Differences in muscle mechanics underlie divergent optimality criteria between feeding and locomotor systems

Abstract

Tetrapod musculoskeletal diversity is usually studied separately in feeding and locomotor systems. However, direct comparisons between these systems promise important insight into how natural selection deploys the same basic musculoskeletal toolkit—connective tissues, bones, nerves, and skeletal muscle—to meet the differing performance criteria of feeding and locomotion. Recent studies using this approach have proposed that the feeding system is optimized for precise application of high forces and the locomotor system is optimized for wide and rapid joint excursions for minimal energetic expenditure. If this hypothesis is correct, then it stands to reason that other anatomical and biomechanical variables within the feeding and locomotor systems should reflect these diverging functions. To test this hypothesis, we compared muscle moment arm lengths, mechanical advantages, and force vector orientations of two jaw elevator muscles (m. temporalis and m. superficial masseter), an elbow flexor (m. brachialis) and extensor (m. triceps‐ lateral head), and a knee flexor (m. biceps femoris‐short head) and extensor (m. vastus lateralis) across 18 species of primates. Our results show that muscles of the feeding system are more orthogonally oriented relative to the resistance arm (mandible) and operate at relatively large moment arms and mechanical advantages. Moreover, these variables show relatively little change across the range of jaw excursion. In contrast, the representative muscles of the locomotor system have much smaller mechanical advantages and, depending on joint position, smaller muscle moment arm lengths and almost parallel orientations relative to the resistance arm. These patterns are consistent regardless of phylogeny, body mass, locomotor mode, and feeding specialization. We argue that these findings reflect fundamental functional dichotomies between tetrapod locomotor and feeding systems. By organizing muscles in a manner such that moment arms and mechanical advantage are relatively small, the locomotor system can produce broad joint excursions and high angular velocities with only small muscular contraction. As such, the anatomical organization of muscles within the limbs allows striding animals to move relatively rapidly and with minimal energetic expenditure. In contrast, the anatomical configuration of muscles in the feeding system, at least m. superficial masseter and m. temporalis, favors their force‐producing capacity at the expense of excursion and velocity.

Muscles of the feeding system are more orthogonally oriented and operate at relatively large moment arms and mechanical advantages. In contrast, the muscles of the locomotor system have almost parallel orientations and smaller mechanical advantages and muscle moment arms. These differences suggest that the feeding system is optimized for the application of high forces, while the locomotor system is optimized for large and rapid joint excursions for minimal energetic expenditure.

1. INTRODUCTION

Evolutionary biomechanical studies of vertebrate feeding and locomotor systems have provided important insights into the ways that natural selection deploys a basic toolkit of musculoskeletal components—connective tissues, bones, nerves, and skeletal muscle—to meet a variety of performance criteria in different lineages (Wainwright, 1994; Thomason, 1997). Most of these studies have focused on explaining cross‐lineage diversity within feeding or locomotor systems, separately. For example, diversity in feeding‐system morphology has been related to variation in feeding behavior and diet in a wide range of vertebrates, including fish, birds, lizards, and mammals (Westneat, 2004; Reilly and McBrayer, 2007; Olsen, 2017), and diversity in locomotor morphology has been linked to variation in locomotor mode, ecology, substrate preference, and overall habitat (Garland and Losos, 1994; Higham, 2007; Reilly et al., 2007; Fabre et al., 2017). In contrast, studies that explicitly compare the two systems are much less common, despite the insight they provide into general principles of musculoskeletal design (English, 1985; Higham, 2007; Ross et al., 2017; Ahn et al., 2018; Granatosky et al., 2019; Olsen, 2019; Anderson and Roberts, 2020).

To explore optimality criteria of the feeding and locomotor systems, Granatosky et al. (2019) compared average joint angular excursions during cyclic behaviors—chewing, walking, and running—in a comparative phylogenetic context across 111 tetrapod species. They found that average limb‐joint angular excursions during cyclic locomotion are greater and more evolutionarily labile than those of the jaw joint during cyclic chewing. Based on these findings, they argued that tetrapod limbed locomotor systems are optimized for fast and energetically efficient application of force over a wider and less predictable range of displacements, the principal aim being to move the organism at varying speeds relative to a substrate whose geometry and mechanical properties need not become more homogenous as locomotion proceeds. In contrast, tetrapod chewing systems are optimized for precise application of force over a narrower, more controlled, and predictable range of displacements, the principal aim being to fracture the substrate, the size, and mechanical properties of which are controlled at ingestion and further reduced and homogenized by the chewing process.

