At its core, comparative biomechanics is a conceptually broad discipline, examining biological systems through the lens of physics. The form of any organism dictates both its response to stressors or external forces, and its interactions with the fluid environment (Vogel, 2011). For example, the muscles of various organisms perform critical movements, and the relative lengths of the input and output lever arms determine whether they perform better at generating forces or at rapid movements (Ritchie, 1954). The simple task of obtaining food presents a staggering diversity of mechanical solutions to the same problem, each with its own associated constraints on other functions. Form–function trade-offs enable examination of evolution in a mechanistic context, particularly for structures with great morphological variety and functional diversity (Arnold, 1983; Higham et al., 2021). In addition to biomimetic inspiration, the simple concepts of comparative biomechanics have transformed our inquiry and examination of the natural world.

The advent of high-speed videography for kinematics (Hedrick, 2008) and micro-computed tomography (micro-CT; James, 2017), together with computational techniques such as finite element analysis (Anderson et al., 2012; Brassey et al., 2013; Bright, 2014; Maas et al., 2012; Polly et al., 2016; Rayfield, 2007; Richmond et al., 2005; Ross, 2005), has proved transformative in comparative biomechanics. Here, I illustrate how this burgeoning field has revolutionized our understanding of the natural world, using the avian bill as a case study. The bill is a morphologically diverse multifunctional appendage (Rico-Guevara et al., 2019a) whose study spans material and fluid biomechanics, ecology, evolutionary biology and neuroscience. Biomechanics is critical to the function of diverse bill shapes in the over 10,000 species of birds (Fig. 1), from those that must withstand the stresses of cracking hard seeds (Olson, 2014; Schluter et al., 1985; Smith, 1987) and head-on impacts (Chhaya et al., 2022a preprint; Lee et al., 2014), to those whose shape reduces drag on movement through fluids (Crandell et al., 2019; Martin and Bhushan, 2016). Bill shape also influences how fluid moves through them, as exemplified by their role in vocalization (Podos et al., 2004; Riede et al., 2016; Trevisan and Mindlin, 2009). Recent studies suggest that trade-offs and constraints have exerted a potent influence on bill evolution (Navalón et al., 2019, 2020), and others suggest that certain key bill traits may be tightly linked to function, such that certain unrelated taxa converge on a similar bill morphology (Pigot et al., 2020). Here, I illustrate, using examples from the above topics, how bill mechanics influence diverse functions, emphasizing general principles to be gleaned from comparative study. Bird bills serve other functions (including preening and visual signalling); here, I primarily illustrate how a biomechanical perspective informs form–function studies on bird bills, and thus biological structures in general.

Fig. 1.

Morphological diversity of bird bills. Top row (left to right): Aethopyga gouldiae1, Napothera malacoptila1, Harpactes erythrocephalus1, Cissa chinensis1, Fratercula corniculata2. Second row (left to right): Passer cinnamomeus2, Aquila nipalensis2, Anastomus oscitans3, Serilophus lunatus4, Phoenicopterus roseus5. Third row (left to right): Recurvirostra avosetta2, Corvus corax2, Spilornis cheela4, Chalcophaps indica4, Thalassarche cauta6. Fourth row (left to right): Ara ararauna7, Phyllergates cucullatus1, Paradoxornis flavirostris3, Stachyris humei1, Batrachostomus moniliger6. Bottom left: Platalea leucorodia5. Fifth row (left to right): Pomatorhinus ferruginosus1, Pyrrhoplectes epauletta1, Nestor notabilis6. Sixth row (left to right): Pomatorhinus superciliaris1, Diomedea epomophora6, Upupa epops5, Gallus gallus4. Bottom right: Pelecanus philippensis6. Photo credits: 1Umesh Srinivasan, 2Anand Krishnan, 3Taksh Sangwan, 4Sutirtha Lahiri, 5Abhijeet Rasal, 6Seshadri KS, 7Arpit Omprakash.

Fig. 1.

