Ontogeny of limb force distribution in squirrel monkeys (Saimiri boliviensis): Insights into the mechanical bases of primate hind limb dominance

Journal of Human Evolution 62 (2012) 473e485

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Ontogeny of limb force distribution in squirrel monkeys (Saimiri boliviensis): Insights into the mechanical bases of primate hind limb dominance Jesse W. Young a, b a b

Department of Anatomy and Neurobiology, Northeastern Ohio Medical University, Rootstown, OH 44272, USA Skeletal Biology Research Focus Area, NEOMED, Rootstown, OH 44272, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 29 June 2011 Accepted 13 January 2012 Available online 3 March 2012

The distribution of peak vertical forces between the forelimbs and the hind limbs is one of the key traits distinguishing primate quadrupedal locomotion from that of other mammals. Whereas most mammals generate greater peak vertical forelimb forces, primates generate greater peak vertical hind limb forces. At the ultimate level, hind limb dominance in limb force distribution is typically interpreted as an adaptation to facilitate fine-branch arboreality. However, the proximate biomechanical bases for primate limb force distribution remain controversial. Three models have been previously proposed. The Center of Mass (COM) Position model attributes primates’ unique mode of limb loading to differences in the position of the whole-body COM relative to the hands and feet. The Active Weight Shift model asserts that primates actively redistribute body weight to their hind limbs by pitching the trunk up via the activation of hind limb retractor muscles. Finally, the Limb Compliance model argues that primates selectively mitigate forelimb forces by maintaining a compliant forelimb and a flat shoulder trajectory. Here, a detailed dataset of ontogenetic changes in morphology and locomotor mechanics in Bolivian squirrel monkeys (Saimiri boliviensis) was employed as a model system to evaluate each of these proposed models in turn. Over the first 10 months of life, squirrel monkeys transitioned from forelimb dominant infants to hind limb dominant juveniles, a change that was precipitated by decreases in peak vertical forelimb forces and increases in peak vertical hind limb forces. Results provided some support for all three of the models, although the COM Position and Active Weight Shift models were most strongly supported by the data. Overall, this study suggests that primates may use a variety of biomechanical strategies to achieve hind limb dominance in limb force distribution. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Locomotor development Center of mass Active weight shift Limb compliance Kinetics Kinematics

Introduction The distribution of peak vertical forces between the forelimbs and the hind limbs has often been cited as one of the key traits distinguishing primate quadrupedal locomotion from that of other mammals (Larson, 1998). Whereas most mammals generate greater peak vertical substrate reaction forces with their forelimbs, primates typically generate greater peak vertical forces with their hind limbs (Kimura et al., 1979; Reynolds, 1985a, b; Kimura, 1992;

E-mail address: [email protected]. Many authors have discussed patterns of peak limb force distribution in terms of “weight-support”, asserting that primates differ from other mammals in supporting a greater proportion of body weight on the hind limbs. However, this association is not necessarily valid. Impulse, calculated as the area under the forceetime curve, is a better metric of each limb’s contribution to weight support, as the total impulse across a stride must sum to body weight times contact duration (Bertram et al. 1997). Therefore, I take the approach of discussing patterns of peak force distribution in terms of limb force distribution, rather than weight support. 1

0047-2484/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jhevol.2012.01.003

Demes et al., 1994; Polk, 2001; Schmitt and Lemelin, 2002, 2004; Schmitt, 2003; Li et al., 2004; Schmitt and Hanna, 2004; Franz et al., 2005; Hanna et al., 2006; Wallace and Demes, 2008; Raichlen et al., 2009)1. A shift from “forelimb dominant” to “hind limb dominant” locomotion has been presented as an adaptive strategy that permitted basal primates to emancipate their forelimbs from a weight-bearing function, facilitating foraging and locomotion in the potentially unstable “fine-branch niche” (Schmitt and Lemelin, 2002; Lemelin and Schmitt, 2007). In support of this hypothesis, Caluromys philander, a South American marsupial known to exploit the fine-branch niche (Julienlaferriere and Atramentowicz, 1990), converges on the primate pattern of greater hind limb loading (Schmitt and Lemelin, 2002; Lemelin and Schmitt, 2007). By contrast, common marmosets (Callithrix jacchus) and cottontop tamarins (Saguinus oedipus), callitrichid primates that show many specializations for movement on large boughs and tree trunks, differ from most other primates in generating greater peak vertical forces on their forelimbs (Schmitt, 2003; J. W. Young, unpublished data). Moreover, studies of a broad sample of arboreal

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and non-arboreal mammals, including primates (Schmitt and Hanna, 2004; Wallace and Demes, 2008), opossums (Lammers and Biknevicius, 2004), and rodents (Schmidt and Fischer, 2010) have shown that individuals show a strong tendency to mitigate forelimb forces and become more hind limb dominant on narrow branch-like trackways. Finally, more terrestrially-adapted primates, such as patas monkeys (Erythrocebus patas) and baboons (Papio spp), tend to distribute peak forces more evenly between the forelimbs and hind limbs (Kimura et al., 1979; Reynolds, 1985b; Demes et al., 1994; Polk, 2001; Young et al., 2007), further suggesting that hind limb dominance in limb force distribution is associated with committed arboreality. Reduction of forelimb loading has also been argued to be a precursor to the evolution of hominin bipedalism (Kimura et al., 1979; Reynolds, 1985b; Kimura, 1987). Despite the importance of hind limb dominance in limb force distribution to theories of primate and human locomotor evolution, the proximate biomechanical bases for peak limb force distribution remain controversial. Three principle mechanical models of primate hind limb dominance have previously been proposed: the Center of Mass Position model (Raichlen et al., 2009), the Active Weight Shift model (Reynolds, 1985a), and the Limb Compliance model (Schmitt, 1999; Schmitt and Hanna, 2004). The principal aim of this study is to use ontogenetic data on limb loading and locomotor mechanics in squirrel monkeys (Saimiri boliviensis) as a model system with which to explore the explanatory power of each of these models in turn. The simplest model attributes primates’ unique mode of limb loading to differences in the position of the center of mass (COM) relative to the position of the hands and feet (Rollinson and Martin 1981; Raichlen et al. 2009). In other words, the limb that is closest to the bulk of an animal’s mass will support a greater proportion of body weight. Mechanically, this phenomenon is similar to the way in which the anterior position of the engine block distributes a greater proportion of vehicle weight on the front wheels of most sedans (Rothbart and Brown, 2006). Although morphological studies have found that the COM in most adult primates is near, or even anterior to, the transverse midline of the trunk (Reynolds, 1974; Wells and DeMenthon, 1987; Turnquist and Wells, 1994; Crompton et al., 1996; Young et al., 2007; Raichlen et al., 2009), adjustments in hand and foot positioning relative to the COM have the potential to alter force distribution between limb pairs, even in the absence of morphological variation in COM position per se (Gray, 1944). Specifically, any shift in morphology or kinematics that decreases the average distance between the feet and COM or increases in the average distance between the hands and the COM has the potential to redistribute body weight and peak forces from the forelimbs to the hind limbs. Reynolds (1985a) presented an alternative model of primate limb force distribution e the Active Weight Shift model. He argued that, in most primates, the average position of the feet during walking is not sufficiently close to the COM to generate observed patterns of forelimbehind limb peak force distribution. Expanding on biomechanical theory first developed by Gray (1944) and Barclay (1953), Reynolds (1985a) instead proposed that primates actively redistribute body weight to their hind limbs by pitching the trunk up via the selective activation of hind limb retractor muscles during early support phase. Reynolds’s (1985a) proposed mechanism is predicated on recognizing that a limb can serve dual functions as either a “strut” or a “lever” during locomotion. A limb acts as a strut when exerting forces solely along its mechanical axis (like the pole of a pole vaulter), and as a lever when exerting forces at right angles to its mechanical axis (like an oar rowing a boat). Limbs acting as struts generate fore-aft reaction forces that vary directly with the limb’s orientation, exerting braking substrate