If Granatosky et al. (2019) hypotheses about the differing optimality criteria between the two systems are correct, then it stands to reason that other anatomical and biomechanical variables in the feeding and locomotor system should reflect these divergent functions. A potentially fruitful analysis would be to explore whether muscle moment arms (e.g., Spoor et al., 1990; Murray et al., 1995; Van Spronsen et al., 1996, 1997), mechanical advantages (e.g., Throckmorton and Dean, 1994; García‐Morales et al., 2003; Biewener et al., 2004; Young, 2005), and force vector orientations (e.g., Crowninshield and Brand, 1981; Osborn, 1993; Van Spronsen et al., 1996; Hsu et al., 2001; Herbert et al., 2015) vary in predictable ways between the locomotor and feeding systems. A muscle moment arm is simply the perpendicular distance between a joint rotational axis and the force vector (i.e., muscle line of action) acting on that joint. This simple metric provides a measure of the effectiveness of a muscle at contributing to a particular motion over a range of positions (Murray et al., 1995; Kuechle et al., 1997; Delp et al., 1999; Sherman et al., 2013). As joints are rotational in nature, the muscle moment arm is multiplied by the force output of the muscle to calculate joint torque (Knudson, 2007). Thus, assuming equal force‐producing capacity of two muscles and ignoring muscle length–tension properties (Dumont and Herrel, 2003; Eng et al., 2009; Gidmark et al., 2013), the joint position with the greatest moment arm will produce the most torque (Knudson, 2007; Sherman et al., 2013). It is important to note that a muscle's moment arm is not static, and through a joint's overall range of motion (RoM) the muscle moment arm can change (Figure 1; Murray et al., 1995; Kuechle et al., 1997; Delp et al., 1999; Sherman et al., 2013; Iriarte‐Diaz et al., 2017). With these considerations in mind, if the feeding system is optimized for producing high forces, then throughout the mandible's RoM the moment arms of the jaw elevator muscles should be maximized.

Figure 1.

Changes in muscle moment arm lengths (a and b) and muscle force vector orientations relative to the resistance arm (c and d) at the jaw (a and c) and elbow (b and d) joints between maximum gape/elbow extension (left) and minimum gape/elbow flexion (right)

While torque‐maximizing properties of moment arms are often discussed (e.g., Cassini and Vizcaíno, 2012; Casanovas‐Vilar and Van Dam, 2013; Sherman et al., 2013), muscles with relatively small moment arms can also provide a functional advantage. In anatomical positions where the moment arm of a muscle is relatively short, a given muscular contraction can produce relatively broad joint excursions or high angular velocities, albeit at lower force (Hildebrand, 1960; Nagano and Komura, 2003; Westneat, 2003, 2004; Knudson, 2007; Crook et al., 2010). Furthermore, for two muscles of the same length, but varying moment arm lengths, the muscle with the shorter moment arm can produce an overall greater range of maximal excursion (Hildebrand, 1960; Nagano and Komura, 2003; Crook et al., 2010). In the locomotor system, arranging muscle anatomical configurations to limit muscle moment arm length could serve to reduce overall transport costs by allowing broad and rapid joint excursions with minimal muscle activation.

Torque‐producing capacity is also dependent on the magnitude of the force produced by a muscle, and this in turn is dependent on the orientation of the force vector of a particular muscle relative to the load or resistance arm (Crowninshield and Brand, 1981; Osborn, 1993; Van Spronsen et al., 1996; Hsu et al., 2001; Herbert et al., 2015). All other things being equal, a muscle that is more perpendicularly oriented relative to the resistance arm will be capable of producing greater joint torque than one with a more parallel alignment (Knudson, 2007). If the goal of a particular biomechanical system is to apply high forces across a range of joint angles, then muscles should be configured in a way such that the force vector remains near perpendicular to the resistance arm throughout a joint's RoM.

The application of torque is also impacted by the mechanical advantage of a muscle relative to the resistance arm. The mechanical advantage of a joint system is determined by the length of the muscle moment arm relative to the length of the resistance arm (Knudson, 2007). The greater the mechanical advantage, the greater the force amplifying potential (Devlin and Wastell, 1986; García‐Morales et al., 2003; Biewener et al., 2004; Young, 2005; Freeman and Lemen, 2008; Casanovas‐Vilar and Van Dam, 2013). In contrast, a joint system with a relatively small mechanical advantage can produce a greater joint rotational velocity of the resistance arm for a given muscular contraction (Hildebrand, 1960; Nagano and Komura, 2003; Knudson, 2007; Crook et al., 2010).

Taken together, small variations in the anatomical configuration of muscle moment arms, mechanical advantage, and force vector orientation can have profound effects on the mechanics of a system. As such, a comparative analysis of these variables between the feeding and locomotor systems should serve as a powerful tool to either support or refute the hypothesis regarding differences in optimality criteria proposed by Granatosky et al. (2019). Specifically, if the feeding system is optimized for precise application of high forces and the locomotor system is optimized for broad and rapid joint excursions for minimal muscle activation, then it is likely that (a) the moment arms of the jaw elevator muscles should be relatively large and close to maximum throughout the range of jaw excursion compared to flexor and extensor musculature of the limbs; (b) the mechanical advantage of jaw elevators should be greater than those of flexor and extensor musculature of the limbs; and (c) the orientation of the jaw elevator muscles relative to the resistance arm should be more orthogonal through the range of jaw excursion compared to flexor and extensor musculature of the limbs. To test these predictions, we compare muscle moment arm, mechanical advantage, and force vector orientation data from jaw elevator muscles and flexor and extensor musculature of the limbs from a sample of 18 species of primates.

