Angular Momentum and Arboreal Stability in CommonMarmosets (Callithrix jacchus)

Brad A. Chadwell1,2 and Jesse W. Young1,2,3*

1Department of Anatomy and Neurobiology, Northeast Ohio Medical University (NEOMED), Rootstown, OH 442722Skeletal Biology Research Focus Area, NEOMED, Rootstown, OH 442723School of Biomedical Sciences, Kent State University, Kent, OH 44240

KEY WORDS balance; torque; center of mass; asymmetrical gaits; primate locomotorevolution

ABSTRACT Despite the importance that concepts ofarboreal stability have in theories of primate locomotorevolution, we currently lack measures of balance per-formance during primate locomotion. We provide thefirst quantitative data on locomotor stability in an arbo-real primate, the common marmoset (Callithrix jacchus),predicting that primates should maximize arboreal sta-bility by minimizing side-to-side angular momentumabout the support (i.e., Lsup). If net Lsup becomes exces-sive, the animal will be unable to arrest its angularmovement and will fall. Using a novel, highly integra-tive experimental procedure we directly measuredwhole-body Lsup in two adult marmosets moving alongnarrow (2.5 cm diameter) and broad (5 cm diameter)poles. Marmosets showed a strong preference for asym-metrical gaits (e.g., gallops and bounds) over symmetri-cal gaits (e.g., walks and runs), with asymmetrical gaits

representing >90% of all strides. Movement on the nar-row support was associated with an increase in more“grounded” gaits (i.e., lacking an aerial phase) and amore even distribution of torque production between thefore- and hind limbs. These adjustments in gait dynam-ics significantly reduced net Lsup on the narrow supportrelative to the broad support. Despite their lack of awell-developed grasping apparatus, marmosets provedadept at producing muscular “grasping” torques aboutthe support, particularly with the hind limbs. We con-tend that asymmetrical gaits permit small-bodied arbo-real mammals, including primates, to expand “effectivegrasp” by gripping the substrate between left and rightlimbs of a girdle. This model of arboreal stability mayhold important implications for understanding primatelocomotor evolution. Am J Phys Anthropol 000:000–000,2014. VC 2014 Wiley Periodicals, Inc.

The origins and subsequent diversification of primatesare intimately linked to arboreality. Because the arbo-real habitat is inherently discontinuous, multidimen-sional, and frequently unstable, primates face a host oflocomotor challenges not encountered by more terrestrialmammals—a fact attested to by the frequency of longbone traumas due to falling in free-ranging arboreal pri-mates (Lovell, 1991). As such, for nearly 100 yearsanthropologists have presented the need to move safelyin an arboreal environment—specifically a narrow-branch arboreal environment—as one of the primaryselective pressures shaping primate locomotor morphol-ogy and behavior (Wood Jones, 1916; Le Gros Clark,1959; Napier, 1967; Cartmill, 1972; Larson, 1998).

Despite the central role that concepts of arboreal sta-bility have played in theories of primate locomotor evolu-tion, we currently lack empirical measures of balanceperformance during primate locomotion. In this study,we provide the first quantitative in vivo data on locomo-tor stability in an arboreal primate, the common marmo-set (Callithrix jacchus). In general, stability can bedefined as the ability of a mechanical system to mini-mize the probability of catastrophic perturbations(Alexander, 2002; Full et al., 2002). We operationalizethis concept by asserting that a primary index of arbo-real stability is the control of the angular momentum ofthe center of mass (CoM) about the support (see alsoLammers and Zurcher, 2011). Angular momentum hasproved a useful metric of stability in a variety of sys-tems, including insect hexapedalism, mammalian quad-rupedalism, human bipedal walking, and robotics (Fullet al., 2002; Goswami and Kallem, 2004; Herr and

Popovic, 2008; Lammers and Zurcher, 2011). We assumethat primates seek to maximize arboreal stability byminimizing side-to-side rolling angular momentum aboutthe support (abbreviated below as Lsup). If Lsup becomestoo large, the animal will be unable to arrest its angularmovement about the support and will fall (Cartmill,1985; Preuschoft, 2002; Lammers and Zurcher, 2011).

We describe a novel, highly integrative experimentalprotocol that integrates kinematic, kinetic, and gait datato directly measure Lsup during locomotion on narrowbranch-like substrates. Our system expands onLammers’ and colleagues research on torque productionand arboreal stability in small, non-primate mammals(Lammers and Gauntner, 2008; Lammers and Zurcher,

Additional Supporting Information may be found in the onlineversion of this article.

Grant sponsor: National Science Foundation; Grant number:BCS-1126790.

*Correspondence to: Jesse W. Young, Department of Anatomy andNeurobiology, Northeast Ohio Medical University, 4209 State Route44, P.O. Box 95, Rootstown, OH 44272. E-mail: jwyoung@neomed.edu

Received 31 August 2014; revised 20 November 2014; accepted 24November 2014

DOI: 10.1002/ajpa.22683Published online 00 Month 2014 in Wiley Online Library

(wileyonlinelibrary.com).

� 2014 WILEY PERIODICALS, INC.

AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 00:00–00 (2014)

2011). We use our system to empirically test severallong-held assumptions about the maintenance of stabil-ity during primate arboreal quadrupedalism. For exam-ple, traveling with a relatively flat and low trajectory ofthe CoM is thought to promote stability by reducing themoment arm of any potential toppling forces (Rose,1973; Cartmill, 1985; Demes et al., 1990). Here, we testthis hypothesis by directly quantifying the associationbetween CoM height and Lsup. Additionally, because oursystem allows us to quantify torque production (i.e.,twisting forces) from individual footfalls, we can addresshypotheses of how primates modulate angular momen-tum control among and within limbs. We test four spe-cific predictions:

(P1) Provided that marmosets do not adjust locomotorbehaviors to facilitate balance across different sub-strates, net change in Lsup over a stride (i.e., DLsup) willbe greater on narrow supports, reflecting the challengeof maintaining stability as branch diameter decreases.Alternatively, similarity in average DLsup measuresacross substrates suggests an ability to increase stabilityvia mechanical changes in locomotor behaviors.

(P2) DLsup will be inversely proportional to the heightof the CoM above the substrate, such that crouched pos-tures are more stable.

(P3) DLsup will be more closely associated with hindlimb torque production than forelimb torque production,reflecting the primacy of the hind limb for maintainingarboreal stability (Cartmill, 1985; Szalay and Dagosto,1988).

(P4) Because marmosets lack a strongly developedgrasping apparatus, torque will be generated primarilyvia the shearing action of substrate reaction forces act-ing about the radius of the support, rather than throughthe independent rotatory action of muscular graspingappendages (see also Lammers and Gauntner, 2008;Lammers, 2009a).

