Comparative limb bone loading in the humerus and femur of the tiger salamander: testing the ‘mixed-chain’ hypothesis for skeletal safety factors

Bones must regularly withstand applied forces, or loads, imposed internally by the contraction of muscles and externally by interactions with the environment. When bones are unable to withstand loads, injury to the skeleton could lead to inferior predator evasion, inability to acquire food, or other detriments including death (Biewener, 1993). Terrestrial locomotion is particularly noteworthy in this context, because limb bones must accommodate the forces imposed by body support and propulsion, generating some of the highest demands upon the skeleton (Biewener, 1993). Despite these demands, bones can normally withstand loads greater than those they typically experience. This ratio between the typical load sustained and the maximum load the structure can withstand is called a ‘safety factor’ (SF), and provides a margin of protection to structures for performing functions with variable demands (Alexander, 1981, 1997, 1998; Diamond, 2002).

SFs for bones commonly allow protection against loads ranging from 2 to 10 times greater than ordinary, with variation across taxa and among the limb bones within a species (Alexander, 1981; Biewener, 1993; Blob et al., 2014; Currey, 2002; Diamond, 2002; Sheffield and Blob, 2011). Several factors contribute to interspecific variation in SFs (Blob and Biewener, 1999; Blob et al., 2014), but explanations for intraspecific variation are less intuitive. For a single structure, the SF is expected to be sufficiently high to prevent it from being compromised by applied loads, but low enough to minimize the energetic costs to produce such a structure (Alexander, 1997).

Yet, the performance of one structure may influence the performance of another within a skeleton. Structures are organized into interconnected systems based on shared biological functions, and the interdependency of structures within a system can limit the performance of individual structures. Alexander (1997) described the integrated nature of structures using a metaphor of chains in which a biological system represents a ‘chain’ composed of inter-connected ‘links’, such as the bones within the leg. Given that a chain's overall strength depends upon the strength of its weakest link, it might be assumed that all components within a system should have comparable biological performance, thus avoiding wasted energy in the production of higher-quality components that would be superseded by the inferior performance of weaker ones (Alexander, 1997). However, Alexander (1997) proposed several scenarios under which variation in SFs, or a ‘mixed-chain’, might be expected within an organism. First, structures that are energetically costly to move or maintain could have lower SFs. Second, structures that experience more variable loading regimes than the rest of the skeleton might have higher SFs, protecting against occasionally higher loads. Third, for species in which all structures of the skeleton exhibit high SFs, there might be greater opportunity for variation in SFs across elements. Diamond (2002) further suggested higher SFs in structures with higher penalties for failure. For instance, a broken nasal bone might impair olfaction, but a broken cranium could be fatal, so greater SFs would be expected for the cranium.

Limited empirical evidence has supported the presence of ‘mixed-chains’ of SFs in the locomotor skeleton. Currey (2002) found a higher incidence of fracture (implying lower SFs) in the distal limb bones of racehorses, compared with proximal bones. Similarly, Blob and Biewener (1999) found lower SFs in the tibia (distal bone) versus the femur (proximal bone) in the hindlimbs of iguanas and alligators. Comparisons between bones of the forelimb and hindlimb are also appropriate to consider in the context of ‘mixed-chains’ because, although the girdles and vertebrae intervene between these limbs, both limbs function to support the body in quadrupeds, and a break in any leg would impair locomotion. However, data for such comparisons are more limited, with a single study finding higher SFs in the humerus versus the femur of alligators (Blob et al., 2014). With respect to proposed factors contributing to ‘mixed-chains’ (Alexander, 1997; Diamond, 2002), the higher humeral SFs of alligators were attributed to the generally high SFs in the limbs of reptiles and the smaller size of the humerus that might make high SFs less costly than for the femur (Blob et al., 2014). However, with such patterns evaluated for only a single species, their generality is unclear.