Compared to some orders of mammals, the ecology, diet, and locomotor behavior of primates are diverse and well‐studied (e.g., Fleagle, 2013; Allen et al., 2015; Marcé‐Nogué et al., 2017; Granatosky, 2018). As such, it is possible to determine whether anatomical variation in muscle moment arm length, mechanical advantage, and force vector relative to resistance arm is driven by differences in broad‐scale biomechanical optimality criteria or ecological considerations (Jaslow, 1987; Demes and Günther, 1989; Vizcaíno et al., 1998; Herrel et al., 2000; Young, 2005; O’Brien et al., 2009; Casanovas‐Vilar and Van Dam, 2013). For example, leaping species may show joint system configurations consistent with the need to generate large take‐off forces (Bobbert and van Zandwijk, 1994; Demes et al., 1999). Alternatively, exudivorus primates may demonstrate anatomical adaptations for large gape that are not consistent with our hypotheses about the force maximizing potential of the feeding system (Eng et al., 2009). Furthermore, primates show a great variation in body size range, which is well documented to drive many aspects of anatomical diversity (e.g., muscle mechanics; Biewener, 1989; Young, 2005; Fellmann, 2012). As such, primates represent an ideal taxonomic group to assess the predictions of this study.

2. MATERIALS AND METHODS

2.1. Specimen preparation

Formalin‐fixed cadaveric primate specimens (one individual per species; Table 1) were obtained from collections in the Department of Organismal Biology and Anatomy at the University of Chicago. Origins of most specimens were unknown, but all specimens were adults and free from any noticeable pathologies or muscle atrophy. For this study, we restricted analyses to uni‐articular muscles that cross joints with actions primarily limited to the sagittal plane. We also chose muscles that have actions consistent with their functional role during feeding and locomotion. Furthermore, only superficial muscles were chosen for analysis to limit irreversible damage to cadaveric specimens during dissection. Based on these considerations, we skinned the specimen and isolated two jaw elevator muscles (m. temporalis and m. superficial masseter), an elbow flexor (m. brachialis) and extensor (m. triceps‐lateral head), and a knee flexor (m. biceps femoris‐short head) and extensor (m. vastus lateralis) for analysis. All muscles were on the right side.

Table 1.

Taxonomic sampling of primate species and information about diet category, intermembral index, and body mass used for linear mixed‐effects models. Only one specimen per species was used for all analyses

Species	Body mass (g)	Diet	Intermembral index
Aotus nancymaae	946	Frugivore	79 a
Callithrix jacchus	255	Exudivore	76
Cebus capucinus	3110	Frugivore	81
Cercocebus atys	8400	Hard object feeder	84
Cercopithecus diana	4550	Frugivore	79
Cercopithecus petaurista	3650	Frugivore	81
Chlorocebus pygerythrus	4195	Omnivore	83
Colobus guereza	8590	Folivore	79
Homo sapiens	70,000	Omnivore	68
Lemur catta	2210	Frugivore	70
Leontopithecus rosalia	609	Insectivore	89
Lophocebus albigena	8750	Frugivore	78
Macaca mulatta	9900	Omnivore	93
Pan troglodytes	53,570	Omnivore	106
Saguinus niger	500	Insectivore	74
Sapajus apella	3085	Hard object feeder	81
Semnopithecus entellus	12,701	Folivore	83
Trachypithecus francoisi	7886	Folivore	80

^aIntermembral index for Aotus nancymaae based on closely related Callicebus torquatus.

2.2. Muscle configuration metrics

Once the muscles were isolated, the jaw, elbow, and knee joints were manipulated to their maximum extended position. Such manipulations required slow and careful application of force and specially modified bar clamps (DWHT83191; DeWalt Manufacturing Company) were used to spread the jaws. In some cases, some additional dissection of connective tissues was required to allow relatively free movement of the joint. The joint was considered maximally extended if osseous features came into contact with one another (e.g., olecranon process came into contact with the olecranon fossa) or there was any indication of soft tissue tearing. Once the joint was considered maximally extended, the joint angle was recorded using a General Tools and Instruments Digital Protractor (Model # 1702; General Tools, New York City, NY; ±0.1°). Manipulation of the joints in this manner resulted in average maximal excursion angles across all species (jaw joint = 101.29° ±7.73°; elbow joint = 169.98 ± 5.57; knee joint = 172.89 ± 4.95) comparable to those already recorded in the literature (Herring and Herring, 1974; Boone and Azen, 1979; Roaas and Andersson, 1982; Günal et al., 1996; Soucie et al., 2011; Hylander, 2013; Fricano and Perry, 2019). From the maximum extended angle position, the excursion of each joint was scaled to determine the angle at 0%, 25%, 50%, 75%, and 100% joint excursion (Figure 1).

At each of the five angular positions for each muscle, moment arm lengths were measured (Tresna Instrument IP67 Digital Calipers; Guilin Guanglu Measuring Instrument, Guangxi Province, China; ±0.03 mm) from the joint axis to the proximal and distal edges of the muscle. The average of these two lengths was used for all subsequent analyses. Additionally, at each of the five angular positions, the angle of each muscle relative to the resistance arm (i.e., mandible, ulna, tibia for m. vastus lateralis, and fibula for m. biceps femoris‐short head) was determined using a General Tools and Instruments Digital Protractor.