reaction forces (SRF) when protracted and propulsive SRF when retracted. In contrast, limbs acting as levers can exert braking or propulsive SRF that are independent of limb orientation. In reality, moving quadrupeds use their limbs as both struts and levers, and realized fore-aft SRF reflect a combination of these modes of action. Reynolds (1985a) asserted that by activating retractor musculature when the hind limb is firmly planted at the beginning of support phase (i.e., by operating the limb as a lever), primates could effectively pitch the trunk up, lifting the anterior portion of the body and redistributing weight from the forelimbs to the hind limbs (Fig. 1). Furthermore, he argued that the tendency of the retractor musculature to potentially accelerate the animal by exerting lever-induced propulsive forces on the ground, a mechanism he referred to as the “Horizontal Lever Effect” (HLE), would be balanced by the braking forces that result from the limb operating as a cranially-displaced strut, a mechanism he referred to as the “Horizontal Strut Effect” (HSE). Provided the HLE and HSE forces are equivalent, the primate will experience no net acceleration and remain at a steady speed (Reynolds, 1985a). As is discussed in more detail below, the degree to which HSE and HLE forces effectively cancel and ensure no net acceleration across a stride has been the subject of much theoretical debate in the primate locomotor literature (Reynolds, 1985a; Li, 2000; Raichlen et al., 2009; Larson and Demes, 2011). Nevertheless, few data exist with which to empirically evaluate Reynolds’s (1985a) model. Schmitt and Hanna (2004) challenged Reynolds’s (1985a) model, asserting that although primates tend to significantly reduce forelimb loading when walking on simulated branches, there is no evidence that hind limb protraction, and therefore requisite strut forces, significantly differ between terrestrial and arboreal substrates. Instead, elaborating on previous studies by Schmitt (1994, 1998, 1999), these authors argued that primates

Figure 1. Schematic illustration of the mechanics of Reynolds’s (1985a) Active Weight Shift model of primate limb force distribution. In the model, activation of hind limb retractor muscles on a firmly planted and protracted hind limb exerts a force (i.e., FHLR) that generates a counter-clockwise moment (i.e., MHLR) about the hip, lifting the anterior end of the trunk upwards, thereby reducing vertical forelimb SRF and increasing vertical hind limb SRF (i.e., SRFv). The braking force induced by the limb behaving as a strut (i.e., the Horizontal Strut Effect, or HSE) cancels out the propulsive force that results from FHLR causing the limb to behave as a lever (i.e., the Horizontal Lever Effect, or HLE), ensuring that the net fore-aft SRF (i.e., SRFFA) is not accelerative. Provided the system is at equilibrium, the magnitude of MHLR can be calculated as the product of HLE and the vertical height of the hip (yhip).

J.W. Young / Journal of Human Evolution 62 (2012) 473e485

mitigate forelimb loading relative to hind limb loading by using “compliant” gaits, marked by a set of kinematic adaptations that together reduce the vertical oscillation of the proximal limb pivot (i.e., shoulder or hip). Reducing the vertical oscillation of the shoulder or hip effectively “flattens” the vertical force trajectory, maintaining impulse (i.e., the area under the forceetime curve) while lowering peak forces. Experimental studies have shown that the use of compliant kinematics allows human runners to significantly reduce peak vertical forces at mid-support while maintaining net impulse and velocity (McMahon et al., 1987). Schmitt and Hanna’s (2004) Limb Compliance model specifically predicts that by increasing forelimb compliance over and above hind limb compliance, primates are able to alter overall patterns of force distribution, leading to hind limb dominance in limb loading. The current study is the first to explicitly test the predictions of the Limb Compliance Model, aside from the Schmitt and Hanna (2004) paper in which the model was originally proposed.

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lifting the anterior end of the trunk via the selective activation of hind limb retractor muscles during early hind limb support phase (Reynolds, 1985a; Fig. 1). If this model is valid, then the ratio of forelimb to hind limb loading should be inversely proportional to hind limb retractor torque at peak vertical hind limb force. Moreover, an ontogenetic increase in relative hind limb loading should be associated with increases in relative hind limb retractor torque at peak vertical hind limb force. The Limb Compliance model predicts that reductions in peak loading should be associated with increased limb compliance (Schmitt, 1999). If this model is valid, peak vertical limb forces should be inversely proportional to limb compliance. Moreover, an ontogenetic increase in relative hind limb loading should be associated with 1) an increase in forelimb compliance, 2) a decrease in hind limb compliance, or 3) a combination of these strategies. Each of these strategies would reduce forelimb peak vertical force relative to hind limb peak vertical force, thereby achieving hind limb dominance in limb loading.

Specific aims and predictions Materials and methods This study employs morphological, kinematic, and kinetic variation in growing Bolivian squirrel monkeys (S. boliviensis) as a model system to explore the biomechanical bases for primate hind limb dominance. Tracking associations between growing bodies and developing locomotor mechanics offers a powerful means of discerning functional relationships that might be obscured in more broad-scale interspecific studies of adult animals (Dial, 2003; Raichlen, 2005; Dial et al., 2008). The ontogenetic squirrel monkey sample is used to evaluate the three previously developed models of primate limb force distribution described above: the COM Position model (Gray, 1944; Raichlen et al., 2009; Larson and Demes, 2011), the Active Weight Shift model (Reynolds, 1985a, b; Larson and Stern, 2009), and the Limb Compliance model (Schmitt, 1998, 1999; Schmitt and Hanna, 2004). Whereas adult squirrel monkeys are hind limb dominant in body weight distribution (Schmidt, 2005), previous work suggests that patterns of weight distribution are not static, but rather change across development. Specifically, a previous study of joint mechanics in the ontogenetic squirrel monkey sample (Young, 2009a) found that the relative magnitude of resultant forelimb forces (scaled to body weight) significantly declined as size increased during development, whereas relative hind limb forces tended to increase with size. On this basis, it is predicted that growing monkeys should transition from forelimb dominant infants to hind limb dominant juveniles and adults. The COM Position model, the Active Weight Shift model, and the Limb Compliance model each support specific hypotheses of how morphology and gait mechanics should change during ontogeny to produce the predicted changes in limb force distribution. Note, however, that the models are not mutually exclusive: primates could conceivably use a combination of strategies to redistribute forces between limb pairs. The COM Position model argues that limb force distribution during a stride is determined by the average position of the COM relative to the average position of the hands and feet during support phase (Gray, 1944; Raichlen et al., 2009; Larson and Demes, 2011). According to this model, an ontogenetic shift from forelimb dominant to hind limb dominant locomotion could be precipitated by 1) a caudal translation of COM position, 2) a cranial translation in average hand position, and 3) a cranial translation in average foot position, or a combination of these strategies. Each of these strategies would have the net effect of decreasing the relative distance between the hind limbs and the COM. The Active Weight Shift model argues that primates actively redistribute body weight from the forelimbs to the hind limbs by