Understanding the prevalence of ‘mixed-chains’ of limb bone SFs could inform how the different functions of forelimbs and hindlimbs contributed to the invasion of land. Fossil evidence suggests that terrestrial capabilities occurred in the forelimb before the hindlimb, and while the forelimbs could have powered propulsion on land in some of the earliest amphibious stem tetrapods (Nyakatura et al., 2014; Pierce et al., 2012), hindlimbs were the primary propulsor on land thereafter for many tetrapods, and may have contributed to hindlimb-driven aquatic locomotion in sarcopterygian fishes (King et al., 2011) and some early stem tetrapods (Pierce et al., 2013). Salamanders are often used as modern locomotor analogs to early stem tetrapods given their morphological and ecological similarities (Gao and Shubin, 2001). Thus, salamanders are an intriguing system to test the ‘mixed-chain’ hypothesis and explore how locomotor function can leave biomechanical signatures in bones, providing a foundation for inferring locomotor capabilities of fossil taxa. Femoral stresses have been evaluated for the tiger salamander Ambystoma tigrinum during terrestrial locomotion (Sheffield and Blob, 2011), but corresponding analyses for the humerus have not been performed. Combined with work on Alligator mississippiensis (Blob et al., 2014), comparisons of locomotor loading between the humerus and femur of A. tigrinum would help identify factors that drive structural and functional diversity within the locomotor system. Additionally, information regarding form–function relationships in the locomotor system of a modern analog to early stem tetrapods can facilitate modeling early stages in the invasion of land.

To more broadly test the prevalence of ‘mixed-chains’ of SFs within the appendicular system, we compared biomechanical properties and loading mechanics during terrestrial locomotion between the humeri and femora of A. tigrinum. Given that its humerus and femur are subequal in size and might require similar energy to move, similar SFs might be expected for these bones (Blob et al., 2014). Alternatively, a ‘mixed-chain’ of SFs might emerge between the limbs in tiger salamanders for several reasons. First, different muscle configurations between salamander limbs (Walthall and Ashley-Ross, 2006) result in fewer muscles that are active during stance spanning the mid-shaft (and contributing to stress) in the humerus than in the femur (Fig. 1), potentially resulting in different sustained loads (the denominator of the SF calculation) between the limbs. Alexander's second condition predicted higher SFs with increased load variation. In another sprawling quadruped, Tiliqua scincoides intermedia, long axis rotation was greater in the humerus (78 deg) than in the femur (53 deg) (Nyakatura et al., 2014), potentially increasing variation in humeral loads. Increased load variation could also result from the non-locomotor roles of the humerus, such as burrowing (Semlitsch, 1983). In addition, relatively high SFs for tiger salamander femora (∼10: Sheffield and Blob, 2011) suggest the potential for variation in SF across salamander limb bones (Alexander, 1997; Blob et al., 2014).

We used a biomechanical model to estimate locomotor stresses (as proxies for loads) and SFs (specifically, ratio of yield stress to mean peak locomotor stress) for the humeri and femora of tiger salamanders by integrating measurements of bone geometry, Vickers hardness (H_V), muscle moment arms and anatomy as well as calculations of ground reaction forces (GRFs) and kinematics. Through our tests of the ‘mixed-chain’ hypothesis of SFs between salamander limb bones, we evaluated (1) whether the femur bore greater stresses because of its greater contribution to acceleration (Kawano and Blob, 2013) or muscular configuration (Walthall and Ashley-Ross, 2006), and (2) whether variation in hardness across a limb bone corresponded with regional differences in locomotor stresses. Moreover, these data establish a foundation for considering ‘mixed-chains’ of limb bone SFs in generalized quadrupeds, in the context of transitions in limb function amongst stem tetrapods.

Bone-loading mechanics were analyzed for adult, male tiger salamanders (Ambystoma tigrinum Green 1825) used in a previous study on GRF production (Kawano and Blob, 2013). Two trials from this earlier study were excluded herein because they generated unrealistic estimates of bone stress (e.g. calculations suggested that limb retractor muscles did not activate during stance). Following completion of experiments, animals were humanely killed with buffered tricane methanesulfonate (MS-222; 2 g l⁻¹), and frozen for subsequent anatomical measurements (Tables 1–3). Experimental and animal care procedures were approved by the Clemson University Institutional Animal Care and Use Committee (protocols 2009-071, 2010-066).

Methods for collecting synchronized 3D kinematic and kinetic data for salamanders have been documented (Kawano and Blob, 2013; Sheffield and Blob, 2011), but are summarized with additional details herein. Dorsal and lateral views of animals walking across a custom-built, multi-axis force platform (K&N Scientific, Guilford, VT, USA) were recorded at 100 Hz with digitally synchronized high-speed digital video cameras (Phantom v4.1, Vision Research Inc., Wayne, NJ, USA). Data on the force production of individual limbs were recorded at 5000 Hz with LabVIEW (v6.1, National Instruments, Austin, TX, USA), and calibrated daily. A 4×9 cm aluminium insert reduced the contact area of the platform, facilitating data collection from isolated limbs (see fig. 1 of Kawano and Blob, 2013). The platform was covered with shelf liner to prevent damage to the salamander’s skin. Data from the force platform and high-speed videos were synchronized with a 1.5 V pulse on the force traces that matched the onset of a light pulse on the lateral video of each trial.

