, the section modulus of the coracoid is expected to be a powerful tool to reveal the origin of powered flight in birds.

Keywords: coracoid, origin of flight, section modulus, strength

The relationship between the body mass (M [g]) and the section modulus of the coracoid normalised by the beam length (Z/C l [mm2]), revealed that the coracoid strength is deemphasised in non‐flapping birds, but is emphasised in flapping birds, especially in soaring birds, to withstand the contractile force produced by flapping muscles. Therefore, the coracoid strength is expected to be an indicator for discriminating the styles of wing‐propelled locomotion.

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1. INTRODUCTION

1.1. Diverse styles of wing‐propelled locomotion in birds

It remains unclear during which stage of evolution the ability of wing‐beat propulsion was acquired in the lineage of theropod dinosaurs to birds (Dial, 2003; Feo et al., 2015; Mayr, 2016, 2017; Pei et al., 2020; Poore et al., 1997; Voeten et al., 2018). Wing beating awakens the backward fluid current to generate a propulsive force on the body (Hildebrand & Goslow, 2003; Pennycuick, 2008; Videler, 2005). Many vertebrates, such as birds (Neornithes, Theropoda), bats (Chiroptera, Mammalia), sea and pig‐nosed turtles (Chelonioidea and Carettochelyidae, Testudinata), sea lions (Pinnipedia, Mammalia), presumably extinct pterosaurs (Pterosauria, Archosauria) and plesiosaurs (Plesiosauria, Sauropterygia) rely on the wing‐beat propulsion for various forms of locomotion (Davenport et al., 2016; Feldkamp, 1987; Padian, 1983; Panyutina et al., 2015; Pennycuick, 2008; Taylor, 1986; Walker, 1971). Among these, the styles of wing‐propelled locomotion (WPL) are especially diverse in birds. Many birds have acquired flight ability, which requires the wings to generate aerodynamic lift and mechanisms to propel the body powered by the wing beat (Hildebrand & Goslow, 2003; Pennycuick, 2008; Videler, 2005). Using this wing‐beat propulsion, many birds, as well as bats, fly forward in the air, mainly relying on powered downstrokes (Hedenström et al., 2009; Hildebrand & Goslow, 2003). Hummingbirds (Trochilidae) exhibit sustained hovering flight to stay in the air using both up‐ and downstrokes for propulsion (Tobalske, 2010). Some diving birds, such as penguins and puffins, use wing‐beat propulsion for swimming, as well as sea and pig‐nosed turtles and sea lions (Hildebrand & Goslow, 2003). Some galliforms (Dial, 2003; Dial & Jackson, 2011; Heers & Dial, 2015; LeBlanc et al., 2018) and columbiforms (Jackson et al., 2011) ascend steep/overhanging slopes by beating their wings to generate propulsive force toward the slope—the chicks, still unskilled in flying with undeveloped wings, do this motion, as do the adults (Tobalske & Dial, 2007). Given the diverse WPL styles among birds, it is important to reveal the evolutionary process of the ability of powered wing‐beat in the lineage of theropod dinosaurs to birds (Burgers & Chiappe, 1999; Chin & Lentink, 2017; Dececchi et al., 2016; Heers & Dial, 2012; Heers et al., 2021; Talori et al., 2019) besides those of the wings to generate aerodynamic lift.

Within the lineage from theropod dinosaurs to modern birds (Neornithes) via pennaraptorans, avialans, pygostylians, ornithothoracines, ornithuromorphs and ornithurines in order, the step‐by‐step evolutionary processes of acquiring anatomical traits related to the wings to generate aerodynamic lift have been assessed by the numerous fossil records (e.g. Brusatte et al., 2015; Pittman et al., 2020; Xu et al., 2014). Continuous miniaturisation of body size (Turner et al., 2007) associated with an increase in the relative arm length (Dececchi & Larsson, 2013) and wing area (Burgers & Chiappe, 1999; Pei et al., 2020) in the lineage is considered to contribute to acquiring the ability of aerodynamic flight. Entire feather structures, starting from mono‐filamentous to radial (down), bilaterally symmetric (contour) and bilaterally asymmetric (flight) feathers in order, as well as hierarchical feather branching (rachis, barbs, barbules and cilia) (Prum & Brush, 2002; Yu et al., 2002), have been also revealed by the numerous fossil records of feathered dinosaurs (e.g. Chen et al., 1998; Hou et al., 1995; Xu et al., 2003). Nudds and Dyke (2010) assessed whether rachis of feathers in fossil avialans, such as Archaeopteryx, Confuciusornis and close relatives, are able to withstand the aerodynamic force required for flight. Feo et al. (2015) have analysed an evolutionary pattern of the barb geometry of flight feathers from the stem taxa to extant birds, which is critical in aerodynamic function. It is considered that the aerodynamic performance of the wing like modern birds has been reinforced after the ornithuromorphs, the stage where all these features are acquired (Feo et al., 2015; Mayr, 2016, 2017).