Data collection and processing Details of the animal sample used in these experiments and the basic procedures for locomotor data collection and processing have been described at length elsewhere (Young 2009b, a), and will be only briefly addressed here. A total of 74 experiments were conducted at the Center for Neotropical Primate Research and Resources (CNPRR: Mobile, AL), including 36 experiments on a flat runway and 38 experiments on a raised 3.2 cm diameter pole (i.e., simulated arboreal substrate). Five female squirrel monkeys comprised the sample for these experiments. Collectively, the monkeys ranged in age from 93 to 293 days and body mass from 219 to 533 g (31e75% of adult female body size: Smith and Jungers, 1997). The squirrel monkeys were filmed at 250 Hz with a digital video camera as they traversed the 1.8 m long flat trackway or raised pole. Two custom-built force platforms were placed in series in the center of the runway to quantify limb SRF. Prior to each experiment, reflective markers were placed over the major limb joints to aid in motion tracking, a procedure that did not require anesthesia. Institutional Animal Care and Use Committees (IACUC) at Stony Brook University and the CNPRR approved all procedures prior to the beginning of this research. Outcome variables To make the results of this study commensurate with the bulk of previous research on primate limb force distribution, only symmetrical walking and running strides were included in the data set. Following Schmitt et al. (2006), symmetrical strides were recognized when touchdowns within a forelimb or hind limb pair were separated by 50
10% of stride duration. Speed Average locomotor speed was calculated from the displacement of the hip or shoulder marker, depending on which marker was visible for the greatest number of frames. To adjust for size-related speed differences across the sample, Froude number (Alexander and Jayes, 1983; Hof, 1996) was calculated as u(gh)2, where u is velocity, g is gravitational acceleration (9.81 m s2), and h is the cube root of body mass. Note that this formula actually yields the square root of the Froude number as originally introduced by Alexander and Jayes (1983). However, both forms of the Froude number are dimensionless ratios that effectively adjust for body size effects on locomotor speed (Hof, 1996; Biewener, 2003). The cube root of body mass was chosen as the

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“height” parameter in the Froude number formula in order to maximize sample sizes. However, Froude numbers calculated using the cube root of body mass were highly correlated with those calculated using other common parameters for the height parameter, such as hind limb length (r ¼ 0.998, p < 0.001) or hip height at mid-support (r ¼ 0.997, p < 0.001). Acceleration As first established by the pioneering theoretical work of Gray (1944), and later empirically confirmed by Lee et al. (1999), acceleration imparts pitching moments about the COM in a moving quadruped, thereby altering reaction forces at the feet and confounding estimates of limb force distribution. Most studies of primate locomotor kinetics have attempted to control for the confounding effects of acceleration by filtering datasets to include only strides where the animals were estimated to be traveling at a constant speed (i.e., steady-state locomotion). Rather than truncating the available data, this study takes the approach of explicitly including acceleration as an explanatory variable. Instantaneous fore-aft acceleration was calculated from kinematic data as:

Axi ¼

xiþ1  2xi þ xi1 Dt 2

where xi, xi-1 and xiþ1 represent, respectively, the x-position of the shoulder/hip marker in frame i and in the immediately preceding and subsequent frames, and Dt represents the inter-frame duration (i.e., 4 ms) (Winter, 2005). Kinematic, rather than kinetic, data were used to calculate accelerations in order to maximize sample size, as only a small subset of trials had kinetic data over an entire locomotor stride. Mean fore-aft acceleration (i.e., net change in fore-aft velocity per second of stride duration) was calculated as the integral of instantaneous acceleration divided by stride duration (Lee et al., 1999). Mean acceleration was made dimensionless by scaling it to gravitational acceleration (9.81 m s2) (Hof, 1996; Lee et al., 1999). Peak vertical limb forces and Vpk ratios Peak vertical forelimb and hind limb forces were defined as the maximum vertical force exerted during periods of single-limb contact, normalized to body weight. Following Demes et al. (1994) and subsequent authors (Schmitt and Lemelin, 2002; Schmitt, 2003; Schmitt and Hanna, 2004; Schmitt and Lemelin, 2004; Schmidt, 2005; Hanna et al., 2006) the ratio of peak forelimb force to peak hind limb force, or “Vpk ratio,” was used as a metric of limb force distribution. Vpk ratios greater than one indicate that forelimb peak forces were greater; values less than one indicate that hind limb peak forces were greater; a Vpk ratio of one indicates that forelimb and hind limb forces were equal. Whereas previous studies have typically calculated Vpk ratios as the quotient of mean forelimb peak force and mean hind limb peak force across several strides, Vpk ratios in this study were calculated within strides, generating a distribution of Vpk ratios for each individual across ontogeny. Whole-body COM position COM position was measured using the reaction board method (Ozkaya and Nordin, 1999; Lammers et al., 2006; Larson and Demes, 2011). In this procedure, a rigid lightweight board, in this case a piece of honeycomb fiberboard, is supported by two nails resting on a platform at one end, and a single nail resting on a scale of equivalent height at the other. The scale is zeroed and the anesthetized animal is placed on its side on the board such that the animal’s craniocaudal axis is parallel to the board’s long axis. Because this system is in mechanical equilibrium, all torques around a given point must cancel out. Therefore, taking the torques around the two-nail pivot,

Mb $xCOM ¼ Rscl $Lbrd where Mb is body mass, xCOM is the craniocaudal position of the COM (relative to two-nail pivot), Rscl is reaction force measured by the scale, and Lbrd is the length of the board between the two supports. Rearranging this equation to solve for xCOM:

xCOM ¼

Rscl Lbrd Mb

Thus, by taking an overhead photo of animal on the board, xCOM can be related to the position of animal’s shoulders and hips and expressed as a percentage of craniocaudal trunk length. Due to possible dangers of repetitively anesthetizing infant and juvenile animals, longitudinal data on COM position in the squirrel monkey sample used in the locomotor experiments were not available. Rather, COM position was measured in a cross-sectional sample of 25 female S. boliviensis individuals taken from the same breeding colony as the locomotor sample. The cross-sectional COM sample completely encompassed the longitudinal locomotor sample in both age and size (age range in the COM sample: 51 days to 8.1 years; body mass range in COM sample: 195e891 g). In order to keep the duration of anesthesia brief, no attempt was made to investigate the effects of varying limb position on whole-body COM position. Rather, all monkeys were placed on the board in a neutral position, with the fore- and hind limbs below their respective girdles and the elbow/knees flexed to approximately 90 . Although this procedure likely underestimates the true variability of wholebody COM position during locomotion, such intra-stride variability is likely minor compared to the ontogenetic variability that was of primary interest in the current study. For example, in a recent study of the relationship between COM position and locomotor kinetics in capuchin monkeys and spider monkeys, Larson and Demes (2011) found that limb movements affected whole-body COM position by no more than 2e3% of trunk length. Moreover, due to the outof-phase movements of contralateral limbs, limb movement per se likely has little effect on whole-body COM position during symmetrical walking and running (Larson and Demes, 2011). Morphometric data from the cross-sectional COM sample were entered into a least-squares multiple regression in which logtransformed COM position was modeled as a function of logtransformed age, body mass, arm length, forearm length, thigh length, and leg length (R2 ¼ 0.81, F[6,18] ¼ 12.6, p < 0.001). Regression coefficients from this model were then used to predict COM position in the longitudinal locomotor sample. Joint kinematics Sagittal plane limb and joint angles were calculated from the digitized video data. Previous studies have calculated average forelimb and hind limb angles, necessary for evaluating the COM Position model, as the midpoint of limb angles at touchdown and liftoff (Raichlen et al., 2009; Larson and Demes, 2011). This convention assumes that limb angular velocity is constant (i.e., zero net angular acceleration during support phase). However, in the current dataset, limb retraction velocity was not constant, but rather peaked during early support phase and tapered towards liftoff (Fig. 2). Therefore, net limb angular acceleration was significantly positive on average (FL ground: 1712
651.1 /s2; FL pole: 7460
770.5 /s2; HL ground: 1274
305.5 /s2; HL pole 6493
1334.2 /s2). In other words, squirrel monkeys tended to retract their limbs more slowly as they approached liftoff, biasing average limb position towards more caudal locations. Average forelimb and hind limb positions were therefore calculated as the arithmetic mean of segmental angles across the entire step. Average limb angles were only calculated when kinematic data were available for >90% of step duration.

