Modulation of limb mechanics in alligators moving across varying grades

Legged locomotion on land often requires animals to transition between level, incline and decline substrates. Graded substrates change the mechanical energy requirement of steady-state locomotion and animals must either perform more work (inclined surfaces) or dissipate more work (declined surfaces) with their limbs to compensate. Most studies of legged animals have focused on steady-state locomotion on level ground (Biewener and Daley, 2007; Birn-Jeffery and Higham, 2014), which establishes an important baseline for relating mechanics and energetics, but does not fully represent the diversity of locomotor conditions encountered in nature.

Data on individual limb forces across grades are available in a small subset of animals, most of which are cursorial species adapted for running. These include horses (Dutto et al., 2004), cats (Gregor et al., 2006), dogs (Lee, 2011), goats (Arnold et al., 2013) and primates (Gottschall and Kram, 2005; Schmidt, 2005). While the strategies that cursorial quadrupeds use to navigate grade changes are well understood, our understanding of how quadrupeds with sprawled postures modulate their limb mechanics when transitioning between grades remains limited. Recent studies in lizards have advanced our understanding of how limb mechanics are used to navigate the challenges of arboreal locomotion (Foster and Higham, 2012; Krause and Fischer, 2013; Wang et al., 2015).

Legged animals use some general strategies to transition between grades. Animals tend to reduce forward speed, increase duty factor and flex their limbs on graded conditions when compared with level (Birn-Jeffery and Higham, 2014). On inclines, most animals decrease stride length and increase stance phase duration relative to level (Carlson-Kuhta et al., 1998; Irschick and Jayne, 1998; Foster and Higham, 2012; Williams et al., 2009), usually resulting in increased vertical or craniocaudal (in the direction of travel) ground reaction forces (GRFs) (Dutto et al., 2004; Gottschall and Kram, 2005; Lammers et al., 2006). On declines, locomotor strategies are more variable, but common changes made by legged animals suggest that stability may be more important than energy modulation when moving downhill. Spatiotemporal characteristics of gait do not follow a general pattern on declines (Birn-Jeffery and Higham, 2014), but limb forces shift to net braking (Lammers et al., 2006; Lee, 2011) and limb joints typically flex more during stance phase relative to level (Jayne and Irschick, 1999; Krause and Fischer, 2013; Leroux et al., 2002; Smith et al., 1998). This increased limb flexion not only allows energy dissipation by large extensor muscles but also is thought to bring the center of mass (COM) closer to the ground and counteract the ‘toppling torques’ encountered when moving across non-level substrate. Overall, strategies to transition between grades depend on context and may be shaped by divergent demands for stability and efficiency.

American alligators, Alligator mississippiensis, are quadrupeds that walk primarily using a ‘walking trot’ and sprawled posture termed ‘semi-upright’ (Bakker, 1971), where proximal limb segments are abducted away from the body and hands, and feet do not lie directly underneath the body. While these general categories of posture serve as a convenient shorthand, the degrees of freedom in jointed systems limit their universal utility (Gatesy and Biewener, 1991). Alligators also have relatively shorter limbs than most terrestrial vertebrates (Blob, 2000) and drag around a large tail that accounts for ∼28% of their total body mass (Willey et al., 2004). These unique characteristics influence limb kinetics during level locomotion compared with other terrestrial quadrupeds. Specifically, mediolateral forces (forces directed toward the body midline) in alligator limbs are 100–140% the magnitude of craniocaudal forces (forces directed in the direction of travel) and hindlimbs support more body weight than forelimbs during walking (Willey et al., 2004), a feature shared broadly with primates (Pontzer et al., 2014), lizards (McElroy et al., 2014) and salamanders (Nyakatura et al., 2019). However, mediolateral forces in cursorial species are often negligible (e.g. Corbee et al., 2014) and forelimbs typically support more body weight in most quadrupeds (Arnold et al., 2013). Alligators and other sprawlers also use non-parasagittal limb movements during walking, which offers another axis of variation to modulate during locomotion across varying grades.