Morphological diversity of bird bills. Top row (left to right): Aethopyga gouldiae1, Napothera malacoptila1, Harpactes erythrocephalus1, Cissa chinensis1, Fratercula corniculata2. Second row (left to right): Passer cinnamomeus2, Aquila nipalensis2, Anastomus oscitans3, Serilophus lunatus4, Phoenicopterus roseus5. Third row (left to right): Recurvirostra avosetta2, Corvus corax2, Spilornis cheela4, Chalcophaps indica4, Thalassarche cauta6. Fourth row (left to right): Ara ararauna7, Phyllergates cucullatus1, Paradoxornis flavirostris3, Stachyris humei1, Batrachostomus moniliger6. Bottom left: Platalea leucorodia5. Fifth row (left to right): Pomatorhinus ferruginosus1, Pyrrhoplectes epauletta1, Nestor notabilis6. Sixth row (left to right): Pomatorhinus superciliaris1, Diomedea epomophora6, Upupa epops5, Gallus gallus4. Bottom right: Pelecanus philippensis6. Photo credits: 1Umesh Srinivasan, 2Anand Krishnan, 3Taksh Sangwan, 4Sutirtha Lahiri, 5Abhijeet Rasal, 6Seshadri KS, 7Arpit Omprakash.

Birds have long played an important role in the art and customs of human civilization, with illustrations dating back to the Paleolithic. Illustrators of birds, from those behind cave paintings and Egyptian tombs to the Mughal courts of India and Western scientists such as Linnaeus (Linnaeus, 1758), have used bird bills as a defining anatomical trait. The sexes of the extinct huia (Heteralocha acutirostris) of New Zealand were originally described as separate species because of dramatically different bill shapes and foraging niches (Buller, 1870). Studying bill shape has proved highly consequential in our understanding of evolution and speciation. Darwin's initial examinations of Galapagos finches (Darwin, 1839) led to the influential later studies of David Lack, Robert Bowman and Peter and Rosemary Grant (Lack, 1947; Bowman, 1961; Grant and Grant, 2006). These studies drew an important mechanistic link between bill morphology and diet, and thus to the probability of survival in harsh environmental conditions. Birds with bills that could crack tougher seeds were more likely to survive food scarcity, shifting the morphology of the population. In parallel, the spectacular adaptive radiation of the Hawaiian honeycreepers was scientifically described in the late 19th century. In spite of their extraordinary divergence in bill morphology, careful examination revealed that they shared a common ancestor (Amadon, 1950; Perkins, 1901).

The twentieth century saw a movement from museum-based natural history toward observations of animals and their behaviour in the wild. This led to an interest in functional morphology, beginning with D'Arcy Thompson's landmark On Growth and Form, which integrated mathematical analyses into morphology (Thompson, 1917). In the latter half of the twentieth century, the functional and mechanical consequences of different forms and feeding strategies received much interest. By then, experiments on human bone identified mechanical response properties to a range of stresses (Evans, 1957; Koch, 1917). Further, comparative anatomy was increasingly blended with mechanical and engineering considerations in the study of biomechanics (Beecher, 1962). Dempster used free-body diagrams to examine forces acting on the human body (Dempster, 1961). Free-body diagrams proved useful as a static (or quasi-static) depiction of the mechanical function of the bill (Bowman, 1961). Although nowadays replaced by finite element models (which enable us to study the distribution of stresses on the bill), the free-body diagram still enables comparison of diverse bill shapes and feeding techniques (Korzun et al., 2003, 2008; Pêgas et al., 2021) (Fig. 2). Walter Bock provided an excellent example of applying this approach to a wide range of bill shapes (Bock, 1966). He treated the jaws of birds as rigid bodies rotating about a pivot, in this case the quadrate bone articulation, whose rotation propels the jaw open. Bock simplified the problem of jaw closing to include the force required and the length of the lever arm. This sets the stage for much of our discussion in upcoming segments, where most mechanical actions performed by the bill can be understood in this simple physical context. The limitations of assuming symmetric loading on the bill and the need to characterize all moving parts of the lever before using free-body diagrams must be acknowledged here, and Bock's work highlighted how a careful analysis of anatomy and natural history must precede any biomechanical analysis. The advance of his model over previous studies was in considering the movement or kinesis of the bill, as well as material inhomogeneity in the bony structures (Bock, 1966). Whereas Hofer examined loads only at the bill tip (Hofer, 1945), Bock examined static loads at various points along the tomium and added an analysis of torques and stress trajectories, introducing the concept of mechanical trade-offs in bill function. In nature, being very good at one function often comes at the expense of another. Sensitivity and resolution trade off against each other in sensory organs, and speed and manoeuvrability typically trade off against each other in flying animals. Bills are no exception to this, and specializations for a certain function result in deficits in others. This has ecological consequences, driving increasing specialization from a ‘generic’ bill morphology, and potentially restricting species to certain niches.