Stance phase kinetics were processed in R (v3.1.2) to generate mediolateral, anteroposterior and vertical components of the GRF, and angles of orientation in the mediolateral and anteroposterior directions. Force magnitudes were normalized to units of body weight (BW) for each animal to standardize for minor differences in body size. Data on GRFs were padded at the beginning and end to avoid edge effects (Smith, 1989), and then filtered with a second-order, zero­-phase, low-pass Butterworth filter using the ‘signal’ package in R. Filter parameters were determined using custom specifications, with normalization to Nyquist frequency to prevent aliasing of data (Smith, 1997). Filtered data were then interpolated to 101 points with a cubic spline using signal::interp1(method=‘spline’). Standardization to 101 points allowed data to be analyzed throughout stance at 1% increments (0%=beginning of stance, 100%=penultimate to swing), facilitating direct comparison between kinematics and kinetics. Fifty and 48 trials were evaluated for the forelimb and hindlimb, respectively, with about 10 trials from each of five individuals for each limb. Comparisons were performed throughout stance, when GRFs were greatest (peak net GRF; Table 4), and during peak tensile stresses (Table 5).

Kinematics were quantified by digitizing coordinate data from the dorsal and lateral (right) views of each trial with DLTdv3 in MATLAB (Hedrick, 2008). High-speed videos were cropped to encompass stance. Joint and anatomical landmarks digitized in each video included: (1) the tip of the longest digit of the manus/pes, (2) the metacarpophalangeal/metatarsophalangeal joint, (3) the wrist/ankle, (4) the elbow/knee, (5) the shoulder/hip and (6) the two points along the midline of the body that were dorsal to the pectoral/pelvic girdles (Fig. S1). Every other frame was digitized for videos longer than 40 frames. Otherwise, every frame was digitized. Digitized coordinates were then smoothed with a quintic spline using pspline::smooth.Pspline. As generalized cross-validation is unreliable for high-speed videos (Walker, 1998), custom smoothing parameters were quantified as the variation of each variable obtained from a single person (S.M.K.) digitizing the first 10 frames of a trial for each limb 3 times. The variance amongst the three digitizing attempts was used as a separate smoothing parameter for each anatomical landmark in each perspective (dorsal and lateral).

Several criteria were used for quality control of data. Trials were excluded if the animal: (1) turned, stopped, or fell on the platform; (2) moved diagonally across the platform; (3) did not have its manus/pes completely on the platform; or (4) had other parts of its body (e.g. head, throat, belly) in contact with the platform during stance. If the peak of the net GRF occurred within ∼5% of the beginning or end of stance, that trial was excluded because the animal's body likely contacted the platform while shifting between its limbs. Acceptable trials had negligible differences in speed between the limbs (Table 6). For trials selected for analysis, data were excluded when the limb overlapped with another body part (e.g. hindlimb during a forelimb trial) to ensure that calculations of GRFs, moments and bone stresses resulted from isolated limbs.

Bone stresses were evaluated using conventions for the anatomical planes of the limbs for sprawling animals, accounting for their rotation during stance (Blob and Biewener, 2001; Butcher and Blob, 2008; Sheffield and Blob, 2011). Bone stresses were analyzed at the mid-shaft, where the most complete records of the biomechanical loading regime are stored (Sanchez et al., 2010) and loads are predicted to be greatest (Biewener and Taylor, 1986). A biomechanical model for calculating locomotor stresses in A. tigrinum femora was applied to the femur data and modified for the humerus. Although data on the loading of A. tigrinum femora during terrestrial locomotion are available (Sheffield and Blob, 2011), new data were collected to directly compare forelimb and hindlimb function within individuals.

where R_GRF is the moment arm of the GRF relative to the joint (obtained from force platform analyses) and r_m is the moment arm of the muscle needed to counter the GRF moment about the joint. Muscles that did not span the mid-shaft could contribute to joint moments countering the GRF, but not to mid-shaft bending stresses (Blob and Biewener, 2001; Sheffield and Blob, 2011). If more than one muscle counteracted the GRF to maintain equilibrium at a joint, a mean moment arm was calculated for the group weighted by the physiological cross-sectional areas (PCSAs) of the contributing muscles (Alexander, 1974; Biewener, 1983; Sheffield and Blob, 2011). Muscular moment arms were measured during post-mortem dissections, while stabilizing the limb in a mid-stance orientation. Detailed descriptions of salamander myology, including origins and insertions of muscles, are given in Walthall and Ashley-Ross (2006).