Once all moment arm lengths and angular muscle orientations were collected, the lengths of the resistance arms were measured as the straight‐line distance between the condyle and infradentale for the jaw joint; the olecranon process and the head of the third metacarpal for the elbow joint; and the superior aspect of the tibial plateau and the head of the third metatarsal for the knee joint. It should be noted that these resistance arm lengths are only estimates of where loading occurs during cyclical locomotion or chewing. Measuring the distance to infradentale on the mandible over‐estimates the length of the resistance arm in primates as most biting and cyclical chewing occur around the second molar (Kay and Hiiemae, 1974; Kay, 1975; Ross et al., 2010).

2.3. Data processing and analysis

Moment arm lengths are size‐dependent, so to compare across species and biomechanical systems all raw measurements were scaled intra‐specifically to the maximum moment arm length for a given muscle. The mechanical advantage of a particular muscle arrangement was calculated within individuals as the ratio of the moment arm length at each position relative to the length of the resistance arm. No scale transformations were required for angular measurements. The change in relative moment arm length and muscle force vector angle was calculated by subtracting the minimum value from the maximum across the range of excursion.

As phylogenetic history may be a relevant confounding variable in studies of anatomical diversity of muscle moment arms across the 18 primate species, we tested for the influence of phylogeny on all variables using both Blomberg's K (Blomberg et al., 2003) and Pagel's λ (Pagel, 1999). All phylogenetic analyses were performed in R (Ver. 3.4.2) using phytools (Revell, 2012) and by pruning a recent super timetree (Hedges et al., 2015) to include only the species in our study. Across all 102 variables collected, only six had a significant (p ≤ 0.05) phylogenetic signal according to Blomberg's K and two according to Pagel's λ [i.e., relative mechanical advantage of m. triceps‐lateral head at 75% and 100% elbow extension, relative mechanical advantage and relative moment arm length of m. brachialis at 100% elbow extension, relative moment arm length of m. temporalis at 0% jaw gape, and change in relative moment arm length of m. brachialis]. Based on these findings, no consideration of phylogeny was included in subsequent statistical testing.

Relative muscle moment arms, mechanical advantages, and the muscle force vector orientations are illustrated for each of the six muscles of interest across the range of joint excursion in Figures 2, 3, 4. Comparing each of these variables independently would become unwieldy, so we only tested whether the maximum relative mechanical advantage was greater in muscles of the feeding system compared to locomotor system, and whether the change in moment arm length and muscle force vector orientation was less in the muscles of the feeding system compared to locomotor system. In addition to being part of the feeding or locomotor system, other variables might influence the anatomical configuration of muscle moment arms, such as diet, locomotor mode, or body mass (Jaslow, 1987; Demes and Günther, 1989; Vizcaíno et al., 1998; Herrel et al., 2000; Young, 2005; O’Brien et al., 2009; Casanovas‐Vilar and Van Dam, 2013). To address this possibility, we calculated a series of linear mixed‐effects models to assess the relationship between the log‐transformed variables of interest with species as a random effect, and joint system (i.e., locomotor vs. feeding), diet [i.e., frugivore, insectivore, hard object feeder, folivore, omnivore, exudivore (Bajpai et al., 2008; Fleagle, 2013; Allen et al., 2015; Marcé‐Nogué et al., 2017)], locomotor mode [as measured by intermembral index; IMI (Fleagle, 2013; Granatosky, 2018)], and log‐transformed body mass as fixed effects (Table 1). The IMI is calculated as the length of the forelimbs (humerus + radius) divided by the length of the hindlimbs (femur + tibia) multiplied by 100. The IMI is used frequently in primatology since it helps predict primate locomotor patterns. When IMI is lower than 100, the forelimbs are shorter than the hindlimbs, which is common for anatomically specialized vertical clinging and leaping species. Anatomically generalized species have IMIs around 100, while arm‐swinging primates have IMIs significantly >100 (Alexander, 1985; Fleagle, 2013, ).

Figure 2.

Dot plots showing moment arm length as a percentage of the maximum moment arm length of the same muscle across the range of joint excursion for two jaw elevator muscles [(a) m. superficial masseter and (b) m. temporalis], an elbow flexor (c; m. brachialis) and extensor (d; m. triceps‐lateral head), and a knee flexor (e; m. biceps femoris‐short head) and extensor (f; m. vastus lateralis). Colored symbols represent individual primate species. Joint movements were standardized across systems such that 0% excursion refers to minimum gape/ maximum elbow and knee flexion and 100% excursion refers to maximum gape/ maximum elbow and knee extension

Figure 3.

Dot plots showing relative mechanical advantage across the range of joint excursion for two jaw elevator muscles [(a) m. superficial masseter and (b) m. temporalis], an elbow flexor (c; m. brachialis) and extensor (d; m. triceps‐lateral head), and a knee flexor (e; m. biceps femoris‐short head) and extensor (f; m. vastus lateralis). Colored symbols represent individual primate species. Joint movements were standardized across systems such that 0% excursion refers to minimum gape/maximum elbow and knee flexion and 100% excursion refers to maximum gape/maximum elbow and knee extension

Figure 4.