0

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FL Angular Velocity (deg/s)

J.W. Young / Journal of Human Evolution 62 (2012) 473e485

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477

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Figure 2. Instantaneous angular velocity of the forelimb (a) and the hind limb (b) during support phase. Values for ground locomotion and pole locomotion are illustrated by solid and dashed lines, respectively. Gray lines and shading indicate 95% confidence bands around mean values.

In order to evaluate the predictions of the Limb Compliance model (Schmitt, 1998, 1999; Schmitt and Hanna, 2004), net shoulder and hip amplitude were also calculated as a measure of limb stiffness. Shoulder and hip amplitudes were normalized to anatomical forelimb and hind limb length, respectively, to adjust for ontogenetic changes in overall size. Forelimb and hind limb “compliance” was then computed as the reciprocal of normalized shoulder and hip amplitudes, such that lower amplitudes equate with greater compliance. Predicted hind limb retractor moment at the hip According to the Active Weight Shift model, primates actively shift body weight off of the forelimbs, and onto the hind limbs, by pitching the trunk via the selective activation of hind limb retractor muscles during early support phase. Reynolds (1985a) showed that, provided that the limb is in mechanical equilibrium, the magnitude of the muscle moment about the hip that causes the trunk to pitch upwards is equal to the product of the “Horizontal Lever Effect” (i.e., HLE e the vector difference between the measured fore-aft SRF and the horizontal forces due to the limb acting as a strut) and the vertical height of the hip (see Fig. 1). Mathematically, the magnitude of the hip retractor muscle moment at peak vertical hind limb force can be calculated as:

  yhip $ SRFFA  HLVpk $sin ðaHL Þ where yhip is the vertical height of the hip, SRFFA is the magnitude of the fore-aft SRF, HLVpk is peak vertical hind limb force, and aHL is the hind limb angle (note that the product of the last two terms is equal to the “Horizontal Strut Effect”). Hind limb retractor moments were divided by body mass to adjust for ontogenetic differences in overall body size (Witte et al., 2002; Moisio et al., 2003; Young, 2009a).

Analytical procedure Because body mass was linearly related to age in all individuals (Young, 2009a), body mass, rather than chronological age, was used as the primary independent variable in all ontogenetic analyses. Moreover, as a result of the precocial nature of squirrel monkey behavioral development (Elias, 1977; Kaack et al., 1979; Boinski and Fragaszy, 1989; Fragaszy et al., 1991; Hartwig, 1995; Young, 2009a), size should have a stronger effect on locomotor mechanics than age per se (Schilling, 2005).

Multiple linear regression analyses were used to test for associations between limb loading, body mass, and any of the predictor variables specified by the three mechanical models, while controlling for Froude number. When the dependent variable was peak limb force, Vpk ratio, or hind limb retractor moment magnitude, mean acceleration was included as a predictor variable in the model. In cases where substrate differences were of interest, for instance when comparing shoulder and hip compliance during locomotion on the ground and the pole (Schmitt, 1998, 1999; Schmitt and Hanna, 2004), substrate type was also included in the model as a categorical variable. In order to make the magnitudes of partial regression coefficients more interpretable across comparisons, all variables were transformed to z-scores prior to analysis, generating standardized partial regression coefficients in the final models. Two sets of tests were performed for each regression model. First tested was whether the predictor variable in question significantly changed with body mass, controlling for Froude number, acceleration, and substrate type as necessary. Second tested was whether the predictor variable was significantly related to either force magnitudes or limb force distribution in the direction predicted by the model. A mixed-effects approach was adopted when fitting all linear regression models (Pinheiro and Bates, 2000; Young et al., 2010), permitting 1) degrees of freedom to be adjusted to account for random variation among individuals and among experimental dates within individuals, and 2) error terms to be adjusted to account for the pseudoreplication that arises from repeatedly measuring the same individuals longitudinally. A likelihood-ratio reformulation of the standard coefficient of determination (i.e., R2) was used to evaluate model fit:

2 R2 ¼  ðlog LUM  log LRM Þ N where N is the number of observations in the sample, log LUM is the log-likelihood of the full model, and log LRM is the log-likelihood of the intercept-only model (Magee, 1990). This formulation of R2 basically quantifies the explanatory power of a given model relative to a null model without predictors. Finally, in order to protect overall error rates from inflation due to multiple comparisons, pvalues from associated sets of statistical tests were adjusted using the Sequential Bonferroni Method (Rice, 1989). All statistical analyses were performed using the R statistical platform (R Development Core Team 2011), supplemented by the nlme package to fit mixed-effects regression models (Pinheiro and Bates, 2000; Pinheiro et al., 2011).

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Results A total of 338 symmetrical strides were analyzed, including 113 strides on the ground and 225 on the 3.2 cm pole.

0.01
0.007, Pole mean
95% CI: 0.02
0.019; Fig. 3c and d). Relative mean acceleration was unrelated to body mass across substrates (all p  0.58). Overall, relative mean acceleration was significantly greater on the ground than on the pole (ANOVA: F[1,63] ¼ 11.0, p ¼ 0.002; Fig. 3c and d).

Froude number and relative mean acceleration Overall patterns of limb force distribution Froude numbers ranged from 0.45 to 2.5 when squirrel monkeys were moving on the ground and 0.42 to 2.8 when squirrel monkeys were moving on the pole (Fig. 3a and b). Froude number was unrelated to body mass during ground locomotion (r ¼ 0.02, p ¼ 0.85), but negatively correlated with body mass during pole locomotion (r ¼ 0.38, p ¼ 0.02), indicating that older and larger monkeys moved at significantly slower relative speeds. Overall, squirrel monkeys moved faster on the pole than on the ground (ANOVA: F[1,67] ¼ 16.8, p < 0.001; Fig. 3a and b), perhaps as a dynamic means of increasing mediolateral stability on narrow substrates (Bruijn et al., 2009; Schmidt and Fischer, 2010). Relative mean acceleration ranged from 0.06 to 0.22 when squirrel monkeys were moving on the ground and 0.25 to 0.15 when squirrel monkeys were moving on the pole (Fig. 3c and d). On average, however, locomotion remained near steady-state on both substrates (i.e., zero acceleration, Ground mean
95% CI:

35 %

Results from mixed-effects multiple regression analyses of peak force data on Froude number and body mass are presented in Table 1. Peak fore- and hind limb vertical forces increased with Froude number across substrates and limbs, as evidenced by significantly positive regression coefficients (Table 1). Peak vertical forelimb forces, however, increased with Froude number at a greater rate than peak vertical hind limbs forces, resulting in positive association between Froude number and Vpk ratio. The effects of acceleration on peak vertical forces differed between foreand hind limbs. Peak vertical forelimb forces decreased with acceleration whereas peak vertical hind limb forces increased. As a result, Vpk ratios declined with increasing acceleration (although the trend did not reach significance during ground locomotion). These data are consistent with previous theoretical and empirical results (Gray, 1944; Lee et al., 1999) showing that acceleration

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Figure 3. Distributions of Froude numbers (a, b) and mean accelerations (c, d) achieved by growing squirrel monkeys during locomotion on the ground (white bars) and the pole (shaded bars).