We test these predictions by examining the gaitdynamics of common marmosets moving over broad andnarrow diameter supports (i.e., elevated poles).Although, through adaptation to gumnivory, marmosetshave become quite derived relative to other primates(Sussman and Kinzey, 1984; Garber, 1992; Hamrick,1998; Young, 2009; Smith and Smith, 2013), as small-bodied arboreal quadrupeds with claw-like tegulae on alldigits except the hallux, marmosets, and other callitri-chids have converged on the general morphotypethought to characterize the early stages of euprimateevolution (Szalay and Dagosto, 1988; Gebo, 2004; Blochet al., 2007; Sargis et al., 2007). As such, empirical dataon marmoset arboreal stability can serve as a baselineagainst which to evaluate balance performance in other,less-derived primates that adhere more closely to thecrown primate bauplan (e.g., an animal with fully devel-oped grasping extremities).

MATERIALS AND METHODS

Experimental protocol

Data were collected from two adult male common mar-mosets (Callithrix jacchus), housed at NEOMED. Beforeeach experiment, marmosets were anesthetized with iso-flurane and the lateral surfaces of the major forelimbjoints (shoulder, elbow, wrist, and fifth metacarpal-phalangeal joint), hind limb joints (hip, knee, ankle, and

fifth metatarsal-phalangeal), and the base, tip, and mid-point of the tail were shaved and marked with retro-reflective tape, to aid in later kinematic analysis. Follow-ing the marker placement, we recorded body mass to thenearest gram. Body mass for the two individuals aver-aged 370 g and 392 g, respectively.

Upon recovery from anesthesia, the marmosets wereencouraged with food rewards to cross a 4 m long set ofhorizontal poles at self-selected speeds (Fig. 1). Two polediameters were used—a “narrow” 2.5 cm pole and a“broad” 5 cm pole. Six custom-built instrumented forcepoles were placed in series in the center of the pole track-way to record locomotor kinetics and two high-speed cam-eras (Xcitex XC-2; Xcitex, Woburn, MA) were located oneither side of the animal to capture their movement pat-terns as they crossed over the force-sensitive region. Vid-eos were recorded at 100–150 frames per second and thekinetic data channels were sampled at 60 scans per frame,resulting in scan rates of 6,000 or 9,000 Hz, respectively.Video and force data were synchronously recorded usingthe ProCapture system.

Data processing

Only complete steady-state strides with minimal accel-eration throughout the stride period were included inour dataset. Strides were considered complete when theanimal’s body weight was entirely supported by the forcepoles during the stride (i.e., from touchdown to subse-quent touchdown of a reference limb), ensuring completemechanical measurement of all the substrate reactionforces (SRFs) and torques affecting the animal’s CoMmovement. A stride was accepted as steady-state if theabsolute forward acceleration across the stride was lessthan or equal to 5% of gravitational acceleration (i.e.,9.81 ms22).

To track and quantify the three dimensional (3D) loco-motor kinematics from both the left and right sides ofthe animals, we calibrated the temporally synchronizedimages from the four cameras to the same coordinatespace using a three-step process (Standen and Lauder,2005). More details on this process are provided in theonline Supporting Information. In the final xyz-coordi-nate system, the xy-axes defined the horizontal planewith the x-axis parallel to the long axis of the pole sub-strate (i.e., the fore-aft [FA] direction) and the y-axis cor-responding to the mediolateral (ML) direction. The z-axis defined the vertical (V) direction. The origin of thesystem was set to the midpoint of the force pole seg-ments at their central axis (Fig. 1). For the strides meet-ing our selection criteria, joint markers on both sides ofthe body were digitized in ProAnalyst software (Xcitex,Woburn, MA). Each digitized feature was subsequentlyfit to a quintic smoothing spline function (tolerance of1 mm2) using a custom MATLAB program, allowing usto mitigate digitizing error and interpolate the positionof a feature for any frames where the marker was notvisible (Walker, 1998).

Force poles consisted of cylindrical wooden dowelsattached to instrumented steel frames that were securedto a removable base. Each pole provided a measure ofthe substrate reaction forces (SRF) in the three axialdirections (i.e., FA, ML, and V) and total torque (stot)about the support (based on the difference in verticalforce registered on the left and right sides of the forcepole). Force poles were calibrated by adapting the meth-ods of Biewener and Full (1992) and Lammers and

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Gautner (2008). More details on these procedures areprovided in the online Supporting Information. Allkinetic analyses were performed using a custom MAT-LAB program. Raw voltages from each force pole werefirst converted to Newtons (N) and corrected for crosstalk between channels using the conversion factorsobtained during the kinetic calibration process (see Sup-porting Information). A low-pass, fourth-order Butter-worth filter was used to remove noise above 75 Hz forthe FA and ML channels and 100 Hz for the two Vchannels.

Gait analyses

For all strides in the dataset, the timing of the initialtouchdown, the subsequent lift-off and the second touch-down for all four limbs were recorded. In cases where alimb was already in contact with a force pole at the startof the stride, the touchdown and lift-off of that stancephase were also noted. Additionally, we identified whichforce poles each foot contacted during its stance phase,allowing us to keep track of which limbs were associated

with the SRF recorded from each pole segment. Coding ofthe footfall timing and force pole identification was per-formed within ProAnalyst. Subsequent gait analyses wereall performed in a custom-written MATLAB program.

Temporal data on limb touchdown events were usedfor subsequent categorical gait coding. Strides in whichthe temporal lag between right and left forelimb stanceperiods, and between right and left hind limb stanceperiods, amounted to 50 6 10% of stride duration werecategorized as symmetrical gaits. All other strides werecategorized as asymmetrical gaits. Symmetrical gaitswere further classified as lateral sequence or diagonalsequence gaits, and asymmetrical gaits as canters, gal-lops, bounds, or half-bounds, based on the temporalphasing of subsequent footfalls. Details of gait codingare provided in the online Supporting Information.

Primary outcome measures

Angular momentum. Our primary metric of stability isthe net change in angular momentum of the center of massabout the support (abbreviated as DLsup). Just as in linear

Fig. 1. Experimental system for recording the mechanics of simulated arboreal locomotion. (a) Schematic illustration of datarecording apparatus. The 0.6 m long array of six strain gage force poles is set in the center of a series of raised horizontal poles,4 m in total length. Lead wires from the strain gages are wired into Wheatstone bridge circuits, resulting in four channels for eachforce pole—one fore-aft (FA) channel, one mediolateral (ML) channel, and two vertical (V) channels from the left and right sides ofthe pole. The difference in force recorded by the two vertical channels provides a measure of rolling torque about the support (i.e.,stot). A signal conditioning chassis excites the Wheatstone bridge circuits and also registers voltage changes in response to forcepole loading. Three-dimensional kinematics are captured by two pairs of high-speed cameras, positioned on either side of the ani-mal. A data collection computer synchronizes the video with the force data and stores bouts of data in response an external triggerpress. (b) A captured video frame of a marmoset galloping through the experimental enclosure on the broad 5 cm substrate. (c) Aclose up of two force poles illustrating the two substrates used: a narrow 2.5 cm diameter pole and a broader 5 cm diameter pole.