Fig. 2.

A hypothetical comparison between finch bills. The hawfinch Coccothraustes coccothraustes, whose seed-cracking bill may be predicted to perform better for dorsoventral loads, and the red crossbill Loxia curvirostra, whose bill is used to pry open pine cones and may thus perform better for mediolateral loads. Static analysis (A) enables us to predict loads at different points of the bill. This leads to experimental measurements of bite force, and kinematic studies using high-speed videography (B). The graphs shown are a mock-up of what such data might be expected to look like. For example, the downward bite force of the hawfinch would be predicted to increase towards the tomium. Next, examination of bill material properties enables us to describe their responses to stresses. The bill of the hawfinch is predicted to perform better (resist deformation) under compressive stresses, whereas that of the crossbill should resist deformation under shear stresses (C). Finally, finite element analysis provides detailed stress distribution patterns (D). In this mock-up of a finite element model, red represents regions of higher stress. The hawfinch is predicted to exhibit lower stresses for dorsoventral loads, whereas the same is predicted in the crossbill for mediolateral loads. Birds were drawn using photographic references by Santiago Caballero Carrera and Daniel Jauvin, sourced from the Macaulay Library (ML319188441, ML202628831; https://www.macaulaylibrary.org/).

Fig. 2.

A hypothetical comparison between finch bills. The hawfinch Coccothraustes coccothraustes, whose seed-cracking bill may be predicted to perform better for dorsoventral loads, and the red crossbill Loxia curvirostra, whose bill is used to pry open pine cones and may thus perform better for mediolateral loads. Static analysis (A) enables us to predict loads at different points of the bill. This leads to experimental measurements of bite force, and kinematic studies using high-speed videography (B). The graphs shown are a mock-up of what such data might be expected to look like. For example, the downward bite force of the hawfinch would be predicted to increase towards the tomium. Next, examination of bill material properties enables us to describe their responses to stresses. The bill of the hawfinch is predicted to perform better (resist deformation) under compressive stresses, whereas that of the crossbill should resist deformation under shear stresses (C). Finally, finite element analysis provides detailed stress distribution patterns (D). In this mock-up of a finite element model, red represents regions of higher stress. The hawfinch is predicted to exhibit lower stresses for dorsoventral loads, whereas the same is predicted in the crossbill for mediolateral loads. Birds were drawn using photographic references by Santiago Caballero Carrera and Daniel Jauvin, sourced from the Macaulay Library (ML319188441, ML202628831; https://www.macaulaylibrary.org/).

Rapid technological progress tremendously impacted comparative studies of the bill. Modern high-speed videography enables us to quantify how birds move their bills when interacting with solids or fluids (Riede et al., 2006; Van Der Meij and Bout, 2006). The ease and precision of 3D kinematic analysis, coupled with experimental measures of bite force (Herrel et al., 2005, 2009), enables us to verify the static measurements of earlier anatomical models. Further, we can now quantify material properties at small spatial scales using nano-indentation (Bonser and Witter, 1993; Seki et al., 2005, 2010). Using 3D printing, biological samples can now be replicated and mechanically tested. Thus, we may examine both microscale toughness and fracture properties in biological materials (Fig. 2). Energy-dispersive X-ray spectroscopy provides the mineral composition of materials, which influences their mechanical properties. Where bill materials are available, bending experiments and the use of digital speckle pattern interferometry and digital image correlation enable us to perform in vitro compressive testing (Soons et al., 2012a), thus integrating laboratory research with field-based natural history.

These advances in biomechanics have been accompanied by major advances in computation, with its attendant analytical power and processing speeds to handle large volumes of data. This has led to renewed interest in macroevolutionary morphological studies on bird bills, particularly based on museum specimens (Cooney et al., 2017; Navalón et al., 2019; Pigot et al., 2020). In addition, CT provides 3D morphological data, and we may virtually dissect and study relevant structures of both extant and extinct species (James, 2017; Lautenschlager et al., 2013). Finite element analysis helps us examine stresses and their transmission patterns across 3D geometries, incorporating information on material properties as well (Fig. 2) (Soons et al., 2010, 2012b, 2015). Finally, computational fluid dynamics, coupled with kinematic data, enables analysis of complex interactions of solid objects such as bills with surrounding fluid media (Crandell et al., 2019). This fusion of older and newer tools perhaps well deserves the name ‘integrative biology’, and informs my subsequent examination of bill form and function.