J.W. Young / Journal of Human Evolution 62 (2012) 473e485 Table 1 Linear mixed-effect regression modeling of overall patterns of limb force distribution in the ontogenetic squirrel monkey sample.a

bb

DF

F ratio

p-value

Sig.c

Forelimb Vpk: Ground Body mass Froude number 0.81 Net acceleration

0.233 0.836 0.350

1, 27 1, 58 1, 58

26.7 263.6 18.9

<0.001 <0.001 <0.001

*** *** ***

Forelimb Vpk: Pole Body mass Froude number Net acceleration

0.179 0.803 0.061

1, 29 1, 148 1, 148

10.7 341.4 7.4

0.003 <0.001 0.008

* ** *

Regression model

R2

0.70

Hind limb Vpk: Ground Body mass Froude number 0.38 Net acceleration

0.429 0.492 0.457

1, 27 1, 47 1, 47

14.2 17.0 9.5

<0.001 <0.001 0.003

** *** *

Hind limb Vpk: Pole Body mass Froude number Net acceleration

0.31

0.425 0.560 0.096

1, 22 1, 137 1, 137

15.1 37.7 6.2

<0.001 <0.001 0.018

** *** *

0.54

0.486 0.666 0.221

1, 25 1, 40 1, 40

20.4 49.5 3.0

<0.001 <0.001 0.090

*** *** NS

0.33

0.476 0.452 0.123

1, 22 1, 130 1, 130

48.4 36.3 8.3

<0.001 <0.001 0.005

*** *** *

Vpk ratio: Ground Body mass Froude number Net acceleration Vpk ratio: Pole Body mass Froude number Net acceleration

a Models are grouped by row, with the dependent variable indicated in italics at the top of each group and the independent variables grouped beneath. b b represents the standardized partial regression coefficients. c Indicates significance following Sequential Bonferroni correction for multiple comparisons: NS not significant; * p < 0.05; ** p < 0.01; *** p < 0.001.

imparts pitching moments to the trunk of a moving quadruped, thereby altering weight distribution and relative force magnitudes at the feet. As documented previously (Young, 2009a), across substrates, peak vertical forelimb forces decreased with size during growth, whereas peak vertical hind limb forces increased. Divergent size-related changes in forelimb and hind limb peak vertical forces resulted in significant declines in Vpk ratio as body mass increased ontogenetically, regardless of substrate (Fig. 4).

Ground Pole

Average Vpk Ratio

1.5

1.0

0.5

0.0 225 grams

325 grams

425 grams

525 grams

Adult Males (950 grams)

Figure 4. Ontogenetic changes in average Vpk ratios in growing squirrel monkeys. Vpk ratios greater than one indicate that peak vertical forelimb forces are greater, Vpk ratios less than one indicate that peak vertical hind limb forces are greater, and a Vpk ratio equal to one indicates equivalent fore- and hind limb peak vertical forces. Bars represent fitted values from mixed-effects multiple regressions of Vpk ratio against body mass, controlling for Froude number and mean acceleration (Table 1). Ground locomotion and pole locomotion are indicated by white and shaded bars, respectively. Vpk ratios for adult male squirrel monkeys were taken from Schmidt (2005).

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COM Position model According to the COM Position model, the horizontal distances between the COM and hands and feet determine the distribution of vertical impulse and peak vertical forces between the limbs. On this model, the caudal shift in limb force distribution observed in the ontogenetic squirrel monkey sample could arise from a caudal shift in COM position, a cranial shift in average hand and foot position, or a combination of these strategies. Whole-body COM position in the cross-sectional morphological sample moved caudally during growth, shifting from approximately 43% of trunk length (from the shoulders to the hips) at the smallest body size to approximately 62% of trunk length at the largest body size (note significant regressions of COM position on body mass in Table 2 and Fig. 5). Predicted COM position similarly moved from 47 to 58% of trunk length over the smaller size range of the longitudinal locomotor sample (Table 2; Fig. 5). On both substrates, Vpk ratios significantly decreased as COM position moved caudally over development (note significantly negative regressions in Table 2), in accordance with the predictions of the COM Position model. Average forelimb and hind limb angles were highly variable across growth (note the low R2 values in Table 2). As such, aside from the tendency for older and larger monkeys to place their forelimbs in more protracted positions during pole locomotion, there were no significant directional changes in average limb position over development. Active weight shift model Reynolds (1985a) argued that passive COM position is insufficient to explain primates’ unusual pattern of body weight support Table 2 Linear mixed-effect regression models evaluating the COM Position model in the ontogenetic squirrel monkey sample.a F ratio

p-value

Sig.b

0.800

1, 23

40.94

<0.001

***

0.65

0.992

1, 64

262.7

<0.001

***

Vpk ratio on Predicted COM position: Ground Predicted COM position 0.389 1, 22 Froude number 0.45 0.722 1, 38 Mean acceleration 0.227 1, 38

13.1 50.8 2.9

0.002 <0.001 0.100

* *** NS

Vpk ratio on Predicted COM position: Pole Predicted COM position 0.384 Froude number 0.30 0.497 Mean acceleration 0.153

1, 22 1, 130 1, 130

14.2 42.6 12.0

0.001 <0.001 <0.001

* *** *

Average forelimb angle: Ground Body mass Froude number 0.16

0.706 0.323

1, 26 1, 64

4.2 22.2

0.052 <0.001

NS ***

Average forelimb angle: Pole Body mass Froude number 0.06

0.326 0.278

1, 27 1, 152

11.7 11.1

0.002 0.001

* *

Average hind limb angle: Ground Body mass Froude number 0.02

0.442 0.106

1, 26 1, 69

2.4 1.5

0.136 0.222

NS NS

Average hind limb angle: Pole Body mass Froude number 0.15

0.135 0.433

1, 30 1, 157

1.5 32.6

0.223 <0.001

NS ***

Measured COM position on massc Predicted COM position on massd

R2

b

0.64

Regression model

DF

a Models are grouped by row, with the dependent variable indicated in italics at the top of each group and the independent variables grouped beneath. b Indicates significance following Sequential Bonferroni correction for multiple comparisons: NS not significant; * p < 0.05; ** p < 0.01; *** p < 0.001. c Data from the cross-sectional sample. Model fit using ordinary least-squares regression. d Data from the longitudinal locomotor sample.

J.W. Young / Journal of Human Evolution 62 (2012) 473e485

COM position (% CC trunk length)

480

40%

decreasing Vpk ratios on both substrates (note significantly negative regressions in Table 3). A common critique of Reynolds’s (1985a) model is that, in addition to pitching the trunk up, greater activation of hind limb retractors has the potential to increase the propulsive impulse of the limb pushing against the ground, causing the animal to accelerate out of steady-state locomotion (e.g., Raichlen et al., 2009). As discussed above, acceleration has the capacity to alter fore- and hind limb forces by imparting pitching moments about an animal’s COM, thereby biasing estimates of limb force distribution (Gray, 1944; Lee et al., 1999). In support of this critique of the model, mean acceleration increased with increasing hind limb retractor moments on both substrates, though the relationship was only significant during pole locomotion (note regression results in Table 3).

