RESEARCH ARTICLE

Comparative limb bone loading in the humerus and femur of thetiger salamander: testing the ‘mixed-chain’ hypothesis for skeletalsafety factorsSandy M. Kawano1,*, D. Ross Economy2, Marian S. Kennedy2, Delphine Dean3 and Richard W. Blob4

ABSTRACTLocomotion imposes some of the highest loads upon the skeleton,and diverse bone designs have evolved to withstand these demands.Excessive loads can fatally injure organisms; however, boneshave a margin of extra protection, called a ‘safety factor’ (SF), toaccommodate loads that are higher than normal. The extent to whichSFs might vary amongst an animal’s limb bones is unclear. If thelimbs are likened to a chain composed of bones as ‘links’, then similarSFs might be expected for all limb bones because failure of thesystemwould be determined by the weakest link, and extra protectionin other links could waste energetic resources. However, Alexanderproposed that a ‘mixed-chain’ of SFs might be found amongst bonesif: (1) their energetic costs differ, (2) some elements face variabledemands, or (3) SFs are generally high. To test whether suchconditions contribute to diversity in limb bone SFs, we compared thebiomechanical properties and locomotor loading of the humerus andfemur in the tiger salamander (Ambystoma tigrinum). Despite highSFs in salamanders and similar sizes of the humerus and femur thatwould suggest similar energetic costs, the humerus had lower bonestresses, higher mechanical hardness and larger SFs. SFs weregreatest in the anatomical regions where yield stresses were highestin the humerus and lowest in the femur. Such intraspecific variationbetween and within bones may relate to their different biomechanicalfunctions, providing insight into the emergence of novel locomotorcapabilities during the invasion of land by tetrapods.

KEY WORDS: Biomechanics, Bone stress, Intraspecific variation,Skeleton, Locomotion, Tetrapod

INTRODUCTIONBones must regularly withstand applied forces, or loads, imposedinternally by the contraction ofmuscles and externally by interactionswith the environment. When bones are unable to withstand loads,injury to the skeleton could lead to inferior predator evasion, inabilityto 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 bodysupport and propulsion, generating some of the highest demandsupon the skeleton (Biewener, 1993). Despite these demands, bonescan normally withstand loads greater than those they typically

experience. This ratio between the typical load sustained and themaximum load the structure can withstand is called a ‘safety factor’(SF), and provides a margin of protection to structures for performingfunctions with variable demands (Alexander, 1981, 1997, 1998;Diamond, 2002).

SFs for bones commonly allow protection against loads rangingfrom 2 to 10 times greater than ordinary, with variation across taxaand 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 interspecificvariation in SFs (Blob and Biewener, 1999; Blob et al., 2014), butexplanations for intraspecific variation are less intuitive. For a singlestructure, the SF is expected to be sufficiently high to prevent it frombeing compromised by applied loads, but low enough to minimizethe 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 organizedinto interconnected systems based on shared biological functions,and the interdependency of structures within a system can limit theperformance of individual structures. Alexander (1997) describedthe integrated nature of structures using a metaphor of chains inwhich a biological system represents a ‘chain’ composed of inter-connected ‘links’, such as the bones within the leg. Given that achain’s overall strength depends upon the strength of its weakestlink, it might be assumed that all components within a system shouldhave comparable biological performance, thus avoiding wastedenergy in the production of higher-quality components that wouldbe superseded by the inferior performance of weaker ones(Alexander, 1997). However, Alexander (1997) proposed severalscenarios under which variation in SFs, or a ‘mixed-chain’, might beexpected within an organism. First, structures that are energeticallycostly to move or maintain could have lower SFs. Second, structuresthat experience more variable loading regimes than the rest of theskeleton might have higher SFs, protecting against occasionallyhigher loads. Third, for species in which all structures of the skeletonexhibit high SFs, there might be greater opportunity for variation inSFs across elements. Diamond (2002) further suggested higher SFsin structures with higher penalties for failure. For instance, a brokennasal bone might impair olfaction, but a broken cranium could befatal, 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 thedistal 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 ofiguanas and alligators. Comparisons between bones of the forelimband hindlimb are also appropriate to consider in the context of‘mixed-chains’ because, although the girdles and vertebraeReceived 10 June 2015; Accepted 9 November 2015

1National Institute for Mathematical and Biological Synthesis, University ofTennessee, Knoxville, TN 37996, USA. 2Department of Materials Science andEngineering, Clemson University, Clemson, SC 29634, USA. 3Department ofBioengineering, Clemson University, Clemson, SC 29634, USA. 4Department ofBiological Sciences, Clemson University, Clemson, SC 29634, USA.

*Author for correspondence (skawano@nimbios.org)

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intervene between these limbs, both limbs function to support thebody in quadrupeds, and a break in any leg would impairlocomotion. However, data for such comparisons are morelimited, with a single study finding higher SFs in the humerusversus the femur of alligators (Blob et al., 2014). With respect toproposed factors contributing to ‘mixed-chains’ (Alexander, 1997;Diamond, 2002), the higher humeral SFs of alligators wereattributed to the generally high SFs in the limbs of reptiles andthe smaller size of the humerus that might make high SFs less costlythan for the femur (Blob et al., 2014). However, with such patternsevaluated 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 hindlimbscontributed to the invasion of land. Fossil evidence suggests thatterrestrial capabilities occurred in the forelimb before the hindlimb,and while the forelimbs could have powered propulsion on land insome of the earliest amphibious stem tetrapods (Nyakatura et al.,2014; Pierce et al., 2012), hindlimbs were the primary propulsor onland thereafter for many tetrapods, and may have contributed tohindlimb-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 earlystem tetrapods given their morphological and ecological similarities(Gao and Shubin, 2001). Thus, salamanders are an intriguing systemto test the ‘mixed-chain’ hypothesis and explore how locomotorfunction can leave biomechanical signatures in bones, providing afoundation for inferring locomotor capabilities of fossil taxa. Femoralstresses have been evaluated for the tiger salamander Ambystomatigrinum during terrestrial locomotion (Sheffield andBlob, 2011), butcorresponding 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 andfemur of A. tigrinum would help identify factors that drive structuraland functional diversity within the locomotor system. Additionally,information regarding form–function relationships in the locomotorsystem of a modern analog to early stem tetrapods can facilitatemodeling early stages in the invasion of land.