Muscles assumed to contribute to humeral joint moments and stresses included retractors and adductors, and elbow and wrist extensors (Fig. 1A,B, Table 2). Forelimb muscle activity patterns were inferred from electromyography (Delvolvé et al., 1997; Székely et al., 1969), anatomical descriptions of Taricha torosa (Walthall and Ashley-Ross, 2006) and direct observations of A. tigrinum. Latissimus dorsi (LD) and coracobrachialis longus (CBL) were considered to retract the humerus (Fig. 1A,B: red). The four bundles of the anconaeus complex were inferred to act as elbow extensors, and subdivided into two functional units according to their anatomical positions: anconaeus scapularis medialis and anconaeus coracoideus (ASMAC; Fig. 1A,B: purple), and anconaeus humeralis lateralis and anconaeus humeralis medialis (AHLAHM; Fig. 1A,B: blue). ASMAC was inferred to exert an additional retractor moment due to its moment arm at the shoulder. Wrist extensors included the flexor digitorum communis (FDC), flexor antebrachii et carpi radialis (FACR), flexor antebrachii et carpi ulnaris (FACU) and a deep complex of carpal plantiflexors (DCF). These muscles were assumed to be active to oppose the moment of the GRF tending to dorsiflex/extend the wrist, with FDC, FACU and FACR also spanning the extensor aspect of the elbow joint (Fig. 1A,B: yellow). Pectoralis (P) and supracoracoideus (SC) insert on the crista ventralis of the humerus (proximal end), and adduct the humerus (Fig. 1A,B: orange). Of these muscles that exert moments about the joints, only three (ASMAC, AHLAHM and CBL) spanned the mid-shaft of the humerus and contributed directly to bone stresses.

The bone loading model for the femur incorporated ankle extensors, and femoral retractors and adductors (Fig. 1C,D, Table 3), with these actions inferred from electromyographic (Ashley-Ross, 1995) and anatomical (Ashley-Ross, 1992) data. The model was detailed in Sheffield and Blob (2011), but a brief summary follows. Caudalipuboischiotibalis (CPIT), caudofemoralis (CDF) and iliofemoralis (ILFM) retract the femur (Fig. 1C,D: red). Ischioflexorius (ISF) is a multi-articular muscle that contributes to femoral retraction, and spans distally to extend the ankle (Fig. 1C,D: magenta). Flexor primordialis communis (FPC) is situated to extend the ankle and knee (Fig. 1C,D: yellow). Three muscles [puboischiotibialis (PIT), pubotibialis (PTB) and puboischiofemoralis externus (PIFE)] contribute to femoral adduction and countering the abductor moment of the GRF (Fig. 1C,D: orange). Muscles that span the mid-shaft and, thus, could contribute to femoral stress include the ISF, PIT, PTB and PIFE. Knee extensors were not incorporated into the biomechanical model because the muscles acting to extend the knee in salamanders (i.e. iliotibialis anterior and posterior) do not have a consistent phase of activity during stance (Ashley-Ross, 1995).

Thus, differences in muscle configuration and PCSA between the limbs could contribute to differences in loading between the humerus and femur. Consequently, these wrist extensors reduce the force that primary elbow extensor muscles (e.g. anconaeus complex) must generate to counter the elbow flexor moments typically imposed by the GRF, without increasing humeral stresses. In contrast, ankle extensors spanning the knee add to its flexor moment, rather than its extensor moment, often requiring elevated (rather than reduced) forces from knee extensors (Sheffield and Blob, 2011). Also, a lower proportion of forelimb muscles contribute to bone stresses. Only 30% of the forelimb muscles considered in the biomechanical model were likely to contribute to humeral stresses (Table 2), with a cumulative PCSA of about 13 mm² (25% of the total PCSA for the forelimb). In contrast, 50% of the hindlimb muscles contributed to femoral stresses (Table 1), with almost 20 mm² constituting about 54% of the total hindlimb PCSA.

The net neutral axis of bending was determined as perpendicular to this axis of peak stress (Sheffield et al., 2011).

where T is calculated as the moment of the GRF vector relative to the long axis of the bone, y is the distance from the centroid of the bone to its cortex and J is the polar moment of area (Table 1), calculated as the sum of the second moments of area in the DV and AP directions (Lieberman et al., 2004).