Here, we quantified the kinetic and kinematic changes used to transition between level, incline and decline walking in alligators. Specifically, we predicted that, similar to other quadrupeds, alligators will (1) support more body weight with their hindlimbs during incline and their forelimbs during decline walking, (2) use their hindlimbs to produce larger propulsive forces during incline walking compared with level walking, (3) use their forelimbs to produce larger braking forces during decline walking compared with level walking. Additionally, given the observation that proximal muscles generate more mechanical work during legged locomotion, we predicted that alligators will primarily modulate their proximal limb joint kinematics to transition across conditions. Finally, we predicted that because of their sprawled posture, alligators will modulate mediolateral kinetics and kinematics to navigate sloped terrain. We tested these predictions by measuring individual limb GRFs as alligators walk at a steady speed across a trackway and 3D high-speed videography to quantify kinematic changes across conditions.

Three female juvenile American alligators, Alligator mississippiensis Daudin 1801 (body mass 524.4±78.4 g, snout–vent length 29.4±0.5 cm; mean±s.d.) were obtained from California State University, San Bernardino, USA, and transferred to an indoor vivarium at University of California Irvine, USA. The vivarium was kept at 28°C with a 12 h:12 h light:dark cycle with the humidity of the vivarium set at 75%. Large tanks within the vivarium allowed animals to fully submerge into water and emerge onto basking platforms ad libitum. Animals were fed weekly and trained to walk across a custom trackway. All animal husbandry and experimental protocols were approved by the University of California Irvine Institutional Animal Care and Use Committee (IACUC).

The trackway (2.5 m×0.3 m) was instrumented with two high-speed video cameras and a small circular force plate (∼0.018 m²) flush-mounted with the ground (Fig. 1A). The trackway was kept in a temperature-controlled room where the environmental temperature was maintained at 28.0±1.0°C (TC1 Controller, Environmental Growth Chambers, Chagrin Falls, OH, USA) with a humidity of 65–70%. This allowed all experiments to be conducted within alligators' preferred temperature range (Smith, 1975; Brattstrom, 1965). Level, incline and decline data were collected over a period of 4 weeks and animal body mass, total length and snout–vent length were measured on each day of data collection to account for minor changes across the span of this study. The substrate was made of acrylic lined with either 100-grit (level) or 120-grit sandpaper (incline and decline).

Joint positions were determined based on kinematic markers placed near each major limb joint's center of rotation. Kinematic markers (OptiTrack Facial Markers 3 mm, NaturalPoint Inc., Corvallis, OR, USA) were painted white and black to facilitate digitization and were placed on the right side of the animal. Forelimb (FL) markers were placed at the third metacarpophalangeal joint, the styloid process of the radius, the lateral epicondyle of the humerus, and directly above the right and left glenoid cavities. Hindlimb (HL) markers were placed at the third metatarsophalangeal joint, the lateral malleolus of the fibula, the lateral epicondyle of the femur, and directly above the right and left acetabula (see Reilly and Elias, 1998). Additional markers were placed along the vertebral column at 30% and 70% gleno-acetabular length. We assumed the marker at 70% along the craniocaudal axis represents COM location in juvenile alligators (Willey et al., 2004) and its displacement over time was used to calculate instantaneous forward walking velocity.