To more broadly test the prevalence of ‘mixed-chains’ of SFswithin the appendicular system, we compared biomechanicalproperties and loading mechanics during terrestrial locomotionbetween the humeri and femora of A. tigrinum. Given that itshumerus and femur are subequal in size and might require similarenergy to move, similar SFs might be expected for these bones(Blob et al., 2014). Alternatively, a ‘mixed-chain’ of SFs mightemerge 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 areactive during stance spanning the mid-shaft (and contributing tostress) in the humerus than in the femur (Fig. 1), potentiallyresulting in different sustained loads (the denominator of the SFcalculation) between the limbs. Alexander’s second conditionpredicted higher SFs with increased load variation. In anothersprawling quadruped, Tiliqua scincoides intermedia, long axisrotation was greater in the humerus (78 deg) than in the femur(53 deg) (Nyakatura et al., 2014), potentially increasing variation inhumeral loads. Increased load variation could also result from thenon-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 variationin 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 tomean peak locomotor stress) for the humeri and femora of tigersalamanders by integrating measurements of bone geometry,Vickers hardness (HV), muscle moment arms and anatomy as wellas calculations of ground reaction forces (GRFs) and kinematics.Through our tests of the ‘mixed-chain’ hypothesis of SFs betweensalamander limb bones, we evaluated (1) whether the femur boregreater stresses because of its greater contribution to acceleration(Kawano and Blob, 2013) or muscular configuration (Walthalland Ashley-Ross, 2006), and (2) whether variation in hardnessacross a limb bone corresponded with regional differences inlocomotor stresses. Moreover, these data establish a foundation forconsidering ‘mixed-chains’ of limb bone SFs in generalizedquadrupeds, in the context of transitions in limb function amongststem tetrapods.

MATERIALS AND METHODSAnimalsBone-loading mechanics were analyzed for adult, male tigersalamanders (Ambystoma tigrinum Green 1825) used in a

List of symbols and abbreviationsAHLAHM anconaeus humeralis lateralis and anconaeus

humeralis medialisAP anteroposteriorASMAC anconaeus scapularis medialis and anconaeus

coracoideusBW body weightCBL coracobrachialis longusCDF caudofemoralisCPIT caudalipuboischiotibialisCV coefficient of variationDCF deep complex of plantar flexors of the carpusDV dorsoventralFm muscular forces (N)FACR flexor antebrachii et carpi radialisFACU flexor antebrachii et carpi ulnarisFDC flexor digitorum communisFE fixed effectFPC flexor primordialis communisGRF ground reaction forceHV Vickers hardnessILFM iliofemoralisISF ischioflexoriusJ polar moment of area (mm4)LD latissimus dorsiLMM linear mixed-effects modelP pectoralisPCSA physiological cross-sectional area (mm2)PIFE puboischiofemoralis externusPIT puboischiotibialisPTB pubotibialisRGRF moment arm of the GRF relative to the joint (m)rc moment arm due to curvaturerm moment arm of the muscle forces (mm)SC supracoracoideusSF safety factorT moment of the GRF vector relative to the

long axis of the boney distance of the centroid from the bone cortex (mm)Θ angle between the muscle and the long axis of the boneσb bending stress (MPa)σyieldstress tensile yield stress (MPa)τ torsional stress (MPa)Ω0

2 analog for coefficient of determination for LMMs

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previous study on GRF production (Kawano and Blob, 2013). Twotrials from this earlier study were excluded herein because theygenerated unrealistic estimates of bone stress (e.g. calculationssuggested that limb retractor muscles did not activate during stance).Following completion of experiments, animals were humanelykilled 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 theClemson University Institutional Animal Care and Use Committee(protocols 2009-071, 2010-066).

Collection of synchronized 3D kinematics and kineticsMethods for collecting synchronized 3D kinematic and kinetic datafor salamanders have been documented (Kawano and Blob, 2013;Sheffield and Blob, 2011), but are summarized with additionaldetails herein. Dorsal and lateral views of animals walking across acustom-built, multi-axis force platform (K&N Scientific, Guilford,VT, USA) were recorded at 100 Hz with digitally synchronizedhigh-speed digital video cameras (Phantom v4.1, Vision ResearchInc., Wayne, NJ, USA). Data on the force production of individuallimbs were recorded at 5000 Hz with LabVIEW (v6.1, NationalInstruments, Austin, TX, USA), and calibrated daily. A 4×9 cmaluminium insert reduced the contact area of the platform,facilitating data collection from isolated limbs (see fig. 1 ofKawano and Blob, 2013). The platform was covered with shelf linerto prevent damage to the salamander’s skin. Data from the forceplatform and high-speed videos were synchronized with a 1.5 Vpulse on the force traces that matched the onset of a light pulse onthe lateral video of each trial.

Stance phase kinetics were processed in R (v3.1.2) to generatemediolateral, anteroposterior and vertical components of the GRF,and angles of orientation in the mediolateral and anteroposterior

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Retractor Elbow/knee extensorAdductor Elbow/knee and wrist/ankle extensors Retractor + ankle extensors

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Fig. 1. Superficial musculature of the forelimbs and hindlimbs of salamanders that were incorporated into the biomechanical model of limb bonestress production. Left, forelimb: A, dorsal; B, ventral. Right, hindlimb: C, dorsal; D, ventral. The illustration is based on myology figures of the Californianewt, Taricha torosa (Walthall and Ashley-Ross, 2006; permission to re-use from John Wiley and Sons, Inc.). Details of these anatomical structures and theirassociated acronyms can be found inWalthall and Ashley-Ross (2006). Muscles active during stancewere assumed to contribute to joint moments to counter theground reaction force (GRF), but could only contribute to bone stress if they spanned the mid-shaft of either the humerus or the femur. Two deep muscles[DCF (deep complex of plantar flexors of the carpus in the forelimb) and ILFM (iliofemoralis) in the hindlimb] were modeled as a wrist extensor and a hip retractor,respectively, but are not illustrated. The top of each figure is oriented in the anterior direction of the animal. Scale bars represent 1 cm.

Table 1. Comparison of anatomical data for the humeri and femora ofAmbystoma tigrinum

Humeri Femora

Length (mm) 15.244±0.463 14.906±0.478Cross-sectional area (mm2) 1.007±0.201 0.879±0.343rc(AP) (mm) 0.099±0.056 0.040±0.031rc(DV) (mm) −0.349±0.128 −0.138±0.103yAP (mm) 1.406±0.089 0.613±0.029yDV (mm) 1.368±0.062 1.000±0.077IAP (mm

4) 0.134±0.048 0.201±0.107IDV (mm

4) 0.191±0.072 0.131±0.048J* (mm4) 0.325±0.118 0.333±0.154

Values are means±s.d. (N=5 individuals for each group). All of the listedvariables except ‘length’were evaluated at themid-shaft of the bone. Statisticalcomparisons were not conducted because of the small sample size.rc, moment arm due to curvature; y, distance from neutral axis to cortex;I, second moment of area; J, polar moment of area; AP, anteroposteriordirection; DV, dorsoventral direction. For rc(AP): positive is concave posterior,negative is concave anterior. For rc(DV): positive is concave ventral, negative isconcave dorsal. *J=IAP+IDV (Lieberman et al., 2004).