Microindentation was used to compare hardness between and within bones. Right humeri and femora were air-dried, mounted in Caroplastic (Carolina Biological, Burlington, NC, USA), a non-infiltrating resin, and sectioned transversely at the mid-shaft. Cut surfaces from the distal half were polished to visualize cross-sectional geometries and prepare for microindentation. Mounted specimens were affixed to a 100×61×2 mm Plexiglas slide with cyanoacrylate glue, and loaded onto an automated polisher (EXAKT Technologies, D-4000, Oklahoma City, OK, USA). Samples were ground with moistened silicon carbide paper of decreasing grit sizes (P800, P1200, P2500, P4000), for 5 min each. Agglomerate-free alumina suspensions were used to polish the specimens to 3.0 μm (Baikalox Type 3.0 CR Alpha), 0.3 μm (Baikalox Type 0.3 CR Alpha) and finally to 0.05 μm (Buehler Micropolish II) using a polishing pad (Buehler, Lake Bluff, IL, USA) for 3 min each. Grinding and oscillation speeds were set at 30 rpm, with a 99.3 g weight applied. Samples were rinsed with deionized water after each step to remove abrasive particulates, air dried and then stored at −20°C for less than 72 h. Prior to indentation, samples were equilibrated to room temperature and cleaned with methanol. These procedures allowed mechanical testing of hydrated bones. H_V was measured with a Digital Display Microhardness Tester (Model HVS-1000B, Beijing, China) configured with a Vickers indenter tip, 0.49 N load and 15 s dwell time, following procedures for microindentation of salamander femora (Sheffield and Blob, 2011). About five indents were performed in the dorsal, ventral, anterior and posterior regions to test for regional heterogeneity in hardness. Data were collected away from cavities and edges of the bone to avoid potential edge effects. No cracks or pile-up were observed.

Sample preparation and testing conditions can influence hardness measurements, but were likely minimal in this study. H_V (1) is consistent for dwell times up to 30 s (Johnson and Rapoff, 2007), (2) does not differ between bones that were fresh versus frozen at −20°C for 3 months and (3) is only 4% lower in bones that are embedded in infiltrating media rather than non-embedded (Evans et al., 1990). We used a non-infiltrating plastic to stabilize the bones and, therefore, expect the difference between mounted and unmounted bones to be minimal. Hardness values have been up to ∼50% higher for bones tested dry rather than wet with a nanoindenter (Hoffler et al., 2005), but only about 9% greater for bones that were dried for 2 days or longer and tested with a microindenter (Johnson and Rapoff, 2007). Our use of a non-infiltrating resin kept the bones hydrated. Although the humerus of individual 1 underwent slightly different testing conditions (0.981 N load, and no data from the posterior region), available data still followed general patterns observed between the humeri and femora (Fig. S3). Also, hardness is consistent for applied loads between 15 and 300 g (Zysset, 2009), encompassing the 0.49 and 0.981 N used in this study. Thus, our protocol likely had minimal effect on hardness comparisons.

H_V, yield stress and SF were reported separately for each of the anatomical regions (Table 7, Table S1). Calculations of yield stresses and SFs were based on dorsal and posterior regions being loaded in tension, and anterior and ventral regions loaded in compression.

Kinetic, kinematic, bone microhardness, safety factor and stress data are available from the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.7f1j1.

Linear mixed-effects models (LMMs), fitted by restricted maximum likelihood via lme4::lmer, were used to evaluate differences within response variables, with individual as a random effect for a random intercepts model (Bates et al., 2014). Random effects represented subsamples of a population and an additional source of variation (e.g. individuals within species) whereas fixed effects were factors to compare (e.g. forelimb versus hindlimb) (Bolker et al., 2009). Regional heterogeneity of H_V within a bone was assessed with anatomical region as a fixed effect. Otherwise, limb bone was the fixed effect. Given that H_V within an anatomical region may vary amongst individuals, anatomical region was also added as a random effect to create a random intercepts and slopes LMM. Pair-wise comparisons between anatomical regions and bones were fitted with a contrast matrix in multcomp::glht. P-values provide limited information regarding the strength of evidence to support conclusions (Anderson et al., 2001), so LMMs were reported in terms of effect sizes and an estimate of precision (e.g. Ω₀²; Xu, 2003), emphasizing the magnitude of the differences and the level of uncertainty in supporting those differences, respectively.