High-speed video cameras with a maximum resolution of 1280×1024 pixels (SC1, Edgertronic, Sanstreak Corp., San Jose, CA, USA) recorded dorsal and lateral views at 200 Hz as animals walked the length of the trackway. Each trial included several steps before and after the force plate, in addition to the step of interest on the force plate. Videographic data were used to determine stance phase duration (SP), swing phase duration (SW) of the pre-force plate step, and SW of the post-force plate step. The average between the two SW values was used to calculate stride duration for each trial, which was then used to calculate stride frequency (=1/stride duration), stride length (=stride frequency×speed) and duty factor (=stance phase duration/stride duration). Coordinates of kinematic markers overlying joint positions were determined by calibrating a 96-point calibration cube with direct-linear transformation software (Hedrick, 2008) in MATLAB (The MathWorks, Natick, MA, USA). 3D position data were used to calculate joint angles of each major limb joint (Fig. 1B), proximal limb joint height (in cm), effective limb length (in cm; the average 3D distance between the proximal limb joint and limb point of contact), step width (in cm; the average mediolateral distance between the proximal limb joint and limb point of contact), and sprawl area [in cm²; the area within the triangle formed by proximal joint height, effective limb length (ELL) and step width] during stance phase (Fig. 1C). Given the limitation of our markers, our analysis is best described as quasi-3D and quasi-static as we are unable to distinguish between the rotational axes used to arrive at a given joint position (Gatesy et al., 2010).

Level data were collected over the course of 3–4 days and once a sufficient number of trials had been collected from each animal, the trackway was modified to a 15 deg incline, and then a 15 deg decline (Fig. 1A). Animals usually walked on a level, incline or decline trackway for any given day of data collection. We did experiments with steeper slopes, but found less reliable GRF data during decline locomotion as steps became more variable and were often impacted by minor slips. Animals were encouraged to walk at their preferred speed via tail taps and allowed to rest after 4–5 consecutive walking bouts. Only trials where animals walked at a constant forward velocity (i.e. steady state), contacted the force plate with either the right FL or right HL in isolation, and remained in view of both cameras were included in our analyses. We considered animals to be walking steadily based on average speed calculated during two different time intervals and the quotient between them. Speed during stance phase (speed_SP) was determined by taking the average instantaneous forward velocity of the COM during limb contact with the force plate. Speed during the total trial (speed_tot) was determined by taking the average instantaneous forward velocity as animals walked the entire length of the trackway. In this study, trials were considered steady state if the speed_SP/speed_tot quotient fell between 0.9 and 1.1. A total of 96 steps from all individuals were analyzed during stance phase of walking across level, incline and decline conditions (n=48 forelimb steps, n=48 hindlimb steps). Alligator steps can be sloppy and often involve toe and finger dragging; therefore, we define stance phase in this study as the time between hand or foot flat on the substrate until the onset of significant wrist palmarflexion (for FL) or when the foot segment was perpendicular to the floor (for HL).

A linear mixed effects (LME) model was used to test for effects of condition (level, incline or decline) on the following dependent variables for each limb: stance phase duration, stride length, duty factor, GRF impulses, average GRF angles (parasagittal and frontal), proximal limb joint height, ELL, sprawl area and net excursion (=start angle−end angle) of each major limb joint during stance phase. Condition was treated as a fixed effect whereas individual alligator was treated as a random effect. We used a sequential Bonferroni correction to account for multiple statistical tests for each limb (LME α=0.006). All variables found to be significantly affected by condition in our LME model were further analyzed using post hoc pairwise comparison Tukey's tests (α=0.05). All statistics were performed using R (lme4 and emmeans packages; https://CRAN.R-project.org/package=lme4, https://CRAN.R-project.org/package=emmeans).

Condition (i.e. level, incline, decline) had no significant effect on speed_SP, stance phase duration, stride length or duty factor for either limb (Table 1). Pooled (FL and HL trials) speed_SP was 0.118±0.026 m s⁻¹ during level walking, 0.116±0.041 m s⁻¹ during incline walking and 0.116±0.028 m s⁻¹ during decline walking, indicating no difference in average locomotor speed as alligators transition across grades.