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mechanics, where change in linear momentum is equal tothe time integral of the applied force (i.e., impulse), the netchange in angular momentum (i.e., angular impulse) canbe calculated as the definite integral of

Pstot, where

Pstot

is the sum of torques across all force poles over time, fromthe beginning to the end of the stride (t1 to t2):

DLsup 5

ðt2

t1

XstotDt:

Angular momentum is quantified in units of N � cm � s.Note that because DLsup and angular impulse are synon-ymous terms, at times we refer to this quantity by eithername, depending on the nature of the discussion.

Center of mass height. CoM position was initiallycalculated as:

mSh1ðmHp2mShÞ � pCoM;

where mSh and mHp equal the midpoint between the leftand right shoulders and hips, respectively, and pCoM isthe average position of the CoM, as a percentage of trunklength from the shoulders to the hips. We estimated pCoMempirically for each animal using the reaction boardmethod (Young, 2012). Details of this procedure can befound in online Supporting Information. Changes in CoMheight during the stride were calculated via cumulativedouble integration of vertical CoM acceleration (whereacceleration was calculated by subtracting body weightfrom the vertical SRF and dividing by body mass: Manter,1938). Integrative constants were optimized using a pathmatching algorithm developed by Daley et al. (2006), asdescribed in the online Supporting Information. MeanCoM height above the support surface over the stride wasour primary metric of vertical posture during locomotion,with lower values indicating a “flatter” CoM trajectory.

Interlimb and intralimb modulation of torque pro-duction. For those strides in which there was no tem-poral overlap between forelimbs and hind limbs on thesame pole, we partitioned summed stot across the forcepoles into independent fore- or hind limb torque. Wethen calculated the portion of whole body DLsup due tothe angular impulse developed by each girdle (i.e.,DLsupFL and DLsupHL).

In stance phases where isolated limbs contacted a givenforce pole segment, we could partition individual limb tor-ques into two components (see Fig. 4 in Lammers,2009b). First, torques can be produced as a result of theshearing components of vertical and mediolateral SRFsacting about the radius of the pole. We refer to this typeof torque as substrate reaction torque (sSRF). Second, ani-mals could use the rotatory action of the muscular grasp-ing limbs to produce torques independent of thoseengendered by the SRF. We refer to this type of torque asmuscular torque (smusc). Following Lammers and Gaunt-ner (2008), we calculated sSRF and smusc as:

sSRF5rCoP3SRFtr

smusc5stot2sSRF;

where rCoP is the radial position of the limb’s center ofpressure (CoP: the point location on the substrate sur-face through which the forces act) along the circumfer-

ence of the force pole, SRFtr is the substrate reactionforce within the transverse plane (i.e., the V and MLcomponents of the total SRF) and 3 indicates the crossproduct of the two vectors. We then evaluated the angu-lar impulse of sSRF and smusc as metrics of the relativeimportance of the two mechanisms to the control of over-all whole-body angular momentum.

Standard force plates estimate the position of the CoPas the moment arm of any external torques applied to theplate. Such calculations assume that linear SRF are theonly source of torques acting about the force transducer.Our force pole system clearly violates this assumption.We therefore kinematically estimated forelimb CoP as apoint in the transverse midpoint of the palm, taken mid-way between the wrist and metacarpal-phalangeal joints.Because the feet were typically held in a digitigrade pos-ture (as seen in most primates: Schmitt and Larson,1995), we modeled hind limb CoP as the transverse mid-point across the metatarsal heads. During fast asymmet-rical gaits, where two fore- or hind limbs contacted thesame force pole as a functional unit, combined limb CoPposition was estimated as the average of the individuallimb CoP positions. In these cases, sSRF and smusc werecalculated for the combined limb pair.

Statistical methods

Categorical differences in gait selection according tosubstrate (e.g., symmetrical vs. asymmetrical gaits onbroad and narrow substrates) were investigated usingFisher’s exact test of row-by-column independence(Sokal and Rohlf, 1995). Variation in continuous meas-ures (e.g., DLsup) associated with gait type and substratediameter was assessed using mixed-effects analyses ofvariance (ANOVA), analyses of covariance (ANCOVA), orregressions depending on the categorical or continuousnature of the predictor variables. The mixed-effectsapproach (Pinheiro and Bates, 2000), allowed us toappropriately adjust degrees of freedom and error termsto account for random variation among individuals andexperimental days. The random factor for all models wasexperiment date nested within animal, guarding againstpseudo-replication errors that could potentially arise byincluding multiple strides from the same animal for thesame experiment date. Post hoc analyses were per-formed using Tukey’s HSD test (Sokal and Rohlf, 1995),modified for mixed-effects model structures.

We used a model selection approach to evaluate therelative importance of various components of whole-bodyangular momentum control (i.e., forelimb torque vs. hindlimb torque), calculating Akaike Information Criteria(AIC) for each model (i.e., predicting DLsup from forelimbtorque alone vs. predicting DLsup from hind limb torquealone). The model with lowest rise in AIC relative to thefull model (i.e., predicting DLsup from forelimb and hindlimb torques together) indicated the best independentpredictor of whole-body DLsup.

Finally, we used paired t-tests to analyze the effects ofa dichotomous predictor variable on a continuous pairedmeasure (e.g., positive stot magnitudes vs. negative stot

magnitudes within individual strides). All statisticalanalyses were performed using the R statistical platform(R Core Team, 2013).

RESULTS

Our final dataset consisted of 63 strides, including 30strides on the broad 5 cm diameter pole, and 33 strides

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on the narrow 2.5 cm diameter pole. Marmosets usedasymmetrical gaits much more frequently than symmet-rical gaits (57 asymmetrical strides vs. 6 symmetrical).Of the 57 asymmetrical strides, most were either canters(34 strides) or gallops (19 strides). Half-bounds and fullbounds were used infrequently (three strides and onestride, respectively). Asymmetrical gait selection differedsignificantly by substrate (P 5 0.01). Gallops and canterswere used with relatively equal frequency on the broadsupport, whereas canters predominated on the narrowsupport (Table 1; Fig. 2).

Symmetrical gaits were only used on the narrow2.5 cm support, where they were split evenly betweenlateral sequence gaits (limb phases: 35–49%) and diago-nal sequence gaits (limb phases: 51–62%; Table 1; Fig.2). The mean limb phase for the symmetrical strides(695% confidence interval) was 46 6 5.2%, a value notsignificantly different from a trot (i.e., where limb phaseequals 50% and contralateral fore- and hind limbs movein synchrony; t[5] 5 0.54, P 5 0.613). Given the distribu-tion of sampled gaits in our dataset, and to create amore balanced design for distributional tests, we classi-fied gaits into three categories for all subsequent analy-ses: symmetrical gaits, gallops/bounds (i.e.,asymmetrical gaits with a whole-body aerial phase), andcanters (i.e., asymmetrical gaits without a whole-bodyaerial phase).

Marmosets used a range of speeds across symmetricaland asymmetrical gaits (symmetrical: 0.53–1.52 ms21;asymmetrical: 0.85–2.01 ms21). Mixed-effects ANOVArevealed a significant main effect for gait type (Fig. 3;F[2,52] 5 3.4, P 5 0.041) but not for substrate diameter(F[1,6] 5 0.78, P 5 0.411). Speed tended to be greatest dur-ing galloping/bounding gaits, though the individual posthoc comparisons did not reach a a� 0.05 level of signifi-cance (P 5 0.053 and 0.096 for comparisons of gallops/bounds with symmetrical strides and canters,respectively).