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directions. Force magnitudes were normalized to units of bodyweight (BW) for each animal to standardize for minor differences inbody size. Data on GRFs were padded at the beginning and end toavoid 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 customspecifications, with normalization to Nyquist frequency to preventaliasing of data (Smith, 1997). Filtered data were then interpolatedto 101 points with a cubic spline using signal::interp1(method=‘spline’). Standardization to 101 points allowed data tobe analyzed throughout stance at 1% increments (0%=beginning ofstance, 100%=penultimate to swing), facilitating direct comparisonbetween kinematics and kinetics. Fifty and 48 trials were evaluatedfor the forelimb and hindlimb, respectively, with about 10 trialsfrom each of five individuals for each limb. Comparisons wereperformed throughout stance, when GRFs were greatest (peak netGRF; 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 inMATLAB (Hedrick, 2008). High-speed videos were cropped toencompass 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 twopoints along the midline of the body that were dorsal to the pectoral/pelvic girdles (Fig. S1). Every other frame was digitized for videoslonger than 40 frames. Otherwise, every frame was digitized.Digitized coordinates were then smoothed with a quintic splineusing pspline::smooth.Pspline. As generalized cross-validation isunreliable for high-speed videos (Walker, 1998), custom smoothingparameters were quantified as the variation of each variableobtained from a single person (S.M.K.) digitizing the first 10frames of a trial for each limb 3 times. The variance amongst thethree digitizing attempts was used as a separate smoothingparameter for each anatomical landmark in each perspective(dorsal and lateral).

Several criteria were used for quality control of data. Trials wereexcluded if the animal: (1) turned, stopped, or fell on the platform;(2) moved diagonally across the platform; (3) did not have itsmanus/pes completely on the platform; or (4) had other parts of itsbody (e.g. head, throat, belly) in contact with the platform duringstance. If the peak of the net GRF occurred within ∼5% of the

Table 2. Comparison of anatomical data for the forelimb muscles of A. tigrinum

rm (mm)

PCSA (mm2) Θ (deg) Shoulder Elbow Wrist Bone stress

Humeral retractorsLD 4.010±0.632 N/A 2.402±0.239 N/A N/A NoCBL 3.092±0.550 6±2.236 4.060±0.991 N/A N/A Yes

Humeral adductorsP 10.105±2.902 N/A 4.342±0.589 N/A N/A NoSC 11.165±2.781 N/A 4.008±1.039 N/A N/A No

Elbow extensorsASMAC* 2.460±0.652 6±2.236 1.820±0.253 1.690±0.380 N/A YesAHLAHM 7.565±1.698 0±0 N/A 1.942±0.735 N/A Yes

Wrist extensorsFDC‡ 6.719±1.603 N/A N/A 1.546±0.382 1.708±0.726 NoFACR‡ 3.150±0.836 N/A N/A 1.356±0.440 1.006±0.326 NoFACU‡ 1.570±0.594 N/A N/A 1.500±0.401 0.948±0.334 NoDCF 2.694±0.971 N/A N/A N/A 0.890±0.293 No

Values are means±s.d. (N=5).PCSA, physiological cross-sectional area; Θ, angle between the muscle and the long axis of the bone; rm, moment arm of the muscle forces about the joint. SeeList of symbols and abbreviations for muscle names. Rightmost column indicates whether the muscle was assumed to contribute to bone stress.Statistical comparisons were not conducted because of the small sample size.*ASMAC also exerts a humeral retractor moment about the shoulder. ‡FDC, FACR and FACU also exert extensor moments at the elbow.

Table 3. Comparisons of anatomical data for the hindlimb muscles of A. tigrinum

rm (mm)

PCSA (mm2) Θ (deg) Hip Knee Ankle Bone stress

Femoral retractorsCPIT 3.708±0.473 N/A 4.072±0.834 N/A N/A NoCDF 4.895±0.915 N/A 5.942±1.198 N/A N/A NoILFM 2.243±0.711 N/A 2.668±0.574 N/A N/A No

Femoral adductorsPIFE 7.357±0.713 11±2.236 2.124±0.185 N/A N/A YesPIT 8.475±0.998 9±2.236 2.946±0.530 3.946±0.730 N/A YesPTB 2.219±0.406 10±0 2.198±0.380 2.308±0.603 N/A Yes

Ankle extensorsISF* 1.595±0.447 8±2.739 5.944±0.635 3.234±0.408 2.668±0.466 YesFPC 6.152±1.321 N/A N/A 1.064±0.188 1.482±0.619 No

Values are means±s.d. (N=5).PCSA, physiological cross-sectional area; Θ, angle between the muscle and the long axis of the bone; rm, moment arm of the muscle forces about the joint. SeeList of symbols and abbreviations for the muscle names. Rightmost column indicates whether the muscle was assumed to contribute to bone stress.Statistical comparisons were not conducted because of the small sample size.*ISF also exerts a hip retractor moment.

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beginning or end of stance, that trial was excluded because theanimal’s body likely contacted the platform while shifting betweenits limbs. Acceptable trials had negligible differences in speedbetween the limbs (Table 6). For trials selected for analysis, datawere excluded when the limb overlapped with another body part(e.g. hindlimb during a forelimb trial) to ensure that calculations ofGRFs, moments and bone stresses resulted from isolated limbs.

Calculation of bone stressesBone stresses were evaluated using conventions for the anatomicalplanes of the limbs for sprawling animals, accounting for theirrotation during stance (Blob and Biewener, 2001; Butcher and Blob,2008; Sheffield and Blob, 2011). Bone stresses were analyzed at themid-shaft, where the most complete records of the biomechanicalloading regime are stored (Sanchez et al., 2010) and loads arepredicted to be greatest (Biewener and Taylor, 1986). Abiomechanical model for calculating locomotor stresses inA. tigrinum femora was applied to the femur data and modified forthe humerus. Although data on the loading of A. tigrinum femoraduring terrestrial locomotion are available (Sheffield and Blob,2011), new data were collected to directly compare forelimb andhindlimb function within individuals.In addition to accounting for bone stresses imposed by the GRF,

mathematical models were used to evaluate the contributions oflimb muscles to bone stress due to moments imposed by the GRF

(Fig. S2). These models incorporated only muscles that are likely tobe active during stance and capable of countering the GRF. Jointswere considered to be in static rotational equilibrium (Biewener,1983), allowing contributions of muscle forces (Fm) to bone stressesto be calculated as:

Fm ¼ RGRF � GRFrm ; ð1Þ

where RGRF is the moment arm of the GRF relative to the joint(obtained from force platform analyses) and rm is the momentarm of the muscle needed to counter the GRF moment about thejoint. Muscles that did not span the mid-shaft could contribute tojoint moments countering the GRF, but not to mid-shaft bendingstresses (Blob and Biewener, 2001; Sheffield and Blob, 2011). Ifmore than one muscle counteracted the GRF to maintainequilibrium at a joint, a mean moment arm was calculated forthe group weighted by the physiological cross-sectional areas(PCSAs) of the contributing muscles (Alexander, 1974;Biewener, 1983; Sheffield and Blob, 2011). Muscular momentarms were measured during post-mortem dissections, whilestabilizing the limb in a mid-stance orientation. Detaileddescriptions of salamander myology, including origins andinsertions of muscles, are given in Walthall and Ashley-Ross(2006).