Half polar plot showing muscle force vector orientations relative to the resistance arm across the range of joint excursion for two jaw elevator muscles [(a) m. superficial masseter and (b) m. temporalis], an elbow flexor (c; m. brachialis) and extensor (d; m. triceps‐lateral head), and a knee flexor (e; m. biceps femoris‐short head) and extensor (f; m. vastus lateralis). Colored symbols represent individual primate species. Joint movements were made comparable between the two systems such that 0% excursion refers to minimum gape/ maximum elbow and knee flexion and 100% excursion refers to maximum gape/ maximum elbow and knee extension. Plots are arranged such that each ring represents a differing level of joint excursion where the innermost ring is 0% excursion and the outermost ring is 100% excursion. Where colored symbols lie on each ring represents the muscle force vector orientation relative to the resistance arm. For example, panel (a) illustrates the force vector orientation of m. superficial masseter relative to the mandible. As the jaw joint moves from minimum (innermost circle) to maximum (outermost circle) gape, the orientation of m. superficial masseter relative to the mandible ranges from ~60° to 120°, but generally retains a near orthogonal position. In contrast, panel (c) illustrates the force vector orientation of m. brachialis relative to the ulna. As the elbow joint moves from maximum flexion (innermost circle) to extension (outermost circle), the orientation of m. brachialis relative to the ulna ranges from ~30° to 160°, a much greater change in muscle force vector orientation compared to m. superficial masseter

As the goal of this study is to investigate the influence of joint system on the anatomical configuration of muscle moment arms, mechanical advantages, and force vector orientations, we constrained comparison of our model to a single null that did not include joint system as a fixed effect. The Burnham and Anderson (2001) approach for model comparison was used and Akaike's information criterion (AIC) generated for each model. Akaike's information criterion provides a measure of the goodness of fit of an estimated model and an operational way of trading off the complexity of an estimated model against how well the model fits the data. The best model has the lowest AIC. Linear mixed‐effects models were constructed and analyzed in R using “lme4” (Bates et al., 2015) following Winter (2013).

3. RESULTS

Linear mixed‐effects models did reveal the importance of considering other variables in addition to joint system—body mass, locomotor mode—when exploring the causes of variation in anatomical configuration of muscle moment arms, mechanical advantages, and force vector orientations (Tables 2 and 3). However, in all cases the inclusion of information about joint system (i.e., feeding or locomotor) in the linear mixed‐effects models resulted in significantly lower AICs (Table 4). Lower AICs indicate that consideration of joint system results in more parsimonious explanations for variation in anatomical configuration of muscle moment arms, mechanical advantages, and force vector orientations than a model that does not include information on joint system.

Table 2.

Interspecific (n = one individual per species) summary statistics (mean ± standard deviation) for the mechanical variables across the range of joint excursion for each of the representative muscles

Variable	Representative muscle	Joint excursion
		100%	75%	50%	25%	0%
Relative moment arm length (%)	m. superficial masseter	79.34 ± 8.74	87.17 ± 8.62	90.54 ± 6.95	96.33 ± 5.82	90.84 ± 11.34
	m. temporalis	84.63 ± 15.70	92.90 ± 8.79	86.79 ± 11.61	89.54 ± 8.25	87.26 ± 12.39
	m. brachialis	58.34 ± 19.12	74.56 ± 17.52	92.72 ± 8.88	75.28 ± 15.19	66.93 ± 25.97
	m. triceps‐lateral head	64.15 ± 26.22	79.91 ± 19.02	85.78 ± 13.76	81.35 ± 17.62	55.54 ± 17.22
	m. biceps femoris‐short head	66.37 ± 21.26	77.22 ± 19.92	91.95 ± 11.35	73.37 ± 19.22	57.39 ± 19.96
	m. vastus lateralis	66.95 ± 23.58	83.66 ± 14.33	87.82 ± 15.44	69.68 ± 13.99	60.54 ± 14.04
Relative mechanical advantage (%)	m. superficial masseter	19.77 ± 5.81	21.63 ± 5.84	22.55 ± 6.20	24.08 ± 7.03	22.68 ± 7.20
	m. temporalis	37.29 ± 7.22	41.51 ± 7.81	38.35 ± 5.69	39.70 ± 5.37	38.77 ± 7.22
	m. brachialis	8.33 ± 4.42	10.42 ± 4.39	12.66 ± 4.68	10.38 ± 4.46	9.15 ± 5.35
	m. triceps‐lateral head	5.19 ± 2.18	6.65 ± 2.61	7.53 ± 3.88	7.11 ± 3.21	4.67 ± 1.94
	m. biceps femoris‐short head	6.89 ± 2.79	8.10 ± 3.26	9.58 ± 3.00	7.59 ± 2.91	5.88 ± 2.52
	m. vastus lateralis	4.74 ± 2.16	6.17 ± 2.60	6.53 ± 2.66	5.05 ± 1.92	4.42 ± 2.01
Muscle force vector orientations relative to the resistance arm (°)	m. superficial masseter	96.92 ± 13.37	85.95 ± 10.14	84.31 ± 6.38	71.44 ± 10.26	62.56 ± 13.54
	m. temporalis	107.60 ± 16.55	108.12 ± 13.01	97.80 ± 11.88	93.46 ± 10.44	92.22 ± 12.54
	m. brachialis	159.63 ± 6.27	112.10 ± 10.09	90.22 ± 9.33	63.73 ± 12.61	39.79 ± 11.23
	m. triceps‐lateral head	160.09 ± 6.74	119.41 ± 5.78	92.51 ± 3.55	66.22 ± 7.05	40.43 ± 9.82
	m. biceps femoris‐short head	160.72 ± 5.49	115.73 ± 12.81	82.67 ± 7.24	54.63 ± 11.66	34.28 ± 8.64
	m. vastus lateralis	164.60 ± 6.05	131.81 ± 17.20	89.38 ± 8.49	64.00 ± 6.34	39.26 ± 9.62

Table 3.