Angular momentum

Total substrate reaction torque (stot) typically fluctu-ated about zero during a stride (Fig. 4, also see MoviesS1-S3 in the online Supporting Information). On aver-age, stot changed direction 4.5 times during a stride(range: 0–10 times). The magnitudes of the net positiveand negative changes in angular momentum (DLsup)induced by these fluctuations in stot were not statisti-cally different from one another on the narrow substrate(paired t-test: t[32] 5 0.628, P 5 0.535), but were so onbroad substrate (paired t-test: t[28] 5 22.45, P 5 0.021).These data suggest that the marmosets exerted morebalanced rolling torques when moving on the narrowsubstrate, perhaps as a means of reducing overall fluctu-ations in Lsup. Indeed, the net change in angularmomentum (DLsup) over a stride was significantly lower

on the narrow substrate (Fig. 5; F[1,6] 5 9.2, P 5 0.023).On the narrow diameter pole, DLsup was significantlyassociated with gait type (F[2,25] 5 5.5, P 5 0.010), suchthat DLsup was higher when marmosets used gallops/bounds than when they used canters or symmetricalgaits (P�0.011). Gait type was not significantly associ-ated with variation in DLsup on the broad diameter pole(F[1,24] 5 0.32, P 5 0.577).

Effects of CoM height

Average CoM height over a stride was significantlyassociated with gait type (F[2,52] 5 3.47, P< 0.039), butnot substrate diameter (F[1,6] 5 1.31, P 5 0.297) (Fig. 6).CoM height was greater during galloping and boundinggaits than during canters or symmetrical gaits (P 50.028 and 0.011, respectively). Contrary to our predic-tions, DLsup was not directly associated with variation inCoM height either across substrates (Fig. 7;F[1,53] 5 0.01, P 5 0.918) or independently within eachsubstrate (all P� 0.848).

Hind limb versus forelimb regulation ofwhole-body angular momentum

On the broad substrate, the net change in angularmomentum (DLsup) associated with hind limb angularimpulse (i.e., DLsupHL) was significantly greater thanthat associated with forelimb angular impulse (i.e.,DLsupFL) (P 5 0.002), whereas on the narrow substrateDLsupFL and DLsupHL magnitudes were statistically simi-lar (P 5 0.677) (Fig. 8). Mixed-effects regression, fit sepa-rately for each pole diameter, revealed that on thebroader substrate DLsup was more closely associatedwith DLsupHL than with DLsupFL (DLsupFL R2: 0.80;DLsupHL R2: 0.93). A model predicting DLsup fromDLsupHL alone also resulted in the lowest rise in AIC rel-ative to a full model that included both DLsupHL thanDLsupFL (DLsupFL model AIC: 8.9; DLsupHL model AIC:222.8; full model AIC: 2196.3). In contrast, on the nar-row substrate, DLsup was slightly better predicted byDLsupFL than DLsupHL (DLsupFL R2: 0.85; DLsupHL R2:0.82), and a model including DLsupFL also resulted in thelowest rise in AIC relative to the full model (DLsupFL

model AIC: 26.7; DLsupHL model AIC: 22.3; full modelAIC: 2151.7) (Fig. 8). In sum, on the broad substrate,whole-body angular momentum was most directly deter-mined by hind limb torque production. On the narrowsubstrate, the two limbs shared a more equal division oflabor, though changes in whole-body angular momentumwere slightly more closely associated with forelimb tor-que production. There were no significant interactionswith gait type (all P� 0.105), indicating that interlimbdifferences in angular momentum control were similaracross gaits.

Mechanism of torque production:sSRF versus smusc

We quantified the relative importance of sSRF versussmusc by measuring the angular impulse imparted byeach mechanism of torque production. A mixed-effectsANOVA revealed a significant interaction betweensource (i.e., smusc or sSRF) and limb girdle (F[1,137] 5 10.7,P 5 0.001), such that whereas smusc angular impulse wasgreater than sSRF angular impulse across limb girdles(all P<0.001), the differentiation between smusc and sSRF

angular impulse was most pronounced in the hind limbs

TABLE 1. Frequency of gait use, grouped by substratea

Asymmetrical Symmetrical

BoundHalf-bound Gallop Canter LS DS

2.5 cm pole 1 (3%) 1 (3%) 4 (12%) 21 (64%) 3 (9%) 3 (9%)5 cm pole – 2 (7%) 15 (50%) 13 (43%) – –

a Frequencies are expressed as absolute counts and, in paren-theses, percentage of total strides within that substrate.

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American Journal of Physical Anthropology

(Fig. 9). Specifically, whereas sSRF angular impulseswere statistically similar between the limb girdles(P 5 0.537), smusc angular impulses were significantlygreater in the hind limbs than in the forelimbs(P 5 0.001).

Because the position of the CoP along the circumfer-ence of the pole is a primary determinant of the effec-tiveness within which animals can exert sSRF or smusc

(Lammers and Gauntner, 2008), we also investigatedvariation in average forelimb and hind limb CoP positionacross substrate diameters. For these analyses, we quan-tified CoP location as angular position relative to the topof the force pole, such that 0� would represent placementdirectly on top of the pole and 90� would representplacement on the lateral extreme of the pole. A mixed-model ANOVA, including substrate diameter and limbgirdle as factors, revealed significant main effects forboth diameter (F[1,6] 5 29.9, P 5 0.002) and limb girdle(F[1,61] 5 76.8, P< 0.001), and no interaction between thetwo (F[1,61] 5 0.06, P 5 0.806). Irrespective of limb girdle,marmosets positioned the extremities closer to the top ofpole when moving on the broad substrate than whenmoving on the narrow substrate (Figs. 10 and 11; allP<0.001). Similarly, irrespective of substrate diameter,marmosets positioned the forelimbs closer to the top of

the pole than the hind limbs (Figs. 10 and 11; allP<0.001). Within the hind limbs, more laterally placedCoP positions were significantly associated with lowersSRF angular impulse (Spearman’s non-parametric corre-lation: q 5 20.42, P 5 0.002), suggesting that limb place-ment may have at least partially accounted for thegreater differentiation between smusc and sSRF angularimpulse in the hind limbs than in the fore limbs.

DISCUSSION

The marmosets in our sample proved adept at limitingfluctuations in angular momentum and maintainingarboreal stability, though not all our specific predictionsregarding angular momentum control were supported.Additionally, it should be noted that DLsup values weresignificantly greater than zero across the dataset (Fig.5), suggesting that rolling plane stability is likely main-tained by managing net angular momentum acrossstrides, rather than within strides. As Lammers andZucher (2011) note, the observation that stability islikely maintained across strides call into question thecommon practice of using the stride as the unit of analy-sis in locomotor studies, suggesting instead that broadcontrol strategies may only be apparent in mechanicaldata collected across bouts of strides. However, suchambitious protocols are difficult in animal research,where measuring extended bouts of locomotor typicallyrequires the use of a treadmill, with potentially biasingeffects (Blaszczyk and Loeb, 1993).