Although the limbs have similar kinematic profiles, numerous differences were identified. At the beginning of stance, the shoulder and hip are adducted by ∼10–15 deg (Fig. 2A), with the wrist and ankle showing similar degrees of extension (Fig. 2B). The femur is more protracted than the humerus until about 80% of stance (Fig. 2C), and the elbow is more flexed than the knee until about 90% of stance (Fig. 2D). Flexion and extension of the elbow and knee follow similar profiles; however, the ankle becomes flexed almost twice as much as the wrist towards mid-stance. Another major difference between the limbs is that the femur remains adducted (e.g. knee closer to the ground than the hip) throughout stance (Fig. 2A), but the humerus becomes abducted (elbow higher than shoulder) after about 30% of stance. Additionally, although both bones begin in a protracted orientation (i.e. distal joint cranial to the girdle for almost all of stance), the humerus is initially nearly perpendicular to the long axis of the body (∼0 deg in Fig. 2C) and retracts at about 10% of stance, whereas retraction of the femur is more evenly split between protracted and retracted orientations (Fig. 2C).

GRF production was generally similar between the forelimbs and hindlimbs (Table 4, Fig. 3), contributing to similarities in the joint moments imposed by the GRF (Fig. 4). The GRF imposes a dorsiflexion (positive) moment about the wrist and ankle (Fig. 4A) due to the anterior position of the GRF relative to these joints. To maintain equilibrium at these joints, wrist and ankle extensors need to be active to counter the flexor moments imposed by the GRF. The primarily vertical orientation of the GRF throughout stance (Fig. 3) tends to impose an abductor moment on the shoulder and hip, though for the latter this shifts to an adductor moment approximately 75% into stance (Fig. 4B). The GRF also imposes a protractor moment about the shoulder and hip, though protraction at the shoulder is lower in magnitude and occurs later in stance (40%) than at the hip (10% stance) (Fig. 4C). Finally, torsional moments imposed by the GRF are similar between the humerus and femur (Fig. 4D), changing from a tendency to impose anterior axial rotation to posterior rotation at about 60% of stance.

Despite these similarities, different configurations of the forelimb and hindlimb influence how the GRF imposes moments on these limbs (Fig. S2). In salamanders (and most quadrupeds), the elbow points posteriorly whereas the knee points anteriorly. However, the GRF is directed essentially vertically for most of stance for both limbs (Fig. 3). Consequently, the flexor/extensor moment of the GRF tends to change in different directions for these joints, shifting from a flexor to an extensor moment for the knee at ∼50% stance, but vice versa for the elbow at ∼75% stance (Fig. 4E). Also, analogous moments were greater in the hindlimb than in the forelimb [e.g. ankle versus wrist in dorsiflexion (Fig. 4A), hip versus shoulder in anteroposterior and dorsoventral rotations (Fig. 4B,C), and knee versus elbow in flexion and extension (Fig. 4E)].

Lower stresses were estimated for locomotor loads upon the humerus, though the difference between the bones was less pronounced for shear (Table 6). Peak tensile and compressive stresses occurred later in stance for the humerus (∼67%) than the femur (∼22%) (Table 6, Fig. 5A,B). This pattern corresponds with the peak net GRF, which also occurred later in stance (∼61%) for the forelimb than the hindlimb (∼33%) (Table 4, Fig. 3). After accounting for variation amongst individuals, total external forces (‘net GRF’) at the time of peak tensile stresses for each bone were 0.061±0.016 BW lower in the humerus, with vertical and anteroposterior components lower by 0.04 and 0.115 BW, respectively (Table 5).

The neutral axis of bending for the humerus was directed such that the posterodorsal region was loaded in tension and the anteroventral region in compression through the time of mid-stance to peak loading (Fig. 5C,D). The neutral axis of bending was aligned closer to the anatomical anteroposterior axis at peak tensile stress for the femur, placing the dorsal portion in tension and the ventral portion in compression. Nonetheless, the anterodorsal cortex of the femur was loaded in tension and the posteroventral cortex in compression at 50% of stance (Fig. 5C,D).

Comparisons indicated higher H_V for the humerus and regional heterogeneity within each bone (Table 7, Table S1). The LMM explained about 68% of the variation in H_V based on Ω₀² (Xu, 2003), an analog of R² for LMMs. The greatest magnitude of H_V, and thus estimated yield stresses, at these mid-shafts was generally in the posterodorsal region (Table 7), corresponding with the typical location of tensile loads about the neutral axis of bending (Fig. 5B).

Femoral SFs ranged from ∼9 to 10 (Table 7), corresponding with the published estimate of 10.5 (Sheffield and Blob, 2011). However, humeral SFs were almost twice those of the femur, ranging from ∼20 to 24. The greatest SFs at femoral mid-shafts were in the dorsal cortex, where H_V was greatest, yet SFs at humeral mid-shafts were greater in the anteroventral region, where H_V was lower (Table 7). This difference was largely due to peak bone stresses that were about two times lower in the humerus (Table 6), although higher yield stresses in the humerus also contributed to SF differences from the femur (Table 7). The worst-case scenario SF (SF_wc) was about two times lower than standard SF calculations for both bones, but still indicated ample margins of safety (∼8–13 for the humerus, ∼3–6 for the femur; Table 7). Biomechanical differences along the dorsoventral and anteroposterior planes of the bones were also reflected in their structural response to bending, as evidenced by second moments of area that were greater in the dorsoventral plane for the humerus and the anteroposterior plane for the femur (Table 1).