The avian bill consists of a bony maxilla and mandible with an outer keratinous rhamphotheca. The dorsal surface of the maxilla is called the culmen, whereas the ventral surface of the mandible is called the gonys. The meeting point of the maxilla and mandible, where most food handling and processing occurs, possesses a ridged biting surface called the tomium. In the absence of teeth, force application by the bill occurs at the tomium, and the rhamphotheca enables stress dissipation synergistically with bone (Lautenschlager et al., 2013; Seki et al., 2005). The keratin of the rhamphotheca is a structurally rigid, glycine-rich 15.5 kDa monomer with a high indentation hardness, representing an impact- and abrasion-resistant material (Bonser, 1996; Frenkel and Gillespie, 1976; Homberger and Brush, 1986; Wang et al., 2016). In many species, keratin forms overlapping scales that are attached to each other and layered over the bone, which may help enhance strength (Hieronymus and Witmer, 2010; Lee et al., 2014; Piro, 2022; Seki et al., 2005).

The discovery of feathered theropod dinosaurs demonstrated that birds evolved by edentulism (loss of teeth) from a toothed theropod ancestor, a feature retained by early avialans together with a rhamphotheca (Miller et al., 2020; Zheng et al., 2020). Genetic switches which reduced the development of dentition may have simultaneously keratinized the outer epidermis of the jaws to form the rhamphotheca (Louchart and Viriot, 2011), a trend seen in turtles and pterosaurs (Beccari et al., 2021; Bestwick et al., 2018; Osi et al., 2011). In non-avian theropods, edentulism coupled with a keratinous rhamphotheca has evolved independently in multiple groups, concomitant with a widespread trend toward herbivory (Lautenschlager et al., 2013; Ma et al., 2017; Meade and Ma, 2022; Norell et al., 2001; Wang et al., 2017; Zanno and Makovicky, 2011). Composite bill structures resist fracturing better than homogeneous materials, and a finite element analysis of the therizinosaur Erlikosaurus andrewsi demonstrated that the rhamphotheca considerably lowered stresses on the jaw during biting (Lautenschlager et al., 2013). Altogether, herbivory may have been a key driver in the evolution of keratinized bills.

However, in early birds, the process of edentulism and the evolution of a lightweight bill was accompanied by a spectacular diversification of shapes and functions (Cooney et al., 2017; Louchart and Viriot, 2011). These massive shape changes are driven by the Bmp4 and calmodulin gene pathways (Abzhanov et al., 2004, 2006), among others (Bhullar et al., 2015). The diversity of functions and specializations in the bill represent adaptations to distinct ecological niches, each shape exerting its own biomechanical constraints. Below, I discuss these trade-offs from the biologist's perspective, focusing on the link between form and function to examine the insights we now have from decades of research on the bill.

Solid biomechanics seeks to understand the resistance of materials to stresses (tensile, compressive or shear) that might cause deformation or fracture. Materials resist or dissipate stress in diverse ways, influenced by their ultrastructure or their geometry (Wainwright, 1992). The jaws of vertebrates experience both compressive and shear stresses during feeding (Therrien et al., 2005). Bills are subject to an additional constraint: being lightweight to support flight. A series of jaw muscles control cranial kinesis of both upper and lower jaws (the upper jaw bends at the nasofrontal hinge). The relative sizes of these muscles and the bones that they attach to determine the force generated by the bill, and the resultant stresses that the bill must withstand. Forces generated by jaw muscles are transmitted via flexibly articulated bones (the quadrate, jugal and pterygoid), which move the jaws (Bock, 1966; Hoese and Westneat, 1996). This facilitates cranial kinesis during diverse tasks such as feeding, singing, etc. In paleognathous birds (ratites), the upper bill is rhynchokinetic, i.e. can bend only at more distal positions (Gussekloo and Bout, 2005). Using the knowledge that bone performs well under compression or tension but relatively poorly under shear, Bock (1966) estimated that the nasofrontal hinge of a crow skull could resist ∼110–175 N forces in compression, but only ∼65–90 N in shear forces.