On the other hand, the origin of the mechanisms to propel the body powered by the wing beat, which should be considered separately from the aerodynamic performance of the wing, are yet to be fully understood. Some studies have hypothesised that flightless stem taxa of the theropod‐avian lineage may have flapped their rudimentary wings to improve their cursorial performance on the hindlimb (Dial, 2003; Dial et al., 2008; Heers & Dial, 2012; Dececchi et al., 2016), which is considered as the origin of wing beat in birds. For the anatomical traits related to the wing beat, the transition of the open margins of the saddle‐shaped glenoid from craniocaudal to dorso‐ventral orientations in the evolution from theropod dinosaurs to modern birds is considered to allow derived dorso‐ventral wing stroke for flapping (Baier et al., 2007; Jenkins, 1993). Some studies have mentioned that the sternal keel has been enlarged independently in sister group with ornithothoracines, some enantiornitheans and ornithuromorphs, for the attachment area of the flapping muscles (mm. pectoralis and supracoracoideus), which can be one of the indices for the origin of flapping flight (Mayr, 2017; Olson, 1976; Olson & Feduccia, 1979). However, these indices are yet to be enough to precisely reconstruct the flapping abilities of extinct taxa. Therefore, we need to find an alternative quantitative index for determining the flapping ability in birds that stands on biomechanics and can also be measured on skeletal remains.

1.2. Mechanical models

In the thoracic skeleton of birds, the sternum and coracoid are rigidly connected (Sy, 1936). Conversely, the articulation between the dorsal end of the coracoid and scapula, which together form the glenoid, is generally not rigidly connected (Sy, 1936). The wing (forelimb) articulates and rotates about the glenoid (Figure 1).

FIGURE 1.

FIGURE 1

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(a) The thoracic skeleton and the flight muscle orientations of birds in left craniolateral view and (b) the coracoid in ventral view with (c) the cross section at the mid‐shaft. The coracoid is bent dorso‐ventrally (green arrow). The mediolateral width (C w [mm]), dorso‐ventral depth (C d [mm]) and craniocaudal beam length (C l [mm]) of the coracoid were measured to estimate the coracoid strength against the bending force. a, acrocoracoid process; co, coracoid; f, furcula; g, glenoid; sc, scapula; st, sternum.

The wing beat in birds is powered by alternating contractions of the mm. pectoralis and supracoracoideus (Hildebrand & Goslow, 2003; Mayr, 2017; Pennycuick, 2008; Poore et al., 1997; Sy, 1936; Videler, 2005). Both muscles arise from the ventral surface of the sternum and run along the ventral surface of the shaft of the coracoid. The former inserts into the ventral side of the deltopectoral crest of the humerus (Pennycuick, 2008; Sy, 1936; Videler, 2005). The latter wraps around the triosseal foramen, which is formed at the coracoid‐scapula‐furcular intersection, and inserts into the proximo‐dorsal side of the deltopectoral crest. The former and latter function in wing depression and elevation, respectively.

While these muscles contract, the coracoid is bent ventrally, and the ventral side of the coracoid is subjected to longitudinal compression (Baier et al., 2007). Therefore, the coracoid is expected to play an important role in withstanding the bending of the thoracic skeleton (Figure 1; Baier et al., 2007; Gray, 1968).

Among the extant birds, the coracoids of the groups with flapping ability tend to be columnar in shape, whereas those of the groups without flapping ability are thin and placoid in shape (e.g. ratites) or slenderer (e.g. dodos and flightless rails) than those of the flapping birds (Appendix S1). Given the difference in shape of the coracoid between birds with and without flapping ability, one can expect that there are differences in the strength of the coracoids between the birds with and without flapping ability to resist the bending caused by the contractile force of flapping muscles.

To compare the strengths of the coracoids widely and quantitatively among birds, the section modulus, which depends on the cross‐section of the columnar structure, is useful in determining the strength or resistance against bending (Goodno & Gere, 2016). In this study, the section modulus of the coracoid in relation to the body mass was used to evaluate the ability of WPL among birds.