Humeri have higher SFs (∼22) than femora (∼10) in salamanders, a disparity greater than that reported in alligators (8.4 for the humerus versus 6.3 for the femur; Blob et al., 2014). The difference between humeral and femoral SFs relates primarily to differences in yield strain for alligators (Blob et al., 2014), but from both lower stresses and structural reinforcement in salamander humeri (Tables 6, 7).

Critical factors that are likely contributing to the relatively lower stresses in the salamander humerus, compared with the femur, include the configuration of joints and disposition of muscles. Because of the range of motion of the arm (Fig. 2) and orientation of the elbow in A. tigrinum, the GRF only exerts a flexor moment at the elbow late in stance (Fig. 4E). This reduces the need for elbow extensors (e.g. anconaeus complex) to counter GRF moments at the elbow, reducing the stress they place on the humerus (Table 2, Fig. 1). Humeral stresses are additionally reduced by contributions of wrist extensors (FDC, FACR, FACU) to the elbow extensor moment, further reducing the force that elbow extensors spanning the humeral mid-shaft must exert. Moreover, adductor muscles contributing to forelimb movement (P and SC) insert proximally on the humerus, and do not contribute to stresses experienced at mid-shaft.

Beyond these stress-reducing characteristics of forelimb musculature in salamanders, H_V of the humerus is generally greater than that of the femur, with different patterns of regional heterogeneity (Table 7, Table S1) between the bones. The highest SFs corresponded with areas loaded in tension (dorsal and posterior) for the femur, but compression (anterior and ventral) for the humerus. Moreover, the femur has a larger second moment of area in the anteroposterior direction (I_AP), but the humerus has a greater second moment of area in the dorsoventral direction (I_DV; Table 1). These results suggest that these limb bones show differences in structure and mechanical response that reduce bending stress in different directions. Given the extent to which humeral SFs (>20) of salamanders are greater than those of the femur (∼10), it is difficult to envisage how the entire magnitude of differences in humeral and femoral SFs of salamanders could be adaptive. Nonetheless, elevated SFs supported by greater H_V and structural modifications suggest the possibility that, to some extent, the high load-bearing capacity of salamander humeri may facilitate the multi-functional role of the forelimbs for locomotor and non-locomotor behaviors (e.g. burrowing).

Comparisons of SFs for the humerus and femur of salamanders provide an additional empirical example of a ‘mixed-chain’ (Alexander, 1997, 1998) within the locomotor skeleton of tetrapods. ‘Mixed-chains’ of SFs were identified between proximal and distal limb bones in horses (Currey, 2002), and iguanas and alligators (Blob and Biewener, 1999). However, data herein reinforce additional patterns observed in alligators (Blob et al., 2014), which demonstrated different SFs between the proximal bones of the forelimb and the hindlimb. As in alligators (Blob et al., 2014), the humerus has a higher SF than the femur in salamanders (Table 7).

Some of the factors proposed by Alexander (1997) that might contribute to differences in SFs between these bones in alligators do not apply to salamanders. For example, alligator humeri are smaller than the femora, which might allow for more economical maintenance of a high SF (Blob et al., 2014). However, the humerus and femur are roughly equal in length in salamanders (Table 1), so Alexander's first condition for ‘mixed-chains’ likely does not apply. Alexander's second condition for ‘mixed-chains’ of SFs also likely does not apply to salamanders. Similar to alligators, the salamander limb bone that was exposed to greater variation in loads (i.e. femur) did not have higher SFs (Table 6), suggesting that elevation of humeral SFs in salamanders likely was not an adaptive response for protection against unpredictable high loads.

SFs for salamander limb bones, like those of alligators, are generally high (>7) compared with those of many taxa, including mammals and birds (Blob et al., 2014). Thus, differences between humeral and femoral SFs for salamanders might simply reflect an increased opportunity for variation in SF across the skeleton (Alexander's third condition). Though this reason has been invoked as a factor contributing to ‘mixed-chains’ in alligators (Blob et al., 2014), data on the limb configuration, muscle disposition and regional heterogeneity of H_V in tiger salamanders also suggest mechanistic reasons for high SFs in limb design. Collectively, the elevated structural and material reinforcement to withstand loads in the humerus, and anatomical features of the forelimb promoting low loads, suggest that stochastic variation associated with large SFs may not completely account for differences in humeral and femoral SFs observed in salamanders.