Table 4. Comparison of GRF parameters at the time of peak net GRF for A. tigrinum

Forelimb Hindlimb

Ω02Mean±s.e.m. FE±s.e.m. t-value Mean±s.e.m. FE±s.e.m. t-value

Time of peak net GRF (%) 61.080±1.008 28.294±1.824 15.511 32.667±1.628 32.786±1.854 17.688 0.732Net GRF (BW) 0.457±0.009 −0.022±0.012 −1.798 0.479±0.010 0.478±0.017 28.266 0.236Vertical GRF (BW) 0.447±0.009 0.007±0.014 0.475 0.439±0.013 0.440±0.020 21.609 0.248Mediolateral GRF (BW) −0.068±0.004 0.002±0.007 0.206 −0.071±0.007 −0.069±0.009 −7.377 0.179Anteroposterior GRF (BW) −0.028±0.008 −0.179±0.012 −15.394 0.151±0.009 0.151±0.008 18.145 0.712Mediolateral angle (deg) −8.671±0.531 0.360±0.964 0.374 −9.271±0.897 −9.031±1.171 −7.712 0.165Anteroposterior angle (deg) −3.206±0.996 −23.225±1.782 −13.036 20.033±1.511 20.018±1.406 14.241 0.646

Values are means±s.e.m. (N=50 and N=48 trials averaged across five individuals for the forelimb and hindlimb, respectively). Timing of the peak net groundreaction force (GRF) is represented as a percentage into the stance phase of the limb cycle. Peak net GRF values were determined for each individual trial, andthen averaged across all trials to produce the mean and s.e.m. Mean values assume all trials were independent.Fixed effect (FE) estimates account for non-independence due to sub-sampling of individuals, and values for the humerus indicate differences from the femurpoint estimates (e.g. net GRF was about 0.02 BW lower in the humerus than in the femur).Statistical analyses were based on the model: lmer(y∼Limb+(1|Individual), REML=True). The hindlimb was treated as the intercept, by default.Ω02 represents a coefficient of determination for linear mixed-effects models (LMMs), whereby values closer to 1.0 indicate stronger concordance between the

data and the LMM.The t-value represents the test statistic based on a t-distribution, and can be used to estimate the likelihood that the differences between the forelimb and hindlimbcould have been derived by chance through a null hypothesis testing framework (note: t-values are not used in inference herein, but are presented forconvenience).

Table 5. GRF parameters at the timing of peak tensile stress for A. tigrinum forelimbs and hindlimbs

Forelimb Hindlimb

Ω02Mean±s.e.m. FE±s.e.m. t-value Mean±s.e.m. FE±s.e.m. t-value

Net GRF (BW) 0.376±0.011 −0.061±0.016 −3.927 0.429±0.013 0.434±0.022 19.919 0.350Vertical GRF (BW) 0.369±0.011 −0.039±0.015 −2.508 0.399±0.014 0.404±0.024 16.991 0.339Mediolateral GRF (BW) −0.052±0.004 0.028±0.010 2.854 −0.081±0.011 −0.081±0.010 −8.019 0.231Anteroposterior GRF (BW) 0.001±0.007 −0.115±0.010 −12.083 0.116±0.006 0.116±0.008 15.002 0.687Mediolateral angle (deg) −8.337±0.628 2.940±1.349 2.180 −11.667±1.522 −11.561±1.714 −6.744 0.280Anteroposterior angle (deg) 0.355±1.029 −16.21±1.495 −10.98 16.820±1.065 16.860±1.392 12.109 0.660

Analyses were based on N=42 and N=29 trials averaged across five individuals for the forelimb and hindlimb, respectively, due to data that were removed duringtimes of overlap with other body structures. FE, fixed effect.GRF parameters were evaluated at the timing of peak tensile stress, and then averaged across all trials to produce the mean and s.e.m. for each limb.Statistical analyses were based on the model: lmer(y∼Limb+(1|Individual), REML=True). The hindlimb was treated as the intercept, by default.The format of statistical analyses follows that described for Table 4. Timings of the peak tensile stress are reported in Table 6.

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Muscles assumed to contribute to humeral joint moments andstresses included retractors and adductors, and elbow and wristextensors (Fig. 1A,B, Table 2). Forelimb muscle activity patternswere inferred from electromyography (Delvolvé et al., 1997;Székely et al., 1969), anatomical descriptions of Taricha torosa(Walthall and Ashley-Ross, 2006) and direct observations ofA. 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 actas elbow extensors, and subdivided into two functional unitsaccording to their anatomical positions: anconaeus scapularismedialis and anconaeus coracoideus (ASMAC; Fig. 1A,B:purple), and anconaeus humeralis lateralis and anconaeushumeralis medialis (AHLAHM; Fig. 1A,B: blue). ASMAC wasinferred to exert an additional retractor moment due to its momentarm at the shoulder. Wrist extensors included the flexor digitorumcommunis (FDC), flexor antebrachii et carpi radialis (FACR),flexor antebrachii et carpi ulnaris (FACU) and a deep complex ofcarpal plantiflexors (DCF). These muscles were assumed to beactive to oppose the moment of the GRF tending to dorsiflex/extend the wrist, with FDC, FACU and FACR also spanning theextensor aspect of the elbow joint (Fig. 1A,B: yellow). Pectoralis(P) and supracoracoideus (SC) insert on the crista ventralis of thehumerus (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-shaftof 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 abrief summary follows. Caudalipuboischiotibalis (CPIT),caudofemoralis (CDF) and iliofemoralis (ILFM) retract the femur(Fig. 1C,D: red). Ischioflexorius (ISF) is a multi-articular musclethat contributes to femoral retraction, and spans distally to extendthe 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) andpuboischiofemoralis externus (PIFE)] contribute to femoraladduction 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 biomechanicalmodel because the muscles acting to extend the knee in salamanders(i.e. iliotibialis anterior and posterior) do not have a consistent phaseof activity during stance (Ashley-Ross, 1995).

Thus, differences in muscle configuration and PCSA betweenthe limbs could contribute to differences in loading between thehumerus and femur. Consequently, these wrist extensors reducethe force that primary elbow extensor muscles (e.g. anconaeuscomplex) must generate to counter the elbow flexor momentstypically imposed by the GRF, without increasing humeral stresses.In contrast, ankle extensors spanning the knee add to its flexormoment, rather than its extensor moment, often requiring elevated(rather than reduced) forces from knee extensors (Sheffield andBlob, 2011). Also, a lower proportion of forelimb musclescontribute to bone stresses. Only 30% of the forelimb musclesconsidered in the biomechanical model were likely to contribute tohumeral stresses (Table 2), with a cumulative PCSA of about13 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 hindlimbPCSA.