2. MATERIALS AND METHODS

2.1. Materials

We used 220 historical bird specimens, representing 209 species, 180 genera, 83 families and 30 orders (Appendix S2). The species were selected to be as varied as possible in taxonomy, style of WPL, and body mass (Appendix S2). This study focuses on the WPL among adult birds, but the ontogenetic shift was not taken into account. Therefore, juvenile specimens were not used in this study.

Some groups, such as Palaeognathae, Rallidae (Gruiformes), Columbiformes, Lari (Charadriiformes), Austrodyptornithes (a group composed of penguins and tube‐nosed seabirds), and Pelecaniformes, are known to contain taxa of multiple WPL styles. Therefore, species of different WPL styles within particular taxonomic group, if available, were selected for the analysis described below to compare the differences in the above‐mentioned indices within each group. The taxa extinct in historic times, such as the dodo (Raphus cucullatus, Columbiformes) and great auk (Pinguinus impennis, Charadriiformes), both known to be flightless birds (Livezey, 1993; Morris, 1857), were used as well.

A digital vernier calliper (0–200 mm; 0.01 mm accuracy: CD‐20CPX; Mitsutoyo Co., Ltd.) and a Martin‐type anthropometer (200–1950 mm; 1 mm accuracy: Takei Scientific Instrument Co., Ltd.) were used for the direct measurements on the skeletal specimens. In some specimens, whose three‐dimensional (3‐D) skeletal profile is available online as an image sequence scanned by X‐ray computed tomography, the measurements were taken on the 3‐D image reconstructed using a 3‐D imaging software, Avizo 8.1 (FEI Visualization Science Group).

2.2. Categories of the WPL style

We followed the literature (Bruderer et al., 2010; Lowi‐Merri et al., 2021) and information on a website ‘Birds of the World’ (Billerman et al., 2022, eds: the latest citation, January 22, 2022) for the WPL styles of the studied species. The studied species were categorised into four different groups based on the use of the wings for locomotion: predominantly flapping flight (‘flap‐flight’, n = 153), wing‐propelled diving (‘wp‐diving’, n = 19), flightless with no flapping ability (‘non‐flapping’, n = 13), and thermal and dynamic soaring (‘soaring’, n = 35) (Appendix S2). The ‘flap‐flight’, ‘soaring’ and ‘wp‐diving’ birds use wing‐beat propulsion for locomotion, although ‘soaring’ birds rely less on the wing beat (Bruderer et al., 2010). Sustained hovering birds, such as hummingbirds (Trochilidae), exhibit high‐frequency wing beats to stay in the air (Tobalske, 2010) and were also included in ‘flap‐flight’. The auks (Alcidae) and dippers (Cinclidae) were categorised as ‘wp‐diving’, although many of them engage in both flapping flight and wing‐propelled diving. Among these, the taxonomic groups that contain multiple WPL styles are as follows: Palaeognathae, Rallidae, Columbiformes (‘flap‐flight’ and ‘non‐flapping’), Austrodyptornithes (‘wp‐diving’ and ‘soaring’), Lari (‘flap‐flight’ and ‘wp‐diving’) and Pelecaniformes (‘flap‐flight’ and ‘soaring’: Appendix S2).

2.3. Body mass data

The body mass (M [g]) was referred from the literature (Dunning, 2008; Shimizu, 2016) for the studied species whose body mass is available. For those whose body mass was not available (e.g. extinct taxa: Appendix S2), the body mass (M) was estimated from the circumference length of the cross‐section of the narrowest portion of the femur (LCF [mm]) using the formula proposed by Field et al. (2013):

LCF=π×Fl+Fs×1+3×Fl+Fs/Fl+Fs210+4−3×Fl+Fs/Fl+Fs2,
lnM=2.40×lnLCF−0.11,

where F l [mm] and F s [mm] are the long and short axes of the femoral section, respectively, by assuming the narrowest femoral cross‐section is ellipsoidal in shape. This formula has been used in various studies for body mass estimation in extinct birds (Handley et al., 2016; Ksepka et al., 2020; Worthy et al., 2016).

2.4. Section modulus of the coracoid

The coracoid was assumed to be a beam structure and bent ventrally by the contraction of flight muscles. The narrowest cross‐section of the coracoid was assumed to be ellipsoid in shape. The mediolateral width (C w [mm]) and dorso‐ventral depth (C d [mm]) of the ellipse were measured (Figure 1), and the section modulus Z [mm3] was calculated using the following formula (Goodno & Gere, 2016):

Z=π×Cw×Cd2/32.

