Tree frogs (Polypedates dennysi) landing on horizontal perches: the effects of perch diameter Free

Natural habitats present a complex array of substrates that differ in shape (Hill et al., 2018; Song et al., 2021), inclination (Endlein et al., 2013; Song et al., 2022), compliance (Hunt et al., 2021) and roughness (Russell and Johnson, 2007; Song et al., 2020). To occupy higher ecological niches, animals must be able to move quickly and effectively with minimal risk of failure (Alexander, 2003). Jumping is a particularly efficient movement employed by many animals to swiftly traverse land (Alexander and Vernon, 1975; Schwaner et al., 2018), negotiate steep terrain (Yuan et al., 2022; Zong et al., 2022), access elevated perches (Goetzke et al., 2019; Hunt et al., 2021) and even navigate the surface of water (Song et al., 2024; Yang et al., 2016). Considerable attention has been paid to the jumping phase (Astley et al., 2015; Brown, 1967; Schwaner et al., 2018; Wang et al., 2014), whereas the landing phase, which is just as crucial as jumping, remains insufficiently understood, especially on challenging terrain such as tree branches (Bijma et al., 2016). A thorough comprehension of landing will enrich our knowledge of the principles for leaping locomotion, thereby advancing jumping robotics (Armour et al., 2007; Zhang et al., 2020) and potentially contributing to improved emergency landing systems for aircraft.

Previous studies have examined the landing of several species on flat surfaces. When cats fall from a height, they consistently employ a technique to attenuate the impact by sequentially contacting the ground with their front and hind feet (Kane and Scher, 1969; Wu et al., 2019; Zhang et al., 2014). As the height of the fall increases, they rely more on their hind feet (Wu et al., 2019). Frogs and toads can land with their front feet first (Gillis et al., 2014; Nauwelaerts and Aerts, 2006) or land on their trunks with limbs extended (Essner et al., 2010). These landing strategies entail specific adaptations, such as aligning the centre of mass with the orientation of the front feet (Azizi et al., 2014) and engaging relevant muscles before landing (Ekstrom and Gillis, 2015; Gillis et al., 2010). As the leap distance increases, the pre-landing elbow extension and post-impact elbow flexion increases (Gillis et al., 2014). In the second tactic, the incorporation of ventral structures enables frogs to cushion the impact during landing effectively (Essner et al., 2010). Quite differently, Anolis lizards first contact the substrates with their hind feet when landing, followed by their front feet (Gilman et al., 2012). In contrast, jumping crested geckos can use their front feet, hind feet or bellies to make initial contact with the ground, with a preference for front feet or nose when landing on sloping surfaces (Higham et al., 2021). The trunks of crested geckos frequently exhibit increased curvature after the initial contact and then move toward the substrate to complete the landing (Higham et al., 2021). These findings highlight the effects of the functional morphology of creatures on their landing techniques and the necessity of taking the target positioning into consideration when studying landing behaviour.

Tree frogs have attracted massive attention because of their adhesive feet (Barnes et al., 2006; Endlein et al., 2013; Federle et al., 2006; Hanna and Barnes, 1991; Persson, 2007) and remarkable jumping abilities (Astley and Roberts, 2014; Kargo et al., 2002; Reilly and Jorgensen, 2011; Wang et al., 2014). Unlike when they are on the ground, animals must exercise heightened caution when manoeuvring in a tree-dwelling environment. They must mitigate the impact and develop reliable grips in landing to avoid lethal falls (Bijma et al., 2016; Herrel et al., 2013; Manzano et al., 2008). Several studies have examined the attachment and locomotion of tree frogs on surfaces resembling plants (Endlein et al., 2017; Herrel et al., 2013; Hill et al., 2018) and found that they can generate robust grips. However, additional investigation is needed to explore their arboreal landing, which involves highly dynamic interactions between the attachment system and the perches.