Statistical parameters derived from linear mixed‐effects models demonstrating the statistical importance of various fixed effects. Values in bold illustrate fixed effects that significantly influence each respective response variable

Response variable	Fixed effect	Estimate	Standard error	t value	F value	p‐value
Change in relative moment arm length	(Intercept)	1.24	0.29	—	—	—
	Joint system	0.32	0.03	9.39	88.12	<0.001
	Diet	0.00	0.00	0.07	0.01	0.944
	Locomotor mode	0.02	0.02	1.15	1.31	0.267
	Body mass	0.00	0.05	−0.05	0.00	0.965
Maximum relative mechanical advantage	(Intercept)	1.91	0.18	—	—	—
	Joint system	−0.55	0.04	−15.45	238.66	< 0.001
	Diet	0.00	0.00	−0.80	0.63	0.428
	Locomotor mode	0.00	0.01	−0.24	0.06	0.814
	Body mass	−0.07	0.03	−2.44	5.98	0.016
Change in muscle force vector orientation	(Intercept)	1.64	0.14	—	—	—
	Joint system	0.63	0.03	21.73	472.27	<0.001
	Diet	0.00	0.00	−1.33	1.78	0.200
	Locomotor mode	0.03	0.01	3.10	9.62	0.006
	Body mass	−0.02	0.02	−0.84	0.71	0.412

Table 4.

Results from comparisons of linear mixed‐effects models. Linear mixed‐effects models were used to assess the relationship between the log‐transformed variables of interest with species as a random effect, and joint system (i.e., locomotor vs. feeding), diet, locomotor mode, and log‐transformed body mass as fixed effects. Model (degrees of freedom = 7) comparison was constrained to a single null (degrees of freedom = 6) that did not include joint system as a fixed effect

Variable	Linear mixed‐effects model	Akaike's information criterion	χ 2 value	Comparison of linear mixed‐effects models (p‐value)
Change in relative moment arm length	Null	14.21	61.44	<0.001
	Model	−45.23
Maximum relative mechanical advantage	Null	68.05	125.95	<0.001
	Model	−55.90
Change in muscle force vector orientation	Null	77.42	181.55	<0.001
	Model	−102.13

For both m. superficial masseter and m. temporalis, the muscle moment arm length remained near maximum regardless of gape angle (Table 2 and Figure 2). In contrast, the relative muscle moment arm lengths for the representative muscles in the locomotor system were reduced to a greater extent over the RoM. For these muscles, moment arm length tended to be greatest at around 50% excursion and was much reduced near maximum elbow or knee flexion and extension. Accordingly, the change in relative muscle moment arm length was significantly lower in the feeding system (m. superficial masseter = 22.32% ± 8.48%; m. temporalis = 24.77% ± 14.0%) compared to the locomotor system (m. brachialis = 48.35% ± 17.53%; m. triceps‐lateral head = 48.37% ± 18.25%; m. biceps femoris‐short head = 46.24% ± 18.05%; m. vastus lateralis = 45.34% ± 14.95%; Table 4 and Figure 5).

Figure 5.

Mean and standard deviation for (a) change in relative moment arm length, (b) maximum relative mechanical advantage, and (c) change in muscle force vector orientation across the 18 primate species. Muscles of the feeding system are presented in orange, and muscles of the locomotor system are presented in blue

There were similar differences in mechanical advantage. In the feeding system, the representative muscles had relatively long muscle moment arms compared to mandible length, hence a large mechanical advantage. As above, the mechanical advantage of m. superficial masseter and m. temporalis varied little across the range of mandible excursion. In contrast, mechanical advantage for representative muscles in the locomotor system was lower and varied considerably depending on elbow or knee joint angle (Table 2 and Figure 3). The maximum mechanical advantage was significantly greater for muscles of the feeding system (m. superficial masseter = 25.13% ± 7.54%; m. temporalis = 44.57% ± 6.33%) compared to the locomotor system (m. brachialis = 13.69% ± 4.88%; m. triceps‐lateral head = 8.70% ± 3.78%; m. biceps femoris‐short head = 10.39% ± 2.90%; m. vastus lateralis = 7.33% ± 2.52%; Table 4 and Figure 5).

The force vector orientations of m. superficial masseter and m. temporalis were close to orthogonal to the mandible throughout the range of jaw excursion. In contrast, force vector orientations of the representative locomotor muscles varied to a greater extent throughout the range of elbow and knee excursion. During maximum elbow and knee flexion and extension, force vector orientations of representative locomotor muscles were in some species near parallel to the resistance arm (Figure 4). Consequently, the change in muscle force vector orientation was significantly lower in the feeding system (m. superficial masseter = 38.74° ± 18.00°; m. temporalis = 27.91° ± 13.15°) than in the locomotor system (m. brachialis = 119.84° ± 15.27°; m. triceps‐lateral head = 119.75° ± 11.54°; m. biceps femoris‐short head = 126.44° ± 9.28°; m. vastus lateralis = 125.72° ± 10.67°; Table 4 and Figure 5).