The strength of the beam structure against bending is inversely proportional to its length (Goodno & Gere, 2016). The craniocaudal coracoid beam length of coracoid exposed from the coraco‐sternal joint was defined as C l (mm) (Appendix S1). Thereafter, the section modulus of the coracoid normalised by the beam length (Z/C l [mm2]) was estimated for each specimen.

In some bird species, the coracoid is not a simple beam structure (Appendix S3). We estimated Z/C l of the coracoid as well as the other bird species, assuming that the strength of the beam structure does not differ significantly whether the clavicle/furcula is fused with the coracoid (see Appendix S3 for further discussion).

2.5. Statistical analyses

The regression lines of the relationship between body mass (log M [g]) and the section modulus of the coracoid normalised by the beam length (log Z/C l [mm2]) was estimated for each flight style of the WPL in birds (‘flap‐flight’, ‘wp‐diving’, ‘non‐flapping’ and ‘soaring’). Phylogenetic generalised least squares (pGLS) (Rohlf, 2001) were used to fit the regression lines using the packages ‘ape’ and ‘nlme’ in R version 4.0.3 (software for statistical analyses: R Foundation for Statistical Computing: R Development Core Team, 2020) (see Appendix S4 for the procedure of selecting the best‐fit regression model in pGLS).

The difference in the plot distributions among the categories of the four WPL styles (‘flap‐flight’, ‘wp‐diving’, ‘non‐flapping’ and ‘soaring’) was tested by phylogenetically‐corrected analysis of covariance (pANCOVA) (Smaers & Rohlf, 2016). The null hypothesis that there is no difference in the normalised section modulus (log Z/C l [mm2]) among the categories was rejected if the p‐value did not exceed 0.05. After conducting pANCOVA, we estimated the predictions of log (Z/C l ) derived by assigning the least square mean (LSM) of covariates log (M) to the pANCOVA model for each WPL style and thereafter conducted Tukey's multiple comparison test for the LSMs of the pairs among the four categories. The null hypothesis that there is no difference in the LSM of log (Z/C l ) between the pairs of WPL styles (‘flap‐flight’ and ‘wp‐diving’, ‘flap‐flight’ and ‘non‐flapping’, ‘flap‐flight’ and ‘soaring’, ‘wp‐diving’ and ‘non‐flapping’, ‘wp‐diving’ and ‘soaring’ and ‘non‐flapping’ and ‘soaring’) was rejected if p‐value did not exceed 0.05. In addition, the residuals of log (Z/C l ) from the best‐fit regression line were estimated for the studied taxa in each WPL styles to compare the intragroup variation within the selected WPL style. In addition to the comparison among the specimens of different WPL styles (‘flap‐flight’, ‘wp‐diving’, ‘non‐flapping’ and ‘soaring’) within all the studied taxa, the residuals from the regression line of (Z/C l ) were compared among the specimens of different WPL styles within particular taxonomic groups, such as Palaeognathae, Rallidae, Columbiformes, Austrodyptornithes, Lari and Pelecaniformes (see Appendix S5 for statistical analyses within particular taxa).

3. RESULTS

In the comparison of the relationship between the M (g) and the section modulus of the coracoid over the coracoid beam length (Z/C l [mm3]) among all studied specimens (Figure 2; Table 1), the assumption of homogeneity of regression slopes was supported (F‐statistic = 1.06, p = 0.369 ≥ 0.05) among the WPL styles (‘flap‐flight’, ‘wp‐diving’, ‘non‐flapping’ and ‘soaring’). According to the pANCOVA, the distributions of the plots among the WPL styles were significantly different (F‐statistic = 16.2, p < 0.0001).

FIGURE 2.

FIGURE 2

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(a) The relationship between the body mass (M [g]) and the section modulus of the coracoid normalised by the beam length (Z/C l [mm2]) and (b) the least square mean of regressions among different styles of wing‐propelled locomotion (WPL): ‘flap‐flight’, ‘wing‐propelled (wp)‐diving’, ‘non‐flapping’ and ‘soaring’. In (b), mean value (horizontal bar), ±standard error (box) and 95% confidence interval (whisker) are shown.

TABLE 1.

Intercept, slope and least square mean (LSM) of regressions among different styles of wing‐propelled locomotion: ‘flap‐flight’, ‘wing‐propelled (wp)‐diving’, ‘non‐flapping’ and ‘soaring’

Comparison Intercept Slope log LSM
‘flap‐flight’ −2.9678 0.7780 −0.3300
‘wp‐diving’ −3.1252 0.8200 −0.3803
‘non‐flapping’ −3.7881 0.8990 −0.7277
‘soaring’ −3.1427 0.8930 −0.1510
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The LSMs of Z/C l in the categories with flapping ability (‘flap‐flight’, ‘wp‐diving’ and ‘soaring’) were >2.2 times larger than that in ‘non‐flapping’ birds (Table 2). Multiple comparisons showed that the LSMs were significantly different (p < 0.05) between ‘non‐flapping’ birds and any categories of the birds with flapping ability (Table 2)—between ‘flap‐flight’ and ‘non‐flapping’ birds (p < 0.0001), between ‘wp‐diving’ and ‘non‐flapping’ birds (p = 3.15 × 10−3), and between ‘non‐flapping’ and ‘soaring’ birds (p < 0.0001).