Bijma et al. (2016) conducted a pioneering study on landing of the frog Trachycephalus resinifictrix on a very slender stick and discovered that the frogs exhibited an equal chance of landing on either their bellies or limbs. Unlike landing on the ground, the frogs significantly adjusted their body orientations before touching the stick. Consequently, we hypothesized that reducing the diameter of the target would cause adjustments in body postures during landing, and that the preference of using body parts in the initial touch would be unaffected. To verify this hypothesis, we comprehensively examined the landing of the tree frog Polypedates dennysi on perches of varying diameter using high-speed cameras and force measuring systems. The findings from this study will advance our understanding of arboreal locomotion and provide valuable insights for developing jumping robots capable of safe landing (Roderick et al., 2021).

Seven individual Chinese flying tree frogs [Polypedates dennysi (Blanford 1881)] acquired from commercial vendors were utilized for experiments in this research (N=7). These specimens had a mass range of 51.6 to 85.1 g and were kept separately in glass containers of 40×40×50 cm. The animals were provided with live crickets as their food source and were exposed to a daily cycle of 12 h:12 h light:dark. The experiments were approved by the Jiangsu Association for Laboratory Animal Science and Jiangsu Forestry Department (approved file no. 2019-152) and were performed under the Guide of the Laboratory Animal Management Ordinance of China. None of the animals were injured in any of the experiments.

As depicted in Fig. 1, a series of stiff, hollowed cylindrical bars with different diameters (16, 32, 64 and 128 mm) but similar lengths (∼350 mm) were horizontally connected to a strain-gauge type force sensor to mimic perches in arboreal environments. All perches were coated with waterproof paper with a consistent roughness of R_a=15.4 μm to ensure that all perches had the same surface properties with just the variation in diameter. Based on pretests, the targets were positioned 190 mm beneath the jumping point, with a horizontal distance of 360 mm. Considering that P. dennysi could land at any position on the perches, the sensor was explicitly designed by taking advantage of Whitstone full bridges (Ştefănescu, 2020) to record three-dimensional forces regardless of the load positions. Fig. 1A defines forces acting on the frogs, as the arrows indicate. F_y represents the force along the centre line of the perch, F_z denotes the vertical force and F_x indicates the force perpendicular to F_y and F_z, with a positive forward direction. The force signals were collected using a NI DAQ model (NI 9178+9237, US) at a sampling rate of 1662 Hz. At the same time, the behaviours of P. dennysi were captured with two orthogonal high-speed cameras at 360 frames s⁻¹ (Blackfly, Teledyne FLIR, USA).

Each frog was subjected to a maximum of three trials every 2 days. The perches were also altered randomly every day to prevent the frogs from becoming habituated to a particular perch. The frogs were placed on the jumping point with their bodies in the x direction and then encouraged to jump by slightly touching their anus with a writing brush (Fig.1A). If the frogs altered their direction more than 15 deg from the x direction before jumping, the trials were discarded. The frogs' weight was assessed before each trial as a rough gauge of the trial's effectiveness. If there was a notable discrepancy between the weight after stabilization and before the trial, the trial was also discarded, and the system was meticulously inspected in preparation for the subsequent trial. Ultimately, every participant completed a total of eight trials.

To look into the landing of P. dennysi on the perches, we first digitized the trajectories of 10 landmarks on their limbs and trunks (i.e. the snout, the vent, the roots of 4 limbs, and the foot centres at four limbs; see Fig. 1A) from the highspeed videos using MATLAB software (Hedrick, 2008). Then, we calculated the kinetic and kinematic parameters, such as the velocities and the body angles from orthogonal camera views. The initial landing positions (ILPs) of frogs were categorized based on the use of limbs and bellies. The ILPs using limbs included a single front foot (SF), double front feet (DF), a single hind foot (SH) and double hind feet (DH). In the trials where the first contact locations were on the belly, we separated the belly length into three equal sections and categorized the belly touch into three groups: anterior belly (AB), middle belly (MB) and posterior belly (PB). Considering that the frog's mass varied significantly due to feeding, consumption and excretion, we normalized the force results by dividing them with the post-stabilization weights (BW, the vertical force after stabilization on the perch; Fig. 1B). When the vertical force fluctuations were less than 10%, the frog was assumed to have attained stability on the perch. The period from the initial contacts to the moment of stabilization was defined as the time expense for P. dennysi to stabilize in landing. The resultant forces were also calculated to assess the impacts of landing better.