In addition to the three conditions promoting ‘mixed-chains’ of SFs proposed by Alexander (1997), higher SFs may be found in structures with higher penalties for failure (Diamond, 2002). Forelimbs and hindlimbs play different roles in legged locomotion (McElroy et al., 2014), which may provide insight into SF variation in salamander limb bones. Although hindlimbs provide the primary propulsion in many non-mammalian quadrupeds, forelimbs still make important contributions to locomotion (Kawano and Blob, 2013; Nyakatura et al., 2014), and loss of locomotor function may be more detrimental for the forelimb. Early work on salamander locomotion (Evans, 1946) demonstrated that forward propulsion could be achieved solely by the forelimbs but not the hindlimbs, suggesting that the forelimbs play a more important locomotor role than passive body support (at least in terrestrial salamanders such as Taricha and Ambystoma). Moreover, there do not appear to be ready examples (among non-bipedal vertebrates) in which the complete loss of the pectoral appendages occurred while the pelvic appendages remained fully intact: when vertebrates lose an entire appendage, it is typically the pelvic appendage (e.g. siren salamanders, amphisbaenids, cetaceans, sirenian mammals, scincid lizards, and fishes from 100 families; Gans, 1975; Lande, 1978; Yamanoue et al., 2010). Even when limb loss is associated with the evolution of fossorial or aquatic life styles (e.g. amphisbaenians and cetaceans), the forelimbs are typically retained rather than the hindlimbs (Caldwell, 2003). Limb reduction, including the loss of digits, can be found in the forelimb rather than the hindlimb in some taxa (Lerista lizards: Skinner et al., 2008), but the loss of proximal limb elements or the entire limb is generally less common for forelimbs. Additional studies are required to verify whether there are strong mechanical or selective advantages for forelimb retention in non-bipedal vertebrates, or whether the conservatism of forelimb retention is due to developmental constraint. For instance, hindlimbs develop after forelimbs (Tanaka and Tickle, 2007), and structural reduction typically occurs in the reverse order from which structures develop (Lande, 1978), potentially making hindlimbs more susceptible to loss via developmental truncation.

Further investigations of how loads vary across limb bones could yield insights into the morphological evolution of limb bones as vertebrates became terrestrial. The vertebrate musculoskeletal system shifted from being essentially weightless as a result of buoyancy underwater to counteracting the effects of gravity on land, drastically shifting the loading regime imposed upon the locomotor structures. This shift may have made the evolution of long, tubular limb bone shafts advantageous compared with their blocky precursors (Currey, 2002). Microanatomical analyses of a wide range of tetrapods have differentiated aquatic and terrestrial lifestyles from limb bone histology (Laurin et al., 2011), facilitating the inference of the locomotor biomechanics of fossil taxa such as the Devonian fish Eusthenopteron (Laurin et al., 2007) and stem stegocephalians (Laurin et al., 2004). Identifying stronger form–function relationships between limb morphology and locomotor movements would facilitate efforts to reconstruct the transition from water to land by tetrapods (Nyakatura et al., 2014; Standen et al., 2014). For instance, the mechanical properties of bones from extant taxa were combined with palaeopathology to theorize the loading conditions that could have fractured the radius in the early stem tetrapod Ossinodus pueri in the context of walking on land (Bishop et al., 2015), suggesting the utility of bone loading data during terrestrial locomotion to address the mechanisms that influenced how vertebrates became terrestrial. Further application of data on locomotor stresses from extant taxa could help answer questions regarding the functional consequences of morphological changes observed in extinct tetrapodomorphs spanning the transition from water to land (Hohn-Schulte et al., 2013; Kawano and Blob, 2013).

We are grateful to Marguerite Butler and Brad Chadwell for advice about smoothing data, and to Chad McMahan and Linda Jenkins for assistance with sample preparation. Earlier drafts were improved by suggestions from Margaret Ptacek, Miriam Ashley-Ross, Andrew Biewener, and two anonymous reviewers. Fig. 1 was produced using figures generously provided by Miriam Ashley-Ross. We also thank Rebecca Nelson, William Mitchell, Patrick McGarity, Lauren Pruitt, Megan Gregory and David Boerma for assistance with video analysis. All experiments were completed at Clemson University. An earlier draft was submitted by S.M.K. as a dissertation chapter in partial fulfillment of a doctoral degree at Clemson University.