TABLE 2.

Result of Tukey's test (difference, standard error [SE], degree of freedom [df], t‐statistic and p‐value) between a pair of different styles of wing‐propelled locomotion: ‘flap‐flight’, ‘wing‐propelled (wp)‐diving’, ‘non‐flapping’ and ‘soaring’

Comparison Difference SE df t‐statistic p‐value
‘flap‐flight’— ‘wp‐diving’ 0.050 0.0721 66.0 0.699 0.8973
‘flap‐flight’—‘non‐flapping’ 0.398 0.0795 209.9 5.005 <0.0001 a
‘flap‐flight’—‘soaring’ 0.179 0.0540 123.7 −3.315 0.0065 a
‘wp‐diving’—‘non‐flapping’ 0.347 0.0981 121.4 3.539 0.0032 a
‘wp‐diving’—‘soaring’ 0.229 0.0794 66.9 −2.889 0.0261 a
‘non‐flapping’—‘soaring’ 0.577 0.0837 171.5 −6.891 <0.0001 a
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a

That the null hypothesis that there was no difference in the section modulus between the categories was rejected (p < 0.05).

Among the categories of the birds with flapping ability (‘flap‐flight’, ‘wp‐diving’ and ‘soaring’), the LSMs were significantly different (p < 0.05) between ‘flap‐flight’ and ‘soaring’ birds (p = 6.52 × 10−3) and between ‘wp‐diving’ and ‘soaring’ birds (p = 2.61 × 10−2) (Table 2). The LSM of Z/C l in ‘soaring’ birds was ~1.5 times larger than those in ‘flap‐flight’ and ‘wp‐diving’ birds (Table 2). Conversely, no significant differences were found between ‘flap‐flight’ and ‘wp‐diving’ birds (p = 0.897) (Table 2).

The residual from the regression line varied by the taxonomic group within each WPL style (Figure 3). Among ‘soaring’ birds, the taxa whose wings are more suitable for soaring in shape (Pennycuick, 2008), such as cranes (Gruidae), albatrosses (Diomedeidae), eagles (Accipitridae), frigatebirds (Fregatidae), pelicans (Pelecanus), storks (Ciconia), and new world vultures (Cathartidae) scored high residuals (−0.13 to 0.38, median = 0.12), compared with those of the other ‘soaring’ birds (−0.53 to 0.14, median = −0.13) (Table S2‐1). Among the ‘wp‐diving’ birds, there was no marked difference in the residual between flightless taxa (e.g. penguins) (−0.20 to 0.26, median = −0.018) and the taxa with flight abilities (e.g. auks) (−0.17 to 0.22, median = 0.011) (Table S2‐1).

FIGURE 3.

FIGURE 3

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The residuals of log (Z/C l ) from the best‐fit regression line with respect to body mass (M [g]) of (a) ‘wp‐diving’ and (b) ‘soaring’ birds. In (a), dark orange plot indicates the taxa with flight ability (e.g., Alcidae), whereas the pale orange plot indicates the taxa without flight ability (e.g., Sphenisciformes). In (b), the taxa whose wings are more suitable for soaring among the ‘soaring’ birds are (C) cranes (Gruidae), (D) albatrosses (Diomedeidae), (E) eagles (Accipitridae), (F) frigatebirds (Fregatidae), (P) pelicans (Pelecanus), (S) storks (Ciconia), (V) new world vultures (Cathartidae), and the other ‘soaring’ birds (O, others).

In the comparison within particular taxonomic groups that contain both ‘flap‐flight’ and ‘non‐flapping’ birds, such as Palaeognathae, Rallidae and Columbiformes, the Z/C l of the birds with flapping ability were larger than the ‘non‐flapping’ birds (Appendix S5, Figure S5A–C). However, the difference in the Z/C l was not so clear between ‘soaring’ brids and the other flapping (‘flap‐flight’ and ‘wp‐diving’) birds in comparison within particular taxa, such as Lari, Austrodyptornithes and Pelecaniformes—the Z/C l of some ‘soaring’ taxa were as large as those of ‘flap‐flight’ and ‘wp‐diving’ birds (Figure S5D–F). As in the comparison among the WPL styles of all studied taxa, the Z/C l were similar between the ‘flap‐flight’ and ‘wp‐diving’ birds in the comparison within particular taxa, such as Lari and Austrodyptornithes (Figure S5D,E).