Statistical analyses were conducted using IBM SPSS 25 (IBM, USA). In particular, we used chi-square analysis (χ²) to ascertain the potential correlation between the preference in initial landing postures and the perch diameters. A linear mixed model (LMM), with individual as the random effect, was used to establish the association between the other parameters describing the landing and the perch diameters. Data transformations were performed once the normality and homogeneity of variance were violated. For example, when examining the impact of ILPs on stabilization time, we ran four LMM tests, each focusing on a specific perch diameter. When all variables were combined, we designated the primary variable as the fixed effect and the secondary variable as the covariate. In the example above, we identified ILPs as the fixed effect, perch diameter as the covariate and individuals as the random effect.

After leaping from a platform and a period of gliding, the P. dennysi approached the horizontal perches (Movie 1) at an average speed of approximately 1.5 m s⁻¹ and then landed on the perches. As shown in Fig. 2A and Movie 1, the tree frogs demonstrated diverse ways to initially engage with the perch, including using a single front foot (SF; Fig. 2A1), double front feet (DF; Fig. 2A2), anterior belly (AB; Fig. 2A3), middle belly (MB; Fig. 2A4), posterior belly (PB; Fig. 2A5), double hind feet (DH; Fig. 2A6) or a single hind foot (SH; Fig. 2A7). When the diameter of the perch increased from 16 mm to 128 mm, the count of frogs initially engaging with DF rose from 8 to 22, while AB decreased from 22 to 8 and MB slightly decreased from 12 to 8 (χ²=14.52, P=0.024). In comparison, the counts of SF, PB, DH and SH remained relatively unchanged (χ²=1.11, P=0.99, Fig. 2B).

The yaw angles of P. dennysi upon touching the perches are displayed in Fig. 2C and Table 1. The yaw angles ranged from 15 to 39 deg in SF and from 15 to 43 deg in SH (Fig. 2C, pink and grey symbols). The yaw angles seemed randomly distributed from 0 to 34 deg on all perches (Fig. 2C, gold, olive and cyan symbols; F≤0.36, P≥0.78) if the bellies were first used. However, the maximum yaw angles increased with perch diameters, ranging from 18 to 33 deg in DF (Fig. 2C, orange symbols) and 6 to 19 deg in DH (Fig. 2C, blue symbols). Fig. 2D displays the pitch angles. When the frogs touched the perches with a front foot, the pitch angle varied from −23 to 7 deg. However, when both front limbs were used, the pitch angle remained consistently negative, ranging from −33 to −2 deg. The pitch angle increased as the initial contact point moved from the anterior belly (−28 to 13 deg) to the hind feet (−9 to 23 deg) (F_6,214.763=20.687, P<0.001), showing no specific correlation with perch diameter (P=0.356).

Fig. 3A,B and Table 2 display the angle formed between the frogs' limbs and the sagittal plane as they touch the perches. If P. dennysi initially made contact with the target using a front foot, the angles between the front limbs and the sagittal plane measured at least 30 deg (range: 30–58 deg), whereas the hind feet had angles ranging from 25 to 64 deg (Fig. 3A,B, pink). When both front feet were used simultaneously, the angle between the front limbs and the sagittal plane decreased (Fig. 3A, orange; F_1,86.287=9.286, P=0.003), varying from 19 to 44 deg, while that of the hind feet also changed (Fig. 3A, orange, range: 14–50 deg; F_1,79.415=18.320, P<0.001). The angle between the front limbs and the sagittal plane increased when the contact position changed from the anterior belly (ranging from 19 to 60 deg) to the hind feet (ranging from 46 to 67 deg in SH) (F_4,125.033=7.18, P<0.001). The angle between the hind limbs and the sagittal plane in AB and MB were comparable (F_1,96.404=0.572, P=0.451), varying from 10 to 60 deg. In PB, the angle between the hind limbs and the sagittal plane varied from 14 to 43 deg, but in DH and SH, they rose to 33–63 deg (Fig. 3A, cyan, blue and grey symbols; F_2,22.037=6.611, P=0.006).