The range of rolling plane angular impulses docu-mented for marmosets—adjusted for body size by divid-ing DLsup by the product of body mass, average CoMheight, and gravitational acceleration—are broadly simi-lar to values previously reported for chipmunks (Tamiassibiricus) running on a simulated arboreal trackway, theonly other quadrupedal mammal for which similar dataare available (marmosets: 20.043 to 0.022 vs. chip-munks: 20.026 to 0.023; chipmunk data from Lammersand Zurcher, 2011). However, peak size-adjusted Lsup inthe marmosets was nearly three times larger than com-parable values reported for walking humans (Herr andPopovic, 2008)—though it is perhaps not surprising that

Fig. 2. Variation in gait selection as a function of substrate diameter. The frequencies of each gait type are expressed as percen-tages of the total number of strides collected on the indicated substrate diameter.

Fig. 3. Interaction plot of average speed differences betweensubstrate diameters, grouped by gait type. Error bars indicate95% confidence intervals about the mean for each cell.

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large, slow moving bipeds would seek to limit side-to-side angular momentum more so than small-bodied,agile arboreal quadrupeds.

We predicted that marmosets would show greaterinstability on the narrow substrate, reflecting the chal-lenge of maintaining balance as branch diameterdecreases. However, DLsup was actually greatest on thebroad substrate (Fig. 5), suggesting greater instabilityon the larger diameter support. Two possible explana-tions could account for this phenomenon. First, it maybe that marmosets could tolerate increased DLsup on the5 cm support because the greater size of the substrate

made it easier to correct balance perturbations. Analysisof average fore- and hind limb CoP positions showed thelarger diameter of the 5 cm pole allowed marmosets tomaintain contact points closer to the top of the support(Figs. 10 and 11), making the broad support functionallymore similar to terrestrial locomotion (Jenkins, 1974).By maintaining limb contacts closer to the top of thepole, vertically oriented forces—which are by far thelargest component of the total resultant force exerted onsubstrate (Fig. 4)—would primarily act perpendicular topole’s surface, allowing the animal to more easily correctbalance disturbances via the application of normal

Fig. 4. Gait mechanics of an exemplar stride (a canter on the narrow 2.5 cm pole; see Supporting Information Movie S2). (a)The gait graph of the stride, where bars indicate the stance phase period of each limb. (b–d) Fore-aft (FA), mediolateral (ML), andvertical (V) substrate reaction forces during the stride. (e, f) Total torque (stot) across the force poles and whole-body angularmomentum about the support (Lsup). Throughout the top four panels, different colors and line styles correspond to footfalls on dif-ferent force poles. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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(rather than shearing) forces. Moreover, due to thelarger radius of the support, the animal would have togenerate proportionally less shearing force to counterany disruptive torques about the support. In sum, itcould be that on the broader support marmosets toler-ated greater DLsup within strides because counteractingany excessive angular momentum during the next stridewould be comparatively easier.

Alternatively, it could be that reduced DLsup on the2.5 cm pole indicates that the marmosets successfullyadjusted their gait mechanics to mitigate the stabilitychallenges that might have occurred on the narrow sup-port. Marmosets significantly altered gait selection whenmoving on the narrow support, eschewing gallops andbounds in favor of symmetrical gaits and canters (Table1, Fig. 2). Young (2009) documented a similar shift awayfrom aerial phase gaits to more grounded asymmetricalgaits as marmosets and squirrel monkeys transitionedfrom locomotion on a flat runway to locomotion on araised pole. The use of more grounded gaits, such ascanters, is thought to reduce both CoM displacementsand the magnitude of peak forces imparted to the sub-strate (Schmitt et al., 2006; Young, 2009). Indeed, in thecurrent dataset, both CoM heights and peak verticalforces were greater during galloping/bounding gaits than

during canters or symmetrical gaits (Fig. 6; allP�0.028). In an arboreal context, such changes couldreduce branch oscillations and thus promote stability(Demes et al., 1990). Additionally, the use of canters andsymmetrical gaits was associated with significantlyreduced DLsup when marmosets were moving on the nar-row support, suggesting that “grounded” gaits canincrease lateral stability as well (Fig. 5). Finally, narrowbranch locomotion was associated with a more equaldivision of whole-body DLsup control between the fore-limbs and the hind limbs (Fig. 8). Though this partiallycontradicts our prediction that the hind limbs would con-sistently play a greater role in controlling whole-bodyangular momentum, it may be that the equal division oflabor on the narrow support permitted more subtle con-trol over DLsup throughout the stride. Indeed, fluctua-tions in stot were more balanced between positive andnegative torques on the narrow substrate.

Increasing joint flexion and moving with a crouchedposture have long been argued to be a primary behav-ioral means of increasing arboreal stability (Napier,1967; Rose, 1973; Schmitt, 2003b; Schmidt and Fischer,2010). Crouched postures are argued to promote stabilityby bringing the CoM closer to the substrate, thus limit-ing the magnitude of any potential toppling torques by

Fig. 5. Interaction plot of average differences in DLsup

between substrate diameters, grouped by gait type. Error barsindicate 95% confidence intervals about the mean.

Fig. 6. Interaction plot of average differences in CoM heightbetween substrate diameters, grouped by gait type. Error barsindicate 95% confidence intervals about the mean.

Fig. 7. Association between net change in angular momentum (DLsup) and CoM height on the narrow (a) and broad (b) diame-ter poles, grouped by gait type.

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shortening their moment arms. We tested this hypothe-sis by examining the correlation between CoM heightand DLsup. Though we found no evidence for a direct cor-relation between these variables, it is noteworthy thatthe variance of DLsup tended to increase in proportion toCoM height (Fig. 7). As such, the highest values of DLsup

were observed when the CoM was furthest from the sub-strate, though the inverse was not true (i.e., that lowvalues of DLsup were only observed when the CoM wasclosest to the substrate). Functionally, this suggests thatalthough high CoM positions may have been associatedwith increased DLsup, marmosets were able to use othermechanisms to limit the destabilizing effects of this rela-tionship. For instance, studies of dynamic stability dur-ing human walking have found that lateral stabilityincreases with speed (Bruijn et al., 2009). Because CoMheight was greatest when marmosets used the fastestgaits (Fig. 6), it may be that the increased dynamic sta-bility conferred by high speeds at times mitigated theinstability that might have resulted from high CoM posi-tions. Future studies of slower moving arboreal animalsmay find a more direct correlation between CoM heightand DLsup.