4. DISCUSSION

According to the comparison among the wide range of bird species, the coracoid strength against dorso‐ventral bending strongly reflects the presence (‘flap‐flight’, ‘wp‐diving’ and ‘soaring’) or absence (‘non‐flapping’) of the ability of WPL. Therefore, sufficient coracoid strength can be regarded as one of the necessary conditions for the propulsion powered by wings in birds, although we cannot simply conclude that the coracoid strength can be used as an indicator for the presence/absence of flying ability in birds. This is because, some birds without flying ability but with powerful flapping ability, such as penguins, which were categorised as ‘wp‐diving’ birds, represented relatively large coracoid strength in relation to body mass.

The relatively enhanced coracoid strength in ‘soaring’ birds, especially in the taxa whose wings are more suitable for soaring, among the other flapping birds may indicate that the coracoids of ‘soaring’ birds likely withstand stronger bending caused by the contraction of flapping muscles (Figure 3). One may consider it unlikely that the coracoid strength in ‘soaring’ birds who maintain the wing posture by continual contraction of flight muscles exceed those of ‘flap‐flight’ birds who propel the body by intermittent contraction of the muscles (Goldspink et al., 1978; Meyers, 1993). However, the taxa whose wings are more suitable for soaring among the ‘soaring’ birds (Pennycuick, 2008), such as albatrosses (Diomedeidae), pelicans (Pelecanus), storks (Ciconia), frigatebirds (Fregatidae), eagles (Accipitridae) and new world vultures (Cathartidae), are characterised by having relatively short sternum, as well as distally developed deltopectoral crest, which result in having relatively obliquely oriented m. pectoralis from the coracoid shaft (Lowi‐Merri et al., 2021; Mayr, 2016) that runs apart from the glenoid among the other birds (Serrano & Chiappe, 2017). Moreover, the furcula of the more frequent soarers tend to curve shallowly and is flattened anterolaterally (Close & Rayfield, 2012; Hui, 2002), whose shape is considered to provide less protraction force and more depression force (Hui, 2002). These traits deviate the line of action of the m. pectoralis from the coracoid shaft and may contribute to increasing the bending moment of the coracoid, which can be one of the reasons why the ‘soaring’ birds show the relatively large coracoid strength among the others.

In contrast, the similarity in coracoid strength between ‘wp‐diving’ and ‘flap‐flight’ birds indicates that there are little differences in the force exerted by flapping muscles between these categories. This result seems to contra the fact that ‘wp‐diving’ birds, such as penguins (Sphenisciformes) and auks (Alcidae), flap powerfully in the water, whose density is ~800 times higher than that of the air (Habib, 2010; Kovacs & Meyers, 2000). However, the muscle contractile force required for the wing‐beat underwater in ‘wp‐diving’ birds may be similar to the force required for ‘flap‐flight’ due to the factors raised below. First, ‘wp‐diving’ birds tend to have relatively small wing area, or to reduce their wing span when swimming underwater. For example, the wing area relative to the body size of penguins is much smaller than those of ‘flap‐flight’ birds of the similar body size—the area is only 8.71 × 10−3 m2 for ‘wp‐diving’ Adélie penguin of ~4850 g in body mass (Dunning, 2008; Sato et al., 2002), whereas the area exceeds 6.19 × 10−2 m2 for ‘flap‐flight’ common loon (Gaviidae, Gaviiformes) of ~4500 g in body mass (Dunning, 2008; Lapsansky et al., 2022). Auks fold their wings by about 50% in wing span when flapping underwater (Johansson & Aldrin, 2002; Kovacs & Meyers, 2000). The reduced wing area and span enable to reduce the moment arm of the hydrodynamic force about the axis of the wing elevation/depression when flapping underwater. In addition, the alcids flap their wings less frequently (~50%) in water than flapping in the air to impart momentum to the surrounding fluid efficiently (Lapsansky et al., 2020). Reducing the moment arm of the hydrodynamic force and the wing beat frequency cause the reduction of the force required in the flapping muscles. According to the quasi‐steady calculation of the hydrodynamic force of the wing in swimming penguins (Harada et al., 2021), the hydrodynamic force of the wing is about 0.50 times body mass, which is much smaller than the aerodynamic force of the wing in ‘flap‐flight’ birds, such as pigeons (~4 times body mass, Ros et al., 2011) and Pacific parrotlets (~2 times body mass, Lentink et al., 2015). Therefore, it is likely that ‘wp‐diving’ birds are not required to exert much larger force than ‘flap‐flight’ birds to flap the wings underwater. Our result does not contradict the studies that compared the strength or robustness of the forelimb bones among birds. Habib (2010) showed that the strength of the forelimb bones in ‘wp‐diving’ birds, especially those engage in both ‘flap‐flight’ and ‘wp‐diving’, does not differ significantly from that of ‘flap‐flight’ birds. Serrano et al. (2020) concluded that the humerus of most volant ‘wp‐diving’ birds, such as some alcids, diving petrels (Procellariidae) and dippers (Cinclidae), were not morphologically different from those of ‘flap‐flight’ birds. Therefore, the coracoid strength in relation to body mass may reflect the lifting force on the wing, and can be a useful tool for estimating the type of WPL in both extant and extinct birds.