We also calculated the angles between the coronal plane of the trunks and the limbs from a side view, as depicted in Fig. 3C,D and Table 1. The P. dennysi raised their hind feet from 8 to 46 deg over the trunk when they were not initially using them to engage with the perches (Fig. 3C). If the hind feet were used first, they may be flexed either upwards or downwards, creating angles between −38 and 38 deg concerning the coronal plane of trunks. The front feet were consistently positioned below the trunk at angles varying from −2 to −42 deg during early encounters when both front feet were utilized. When using a single front foot, the angles between the front limbs and the coronal plane of trunks ranged from −29 to 19 deg. However, when the anterior or middle bellies were employed, the angles varied between −35 and 40 deg, either negative or positive. As the initial contact location migrated from the posterior belly to the hindfoot, the angles between the front limbs and the coronal plane of trunks tended to become more positive (−0.5 to 16 deg in SH).

Fig. 4A shows the time P. dennysi took to land steadily on perches. On perches with a diameter of 16 mm, the time to stabilize fell from 0.95±0.23 s (SF; mean±s.d.) to 0.68±0.25 s (MB) and subsequently increased to 1.28±0.08 s (SH) as the initial contact position changed from front feet to hind feet (F_6,47.112=7.146, P<0.001). As the diameter of the perches increased, the stabilization time tendencies over the ILPs resembled those on the 16 mm perch, albeit with reduced values. The stability period on the 128 mm perch reduced from 0.57±0.16 s in SF landing to 0.23±0.06 s in MB landing and subsequently increased to 0.43±0.16 s in SH landing (F_6,47.793=4.283, P=0.002, after square root transformation). Fig. 4B,C shows the maximum forces in the fore–aft and vertical directions. The maximum fore–aft forces for all ILPs rose when the diameter of the target perches grew (F_3,214.69=22.717, P<0.001, after square root transformation) and increased when the initial contact position switched from the front feet to the hind feet (F_6,214.69=34.298, P<0.001). The frogs experienced an increase in maximal fore-aft force from 2.87±1.11 BW in SF to 6.42±0.49 BW in SH when it landed on the 16 mm perch (F_6,47.652=7.803, P<0.001). On the 128 mm perch, the most significant fore–aft force rose from 3.95±0.96 BW in SF to 7.90±0.96 BW in SH (F_6,46.923=10, P<0.001, after square root transformation). Some individuals exerted a fore–aft force over 13.5 times their body weight. Shifting from the front feet to the hind feet resulted in an initial rise followed by a drop in peak vertical forces. During landing on the 16 mm perch, the highest vertical force rose from 4.0±0.69 BW in SF to 6.87±0.95 BW in MB and decreased to 4.69±0.16 BW in SH (F_6,49=11.492, P<0.001 after reciprocal transformation). While landing on the 128 mm perch, the maximum vertical force rose from 4.10±0.56 BW in SF to 12.62±2.34 BW in MB and, after that, dropped to 7.71±3.51 BW in SH (F_6,46.221=15.835, P<0.001, after square root transformation).

Arboreal creatures that perform jumping manoeuvres need stable landings to stay safe. Firstly, jumping animals must securely grip their target surface to avoid falling, which could be fatal for many species. Although several animals have adapted methods to lessen the impact force of falling (Jusufi et al., 2008), the energy required to ascend back to their habitat is substantial. It is also crucial to avoid injury to body tissues during landing (Günther et al., 1991). Using their claws and tails, lizards (Siddall et al., 2021) and squirrels (Hunt et al., 2021) can safely land on steep targets. In this work, tree frogs P. dennysi, which have neither claws nor tails, demonstrated exceptional precision in landing on horizontally placed perches with varying diameters (16, 32, 64, and 128 mm) (Movie 1). They never missed the targets nor fell from the perches after landing. It was shown that such a safe landing benefits from their ability to generate adhesion (Bijma et al., 2016). Here, we further highlight the significance of the adjustment of body posture during landing.