We observed no significant differences in FL vertical impulse (LME, P=0.968), HL vertical impulse (P=0.110), FL mediolateral impulse (P=0.711) or HL mediolateral impulse (P=0.112) due to condition. However, craniocaudal impulse decreased significantly during decline walking and increased during incline walking (relative to level) for both limbs (FL LME, P<0.0001; HL LME, P<0.0001) (Fig. 2, Table 2). Consistent with these data, we found that average parasagittal GRF angle (θ_parasagittal) in both limbs became more negative during decline walking (indicating an increased braking effort) and more positive during incline walking (indicating a more propulsive effort) for each limb (FL LME, P<0.0001; HL LME, P<0.0001; Fig. 3A). We also found no significant differences in average frontal GRF angle (θ_frontal) due to condition for either limb (FL LME, P=0.416; HL LME, P=0.919; Fig. 3B).

Condition had no significant effect on shoulder height (LME, P=0.22) or hip height (P=0.84) (Fig. 4). ELL increased significantly during decline locomotion relative to the other two conditions in both limbs (FL P=0.002; HL P=0.005). Consistent with these data, we found that sprawl area significantly increased during decline relative to the other two conditions in both limbs (FL P=0.002; HL P=0.004), indicating alligator limbs are more abducted during decline walking.

We observed significant inter- and intra-individual variation in joint kinematics during stance phase of walking in alligators (Figs S1 and S2). With the exception of wrist net excursion during decline (Fig. 5, Table 3), most joint kinematic variables tested (e.g. start/end angles, joint flexion/extension) yielded non-significant results when run through our LME model. We found that the wrist has a net dorsiflexion excursion during level and incline walking (−8.8±7.5 deg and −10.8±7.7 deg, respectively), but shifts to a net palmarflexion excursion (1.4±14.0 deg) during decline walking (LME, P=0.005).

We predicted that alligators would support a larger proportion of their body weight with their hindlimbs during incline walking and their forelimbs during decline walking. This prediction was partly based on the assumption that juvenile alligators had a COM closer to their hindlimbs (Willey et al., 2004). However, we found that vertical impulses were statistically similar between forelimbs and hindlimbs during level walking in the alligators used in this study (Table 2). Recent work shows that COM position shifts its craniocaudal position across the size range in alligators (Iijima et al., 2021); therefore, it is possible that the alligators used in this study (body mass range 0.47–0.61 kg) have a COM closer to 50% of their gleno-acetabular length.

Regardless of COM distribution, other quadrupeds such as horses (Dutto et al., 2004), dogs (Lee, 2011) and goats (Arnold et al., 2013) shift body weight support between limb pairs during graded locomotion when compared with level locomotion. This pattern is also observed in primates when comparing the relative role of limb pairs during walking versus climbing (Hanna et al., 2017). However, we did not observe significant differences in vertical impulses for either limb in alligators due to condition (Table 2). This suggests a 15 deg locomotor grade does not shift the relative contributions of the forelimb and hindlimb in juvenile alligators. It remains unclear whether differences in body weight support across grades between alligators and other quadrupeds are due to differences in body plan (i.e. relative body mass, COM distribution), limb posture or a combination of the two. Future work manipulating COM position with the addition of extrinsic loads in quadrupeds of varying sizes is needed to properly address the effect of COM position on limb mechanics during locomotion. In general, alligators seem to maintain consistent vertical impulses across conditions while selectively modulating craniocaudal impulses to maintain forward speed as they transition between grades (see below). This allows alligators to manage the increase in total GRF magnitude necessary for graded locomotion while prioritizing speed maintenance when transitioning between grades.