Measured Position Predicted Position

45%

50%

55% 60% 65%

200

400

600

Limb compliance model

800

Body mass (g) Figure 5. Ontogenetic changes in whole-body COM position in growing squirrel monkeys. COM position is expressed as a percentage of craniocaudal trunk length from the shoulders to the hips, such that values less than 50% indicate that the COM is closer to the shoulders and values greater than 50% indicate that the COM is closer to the hips. Large darkly shaded circles represent values measured in the cross-sectional morphological sample, whereas smaller lightly shaded circles represent predicted values for the longitudinal locomotor sample (see text for methodological details). Data are plotted on logarithmic axes.

and limb force distribution. Rather, his Active Weight Shift model posits that primates use hind limb retractor muscles to pitch the trunk upwards, thereby shifting body weight support from the forelimbs to the hind limbs (Fig. 1). On both substrates, normalized hind limb retractor moments at peak vertical hind limb force significantly increased with body mass during development (note significantly positive regressions in Table 3). As predicted by the Active Weight Shift model, increases in normalized hind limb retractor moments were associated with

Table 3 Linear mixed-effect regression models evaluating the Active Weight Shift model in the ontogenetic squirrel monkey sample.a Regression model

R2

b

Normalized HL retractor moment: Ground Body mass 0.704 Froude number 0.36 0.506 Mean acceleration 0.611 Normalized HL retractor moment: Pole Body mass 0.500 Froude number 0.16 0.131 Mean acceleration 0.201

F ratio

p-value

Sig.b

1, 15 1, 17 1, 17

13.8 6.0 3.2

0.002 0.025 0.093

* NS NS

1, 19 1, 62 1, 62

10.4 0.9 8.0

0.008 0.454 0.006

* NS *

0.007

*

0.005 0.229

* NS

25.7

<0.001

***

10.3 3.6

0.002 0.062

* NS

DF

Vpk ratio on normalized HL retractor moment: Ground Hind limb retractor 0.244 1, 14 10.2 moment Froude number 0.49 0.411 1, 14 10.8 Mean acceleration 0.230 1, 14 1.6 Vpk ratio on normalized HL retractor moment: Pole Hind limb retractor 0.334 1, 60 moment Froude number 0.38 0.312 1, 60 Mean acceleration 0.091 1, 60

a Models are grouped by row, with the dependent variable indicated in italics at the top of each group and the independent variables grouped beneath. b Indicates significance following Sequential Bonferroni correction for multiple comparisons: NS not significant; * p < 0.05; ** p < 0.01; *** p < 0.001.

The Limb Compliance model predicts that greater use of compliant limb kinematics, quantified here as the inverse of normalized shoulder and hip amplitude during support phase, has the potential to mitigate peak vertical forces and alter force distribution between the limbs. Specifically, increases in forelimb compliance relative to hind limb compliance should be associated with lower Vpk ratios. To evaluate these predictions, data are presented below on 1) size-related changes in forelimb compliance and hind limb compliance, and 2) associations between each of these parameters and either peak limb forces or Vpk ratios during growth. Regardless of substrate, forelimb compliance significantly increased with size over development, indicating that squirrel monkeys adopted a more compliant gait as they grew older and larger (note significantly positive regression of forelimb compliance on body mass in Table 4). In contrast, hind limb compliance did not significantly vary with body mass during ontogeny (note regression results in Table 4). These data are consistent with the results of a previous study of this sample, showing that squirrel monkeys use significantly more flexed elbow postures as they mature, whereas knee angles do not vary with body size (Young, 2009a). Nevertheless, despite divergent ontogenetic trends, both forelimb and hind limb compliance were significantly greater on the pole than on the ground (ANCOVA controlling for Froude number and body mass; note significantly positive substrate effect for both forelimb and hind limb compliance in Table 4), replicating Schmitt et al.’s earlier findings that primates adopt a more compliant gait during locomotion on narrow substrates (Schmitt, 1998, 1999; Schmitt and Hanna, 2004). Increasing forelimb compliance was associated with decreased peak vertical forelimb forces on both substrates (although the relationship was not significant during pole locomotion after adjusting p-values to control experiment-wise error rates; see Table 4), replicating Schmitt’s previous findings (Schmitt, 1998, 1999). In contrast, peak vertical hind limb forces were not related to hind limb compliance on either substrate (note regression results in Table 4) although this could reflect the lack of variability in normalized hip amplitude over development. Despite significant increases in forelimb compliance relative to hind limb compliance during ontogeny, and a significant relationship between increasing forelimb compliance and decreased peak vertical forelimb forces, after p-values were adjusted to control experiment-wise error rates, Vpk ratios were not significantly related to shoulder/hip compliance ratios on either substrate, belying the expectations of the Limb Compliance model of limb force distribution.

J.W. Young / Journal of Human Evolution 62 (2012) 473e485 Table 4 Linear mixed-effect regression models evaluating the Limb Compliance model in the ontogenetic squirrel monkey sample.a

b

DF

Normalized forelimb compliance Body mass Froude number 0.08 Substrate

0.443 0.205 0.691

Normalized hind limb compliance Body mass Froude number 0.04 Substrate

0.173 0.165 0.900

Regression model

R2

F ratio

p-value

Sig.b

1, 50 1, 178 1, 50

21.6 7.7 16.4

<0.001 0.006 <0.001

*** NS ***

1, 51 1, 181 1, 51

2.1 2.9 16.9

0.157 0.092 <0.001

NS NS ***

<0.001

***

<0.001 <0.001

*** ***

0.018

NS

<0.001 0.028

*** NS

0.673

NS

<0.001 0.465

* NS

0.481

NS

<0.001 0.019

*** NS

0.011

NS

<0.001 0.098

*** NS

0.6

0.455

NS

36.0 9.4

<0.001 0.003

*** *

Forelimb Vpk on normalized forelimb compliance: Ground Normalized forelimb 0.130 1, 52 14.7 compliance Froude number 0.82 0.767 1, 52 224.0 Mean acceleration 0.417 1, 52 29.8 Forelimb Vpk on normalized forelimb compliance: Pole Normalized forelimb 0.097 1, 126 5.8 compliance Froude number 0.68 0.811 1, 126 311.6 Mean acceleration 0.051 1, 126 4.9 Hind limb Vpk on normalized hind limb compliance: Ground Normalized hind limb 0.046 1, 41 0.2 compliance Froude number 0.18 0.438 1, 41 14.0 Mean acceleration 0.116 1, 41 0.5 Hind limb Vpk on normalized hind limb compliance: Pole Normalized hind limb 0.031 1, 120 0.5 compliance Froude number 0.18 0.602 1, 120 32.8 Mean acceleration 0.094 1, 120 5.7 Vpk ratio on forelimb/hind limb compliance ratio: Ground Shoulder/hip compliance 0.198 1, 34 7.2 ratio Froude number 0.50 0.660 1, 34 61.1 Mean acceleration 0.209 1, 34 2.9 Vpk ratio on forelimb/hind limb compliance ratio: Pole Shoulder/hip compliance 0.039 1, 109 ratio Froude number 0.23 0.497 1, 109 Mean acceleration 0.147 1, 109

a Models are grouped by row, with the dependent variable indicated in italics at the top of each group and the independent variables grouped beneath. b Indicates significance following Sequential Bonferroni correction for multiple comparisons: NS not significant; * p < 0.05; ** p < 0.01; *** p < 0.001.

Discussion Vpk ratios in growing squirrel monkeys significantly declined over the first 10 months of life (Fig. 4), indicating that the monkeys transitioned from forelimb dominant infants to hind limb dominant juveniles and adults (Schmidt, 2005). Across gaits and substrates, declining Vpk ratios resulted from decreases in forelimb peak vertical forces alongside concomitant increases in hind limb peak vertical forces. This study tested the power of three previously developed models of primate hind limb dominance e the COM Position model, the Active Weight Shift model, and Limb Compliance model e to explain the observed ontogenetic changes in limb force distribution. Each of these models makes specific, though not mutually exclusive, predictions about the proximate biomechanical strategies primates use to achieve hind limb dominance in limb force distribution. Are ontogenetic changes in limb force distribution determined by COM position? The COM Position model predicts that limb force distribution varies as a function of the horizontal distance between the COM