Long, mobile digits adapted for grasping are oftencited as a key morphological trait defining the Order Pri-mates (Le Gros Clark, 1959; Dagosto, 2007). Function-ally, grasping extremities are thought to facilitateadhesion and balance on narrow substrates by allowing

primates to generate stabilizing muscular torques aboutthe support (Napier, 1967; Cartmill, 1985; Preuschoftet al., 1995). Through adaptation to gumnivory, marmo-set autopodial anatomy has become quite derived rela-tive to other crown primates, being characterized byclaw-like tegulae on every digit but the hallux, relativelynarrow apical pads, and a relatively short hallux withdiminished adductor musculature (Beattie, 1927; Midlo,1934; Hamrick, 1998). These derived changes in marmo-set autopodial morphology may limit grasping abilitywhen locomoting in a small branch environment (Ham-rick, 1998; Schmitt, 2003a). We thus predicted that lim-ited grasping morphology would require marmosets toproduce angular impulse primarily through substratereaction forces (i.e., sSRF) rather than the independentrotatory action of muscular grasping limbs (i.e., smusc).

In contradiction to this prediction, across limb girdlesand substrate diameters, angular impulse was predomi-nantly generated via smusc, with the discrepancybetween smusc and sSRF being particularly pronounced inthe hind limbs (Fig. 9). Despite their limited develop-ment of typical primate grasping morphology, marmosetswere thus nonetheless able to control lateral stabilityvia primarily muscular torque production. We contendthat the discrepancy between our prediction and ourfindings results from the marmosets’ predominant use ofasymmetrical gaits. Most hypotheses of primate locomo-tor evolution typically assume (either implicitly orexplicitly) that early primates and their ancestors wereusing symmetrical gaits, where footfalls would be spacedin time and each limb would function more or less inde-pendently (e.g., Cartmill, 1972; Szalay and Dagosto,1988; Sussman, 1991; Larson, 1998). In such a situation,individual extremities would be responsible for produc-ing the torques required to regulate whole-body angularmomentum, making grasping morphologies beneficial.During asymmetrical gaits, however, the two limbs of agirdle function together, producing substrate reactionforces and torques as a single unit. As such, the fore-limbs and hind limbs of a cantering, galloping, or bound-ing primate could be considered to represent unified“functional extremities,” expanding “effective” grasp asthe animal grips the substrate between the left andright limbs of the girdle. Moreover, because hind limbstypically have shorter lead durations than forelimbs dur-ing asymmetrical gaits, particularly among small mam-mals (Dagg, 1973; Hildebrand, 1977), the tendency for

Fig. 9. Interaction plot of the average differences in DLsup

accounted for by smusc versus sSRF in forelimbs and hind limb.Error bars indicate 95% confidence intervals about the mean.

Fig. 10. Interaction plot of average differences in angularCoP position between substrate diameters, grouped by limb gir-dle. Error bars indicate 95% confidence intervals about themean.

Fig. 8. Interaction plot of average differences in forelimband hind limb angular impulse (i.e., DLsup) grouped by sub-strate diameter. Error bars indicate 95% confidence intervalsabout the mean.

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the two limbs in a girdle to function as a single extrem-ity is likely to be most pronounced in the hind limbs. Inthe current dataset, average hind limb lead durations(scaled to trailing limb duty factors, following Hilde-brand, 1977) were approximately half of average fore-limb lead durations (forelimbs: 52.2%; hind limbs:26.2%), a difference that was significant on both sub-strates (all P� 0.001). Additionally, the relatively lowposition of the hind limbs on the pole (Figs. 10 and 11)could have permitted the animals to more effectivelygrip the substrate between the right and left feet byexerting opposing normal forces, further facilitatingsmusc production (Cartmill, 1974). The use of paired leftand right limbs as unified grasping organs may alsoexplain the frequent use of trot-like symmetrical gaits inmarmosets and other callitrichids (Arms et al., 2002;Schmitt, 2003a; Nyakatura et al., 2008; Nyakatura andHeymann, 2010; this study), as well as during arboreallocomotion in other small non-grasping mammals, suchas opossums (Lammers and Gauntner, 2008). In a trot-ting gait, left and right fore- and hind limbs are pairedacross limb girdles, in this case permitting contralateralforelimb-hind limb pairs to act as unified “functionalextremities.” Indeed, Lammers and Gauntner (2008)showed that average smusc exceeded average sSRF in trot-ting gray short-tailed opossums (Monodelphis domestica)moving over instrumented poles, supporting our conten-

tion that paired limb use permits non-grasping mammalto effectively control torque production about thesubstrate.

In summary, the use of asymmetrical gaits allowedmarmosets to create functional grasping appendages,facilitating the production of muscular torques about thesubstrate despite their relatively poor development oftypical primate grasping morphology. This hypothesizedrelationship between asymmetrical gaits and the crea-tion of functional grasping appendages may explain thefrequent use of asymmetrical gaits in other small-bodiedarboreal mammals, including didelphid marsupials(Pridmore, 1994), tree squirrels (Youlatos and Samaras,2010), tree shrews (Jenkins, 1974), mouse lemurs (Sha-piro et al., 2014), and other callitrichids (Fleagle andMittermeier, 1980; Garber, 1991; Rosenberger and Staf-ford, 1994; Nyakatura and Heymann, 2010). As notedabove, high speed asymmetrical gaits also conferdynamic stability, further mitigating arboreal balancedisruptions (Bruijn et al., 2009). Moreover, postcranialfeatures of Eocene primates and other closely relatedarchontan taxa suggest that asymmetrical gaits mayhave been a critical component of the locomotor reper-toire of stem primates and their ancestors (Gregory,1920; Dagosto, 1993, 2007; Bloch and Boyer, 2007), par-ticularly during those stages of primate evolution whenoverall body sizes were small and a powerful pedal

Fig. 11. Anterior view of mean CoP positions for right limbs (dark-shaded symbols) and left limbs (light-shaded symbols),grouped by substrate diameter and gait type. Radial lines on each pole are spaced at 30� intervals. Symbols are plotted at differentlevels along the circumference of the pole to more easily distinguish among gait types. All calculations involving CoP positionassumed a location on the surface of the pole.

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grasping apparatus had yet to be developed (Gebo, 2004;Sargis et al., 2007).

However, because substrate reaction forces are typi-cally greater during high-speed locomotion, an inevitabletrade-off is reached as overall body size increases rela-tive to branch diameter. At some point, either branchintegrity would be compromised or angular momentumin other planes would become excessive (e.g., pitchingmomentum in the sagittal plane), and the use of asym-metrical gaits would be detrimental to arboreal stability.In these situations, grasping extremities should confersome selective performance advantage. Becausebranches are not vanishingly small, small-bodied arbo-real mammals are less likely to encounter such challeng-ing substrates on a frequent basis. We acknowledge thatgrasping extremities can serve functions beyond themaintenance of balance during horizontal arboreal loco-motion, and are also likely to be critical for climbing andthe traversal of oblique supports (Reghem et al., 2012;Birn-Jeffery and Higham, 2014). Nevertheless, we sug-gest that in general there may have therefore been a“body size threshold” during primate locomotor evolu-tion, past which powerful grasping extremities andbehavioral adjustments—such as the use of compliantgait kinematics (Schmitt, 1999, 2003b) and specific foot-fall patterns, such as diagonal sequence gaits (Stevens,2006, 2007)—became critical adaptations for maintain-ing arboreal stability, facilitating early primates’ success-ful restriction to the arboreal habitat (Orkin andPontzer, 2011).