Forces acting on the bones were resolved into axial and transversecomponents. These were combined with bone length, cross-sectional area, second and polar moments of area, and thebending moment arms imposed by shaft curvature (rc: Biewener,1983) (Table 1) to calculate axial compressive stress and bendingstresses in the anteroposterior plane (σb,AP, influenced by humeralretractors) and dorsoventral plane (σb,DV, influenced by elbowextensors) (Blob and Biewener, 2001). The second moment of area(reflecting resistance to bending) and polar moment of area(reflecting resistance to torsion) (Lieberman et al., 2004) weremeasured with BoneJ (Doube et al., 2010) in ImageJ64 (v1.47t,Bethesda, MD, USA). The magnitude of the net bending stress atthe mid-shaft was calculated as the vector sum of stresses in twoplanes, allowing the orientation of peak bending stress (relative tothe AP axis) to be calculated as:

ab;net ¼ tan�1 sb;DVsb;AP

� �: ð2Þ

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

Table 6. Timings and magnitudes of peak bone stresses for A. tigrinum, with average speed during stance

Humerus Femur

Ω02Mean±s.e.m. CV FE±s.e.m. t-value Mean±s.e.m. CV FE±s.e.m. t-value

Peak tensile stress (MPa) 7.006±0.282 0.285 −5.531±0.740 −7.471 12.505±1.051 0.582 12.537±1.939 6.464 0.641Peak compressive stress (MPa) −7.376±0.292 −0.280 10.014±0.911 10.993 −17.294±1.305 −0.523 −17.410±2.370 −7.346 0.712Peak axial stress (MPa) −0.930±0.063 −0.476 1.625±0.098 16.569 −2.495±0.161 −0.448 −2.555±0.349 −7.322 0.832Peak shear stress (MPa) −3.261±0.171 −0.371 0.412±0.272 1.510 −3.704±0.360 −0.673 −3.672±0.720 −5.101 0.549Time of peak tensile stress (%) 66.540±1.508 0.160 44.335±2.716 16.330 22.188±2.299 0.718 22.205±2.057 10.790 0.739Time of peak axial stress (%) 36.540±1.589 0.308 16.959±1.673 10.130 19.458±0.589 0.210 19.581±1.581 12.390 0.547Time of peak compressive stress (%) 65.640±1.446 0.156 47.586±1.525 31.210 17.875±0.689 0.267 18.054±1.753 10.300 0.915Time of peak shear stress (%) 24.560±1.484 0.427 −5.433±2.328 −2.334 29.938±1.841 0.426 29.993±1.909 15.710 0.091Average speed during stance (cm s−1) 10.347±0.311 0.213 −0.177±0.564 −0.315 10.613±0.493 0.322 10.524±0.549 19.156 0.097

Values are means±s.e.m. (N=50 and N=48 trials averaged across five individuals for the humerus and femur, respectively). FE, fixed effect; CV, coefficient ofvariation (=s.d./mean).Timings of peak stresses are represented as a percentage into the stance phase of the limb cycle. Peak stress values were determined for each individual trial,and then averaged across all trials to produce the mean and s.e.m.Statistical analyses were based on the model: lmer(y∼Bone+(1|Individual), REML=True). The femur was treated as the intercept, by default.The format of statistical analyses follows that described for Table 4.

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Torsional stresses (τ) produced by the GRF were calculated as:

t ¼ TðyJÞ; ð3Þ

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

Mechanical testing of salamander humeri and femoraMicroindentation was used to compare hardness between andwithin bones. Right humeri and femora were air-dried, mounted inCaroplastic (Carolina Biological, Burlington, NC, USA), a non-infiltrating resin, and sectioned transversely at the mid-shaft. Cutsurfaces from the distal half were polished to visualize cross-sectional geometries and prepare for microindentation. Mountedspecimens were affixed to a 100×61×2 mm Plexiglas slide withcyanoacrylate glue, and loaded onto an automated polisher(EXAKT Technologies, D-4000, Oklahoma City, OK, USA).Samples were ground with moistened silicon carbide paper ofdecreasing grit sizes (P800, P1200, P2500, P4000), for 5 min each.Agglomerate-free alumina suspensions were used to polish thespecimens 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 (BuehlerMicropolish II) using a polishing pad (Buehler, Lake Bluff, IL,USA) for 3 min each. Grinding and oscillation speeds were set at30 rpm, with a 99.3 g weight applied. Samples were rinsed withdeionized water after each step to remove abrasive particulates, airdried and then stored at −20°C for less than 72 h. Prior toindentation, samples were equilibrated to room temperature andcleaned with methanol. These procedures allowed mechanicaltesting of hydrated bones. HV was measured with a Digital DisplayMicrohardness Tester (Model HVS-1000B, Beijing, China)configured with a Vickers indenter tip, 0.49 N load and 15 sdwell time, following procedures for microindentation ofsalamander femora (Sheffield and Blob, 2011). About fiveindents were performed in the dorsal, ventral, anterior andposterior regions to test for regional heterogeneity in hardness.Data were collected away from cavities and edges of the bone toavoid 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. HV (1) isconsistent 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 areembedded in infiltrating media rather than non-embedded (Evanset al., 1990). We used a non-infiltrating plastic to stabilize the bonesand, therefore, expect the difference between mounted andunmounted bones to be minimal. Hardness values have been upto ∼50% higher for bones tested dry rather than wet with ananoindenter (Hoffler et al., 2005), but only about 9% greater forbones that were dried for 2 days or longer and tested with amicroindenter (Johnson and Rapoff, 2007). Our use of a non-infiltrating resin kept the bones hydrated. Although the humerus ofindividual 1 underwent slightly different testing conditions(0.981 N load, and no data from the posterior region), availabledata still followed general patterns observed between the humeri andfemora (Fig. S3). Also, hardness is consistent for applied loadsbetween 15 and 300 g (Zysset, 2009), encompassing the 0.49 and0.981 N used in this study. Thus, our protocol likely had minimaleffect on hardness comparisons.

HV data were entered into a linear regression equation (Wilsonet al., 2009), derived using empirical data from various tetrapodbones (Hodgskinson et al., 1989), to estimate tensile yield stress(σyieldstress; MPa):

syieldstress ¼ 32:571þ 2:702� HV: ð4Þ

Tensile yield stress has important consequences for organismsbecause bone failure tends to occur on the tensile side duringbending (Currey, 2002). Compressive yield stress was alsoestimated from HV to evaluate regional heterogeneity of bonebiomechanics. Data on compressive yield stress are not available forsalamanders, so estimates were based on the assumption that tensileyield stresses are 25% lower than compressive yield stresses(Currey, 1984). SFs were then calculated as:

SF ¼ syieldstressmean peak stress

ð5Þ

and ‘worst-case’ scenario estimates (SFWC) as:

SFWC ¼ syieldstress � 2� s:d:syieldstressmean peak stressþ 2� s:d:smean peak stress :

ð6Þ

HV, yield stress and SF were reported separately for each of theanatomical regions (Table 7, Table S1). Calculations of yield stressesand SFs were based on dorsal and posterior regions being loaded intension, and anterior and ventral regions loaded in compression.