4. DISCUSSION

Our results demonstrate significant differences in the anatomical configurations of muscle moment arms, mechanical advantages, and force vector orientations between representative muscles of the feeding and locomotor systems of primates. Specifically, the largest jaw elevator muscles of the feeding system are more orthogonally oriented relative to the resistance arm (the mandible) and operate at relatively larger moment arms and mechanical advantages. Moreover, these variables change little across the range of jaw excursion. In contrast, the representative muscles of the locomotor system tend to have much smaller mechanical advantages and, depending on joint position, smaller muscle moment arm lengths and almost parallel orientations relative to the resistance arm. These patterns are consistent regardless of phylogeny, body mass, locomotor mode, and feeding specialization. As outlined in greater detail above, if the goal of a particular biomechanical system is to apply high forces across a range of joint angles, then muscles should be configured so that the force vector remains near perpendicular to the resistance arm, and the muscle moment arm and mechanical advantage are near maximum throughout their joint's RoM (Knudson, 2007; Casanovas‐Vilar and Van Dam, 2013; Sherman et al., 2013). In contrast, if a biomechanical system is designed for broad joint excursions and rapid joint rotational velocities, then relatively short muscle moment arms and small mechanical advantages are preferable (Nagano and Komura, 2003; Crook et al., 2010; Sherman et al., 2013). Based on these principles, we believe that our results highlight a fundamental functional dichotomy between cyclical behaviors performed by the feeding and locomotor systems, namely the feeding system is more strongly optimized for the generation of high bite forces and precisely controlled bite force and jaw displacement during cyclic chewing, whereas the locomotor system is optimized for speed and energetic efficiency during cyclic walking and running.

The energetic costs of locomotion can be quite high [reaching upwards of 34% of an animal's daily energy costs (Hoyt and Kenagy, 1988; Karasov, 1992); in humans, they represent approximately 8.5 times the cost of cyclic chewing (20.7 ± 9.86 J/sec during chewing vs. ~175 J/sec during locomotion) (Hanna and Wall, 2016)]. It is therefore no surprise that tetrapods seem to have adopted a range of strategies to reduce locomotor costs (Alexander, 1990; Kram and Taylor, 1990; Alexander, 1991, 1991,1991, 1991; Biewener, 1998; Hoyt et al., 2000; Reilly et al., 2007). One of these strategies—increases in total step length and stance duration—is directly linked to the relatively broad limb‐joint excursions. Lengthening steps through increased joint excursion reduces the frequency of muscle activation over a given distance moved, reducing the metabolic cost of locomotion (Roberts et al., 1998; Reilly et al., 2007; Pontzer, 2007, 2016). By organizing muscles in a manner such that moment arms and mechanical advantage are relatively small, the locomotor system can produce relatively broad joint excursions and high angular velocities for a given muscular contraction compared to the feeding system. As such, the anatomical organization of muscles within the limbs can allow a striding animal to get from one location to another relatively rapidly and with minimal energetic expenditure (Hildebrand, 1960; Nagano and Komura, 2003; Crook et al., 2010), negating the extra muscular force required to support the body associated with higher running speeds (Biewener et al., 2004). This simplistic explanation potentially only applies to relatively large quadrupedal animals and small leaping animals may violate these predictions. However, our analysis including IMI as a proxy for locomotor mode revealed no significant impact of locomotor mode on our measures within primates (Table 3).

In contrast, the anatomical configuration of muscles in the feeding system, at least m. superficial masseter and m. temporalis, favors their force‐producing capacity at the expense of excursion and velocity. Mechanical advantage of these jaw elevators was relatively larger than for any muscles of the locomotor system. This difference is even more striking considering that measuring mandible load arm all the way to infradentale over‐estimates the length of the resistance arm in primates (Kay and Hiiemae, 1974; Kay, 1975; Ross et al., 2010). Furthermore, muscle moment arms remained near maximum and force vector orientation remained near orthogonal throughout the range of jaw excursion. These patterns were true for all species regardless of dietary specialization or degree of prognathism (e.g., Pan troglodytes vs. Homo sapiens; Van Spronsen et al., 1996). Taken together, these mechanical variables give the jaw elevator muscles the “anatomical potential” to produce high forces regardless of joint angle, ignoring length–tension properties (Dumont and Herrel, 2003; Eng et al., 2009; Gidmark et al., 2013). This force‐producing capacity is important for both fracturing the substrate during ingestion and then further homogenizing the food item into a swallow‐safe bolus during cyclic chewing (Kay and Hiiemae, 1974; Ross and Iriarte‐Diaz, 2014).

The anatomical configuration of the primate feeding system is associated with a trade‐off. Specifically, for a given muscle contraction the mandible goes through a lower joint angular excursion than observed in the locomotor system (Nagano et al., 2007; Crook et al., 2010), making it difficult to achieve rapid movements of the mandible. Yet, unlike the locomotor system, where the ability to move the musculoskeletal components at a range of frequencies is an important aspect of system performance, primate feeding systems appear to be optimized to operate within a relatively narrow and slow frequency band (Ross et al., 2009; Thompson et al., 2011; Ross and Iriarte‐Diaz, 2014).