We predicted alligators would use their hindlimbs to produce larger propulsive forces during incline walking and their forelimbs to produce larger braking forces during decline walking (when compared with level walking). As predicted for the hindlimb, we found that θ_parasagittal increased from 7 deg for level walking to 22 deg for incline walking, indicating a stronger propulsive effort by the hindlimb when walking uphill. As predicted for the forelimb, we found that θ_parasagittal decreased from −5 deg for level walking to −22 deg for decline walking, indicating a stronger braking effort by the forelimb when walking downhill (Fig. 3). These results are consistent with individual limb data from dogs (Lee, 2011), horses (Dutto et al., 2004) and opossums (Lammers et al., 2006) moving across varying grades. In general, it seems that the hindlimbs of quadrupeds are better suited for propulsive force generation, whereas the forelimbs are better suited for braking. This is consistent with anatomical data in mammalian quadrupeds showing significantly more extensor muscle mass in the hindlimbs when compared with the forelimbs (Kilbourne and Hoffman, 2013), a pattern also observed in alligators (Allen et al., 2010, 2014). Alligators may modulate limb muscle recruitment or function (length trajectories) to maintain similar limb forces despite the dimensional disparity among forelimbs and hindlimbs. Future work measuring in vivo muscle function in forelimb and hindlimb muscles during quadrupedal locomotion will likely reveal how mechanical function shapes the physiology and control of limb muscles.

We predicted alligators would primarily modulate proximal limb joint kinematics to transition across conditions. Most legged animals increase hip retraction (i.e. extension) on inclines (Carlson-Kuhta et al., 1998; Hoyt et al., 2002; Jayne and Irschick, 1999; Reznick et al., 2021) and protract (i.e. flex) limbs more on decline relative to level walking (Jayne and Irschick, 1999; Reznick et al., 2021; Smith et al., 1998). We found some support for alligators increasing hip retraction during incline when compared with level walking (Fig. 5), but this difference was not statistically significant (Table 3). We did however observe that the range of joint angles used tended to increase during incline walking compared with level locomotion (Fig. 5, Table 3). This pattern is consistent with the need to increase positive mechanical work production when walking up an incline and is most noticeable for the joints of the hindlimb. A similar pattern has also been observed in geckos (Birn-Jeffery and Higham, 2016) and goats (Arnold et al., 2013).

Our observation that alligators used a more sprawled limb posture during decline walking suggests that alligators may use movements outside of the parasagittal plane to improve static stability by increasing the base of support when walking downhill. Most legged vertebrates studied to date have parasagittal limb motions during locomotion and increase stability on grades by decreasing proximal joint height and bringing their COM closer to the ground (Birn-Jeffery and Higham, 2014). Decreased proximal joint height in upright animals causes increased limb joint flexion and decreased effective mechanical advantage across limb joints (Arnold et al., 2005; Biewener, 1989). Alligators and other sprawlers likely benefit from non-parasagittal limb movements as a mechanism for increasing stability without flexing their limbs. This interpretation is nicely exemplified by the limb posture in polypedal organisms (Martinez, 1996) or robots (Krummel et al., 2014), where non-parasagittal changes in posture are often associated with increased stability. It is also possible that the large tail of alligators, which drags on the substrate during locomotion, contributes to passive stability, which may alleviate the need for kinematic modulation of limbs across grades. Future work on the non-parasagittal limb movements used by sprawling species transitioning between grades is needed to support this notion.

In this study, we examined how alligators transition between level, incline and decline walking. We measured individual limb forces and 3D kinematics as alligators walked steadily across level, 15 deg incline and 15 deg decline conditions. We compared our results with strategies used by other legged animals in an effort to identify which features of an animal's body plan and locomotor mechanics effect overall limb function. We found that juvenile alligators maintain spatiotemporal characteristics of gait and locomotor speed by selectively modulating craniocaudal impulses (relative to level locomotion) when transitioning between grades. Alligators seem to accomplish this using a variety of kinematic strategies, but consistently sprawl both limb pairs outside of the parasagittal plane during decline walking. This latter result suggests alligators and other sprawling species likely benefit from movements outside of the parasagittal plane as another axis of variation to modulate when transitioning between graded substrates.

The authors would like to thank T. Owerkowicz for providing the alligators for the study. We thank members of the Azizi Lab for helpful comments on an early draft of the manuscript. Thank you to J. R. Hutchinson and one other anonymous reviewer for their comments that significantly improved the paper.

This article has an associated ECR Spotlight interview with Adrien Arias.