CONCLUSIONS AND DIRECTIONS FOR FUTURERESEARCH

The primary goal of this study was to introduce anovel conceptual and experimental framework withwhich to evaluate stability during primate quadrupedallocomotion. As illustrated by our case study of commonmarmosets, this system has the potential to provide newempirical insight into the performance benefits of mor-phological and behavioral features that have long beenargued to be critical elements of primate quadrupedal-ism. Ongoing research in our laboratory is using thisframework to examine locomotor stability in other pri-mates for whom symmetrical gaits are more common(e.g., squirrel monkeys, Saimiri boliviensis). To bettermodel the complexity of wild primate locomotion, futurestudies should also consider how intermittent locomotion(vs. the continuous steady-state strides studied here)and greater substrate variability impact the quantitativemetrics of primate stability introduced here. Such dataare required to fully explore the links among morphology(broadly defined here to include both locomotor anatomyand behavior), function (the production of forces and tor-ques), and performance (the maintenance of arborealstability). Organizing research questions along this mor-phology–function–performance axis is a crucial step inestablishing the adaptive nature of a given feature(Arnold, 1983; Lauder, 1996), and is thus critical tounderstanding primate locomotor evolution.

ACKNOWLEDGMENTS

The authors thank Nathan Michael, Timothy O’Neill,Kyle Resnick, and Gabrielle Russo for help with animalexperiments and data processing. Nicolay Hristov pro-vided invaluable advice on animal training. The NEOMEDComparative Biomechanics Journal Club, the associate

editor, and the two external reviewers provided helpfulcomments on a previous draft of this manuscript. Researchsupported by NSF-BCS 1126790 and the NEOMEDDepartment of Anatomy and Neurobiology.

LITERATURE CITED

Alexander RM. 2002. Stability and manoeuverability of terres-trial vertebrates. Integr Comp Biol 42:158–164.

Arms A, Voges D, Fischer MS, Preuschoft H. 2002. Arboreallocomotion in small new-world primates. Z Morphol Anthropol83:243–263.

Arnold SJ. 1983. Morphology, performance and fitness. Am Zool23:347–361.

Beattie J. 1927. The anatomy of the common marmoset. ProcZool Soc (Lond) 27:593–718.

Biewener AA, Full RJ. 1992. Force platform and kinematicanalysis. In: Biewener AA, editor. Biomechanics: structuresand systems. Oxford: Oxford University Press. p 45–73.

Birn-Jeffery AV, Higham TE. 2014. The scaling of uphill anddownhill locomotion in legged animals. Integr Comp Biol 54:1159–1172.

Blaszczyk J, Loeb GE. 1993. Why cats pace on the treadmill.Physiol Behav 53:501–507.

Bloch J, Silcox M, Boyer D, Sargis E. 2007. New Paleocene skel-etons and the relationship of plesiadapiforms to crown-cladeprimates. Proc Natl Acad Sci USA 104:1159.

Bloch JI, Boyer DM. 2007. New skeletons of Paleocene-EocenePlesiadapiformes: a diversity of arboreal positional behaviorsin early primates. In: Ravosa MJ, Dagosto M, editors. Pri-mate origins: adaptations and evolution. New York, NY:Springer. p 535–581.

Bruijn S, van Die€en J, Meijer O, Beek P. 2009. Is slow walkingmore stable? J Biomech 42:1506–1512.

Cartmill M. 1972. Arboreal adaptations and the origin of theOrder Primates. In: Tuttle R, editor. The functional and evo-lutionary biology of primates. Chicago: Aldine. p 97–122.

Cartmill M. 1974. Pads and claws in arboreal locomotion. In:Jenkins FA, editor. Primate locomotion. New York, NY: Aca-demic Press. p 45–83.

Cartmill M. 1985. Climbing. In: Hildebrand M, Bramble DM,Liem KF, Wake DB, editors. Functional vertebrate morphol-ogy. Cambridge: Harvard University Press. p 73–88.

Dagg AI. 1973. Gaits in mammals. Mammal Rev 3:135–154.Dagosto M. 1993. Postcranial anatomy and locomotor behavior

in Eocene primates. In: Gebo DL, editor. Postcranial adapta-tion in nonhuman primates. Dekalb, IL: Northern IllinoisUniversity Press. p 199–219.

Dagosto M. 2007. The postcranial morphotype of primates. In:Ravosa MJ, Dagosto M, editors. Primate origins: adaptationsand evolution. New York, NY: Springer. p 489–534.

Daley M, Usherwood J, Felix G, Biewener A. 2006. Runningover rough terrain: guinea fowl maintain dynamic stabilitydespite a large unexpected change in substrate height. J ExpBiol 209:171–187.

Demes B, Jungers WL, Nieschalk U. 1990. Size- and speed-related aspects of quadrupedal walking in slender and slowlorises. In: Jouffroy FK, Stack MH, Niemetz C, editors. Grav-ity, posture and locomotion in primates. Florence: Il Sedice-simo. p 175–197.

Fleagle JG, Mittermeier RA. 1980. Locomotor behavior, bodysize, and comparative ecology of seven Surinam monkeys. AmJ Phys Anthropol 52:301–314.

Full RJ, Kubow T, Schmitt J, Holmes P, Koditschek D. 2002.Quantifying dynamic stability and maneuverability in leggedlocomotion. Integr Comp Biol 42:149–157.

Garber PA. 1991. A comparative study of positional behavior inthree species of tamarin monkey. Primates 32:219–230.

Garber PA. 1992. Vertical clinging, small body size, and the evo-lution of feeding adaptations in the Callitrichinae. Am J PhysAnthropol 88:469–482.

Gebo DL. 2004. A shrew-sized origin for primates. Yrbk PhysAnthropol 47:40–62.

MECHANICS OF ARBOREAL STABILITY IN MARMOSETS 11

American Journal of Physical Anthropology

Goswami A, Kallem V. 2004. Rate of change of angular momen-tum and balance maintenance of bieped robots. Proceedingsof the IEEE International Conference on Robotics and Auto-mation:3785–3790 (doi: 3710.1109/ROBOT.2004.1308858).

Gregory WK. 1920. On the structure and relations of Notharctus,an American Eocene primate. Mem Am Mus Nat Hist 3:51–243.

Hamrick MW. 1998. Functional and adaptive significance of pri-mate pads and claws: evidence from new world anthropoids.Am J Phys Anthropol 106:113–127.

Herr H, Popovic M. 2008. Angular momentum in human walk-ing. J Exp Biol 211:467–481.

Hildebrand M. 1977. Analysis of asymmetrical gaits. J Mammal58:131–156.

Jenkins FA. 1974. Tree shrew locomotion and the origins of pri-mate arborealism. In: Jenkins FA, editor. Primate locomotion.New York, NY: Academic Press. p 85–115.