Table 7. Regional heterogeneity of hardness values and safety factors across the limb bone mid-shafts of A. tigrinum

Humerus Femur

Anterior Dorsal Posterior Ventral Anterior Dorsal Posterior Ventral

HV 36.3±0.9 41.7±1.5 44.4±1.2 36.6±0.9 33.7±1.2 36.0±1.1 34.6±0.9 31.5±1.1HV sample sizes 23 24 20 22 25 25 25 24Mean yield stress (MPa)* 174.1±3.3 145.2±4.0 152.6±3.2 175.4±3.2 164.8±4.2 129.8±3.0 126.1±2.4 156.7±4.1Standard SF 23.6±0.5 20.7±0.6 21.8±0.5 23.8±0.4 9.5±0.2 10.4±0.2 10.1±0.2 9.1±0.2CV of SF 0.092 0.136 0.095 0.085 0.128 0.117 0.095 0.128SFWC 12.3±0.3 8.1±0.3 9.5±0.2 12.6±0.3 5.7±0.2 3.7±0.1 3.8±0.1 5.4±0.2

Values represent means±s.e.m.HV, Vickers hardness; SFWC, worst case SF.*Mean yield stress for dorsal and posterior regions (under tension) was calculated using the equation: 32.571+2.702×HV (Wilson et al., 2009). For anterior andventral regions (under compression), it was calculated as (tensile yield stress)/0.75.Statistical analyses were based on the model: lmer(y∼Bone/AnatomicalLocation+(1+AnatomicalLocation|Individual), REML=True).Statistical comparisons can be found in Table S1.

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

Statistical analysesLinear mixed-effects models (LMMs), fitted by restrictedmaximumlikelihood via lme4::lmer, were used to evaluate differences withinresponse variables, with individual as a random effect for a randomintercepts model (Bates et al., 2014). Random effects representedsubsamples of a population and an additional source of variation(e.g. individuals within species) whereas fixed effects were factorsto compare (e.g. forelimb versus hindlimb) (Bolker et al., 2009).Regional heterogeneity of HV within a bone was assessed withanatomical region as a fixed effect. Otherwise, limb bone was thefixed effect. Given that HV within an anatomical region may varyamongst individuals, anatomical region was also added as a randomeffect to create a random intercepts and slopes LMM. Pair-wisecomparisons between anatomical regions and bones were fitted witha contrast matrix in multcomp::glht. P-values provide limitedinformation regarding the strength of evidence to supportconclusions (Anderson et al., 2001), so LMMs were reported interms of effect sizes and an estimate of precision (e.g. Ω0

2; Xu,2003), emphasizing the magnitude of the differences and the levelof uncertainty in supporting those differences, respectively.

RESULTSKinematic comparison of forelimbs and hindlimbsAlthough the limbs have similar kinematic profiles, numerousdifferences were identified. At the beginning of stance, the shoulderand hip are adducted by ∼10–15 deg (Fig. 2A), with the wrist andankle showing similar degrees of extension (Fig. 2B). The femur ismore protracted than the humerus until about 80% of stance

(Fig. 2C), and the elbow is more flexed than the knee until about90% of stance (Fig. 2D). Flexion and extension of the elbow andknee follow similar profiles; however, the ankle becomes flexedalmost twice as much as the wrist towards mid-stance. Anothermajor difference between the limbs is that the femur remainsadducted (e.g. knee closer to the ground than the hip) throughoutstance (Fig. 2A), but the humerus becomes abducted (elbow higherthan shoulder) after about 30% of stance. Additionally, althoughboth bones begin in a protracted orientation (i.e. distal joint cranialto the girdle for almost all of stance), the humerus is initially nearlyperpendicular to the long axis of the body (∼0 deg in Fig. 2C) andretracts at about 10% of stance, whereas retraction of the femur ismore evenly split between protracted and retracted orientations(Fig. 2C).

Moments produced by the GRF about limb jointsGRF production was generally similar between the forelimbs andhindlimbs (Table 4, Fig. 3), contributing to similarities in the jointmoments imposed by the GRF (Fig. 4). The GRF imposes adorsiflexion (positive) moment about the wrist and ankle (Fig. 4A)due to the anterior position of the GRF relative to these joints. Tomaintain equilibrium at these joints, wrist and ankle extensors needto 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 andhip, though for the latter this shifts to an adductor momentapproximately 75% into stance (Fig. 4B). The GRF also imposes aprotractor moment about the shoulder and hip, though protraction atthe shoulder is lower in magnitude and occurs later in stance (40%)than at the hip (10% stance) (Fig. 4C). Finally, torsional momentsimposed by the GRF are similar between the humerus and femur(Fig. 4D), changing from a tendency to impose anterior axialrotation to posterior rotation at about 60% of stance.

Pro

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C DProtraction

Adduction

Abduction

Flexion

Extension

Flexion

Extension

Stance (%)25 50 75 100 0 25 50 75 100

0 25 50 75 100 0 25 50 75 100

Hindlimb

Fig. 2. Comparison of stance phasekinematic profiles between theforelimbs and hindlimbs of tigersalamanders, Ambystoma tigrinum.Lines and adjacent shading representmeans±s.e.m. pooled across all trials forthe forelimbs (N=50) and hindlimbs(N=48), with all trials normalized as apercentage of stance. Negative values arehighlighted in gray, and indicate adductionin A and retraction in C. Kinematiccomparisons include: (A) abduction/adduction angle of the limbs,(B) extension/flexion of the wrists andankles, (C) protraction/retraction angle ofthe limbs and (D) extension/flexion of theelbows and knees. See Fig. S1 forillustration of these kinematic angles.

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Despite these similarities, different configurations of the forelimband hindlimb influence how the GRF imposes moments on theselimbs (Fig. S2). In salamanders (and most quadrupeds), the elbowpoints posteriorly whereas the knee points anteriorly. However, theGRF is directed essentially vertically for most of stance for bothlimbs (Fig. 3). Consequently, the flexor/extensor moment of theGRF tends to change in different directions for these joints, shiftingfrom 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 theforelimb [e.g. ankle versus wrist in dorsiflexion (Fig. 4A), hip versusshoulder in anteroposterior and dorsoventral rotations (Fig. 4B,C),and knee versus elbow in flexion and extension (Fig. 4E)].

Comparison of bone stressesLower stresses were estimated for locomotor loads upon thehumerus, though the difference between the bones was lesspronounced for shear (Table 6). Peak tensile and compressivestresses occurred later in stance for the humerus (∼67%) than thefemur (∼22%) (Table 6, Fig. 5A,B). This pattern corresponds withthe peak net GRF, which also occurred later in stance (∼61%) for the

forelimb than the hindlimb (∼33%) (Table 4, Fig. 3). Afteraccounting for variation amongst individuals, total external forces(‘net GRF’) at the time of peak tensile stresses for each bone were0.061±0.016 BW lower in the humerus, with vertical andanteroposterior components lower by 0.04 and 0.115 BW,respectively (Table 5).