4.1. Limitations

Besides the positive notes raised above, there are some limitations to this study. The first concern is the simplification in estimating the section modulus of the coracoid and the body mass by assuming that the coracoid and femur are elliptical in cross‐section. This simplification of the cross‐sections of the long bones of animals has been widely employed in many other studies on estimating the section modulus (Blanco & Jones, 2005; Habib, 2010). Among these, the assumption on the femur cross‐section is widely accepted among studies estimating body mass from the femur (Campbell & Marcus, 1992; Field et al., 2013). Therefore, we consider that the error caused by this assumption is limited.

Another concern is the ambiguity in the categorisation of WPL styles among birds recognised in this study (Baliga et al., 2019; Bruderer et al., 2010; Pennycuick, 2008). The WPL of birds was simplified to four styles in this study, and each bird species was categorised into a single style of WPL. However, many bird species exhibit multiple flight behaviours (Baliga et al., 2019), and the styles of WPL vary according to the ontogenetic stage in some taxa (Dial & Jackson, 2011; Heers & Dial, 2015; Jackson et al., 2011; LeBlanc et al., 2018). For example, young chukar (Alectoris) employ wing‐assisted incline running, though adult chukars employ both ‘flap‐flight’ and wing‐assisted incline running (Dial, 2003). Furthermore, puffins (Fratercula) employ both ‘flap‐flight’ and ‘wp‐diving’ (Kovacs & Meyers, 2000). The difference in the coracoid strength, which was not clear between WPL styles in some taxa, such as Lari, Austrodyptornithes and Pelecaniformes (Appendix S5), may be due to such ambiguity of categorising WPL styles. The styles of the WPL can also be re‐categorised based on other factors, such as the wing span, wing area, and wing‐beat frequency (Bruderer et al., 2010; Rader et al., 2020; Warham, 1977). Therefore, whether the categorisation fits the natural ecology of birds must be considered carefully. Furthermore, the index used in this study should be compared with the actual stress that is distributed in the coracoid or with the wing load in vivo. These points will be postponed for future studies. However, although there are some limitations raised above, the strength of the coracoid against dorso‐ventral bending can be a powerful tool to reliably estimate the presence/absence of flapping ability in birds based on their skeletal morphology.

4.2. Application to extinct taxa

Although there are some limitations raised above, the coracoid strength in relation to body mass can be a powerful index to evaluate the WPL styles of flapping abilities in extinct neornithean and even ornithurine birds. In particular, it is worth testing whether the giant birds, such as Argentavis (Accipitriformes) and Pelagornis (Odontopterigiformes: Goto et al., 2022) employed ‘soaring’ or ‘flap‐flight’; whether the Ichthyornis (Clarke, 2004; Hinić‐Frlog & Motani, 2010), Hesperornis (Lucas, 1903; Marsh, 1880; Townsend, 1909), and plotopterids (Suliformes: Dyke et al., 2011; Watanabe et al., 2020) swam using wing‐ or hindlimb propulsions; and process of flightless evolutions in rallids (Gruiformes: Gaspar et al., 2020) and paleognathans (Mitchell et al., 2014).