Lammers AR. 2009a. The effects of substrate texture on themechanics of quadrupedal arboreal locomotion in the grayshort-tailed opossum (Monodelphis domestica). J Exp Zool311A:813–823.

Lammers AR. 2009b. Mechanics of generating friction duringlocomotion on rough and smooth arboreal trackways. J ExpBiol 212(Pt 8):1163–1169.

Lammers AR, Gauntner T. 2008. Mechanics of torque genera-tion during quadrupedal arboreal locomotion. J Biomech 41:2388–2395.

Lammers AR, Zurcher U. 2011. Torque around the center ofmass: dynamic stability during quadrupedal arboreal locomo-tion in the Siberian chipmunk (Tamias sibiricus). Zoology114:95–103.

Larson SG. 1998. Unique aspects of quadrupedal locomotion innonhuman primates. In: Strasser E, Fleagle J, RosenbergerA, McHenry H, editors. Primate locomotion. New York, NY:Plenum Press. p 157–173.

Lauder GV. 1996. The argument from design. In: Rose MR,Lauder GV, editors. Adaptation. San Diego, CA: AcademicPress. p 55–91.

Le Gros Clark WE. 1959. The antecedents of man: an introduc-tion to the evolution of the primates. Edinburgh: EdinburghUniversity Press.

Lovell NC. 1991. An evolutionary framework for assessing ill-ness and injury in nonhuman primates. Yrbk Phys Anthropol34:117–155.

Manter JT. 1938. The dynamics of quadrupedal walking. J ExpBiol 45:522–540.

Midlo C. 1934. Form of hand and foot in primates. Am J PhysAnthropol 19:337–389.

Napier JR. 1967. Evolutionary aspects of primate locomotion.Am J Phys Anthropol 27:333–342.

Nyakatura J, Fischer MS, Schmidt M. 2008. Gait parameteradjustments of cotton-top tamarins (Saguinus oedipus, Calli-trichidae) to locomotion on inclined arboreal substrates. Am JPhys Anthropol 135:13–26.

Nyakatura JA, Heymann EW. 2010. Effects of support size andorientation on symmetric gaits in free-ranging tamarins ofAmazonian Peru: implications for the functional significanceof primate gait sequence patterns. J Hum Evol 58:242–251.

Orkin JD, Pontzer H. 2011. The narrow niche hypothesis: graysquirrels shed new light on primate origins. Am J PhysAnthropol 144:617–624.

Pinheiro JC, Bates DM. 2000. Mixed-effects models in S and S-PLUS. New York, NY: Springer.

Preuschoft H. 2002. What does “arboreal locomotion” meanexactly and what are the relationships between “climbing”environment and morphology? Z Morphol Anthropol 83:171–188.

Preuschoft H, Witte H, Fischer M. 1995. Locomotion in noctur-nal prosimians. In: Alterman L, Doyle G, Izard MK, editors.Creatures of the dark: the nocturnal prosimians. New York,NY: Plenum Press. p 453–472.

Pridmore PA. 1994. Locomotion in Dromiciops australis (Marsu-pialia: Microbiotheriidae). Aust J Zool 42:679–699.

R Core Team. 2013. R: a language and environment for statisti-cal computing. 2.15.3 ed. Vienna, Austria: R Foundation forStatistical Computing.

Reghem E, Byron C, Bels V, Pouydebat E. 2012. Hand posturein the grey mouse lemur during arboreal locomotion on nar-row branches. J Zool 288:76–81.

Rose MD. 1973. Quadrupedalism in primates. Primates 14:337–357.

Rosenberger A, Stafford BJ. 1994. Locomotion in captive Leon-topithecus and Callimico: a multimedia study. Am J PhysAnthropol 94:379–394.

Sargis EJ, Boyer DM, Bloch JI, Sargis EJ. 2007. Evolution ofpedal grasping in Primates. J Hum Evol 53:103–107.

Schmidt A, Fischer MS. 2010. Arboreal locomotion in rats—thechallenge of maintaining stability. J Exp Biol 213:3615–3624.

Schmitt D. 1999. Compliant walking in primates. J Zool Lond248:149–160.

Schmitt D. 2003a. Evolutionary implications of the unusualwalking mechanics of the common marmoset (C. jacchus). AmJ Phys Anthropol 122:28–37.

Schmitt D. 2003b. Substrate size and primate forelimb mechan-ics: implications for understanding the evolution of primatelocomotion. Int J Primatol 24:1023–1036.

Schmitt D, Cartmill M, Griffin TM, Hanna JB, Lemelin P. 2006.Adaptive value of ambling gaits in primates and other mam-mals. J Exp Biol 209:2042–2049.

Schmitt D, Larson SG. 1995. Heel contact as a function of sub-strate type and speed in primates. Am J Phys Anthropol 96:39–50.

Shapiro LJ, Kemp AD, Young JW. 2014. Kinematic adjustmentsto substrate size and orientation during asymmetrical gaits inmouse lemurs (Microcebus murinus). Am J Phys Anthropol153(Suppl. 58):237.

Smith JM, Smith AC. 2013. An investigation of ecological corre-lates with hand and foot morphology in callitrichid primates.Am J Phys Anthropol 152:447–458.

Sokal RR, Rohlf FJ. 1995. Biometry. New York, NY: W.H.Freeman.

Standen EM, Lauder GV. 2005. Dorsal and anal fin function inbluegill sunfish Lepomis macrochirus: three-dimensionalkinematics during propulsion and maneuvering. J Exp Biol208:2753–2763.

Stevens NJ. 2006. Stability, limb coordination and substratetype: the ecorelevance of gait sequence pattern in primates.J Exp Zool 305A:953–963.

Stevens NJ. 2007. The effect of branch diameter on primategait sequence pattern. Am J Primatol 70:1–7.

Sussman RW. 1991. Primate origins and the evolution of angio-sperms. Am J Primatol 23:209–223.

Sussman RW, Kinzey WG. 1984. The ecological role of the Calli-trichidae: a review. Am J Phys Anthropol 64:419–449.

Szalay FS, Dagosto M. 1988. Evolution of hallucial grasping inthe primates. J Hum Evol 17:1–33.

Walker JA. 1998. Estimating velocities and accelerations of ani-mal locomotion: a simulation experiment comparing numeri-cal differentiation algorithms. J Exp Biol 201:981–995.

Wood Jones F. 1916. Arboreal man. London: E. Arnold.Youlatos D, Samaras A. 2010. Arboreal locomotor and postural

behaviour of European red squirrels (Sciurus vulgaris L.) innorthern Greece. J Ethol 29:235–242.

Young JW. 2009. Substrate determines asymmetrical gaitdynamics in marmosets (Callithrix jacchus) and squirrelmonkeys (Saimiri boliviensis). Am J Phys Anthropol 138:403–420.

Young JW. 2012. Ontogeny of limb force distribution in squirrelmonkeys (Saimiri boliviensis): insights into the mechanicalbases of primate hind limb dominance. J Hum Evol 62:473–485.

12 B.A. CHADWELL AND J.W. YOUNG

American Journal of Physical Anthropology