Bock (1966) also conducted a detailed examination of the structure of bone within the bill in relation to the stress trajectories experienced during loading. He found that areas of higher compressive stress (crowding of stress trajectories) coincided with the presence of compact bone, whereas areas with lower stress possessed spongy, lightweight trabecular bone. Trabecular bone importantly provides resistance to bending stresses (Seki et al., 2005). Again, the trade-off is evident; strength to perform one function may result in structural weakness in others, and also trade off against weight (critical for a flying bird). The combination of bony materials renders the avian bill robust yet lightweight, even without considering the keratinous rhamphotheca (Bock, 1966).

Bird bills also serve as a probing tool where loads emerge from moving the bill against dense mud or into crevices in tree trunks, as a head-butting implement where compressive stresses result from contact between two birds, as a seed-cracker where massive forces must be exerted in order to crush tough seeds, and as a chisel used to excavate holes in wood, just to name a few of their diverse functions. Many functions impose great physical demands on the bill, and hypertrophied jaw and neck muscles perform the work of actuating the bill against a substrate (Deeming et al., 2022; Heckeberg et al., 2021; Van Der Meij and Bout, 2008). These forces could easily fracture the bill if the resultant stresses are not dissipated. If the bill is approximated to a simple cylindrical beam loaded either axially (as during pecking) or transversely (as during biting), one might consider the stress trajectories as radiating dorsoventrally and posteriorly from the point of contact, eventually approaching the base of the skull and braincase, and it is thus critical for some dissipation to occur (Brassey et al., 2013). In their simplest form, these forces may be represented as buckling stress (predicted under Euler's Law) and shear stress (Chhaya et al., 2022a preprint), each of which could result in material failure when they cross a critical threshold.

The bill could theoretically, therefore, be highly susceptible to fracture or buckling during physically demanding tasks. How do bird bills support these demanding functions, and yet remain lightweight enough for flight? The keratinized rhamphotheca over the trabecular ‘spongy’ bone appears to represent a key step in the evolution of lightweight, fracture-resistant bills. This ‘sandwich’ composite structure lowers stresses experienced by the bill during compressive or shear loading, and stops fracture propagation before it reaches the bony layers of the bill. Fracture of the keratin occurs by scale displacement when strains are lower, and the scales themselves fail at higher strains (Genbrugge et al., 2012; Seki, 2009; Seki et al., 2005, 2010; Soons et al., 2012b). Wear and tear of the rhamphotheca thus protects the bony portions of the bill from injury (Hieronymus and Witmer, 2010; Lee et al., 2014). In addition to strength arising from the synergistic effects of a composite structure, bills may further be reinforced by the incorporation of minerals and pigments into the rhamphotheca. Melanin increases the hardness of keratin, thereby improving its resistance to fracture and particularly abrasion (Bonser and Witter, 1993). By increasing the abrasion resistance of bills, birds may compensate to some degree for damage over time, eventually replacing the keratin to provide a new surface. This presents advantages over teeth, which cannot be replaced. Further, the bill of the Toco toucan (Ramphastos toco) contains mineral deposits which increase the Young's modulus (Seki et al., 2005). Bird bill keratin normally contains calcium phosphate (hydroxyapatite) (Pautard, 1963). Mineralization increases material hardness, as in insect mandibles and ovipositors where zinc enrichment improves resistance to material stresses (Gundiah and Jaddivada, 2020). However, this field still largely operates outside of the ecological context of bill use, and eco-mechanical studies relating behaviour and morphology to the biochemical structure of bills represent an important frontier for future research.