The neutral axis of bending for the humerus was directed suchthat the posterodorsal region was loaded in tension and theanteroventral region in compression through the time ofmid-stance to peak loading (Fig. 5C,D). The neutral axis ofbending was aligned closer to the anatomical anteroposterior axis atpeak tensile stress for the femur, placing the dorsal portion intension and the ventral portion in compression. Nonetheless, theanterodorsal cortex of the femur was loaded in tension and theposteroventral cortex in compression at 50% of stance (Fig. 5C,D).

Biomechanical properties and SFs of the salamander humeriand femoraComparisons indicated higher HV for the humerus and regionalheterogeneity within each bone (Table 7, Table S1). The LMMexplained about 68% of the variation inHV based onΩ0

2 (Xu, 2003),

Forelimb

Stance (%)

Hindlimb

0 25 50 75 100 0 25 50 75 100

0 25 50 75 100 0 25 50 75 100

0 25 50 75 100 0 25 50 75 100

Ant

erop

oste

rior a

ngle

(deg

)

−40

−20

0

20

40

Ant

erop

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rior (

BW

)

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0

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0.2

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GR

F (B

W)

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cal (

BW

)

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0.2

0.3

0.4

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tera

l (B

W)

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Med

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tera

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eg)

−20

−10

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Posterior

Anterior

Medial

Lateral

Posterior

Anterior

Medial

Lateral

Vertical Vertical Fig. 3. GRF production by the forelimband hindlimb of A. tigrinum throughoutstance. Lines and adjacent shadingrepresent means±s.e.m. pooled across alltrials for the forelimbs (N=50) andhindlimbs (N=48), with all trials normalizedas a percentage of stance.Anteroposterior angles were set relative tovertical (0 deg), so that negative valuesindicate a GRF directed posteriorly.Mediolateral angles were also relative tovertical (0 deg), so that negative valuesindicate a GRF directly medially. Grayrectangles distinguish negative valueswithin each plot. Although the peak valuesfor the net GRF and the verticalcomponent were similar (∼0.45 bodyweight, BW) and the GRF remainedmedial, positive anterior valuesthroughout stance indicate that thehindlimbs had a greater acceleratory rolethan the forelimbs.

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an analog of R2 for LMMs. The greatest magnitude of HV, and thusestimated yield stresses, at these mid-shafts was generally in theposterodorsal region (Table 7), corresponding with the typicallocation of tensile loads about the neutral axis of bending (Fig. 5B).

Femoral SFs ranged from ∼9 to 10 (Table 7), corresponding withthe 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 dorsalcortex, where HV was greatest, yet SFs at humeral mid-shafts weregreater in the anteroventral region, where HV was lower (Table 7).This differencewas largely due to peak bone stresses that were abouttwo times lower in the humerus (Table 6), although higher yieldstresses in the humerus also contributed to SF differences from thefemur (Table 7). The worst-case scenario SF (SFwc) was about twotimes lower than standard SF calculations for both bones, but stillindicated ample margins of safety (∼8–13 for the humerus, ∼3–6for the femur; Table 7). Biomechanical differences along thedorsoventral and anteroposterior planes of the bones were alsoreflected in their structural response to bending, as evidenced bysecond moments of area that were greater in the dorsoventral planefor the humerus and the anteroposterior plane for the femur(Table 1).

DISCUSSIONMechanisms underlying elevated SFs in salamander humeriHumeri have higher SFs (∼22) than femora (∼10) in salamanders, adisparity greater than that reported in alligators (8.4 for the humerusversus 6.3 for the femur; Blob et al., 2014). The difference betweenhumeral and femoral SFs relates primarily to differences in yieldstrain for alligators (Blob et al., 2014), but from both lower stressesand structural reinforcement in salamander humeri (Tables 6, 7).

Critical factors that are likely contributing to the relatively lowerstresses 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 ofthe elbow in A. tigrinum, the GRF only exerts a flexor moment at theelbow late in stance (Fig. 4E). This reduces the need for elbowextensors (e.g. anconaeus complex) to counter GRF moments at theelbow, reducing the stress they place on the humerus (Table 2,Fig. 1). Humeral stresses are additionally reduced by contributionsof wrist extensors (FDC, FACR, FACU) to the elbow extensormoment, further reducing the force that elbow extensors spanningthe humeral mid-shaft must exert. Moreover, adductor musclescontributing to forelimb movement (P and SC) insert proximally onthe humerus, and do not contribute to stresses experienced at mid-shaft.

Beyond these stress-reducing characteristics of forelimbmusculature in salamanders, HV of the humerus is generally greaterthan that of the femur, with different patterns of regionalheterogeneity (Table 7, Table S1) between the bones. The highestSFs 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 theanteroposterior direction (IAP), but the humerus has a greater secondmoment of area in the dorsoventral direction (IDV; Table 1). Theseresults suggest that these limb bones show differences in structure andmechanical response that reduce bending stress in different directions.Given the extent to which humeral SFs (>20) of salamanders aregreater than those of the femur (∼10), it is difficult to envisage howthe entire magnitude of differences in humeral and femoral SFs ofsalamanders could be adaptive. Nonetheless, elevated SFs supportedby greaterHVand structuralmodifications suggest the possibility that,

0.00075

0.00050

0.00025

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0.006

0.004

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Forelimb

Stance (%)

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Rotate anteriorly

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Plantarflexion

DorsiflexionA

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ow/k

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(N m

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one

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(N m

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irdle−A

P ax

is (N

m)

Gird

le−D

V a

xis

(N m

)W

rist/a

nkle

(N m

)

Fig. 4. Comparison of moments exerted by the GRF for the forelimb andhindlimbofA. tigrinum. Lines representmean values obtained fromdata pooledacross all trials for the forelimbs (N=50) and hindlimbs (N=48), with the shadingdepicting the standard error. Negative values are highlighted in gray, and thedirections of rotation indicated by positive and negative values are labeled in thepanels. Girdle refers to the shoulder and hip. AP, anteroposterior; DV,dorsoventral.SeeFig.S2 for illustrationofGRFmomentarmsrelative to limb joints.

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to some extent, the high load-bearing capacity of salamander humerimay facilitate the multi-functional role of the forelimbs for locomotorand non-locomotor behaviors (e.g. burrowing).

Relevance of ‘mixed chains’ to tetrapod evolutionComparisons of SFs for the humerus and femur of salamandersprovide an additional empirical example of a ‘mixed-chain’(Alexander, 1997, 1998) within the locomotor skeleton oftetrapods. ‘Mixed-chains’ of SFs were identified betweenproximal and distal limb bones in horses (Currey, 2002), andiguanas and alligators (Blob and Biewener, 1999). However, dataherein reinforce additional patterns observed in alligators (Blobet al., 2014), which demonstrated different SFs between theproximal bones of the forelimb and the hindlimb. As in alligators(Blob et al., 2014), the humerus has a higher SF than the femur insalamanders (Table 7).Some of the factors proposed by Alexander (1997) that might

contribute to differences in SFs between these bones in alligators donot apply to salamanders. For example, alligator humeri are smallerthan the femora, which might allow for more economicalmaintenance of a high SF (Blob et al., 2014). However, thehumerus and femur are roughly equal in length in salamanders(Table 1), so Alexander’s first condition for ‘mixed-chains’ likelydoes 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 inloads (i.e. femur) did not have higher SFs (Table 6), suggesting thatelevation of humeral SFs in salamanders likely was not an adaptiveresponse for protection against unpredictable high loads.