Prior research has demonstrated that frogs and toads can land on a flat surface using their front feet (Gillis et al., 2014; Nauwelaerts and Aerts, 2006) or bellies with limbs extended (Essner et al., 2010). A recent study on T. resinifictrix suggested that, in addition to the front feet and bellies, the hind feet also play a role in tree frogs landing on perches (Bijma et al., 2016). The tree frogs in this work could initiate engagement with the target using either their limbs or trunk, including a single front foot, double front feet, anterior belly, middle belly, posterior belly, double hind feet or single hind foot (Fig. 2A). However, two unusual landing modes reported by Bijma et al. (2016) were not observed in this study: (1) frogs leaping over the target and reaching back with their front feet to make contact with the target (see fig. 4b in Bijma et al., 2016) or (2) frogs extending their hind feet forward to make contact with the target before reaching it (see fig. 4d in Bijma et al., 2016). Notably, the targets in their investigation were narrower (10 mm) and situated at different distances from the jumping point. Additionally, the animal species was also different. Therefore, the discrepancy could be due to the goal variance, but further thorough analysis is necessary.

In all experiments, frogs made contact with perches using a single front foot in less than one-seventh of the total number of trials; similarly, the number of trials where frogs initiated contact with the perches using their hind feet or posterior bellies was low. Polypedates dennysi prefers using twin front feet or the abdomen area. Unlike our initial hypotheses, increasing the perch diameter led to a significant preference for using both front feet (DF) to engage with the perches, as shown in Fig. 2. Landing on small things is more likely to fail when utilizing limbs owing to the restricted surface area on the arms and footpads compared with the abdomen. The abdominal area has a larger surface area and increased flexibility, enabling more accurate and efficient targeting of small landing sites.

Tree frogs tend to sway or yaw when they approach perches. Notably, we found that they tended to turn towards the base of the perches in this work. It is unclear if this inclination results from visual impact of the root fixation. We did not continue researching the matter and instead determined the absolute values of the yaw angle, as depicted in Fig. 2C. Trachycephalus resinifictrix consistently adjusts its position while landing on a horizontally mounted perch to align with it (Bijma et al., 2016). We found similar deviations in P. dennysi but they were not as straightforward as those observed in T. resinifictrix. When P. dennysi made contact with the perches with a single front or hind foot, the body had a yaw angle of at least 15 deg. However, extending the limbs on duty resulted in smaller angles between the limbs and the mesopendicular plane of perches. For other ILPs, the yaw angles were far smaller, barely exceeding 30 deg. Unlike the yaw angles in belly landings, which were not linked with the diameter of the perches, the yaw angles for foot landings noticeably rose as the perch diameters grew. Large yaw angles hinder the ability of both limbs to simultaneously touch small perches effectively. However, perches larger than the space between frogs' limbs offer more surface, reducing the likelihood of missing the target. This explains why tree frogs tended to land with both front feet on more prominent perches more often, as mentioned earlier.

Because all perches were set to be 190 mm beneath the take-off point, the P. dennysi were initially supposed to adopt diving postures (i.e. head down) to touch the perches. The experimental results indicated that tree frogs favoured diving postures while making initial contact with perches using the front limbs. Particularly in DF, the pitch angles were negative, and the double front limbs on duty were positioned beneath the trunk and less extended. Such posture might help align the centre of mass with the orientation of the front feet (Azizi et al., 2014). Frogs in belly landings showed equal possibilities of encountering the perches with positive or negative pitch angles. The front feet could be positioned below or above the coronal plane, while the hind feet were placed above the coronal plane. When the initial contact position shifted to the hind limbs, the pitch angles tended to be more positive. The front limbs were more inclined to be fully extended and aligned above the coronal plane, whereas the hind limbs were more inclined to be aligned below it. It has been previously found that frogs and toads may activate appropriate muscles before landing (Ekstrom and Gillis, 2015; Gillis et al., 2010). The above adjustment reveals the animals' adaptability in modifying body positions and limb orientations for aboral landing.