In addition to neornithean and ornithurine birds, this new index can potentially be applied to other flying tetrapods, such as bats (Chiroptera, Mammalia) and pterosaurs (Pterosauria, Archosauria). Clavicles of bats can potentially function as struts within the shoulder girdle to withstand the bending caused by flapping muscles like the coracoids of birds (Panyutina et al., 2015). Therefore, the clavicular strength can potentially be an index to evaluate the WPL styles in bats. Likewise, if the coracoid functions to withstand the bending caused by flapping muscles in pterosaurs (Padian, 1983), the strength can also be a reference for their WPL styles. Particularly, the strength of plate‐like coracoids against bending force in the largest group of pterosaurs, such as Pteranodon, Nyctosaurus and Quetzalcoatlus (Jensen & Padian, 1989) would be one of the clues to answer a controversial whether they had flight ability (Witton & Habib, 2010).

Furthermore, this new index is highly expected to contribute to reconstructing the origin of powered flight in the lineage from feathered theropod dinosaurs to modern birds (Neornithes) via pennaraptorans, avialans, pygostylians, ornithothoracines and ornithuromorphs in order (e.g., Pittman et al., 2020: Appendix S6). According to Baier et al. (2007), the ligament that connects the shoulders and arms likely begins to transmit the force exerted by the m. pectoralis to the coracoid in the descendants of the common ancestor of Jeholornis and pygostylians, and this ligament‐based force balance to the force of the pectoral muscle is perfectly established in ornithothoracines. Although the non‐neornithean feathered theropod dinosaurs are not phylogenetically bracketed (Witmer, 1995) by the studied bird species, the coracoid seems to gradually increase in size relative to the femoral length, and gradually shifts from placoid to columnar in shape (Appendix S6; Balanoff & Norell, 2012; Chiappe et al., 1999; Clarke, 2004; Lefèvre et al., 2014; O'Connor et al., 2019; Olson, 1976; Wang et al., 2020; Xu et al., 2003; Zhou & Zhang, 2002). In ornithothoracines, the coracoids seem to become thicker dorso‐ventrally relative to the mediolateral width at the mid‐section as in modern birds with flapping abilities, and likely have evolved a triosseal foramen (O'Connor et al., 2011), which implies that the m. supracoracoideus runs along the shaft of coracoid (Appendix S6). We therefore consider that our index can be applied at least to the ornithothoracines, and presumably to the more basal avialans whose coracoid become columnar in shape, such as Jeholornis (Appendix S6; Lefèvre et al., 2014; O'Connor et al., 2011). Our index for coracoid strength may provide a powerful theoretical framework for reconstructing the origin of the pre‐flight flapping ability (Heers & Dial, 2012; Heers et al., 2021) and the powered flight.

5. CONCLUSIONS

The section modulus of coracoid in relation to the body mass of 220 specimens, variable in WPL styles and taxonomy representing 209 species, 180 genera, 83 families and 30 orders, were compared to test the relationship between WPL and skeletal morphology in extant birds. We found that the index was emphasised in flapping birds, especially in the soaring birds, whereas it was de‐emphasised in non‐flapping birds. These results reflect the difference in the requirement of coracoids to withstand the bending force caused by flapping muscles, such as the pectoralis and supracoracoideus muscles. The index is expected to be a powerful tool for reliably reconstructing the ability of WPL in extinct birds, as well as in the lineage from theropod dinosaurs to modern birds.

AUTHOR CONTRIBUTIONS

All the measurements and analyses were conducted by Takumi Akeda, the study was designed by Shin‐ichi Fujiwara and the manuscript was developed by both authors. Neither author has any conflict of interest to declare.

Supporting information

Appendix S1.

Click here for additional data file. (11.4MB, pdf)

ACKNOWLEDGMENTS

The authors thank T. Yamasaki (Yamashina Institute for Ornithology [YIO]), I. Nishiumi, M. Manabe (National Museum of Nature and Science [NSM]), M. Nimi (NUM), H. Kashiwagi (Nagoya City Science Museum) and N. Nakai (Nagoya University) for providing specimens for this study; T. Imamura (YIO) for CT‐scanning the studied specimens; M. Hioki, T. Imamura (YIO), A. Higuchi and C. Sakata (NSM) for their assistance during our measurements in their institutes; S. Hayashi (Nagoya University) for improving advices of statistical analyses; an anonymous reviewer for his/her improving comments prior to submitting the manuscript; T. Naganuma and his cat (Abiko Hotel) for providing the authors for the comfort stay in Abiko; and the members of Laboratory of Geobiology (Nagoya University) for their improving comments. Special thanks go to the editor and two anonymous reviewers who gave us improving comments for this study. This study is supported by Japan Society for the Promotion of Science (grant no. 17K17794).

Akeda, T. & Fujiwara, S‐i. (2023) Coracoid strength as an indicator of wing‐beat propulsion in birds. Journal of Anatomy, 242, 436–446. Available from: 10.1111/joa.13788

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