Of course, the individual components of the bill ultimately give rise to distinct bill geometries (Al-Mosleh et al., 2021), which strongly influence stresses experienced during feeding or other functions (Rayfield, 2011), and thus bill shape evolution (Olsen, 2017; Reddy et al., 2012). Simply put, a thin, slender bill will not be very efficient at cracking hard seeds. This requires both musculature and a bill surface (tomium) that can generate high pressures, and a wide, deep bill that can withstand the resultant compressive and shear stresses (Field, 2019; Herrel et al., 2005; Soons et al., 2010). For example, the massive bill of the extinct Hawaiian honeycreeper Chloridops kona could crack seeds of the naio Myoporum sandwicense, which required forces in excess of 400 N (Olson, 2014; Perkins, 1893), and the finches Pyrenestes ostrinus (146 N force) and Coccothraustes coccothraustes (>400 N force) similarly feed on extremely tough materials (Sims, 1955; Smith, 1987, 1990). Such forces no doubt result in significant compressive and shear stress, particularly at the tomium, and may have driven repeated evolution of massive bills in finches, exemplified by Crithagra concolor of São Tomé (Melo et al., 2017). In contrast, the bills of the Hawaiian honeycreepers Rhodacanthis palmeri (now extinct) and Loxioides bailleui serve(d) to cut bean pods of Acacia koa and Sophora chrysophylla, respectively, rather than crush seeds (Perkins, 1893).

In seed-crushing bills, high bite force risks fracturing the bone. Bite forces are often higher toward the rear of the bill, but the fracture point owing to increased shear stress sets a constraint on the maximum force the bill can exert, and muscles, head and jaw-closing apparatus appear arranged to accommodate these constraints (Carril et al., 2015; Genbrugge et al., 2011; Rao et al., 2018; Soons et al., 2010, 2015). Bowman concluded that either a heavily curved bill or one with a thickened base could potentially support fracture resistance during seed cracking (Bowman, 1961). In the decurved bill of a cardinal (Cardinalis cardinalis), increased bill depth increases the moment arm of the force generated by the muscles, and hence torque, leading to increased bite force. Simultaneously, the bill withstands shear stresses at the base. The deep bill of the evening grosbeak (Coccothraustes vespertinus) exerts high compression with low shear (Bock, 1966). Bowman's (1961) and Bock's (1966) studies served as a prelude to Grant and Grant's (2006) study of the ecological consequences of bill shape, which informed our understanding of evolution. Recent studies using finite element analysis have found that the deep and wide bills of several species of Darwin's finches exhibit enhanced stress dissipation (Genbrugge et al., 2012; Herrel et al., 2005; Soons et al., 2010, 2015). Bill morphology in seed-eating birds supports resource partitioning, seed selection and surviving scarcity of food, further demonstrating how comparative biomechanics informs evolutionary biology (Abbott et al., 1975; Benkman and Pulliam, 1988; Foster et al., 2008; Grant and Grant, 2006; Hespenheide, 1966; Kear, 1962; Schluter et al., 1985; Smith, 1987, 1990; Willson, 1972).

In general, bills that are ‘buttressed’ or reinforced both dorsoventrally and mediolaterally perform well under compressive loads. These specializations impose trade-offs on other functions. For a given input arm length, a shorter output lever arm is important to increase mechanical advantage and thus generate greater force (Fig. 3). It thus stands to reason that a bill that cracks hard seeds, such as that of a parrot or finch, is also shorter in the dimension of length (Bock, 1966; Homberger, 2003). However, this geometric configuration potentially prioritizes force over jaw-closing velocity (Corbin et al., 2015; Herrel et al., 2009), which can impact a number of other behaviours. Birds with slender bills, such as insectivores that catch moving prey, prioritize closing velocity (or the velocity ratio), and thus possess longer output lever arms relative to input lever arms (Beecher, 1962; Lederer, 1975). Cracking of seeds in finches often also involves lateral movement of the bill, and the extent of this lateral movement differs between greenfinches (Chloris chloris) (with a lower husking time and a larger lateral movement) and Java sparrows (Padda oryzivora) (Van Der Meij and Bout, 2006; Van Der Meij et al., 2004). Crossbills (Loxia) use their unique bills in a lateral motion to open pine cones (Benkman, 1993), and specialization for mediolateral strength putatively reduces dorsoventral bite force. Analysis of kinematics and bite force coupled with finite element models and nanoindentation will help us better understand how bills withstand both compressive and shear stresses, and whether they trade off between dorsoventral and mediolateral strength (Fig. 2). Additionally, XROMM (X-ray reconstruction of moving morphology) technology provides a way to quantify the actions of the jaw musculature (Dawson et al., 2011), which in turn will help better understand the lever biomechanics employed to generate different kinds of forces.

Fig. 3.