The use of primates in this study allowed us to assess whether anatomical variation in muscle moment arm length, mechanical advantage, and force vector relative to resistance arm was driven by differences in broad‐scale biomechanical optimality criteria or ecological considerations, such as phylogeny, body mass, locomotor mode, and/or diet (Jaslow, 1987; Demes and Günther, 1989; Vizcaíno et al., 1998; Herrel et al., 2000; Young, 2005; O’Brien et al., 2009; Casanovas‐Vilar and Van Dam, 2013). While there was some influence of body mass and locomotor mode on the anatomical configurations of the joint systems, these effects were minimal compared to the cross‐system comparisons (i.e., locomotor vs. feeding). This is not to imply that these ecological and phylogenetic variables do not influence the anatomical configurations of joints. More detailed intersystem comparisons would reveal predictable patterns in muscle moment arm lengths, mechanical advantages, and force vector orientations based on diet, locomotor mode, and/or body mass. The narrow sampling in this study precludes such in‐depth analyses, and future studies should explore these potentials in more detail.

A study of this nature is faced with several limitations that reduce its broad‐scale applicability. First, although our sample of 18 primate species is large, and to our knowledge represents the largest collection of data on interspecific muscle moment arms, mechanical advantages, and force vector orientations to date, it has its limitations. A sample of 18 primate species does not capture variation across primates, let alone across mammals or tetrapods as a whole. For example, it is possible that predatory species that rely on quick jaw closing to catch prey may have jaw elevator muscles that more closely resemble the locomotor system than the feeding system of most primates that are ominivorous (Maynard and Savage, 1957; Smith, 1993; Koolstra and van Eijden, 1995). Furthermore, our ability to only sample one individual per species does not capture intraspecific variation. We hope that these data will spark future interest and motivate studies to increase phylogenetic, locomotor, and dietary diversity, especially utilizing less invasive diceCT data (Orsbon et al., 2018) and dynamic estimates based on computer models (White et al., 1989; Hutchinson et al., 2005, 2011; O’Neill et al., 2013; Iriarte‐Diaz et al., 2017). The muscles selected for this study also do not capture the full range of functional diversity within the feeding and locomotor systems. For example, it would be of interest to take the same measurements from bi‐articular muscles (e.g., MacFadden and Brown, 2007) including jaw depressors (e.g., van Eijden et al., 1997), hip rotators (e.g., Delp et al., 1999; Vaarbakken et al., 2015), or intrinsic muscles of the hands and feet (e.g., Smutz et al., 1998). However, as the goal of this study was to directly compare muscles of the feeding and locomotor systems, this required certain sampling limitations to assure biologically relevant comparisons. It is also the case that this study takes a rather simplistic view of muscle function. Specifically, we treat all muscles as if they have similar contractile properties, internal architecture, physiological cross‐sectional area, fiber types, and activity patterns. Some of these variables are known to vary between the feeding and locomotor systems (e.g., Hoh, 2002; Österlund et al., 2011; Anderson and Roberts, 2020) and have effects on an individual muscle's ability to generate force or speed (Narici et al., 1992; Morse et al., 2005; Knudson, 2007; Eng et al., 2009; Taylor and Vinyard, 2009; Guimarães et al., 2013). Furthermore, this study ignores length–tension properties of muscles (Dumont and Herrel, 2003; Eng et al., 2009; Gidmark et al., 2013) and muscle architecture dynamics (Laird et al., 2020). However, such considerations are beyond the scope of this study as it was our intent to simply explore the “anatomical potential” for certain muscle configurations to produces high forces vs. wide excursion.

4.1. Conclusions

In this study, we demonstrate that compared with the locomotor system, muscles of the feeding system are oriented more orthogonally to the resistance arm (the mandible) and show relatively larger moment arms and mechanical advantages regardless of jaw joint excursion. In contrast, the representative muscles of the locomotor system have much smaller mechanical advantages, and, depending on joint position, can have small muscle moment arm lengths and an almost parallel orientation relative to the resistance arm. These findings are in accordance with optimality criteria proposed by Granatosky et al. (2019); that is, that the feeding system is more optimized for precise application of high forces and the locomotor system is more optimized for broad and rapid joint excursions for minimal energetic expenditure. This study adds to growing literature that explicitly compares the two systems to provide insight into general principles of musculoskeletal design (English, 1985; Higham, 2007; Ross et al., 2017; Ahn et al., 2018; Granatosky et al., 2019; Olsen, 2019). Future studies aimed at testing differences in feeding and locomotor energetic expenditure and muscle activity patterns could provide additional evidence to further test whether the feeding system is optimized for the application of high forces and the locomotor system is optimized for large and rapid joint excursions for minimal energetic expenditure.

AUTHOR CONTRIBUTIONS

MCG and CFR designed the study. MCG collected and analyzed data. MCG and CFR wrote and edited the manuscript.

Granatosky MC, Ross CF. Differences in muscle mechanics underlie divergent optimality criteria between feeding and locomotor systems. J. Anat. 2020;237:1072–1086. 10.1111/joa.13279

DATA AVAILABILITY STATEMENT

Raw data will be uploaded as a Supplemental Table at the time of publication.