SFs for salamander limb bones, like those of alligators, aregenerally high (>7) compared with those of many taxa, includingmammals and birds (Blob et al., 2014). Thus, differences betweenhumeral and femoral SFs for salamanders might simply reflect anincreased opportunity for variation in SF across the skeleton(Alexander’s third condition). Though this reason has been invokedas a factor contributing to ‘mixed-chains’ in alligators (Blob et al.,2014), data on the limb configuration, muscle disposition andregional heterogeneity of HV in tiger salamanders also suggestmechanistic reasons for high SFs in limb design. Collectively, theelevated structural and material reinforcement to withstand loads inthe humerus, and anatomical features of the forelimb promoting lowloads, suggest that stochastic variation associated with large SFsmay not completely account for differences in humeral and femoralSFs observed in salamanders.

In addition to the three conditions promoting ‘mixed-chains’ ofSFs proposed by Alexander (1997), higher SFs may be found instructures with higher penalties for failure (Diamond, 2002).Forelimbs and hindlimbs play different roles in legged

D Right humerus: peak stress

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Fig. 5. Bone stresses are lower in the humerus than in the femur for A. tigrinum, and vary in magnitude across these bones. Maximum (A) tensilestress and (B) compressive stress, and (C) the angle of the neutral axis of bending from the anatomical AP axis. (D) Orientation of the neutral axis of bending (solidred line) relative to the AP axis (dashed black line) at peak tensile stress (top) and 50% of stance (bottom), mapped onto cross-sections of the humeral andfemoral mid-shafts. Dark regions of the bone are in compression and light regions are in tension. Compared with the humerus, magnitudes of the peak tensile(A) and compressive (B) stresses are about 1.7 and 2.3 times greater, respectively, in the femur. At both 50% of stance and the timing of the peak tensile stress(C,D), the absolute angle of the neutral axis is greater than 30 deg for the humerus but less than 20 deg for the femur.

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locomotion (McElroy et al., 2014), which may provide insight intoSF variation in salamander limb bones. Although hindlimbs providethe primary propulsion in many non-mammalian quadrupeds,forelimbs still make important contributions to locomotion(Kawano and Blob, 2013; Nyakatura et al., 2014), and loss oflocomotor function may be more detrimental for the forelimb. Earlywork on salamander locomotion (Evans, 1946) demonstrated thatforward propulsion could be achieved solely by the forelimbs butnot the hindlimbs, suggesting that the forelimbs play a moreimportant locomotor role than passive body support (at least interrestrial salamanders such as Taricha and Ambystoma). Moreover,there do not appear to be ready examples (among non-bipedalvertebrates) in which the complete loss of the pectoral appendagesoccurred while the pelvic appendages remained fully intact: whenvertebrates lose an entire appendage, it is typically the pelvicappendage (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 limbloss is associated with the evolution of fossorial or aquatic life styles(e.g. amphisbaenians and cetaceans), the forelimbs are typicallyretained rather than the hindlimbs (Caldwell, 2003). Limbreduction, including the loss of digits, can be found in theforelimb rather than the hindlimb in some taxa (Lerista lizards:Skinner et al., 2008), but the loss of proximal limb elements or theentire limb is generally less common for forelimbs. Additionalstudies are required to verify whether there are strong mechanical orselective advantages for forelimb retention in non-bipedalvertebrates, or whether the conservatism of forelimb retention isdue to developmental constraint. For instance, hindlimbs developafter forelimbs (Tanaka and Tickle, 2007), and structural reductiontypically occurs in the reverse order from which structures develop(Lande, 1978), potentially making hindlimbs more susceptible toloss via developmental truncation.Further investigations of how loads vary across limb bones could

yield insights into the morphological evolution of limb bones asvertebrates became terrestrial. The vertebrate musculoskeletalsystem shifted from being essentially weightless as a result ofbuoyancy underwater to counteracting the effects of gravity on land,drastically shifting the loading regime imposed upon the locomotorstructures. This shift may have made the evolution of long, tubularlimb bone shafts advantageous compared with their blockyprecursors (Currey, 2002). Microanatomical analyses of a widerange of tetrapods have differentiated aquatic and terrestriallifestyles from limb bone histology (Laurin et al., 2011),facilitating the inference of the locomotor biomechanics of fossiltaxa such as the Devonian fish Eusthenopteron (Laurin et al., 2007)and stem stegocephalians (Laurin et al., 2004). Identifying strongerform–function relationships between limb morphology andlocomotor movements would facilitate efforts to reconstruct thetransition from water to land by tetrapods (Nyakatura et al., 2014;Standen et al., 2014). For instance, the mechanical properties ofbones from extant taxa were combined with palaeopathology totheorize the loading conditions that could have fractured the radiusin the early stem tetrapod Ossinodus pueri in the context of walkingon land (Bishop et al., 2015), suggesting the utility of bone loadingdata during terrestrial locomotion to address the mechanisms thatinfluenced how vertebrates became terrestrial. Further application ofdata on locomotor stresses from extant taxa could help answerquestions regarding the functional consequences of morphologicalchanges observed in extinct tetrapodomorphs spanning thetransition from water to land (Hohn-Schulte et al., 2013; Kawanoand Blob, 2013).

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

Competing interestsThe authors declare no competing or financial interests.

Author contributionsS.M.K. collected and analyzed the data, D.R.E., M.S.K. and D.D. provided themechanical testing equipment, and trained/supervised S.M.K. inmechanical testing.R.W.B. developed the biomechanical model, provided equipment for quantifyingkinematics and kinetics, and supervised analyses. S.M.K. and R.W.B. led theconception and design of the research. All authors contributed to writing themanuscript.

FundingFunding was provided by the American Society of Ichthyologists and HerpetologistsGaige and Raney Awards (S.M.K.), Sigma Xi Grants-in-Aid of Research (S.M.K.),Clemson University (S.M.K.), and National Science Foundation (IOS 0517240 andIOS 0817794, to R.W.B.). Data analysis andmanuscript preparation were completedwhile S.M.K. was a Postdoctoral Fellowat the National Institute for Mathematical andBiological Synthesis (sponsored by National Science Foundation Award DBI-1300426 and the University of Tennessee, Knoxville).

Supplementary informationSupplementary information available online athttp://jeb.biologists.org/lookup/suppl/doi:10.1242/jeb.125799/-/DC1

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