481

vector (i.e., the center of gravity) and the center of pressure of the hands and feet (Gray, 1944; Rollinson and Martin, 1981; Raichlen et al., 2009). According to this model, any shift in morphology or kinematics that decreases the average distance between the feet and COM or increases in the average distance between the hands and the COM has the potential to redistribute body weight and peak forces from the forelimbs to the hind limbs. Previous studies of adult individuals have shown that natural and experimental variation in relative COM position significantly affects limb force distribution in primates and other mammals, often in the direction predicted by the COM Position model. For instance, quadrupeds who naturally vary in the craniocaudal position of the COM, such as different breeds of domestic dog (Lee et al., 1999; Bertram et al., 2000) or fat-tailed dwarf lemurs undergoing seasonal variation in tail mass associated with torpor (Lemelin and Schmitt, 2004), show increased hind limb loading with more caudal COM positions. Experimental studies in which the position of the COM relative to the hands and feet was experimentally translated by means of external weights or locomotion on angled substrates have shown similar results (Lee et al., 2004; Lammers et al., 2006; Young et al., 2007; Lee, 2011). Finally, in a direct test of the COM Position model, Raichlen et al. (2009) found that the average position of the hands and feet relative to the COM accurately predicted patterns of body weight support in walking chimpanzees. In the same study, Raichlen et al. (2009) also reviewed evidence showing that primates, as an order, tend to show more protracted hind limb positions and less retracted forelimb positions than other quadrupedal mammals. These data suggest primates tend to place their hind limbs closer to the COM than their forelimbs, exacerbating any influence of a relatively posterior COM position on increased hind limb loading. However, more recent studies by Larson et al. (Larson and Stern, 2009; Larson and Demes 2011) have shown that 1) COM position relative to the hands and feet fails to predict patterns of weight distribution in capuchin and spider monkeys, 2) on average, most primates maintain neutral forelimb and hind limb postures during support phase (i.e., neither excessively protracted nor retracted), and 3) with the possible exception of the great apes, limb positions relative to the COM appear to be uncorrelated with patterns of fore/ hind weight support. Larson and Demes (2011) argue that, altogether, these results suggest that different primate radiations may use divergent strategies to achieve hind limb dominance in weight support. Specifically, they suggest that whereas passive COM position may, at least partially, explain fore/hind force distribution in the great apes, some additional “active” mechanism of body weight distribution is required to account for hind limb dominance in other primate clades. Nevertheless, despite the ambiguous relationship between COM position and patterns of fore/hind loading across primates, declining Vpk ratios during squirrel monkey ontogeny were coincident with a caudal translation of the estimated position of the whole-body COM, which moved from 47% of shoulder-to-hip trunk length among the youngest and smallest monkeys in the longitudinal locomotor sample to 58% of trunk length among the oldest and largest monkeys (Fig. 5). These results should be interpreted with some caution, as 1) direct measurements of COM position in the individuals used in the locomotor experiments were not available, and 2) estimates of COM position did not incorporate the dynamic effects of limb movements on instantaneous COM position during locomotion. Nevertheless, the overall finding that COM position moves caudally during growth is buoyed by the results of previous studies showing that similar caudal shifts in whole-body COM occur in growing rhesus macaques (Grand, 1977, 1983; Turnquist and Wells, 1994), yellow

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J.W. Young / Journal of Human Evolution 62 (2012) 473e485

baboons (Raichlen, 2004), humans (Wells et al., 2002), and dogs (Biknevicius et al., 1997). During locomotion on the pole, squirrel monkeys also placed their forelimbs in more cranial average positions as they grew older and larger. Placing the forelimbs in a more cranial position would exacerbate the effects of the caudal translation in COM position, further increasing the relative distance between the COM and forelimbs, thereby increasing the relative vertical forces on the hind limbs. In short, the current study provided general support for the argument that whole-body COM position is related to patterns of fore/hind limb loading in the manner predicted by the COM Position model. Are ontogenetic changes in limb force distribution determined by active weight shift? Reynolds (1985a) argued that primates actively redistribute body weight to the hind limbs by pitching the trunk dorsally via the activation of hind limb retractor musculature during early support phase, when the hind limb is highly protracted (Fig. 1). In support of the Active Weight Shift model, the current study showed that 1) regardless of substrate, hind limb retractor moments at peak vertical hind limb force increased as squirrel monkeys aged, and 2) Vpk ratios significantly decreased with increasing hind limb retractor moments. It should be noted that the methods used in this study provide, at best, a tangential test of the Active Weight Shift model. A more complete test of the model would necessitate not only kinetic data on substrate reaction forces and kinematic data on limb posture, but electromyographic and sonomicrometric measures of hind limb retractor muscle work (e.g., Biewener, 1998), permitting a holistic test of how muscle activation affects limb force distribution. Nevertheless, when taken together, the results reported here suggest that increasing reliance on Reynolds’s (1985a) active weight shift mechanism may be at least partially responsible for the transition from forelimb dominance to hind limb dominance observed during squirrel monkey growth. Previous studies have provided mixed evidence regarding Reynolds’s (1985a) model. In support of Reynolds’ (1985a) hypothesis, Reynolds (1987) and Larson et al. (2001) found that primates exhibit pronounced degrees of hind limb protraction at touchdown, higher than any other mammalian group with the exception of marsupials. High levels of hind limb protraction at touchdown would be required to generate strut-produced braking forces of sufficient magnitude to counteract the propulsive effects of strong activation of hind limb retractor muscles. Electromyographic (EMG) studies have also presented data congruent with Reynolds’s (1985a) hypothesis. Kimura et al. (1979) and Ishida et al. (1985) found that in several species of anthropoid primates, the long head of m. biceps femoris, an important hind limb retractor, was active across the initial half of support phase during walking, as Reynolds (1985a) predicted. The long head of m. biceps femoris has also been shown to be active in orangutans (Pongo pygmaeus) during the latter half of swing phase and the first half of support phase (Stern and Susman, 1981). More recently, Larson and Stern (2009) found that hip retractor muscles were active across the first two-thirds of support phase during walking in an eclectic sample of prosimian and catarrhine primates. The great apes, which tended to show the highest levels of retractor activity, also exhibit the greatest degree hind limb dominance in force distribution (Kimura et al., 1979; Reynolds, 1985b; Demes et al., 1994). However, recent biomechanical theory and data challenge Reynolds’s (1985a) hypothesis. As discussed above, in addition to pitching the trunk up, greater activation of hind limb retractors has the potential to increase the propulsive impulse of the limb pushing against the ground, causing the animal to accelerate. Reynolds