Fig. 4A illustrates the time tree frogs need to stabilize themselves during landing using different ILPs. The time needed for stabilization significantly varies with changes in the target perch diameter and landing approach. In all cases, tree frogs can stabilize their bodies in less than 1.5 s. And, as the diameter of the target increases, the required stabilization time decreases significantly. Smaller targets give tree frogs a smaller contact area, necessitating additional limb movements or body deformations to establish engagement. When landing on the same targets, landings involving initial contact with the abdomen require a shorter stabilization time compared with landings involving limb-initiated contact. This could be attributed to the simultaneous bending of the front and hind feet towards the target, facilitating quick adhesion while alleviating impacts when the abdomen is used for initial contact. However, when the initial contact is established with the front or hind feet, other body parts can only swing in a single direction to increase body contact with the target perch.

Fig. 4B,C shows the peak fore–aft and vertical forces indicating the maximum impact forces experienced by tree frogs throughout the landing process. The maximal impact forces are affected by the landing posture and the diameter of the target. For all ILPs, the maximum horizontal impact force increases with an increase in the diameter of the target. When the tree frog establishes initial contact with the target using a single front foot, a hind limb or double hind feet, the maximum vertical impact forces were not significantly affected by the perch diameter. However, as the diameter of the targets grows, so does the maximum vertical impact force. On all perches, the peak fore–aft impact force was smallest when the frogs landed with front feet (i.e. SF), but increased when the bellies were initially used and reached more than six times body weight when a single hind foot was used for initial contact. Namely, the maximal fore–aft impact force increases when the first touching point shifts from the front feet to the torso and hind feet. The maximum vertical impact force, on the other hand, shows an increasing tendency followed by a declining trend. Notably, the changing trend of the maximum vertical impact force is correlated to the stabilization time. The results here also help to explain why the tree frogs prefer to land with double front feet on large perches but use bellies on small targets (Fig. 2). Tree frogs can stabilize relatively quickly without generating large impact forces (Fig. 4).

Several reasons can be suggested for the observed link between the maximal impact forces, ILPs and target diameters. First, as previously stated, when tree frogs make initial contact with the target perch using their front feet, the back half of their body spins downward, creating centrifugal motion in the backward direction (the clockwise direction), which diminishes the impact force. Conversely, when tree frogs make initial contact with an object with their hind feet, the front half of their body spins downward, creating a centrifugal force in the forward direction and boosting the impact force. In addition, when tree frogs first make contact with the target with their front feet, the limbs contract, helping to cushion the impact. However, they cannot use limb deformation for cushioning when using their hind feet for initial contact.

The largest vertical impact force can reach up to 16 times body weight when the tree frog makes initial contact with the mid-body on a 128 mm round perch. When the hind feet make first contact with a 128 mm round perch, the largest fore–aft impact force can exceed 14 times body weight and far beyond the ability of frogs estimated from the quasi-static measurements (Endlein et al., 2017; Meng et al., 2019). Presumably, the whole-body adhesion stated above and the rate-dependent adhesion (Song et al., 2023) might account for the ability of frogs to bear such high forces, but it requires more systematic investigation.

Studies on animal locomotor performance are only helpful when undertaken in an ecologically appropriate environment (Irschick and Garland, 2001). This study investigated the landing performance of P. dennysi tree frogs on perches of different diameters, offering valuable information into their landing biomechanics. Our research indicates that tree frogs exhibit specific initial landing postures (ILPs) based on the diameter of the perch. They seem to favour using their belly area on narrower platforms and double front feet on wider perches. The angles between the limbs and trunk changed with the ILPs, indicating that tree frogs may adjust their body position while landing. Subsequently, the time required for stabilization during landing varied greatly. The impact forces of tree frogs varied with both perch diameter and ILP, with smaller perches resulting in lower impact forces. These findings highlight the necessity of considering perch diameter and landing style when studying the biomechanics of arboreal locomotion. Further research in this area could help us to understand arboreal landing biomechanics and inspire advances in biological and technical areas.

We thank Zhouyi Wang for his support in this study and the reviewers for their constructive suggestions.