(1985a) argued that if the hind limb were sufficiently protracted, the braking impulse resulting from the limb functioning as a cranially-displaced strut should sufficiently negate the propulsive impulse resulting from the limb functioning as a lever, thus ensuring that the net horizontal impulse was low and that the animal maintains a steady rate of speed. Nevertheless, according to Reynolds’s (1985a) own calculations, net propulsive impulse across the stride would never sum to zero e even if the hind limb were highly protracted at the moment of peak force (Raichlen et al., 2009). Therefore, locomotion could not be strictly steady-state and measures of limb force distribution would be confounded by unbalanced pitching torques around the COM (Gray, 1944; Lee et al., 1999). Indeed, the current results illustrated that increased hind limb retractor moments were associated with increased acceleration on both substrates (though significantly so only during pole locomotion). These data suggest that Reynolds’s (1985a) contention that strut-produced braking impulses are sufficient to negate leverproduced propulsive forces may not be correct. Nevertheless, multiple force plate records of individual limb force production during a stride (e.g., Bertram et al., 1997; Lee et al., 1999, 2004) would be required to fully evaluate such relationships. A second critique of Reynolds’s (1985a) model is that, as noted by Li (2000), retractor musculature may be required to contract isometrically, or even perform negative work, in order to keep the protracted hind limb from collapsing into flexion during early support phase under the weight of the body, particularly if body weight is being primarily supported by the hind limbs. Therefore, EMG and mechanical evidence that hind limb retractor muscles are active during early support phase is difficult to functionally interpret without concurrent data on changes in retractor muscle fascicle lengths. Finally, Reynolds’s (1985a) mechanism requires that fore- and hind limbs support phases substantially overlap, permitting sufficient time for the requisite redistribution of forces between limb pairs. For this reason, the Active Weight Shift model is most applicable to limb force distribution during walking. Primates, however, tend to generate greater peak vertical forces on the hind limbs across all gaits, including gaits with little or no overlap between fore- and hind limb support phases, such as ambling (i.e., “grounded running”: Wallace and Demes, 2008) and galloping (Kimura, 1992; Demes et al., 1994; Hanna et al., 2006). Are ontogenetic changes in limb force distribution determined by limb compliance? According to the Limb Compliance model (Schmitt and Hanna, 2004), an ontogenetic transition to greater hind limb dominance in limb force distribution should result from increased forelimb compliance, decreased hind limb compliance, or a combination of these strategies. The results of this study showed that squirrel monkeys increased levels of forelimb compliance and maintained levels of hind limb compliance as they grew. Moreover, greater levels of forelimb compliance were associated with lower forelimb peak vertical forces replicating previous research by Schmitt (1998, 1999). Nevertheless, after pvalues were adjusted to control experiment-wise error rates, the ratio of forelimb compliance to hind limb compliance was not significantly associated with Vpk ratios on either substrate, belying the predictions of the Limb Compliance model. However, the current study did support Schmitt’s (1998, 1999) contention that primates should increase the use of compliant gait mechanics on narrow substrates. Aside from Schmitt and Hanna’s (2004) original paper, in which the authors presented data showing that many primates decrease both Vpk ratios and increase forelimb and hind limb compliance when transitioning from ground locomotion to pole locomotion, no

J.W. Young / Journal of Human Evolution 62 (2012) 473e485

previous study has explicitly tested the predictions of the Limb Compliance model. In tangential support of the model, Larney and Larson (2004) found that primates exhibit substantially more limb compliance than most other mammals, particularly in the forelimb. How varying degrees of forelimb and hind limb compliance are related to patterns of limb force distribution across primates and other mammals remains to be tested. Ontogeny of limb force distribution in other animals Although the current study is the first to examine the ontogeny of limb force distribution in a detailed biomechanical context, previous work by Kimura (1987; 2000) and Biknevicius et al. (1997) corroborates some of the findings presented here. Kimura (1987, 2000) examined the ontogeny of vertical force distribution in chimpanzees and Japanese macaques. The typical primate pattern of hind limb dominance during locomotion was evident in chimpanzees throughout development and in macaques from three months of age onwards. Prior to this age, infant macaques distributed vertical peak forces equally between the forelimbs and hind limbs. Interestingly, during the first year of life, standing chimpanzees supported more body weight on their forelimbs than their hind limbs. Kimura (1987) argued that the ontogenetic change in static body weight support resulted from decreasing relative head mass in the growing chimpanzees and a corresponding caudal shift in COM position. The finding that infant chimpanzees are forelimb dominant when standing but hind limb dominant when walking implies that chimpanzees must use a dynamic mechanism to redistribute forces between then hands and feet during locomotion, reinforcing the notion that primates may be using a range of biomechanical strategies to achieve hind limb dominance (Larson and Demes, 2011). Previous research has also shown that ontogenetic changes in limb force distribution are not limited to primates. In a longitudinal study of growing domestic dogs, Biknevicius et al. (1997) found that relative forelimb peak vertical forces remained static across growth whereas relative hind limb peak vertical forces significantly increased with body mass, a difference the authors attributed to developmental changes in body composition and corresponding whole-body COM translation.

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position and hind limb retractor moment magnitudes were the most robust predictors of ontogenetic changes in limb force distribution across substrates. Overall, the results of this study suggest that primates may use a variety of biomechanical strategies to achieve hind limb dominance in limb force distribution (see also Larson and Demes, 2011). It should be stressed that the current results are strictly valid only in the context of ontogenetic changes in squirrel monkey limb force distribution. Nevertheless, the use of locomotor ontogeny as a model system to investigate functional models of animal performance offers many advantages over the more common interspecific comparisons of adult animals (Hurov, 1991; Raichlen, 2005; Shapiro and Raichlen, 2005, 2006; Young, 2009b). In a developing animal, somatic growth can be explicitly associated with changes in performance, permitting a tightly-controlled test of form-function links that are free from the sampling error typically engendered by comparing multiple individuals, let alone multiple taxonomic groups. In the context of this study, detailed morphological, kinematic, and kinetic measurements, combined with the mixed-effects modeling approach, allowed an examination of the mechanical bases for ontogenetic variation in limb force distribution at an intraindividual level. The ability of each of the proposed mechanical models to explain such changes can, by analogy, inform our understanding of the likely mechanical bases for hind limb dominance across primates. Future research should continue to examine the ontogeny of locomotor kinetics in other primates and non-primate quadrupeds. Previous research with macaques, chimpanzees, and dogs suggests that ontogenetic changes in limb force distribution may be common to many mammals (Kimura, 1987, 2000; Biknevicius et al., 1997), highlighting the potential for additional studies to provide insight into the biomechanical bases of limb force distribution. Finally, it is critical that future studies of primate locomotion move away from characterizing single-limb forces at single points in time. Holistic descriptions of impulse development across all four limbs over entire strides (e.g., Bertram et al., 1997; Lee et al., 1999, 2004), in combination with quantitative data on limb kinematics and muscle work, will be crucial to understanding how primates and other mammals dynamically adjust limb force distribution to cope with substrate properties, stability and locomotor demands.

Conclusions This study used longitudinal data on somatic growth and locomotor development in Bolivian squirrel monkeys as a model system to address the biomechanical bases of “hind limb dominance” in primate limb force distribution. Three previously developed models of primate locomotor kinetics were evaluated: the COM Position model (Gray, 1944; Raichlen et al., 2009), the Active Weight Shift model (Reynolds, 1985a), and the Limb Compliance model (Schmitt and Hanna, 2004). It should be noted that these models are not mutually exclusive. For instance, lowering the average height of the shoulders relative to the hips, as in the Limb Compliance model, has the potential to decrease the distance between the hind limbs and the wholebody COM (see also Stern, 1975), thereby increasing hind limb dominance via the mechanism predicted under the COM Position model. Results provided some support for all three models. Ontogenetic changes in COM position, hind limb retractor muscle moments, and forelimb compliance were consistent with the predictions of the COM Position model, the Active Weight Shift model, and the Limb Compliance model, respectively. Additionally, each of these factors was able to explain some of the variation in limb loading in the fashion predicted by each of the respective models, although COM

Acknowledgements This work was greatly improved by comments from Brigitte Demes, Audrone Biknevicius, William Jungers, Susan Larson, and Liza Shapiro. Comments from Mark Teaford and three anonymous reviews substantially improved the final manuscript. Liza Shapiro kindly assisted with center of mass measurements on the crosssectional squirrel monkey sample. Robert Danczak, Michael Pante, and Bartholomew White assisted with digitizing locomotor videos. Animal research was carried out at an NIH-funded National Primate Research Center, where I received generous help from many individuals, including: Bethany Brock, Heather Hyer, Leigh Ann Long, Virginia Parks, Seth Pollack, Lawrence Williams, and Cindy Van Hook. Ty Hedrick provided software for kinematic analysis (Hedrick, 2008). Brigitte Demes and Daniel Riskin assisted with force plate construction and Daniel Talley assisted with runway construction. Stephen Nash generously provided the drawing of the monkey limb used to construct Fig. 1, sparing journal readers from my egregious lack of artistic talent. Funding was provided by the L.S.B. Leakey Foundation (Grant 38648), the Interdepartmental Doctoral Program in Anthropological Sciences at Stony Brook University, and NEOMED.

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