Nonlinear variation in clinging performance with surface roughness in geckos

Abstract Understanding the challenges faced by organisms moving within their environment is essential to comprehending the evolution of locomotor morphology and habitat use. Geckos have developed adhesive toe pads that enable exploitation of a wide range of microhabitats. These toe pads, and their adhesive mechanisms, have typically been studied using a range of artificial substrates, usually significantly smoother than those available in nature. Although these studies have been fundamental in understanding the mechanisms of attachment in geckos, it is unclear whether gecko attachment simply gradually declines with increased roughness as some researchers have suggested, or whether the interaction between the gekkotan adhesive system and surface roughness produces nonlinear relationships. To understand ecological challenges faced in their natural habitats, it is essential to use test surfaces that are more like surfaces used by geckos in nature. We tested gecko shear force (i.e., frictional force) generation as a measure of clinging performance on three artificial substrates. We selected substrates that exhibit microtopographies with peak‐to‐valley heights similar to those of substrates used in nature, to investigate performance on a range of smooth surfaces (glass), and fine‐grained (fine sandpaper) to rough (coarse sandpaper). We found that shear force did not decline monotonically with roughness, but varied nonlinearly among substrates. Clinging performance was greater on glass and coarse sandpaper than on fine sandpaper, and clinging performance was not significantly different between glass and coarse sandpaper. Our results demonstrate that performance on different substrates varies, probably depending on the underlying mechanisms of the adhesive apparatus in geckos.

locomotor performance in various habitats, and variation in physiological and morphological characters may, in turn, increase performance in certain habitats (Kohlsdorf et al., 2004). Therefore, studies of ecological morphology and evolution often link morphology, performance, and ecology to suggest adaptation (Hagey, Puthoff, Crandell, Autumn, & Harmon, 2016;Wainwright & Reilly, 1994).
Natural substrates are usually structurally and chemically substantially different from those used in laboratories (Russell & Johnson, 2007Stark et al., 2015). A few recent studies have examined the surface topography of natural substrates and how it affects adhesion in geckos, highlighting the unpredictability (i.e., nonuniform amplitude and wavelengths of asperities creating varying undulance) of natural substrates, especially in comparison with artificial substrates previously used in gecko adhesion studies (Cole, Jones, & Harris, 2005;Naylor & Higham, 2019;Russell & Johnson, 2014;Vanhooydonck et al., 2005). Other studies have also stressed the importance of using ecologically relevant substrates to better understand performance in insects (Bullock & Federle, 2011), tree frogs (Langowski et al., 2019), and geckos (Hagey et al., 2014;Higham, Russell, Niewiarowski, Wright, & Speck, 2019;Peattie, 2007). Most recently, Higham et al. (2019) summarized the importance, methods, and reasons for including ecological parameters like surface characteristics in gecko adhesion studies.
When setal fields are first deployed, spatulae make direct contact with the surface microtopography, and they go through a proximal pull, undergoing a preloading phase. This enables the generation of shear forces and increases the overall strength of the bond (Autumn, 2007;Autumn et al., 2000;Russell & Johnson, 2007). Hence, substrate surface microtopography has a major influence on the area available for attachment from a single spatula to the whole setal field and significantly influences the magnitude of force generated by the adhesive apparatus (Russell & Johnson, 2007). The peak-to-valley heights of the surface topology are one way to estimate roughness and therefore are also one way to assess the area available for setal contact at different microtopographies. Investigating the performance of geckos on surfaces with specific kinds of micro-and nanotopography is an important element of understanding adhesion in nature (Gamble et al., 2012;Russell & Johnson, 2007. Although studies on smooth artificial surfaces have been important for unraveling the physical principles behind gecko adhesion, it is not clear if such studies can be used to estimate performance, or relative performance, of different species of geckos on rougher or nonuniform surfaces, such as those they encounter in their natural environment.
Based on mechanisms predicted from observing gecko adhesion on artificial surfaces that are uniform and allow a very high proportion (nearing 100%, Russell & Johnson, 2007) of setae to make contact, we might expect a consistent decline in gecko attachment force with increasing roughness, presumably as setal fields find less purchase on uneven surfaces (Cole et al., 2005;Fuller & Tabor, 1975; Figure 1a). Researchers have, however, found that setal fields can accommodate rougher surfaces, even though they are thought to have evolved for adhering to smooth substrates (e.g., Rhoptropus cf. biporosus; Russell & Johnson, 2014). In addition, recent studies have highlighted a multifunctional and synergistic relationship between claws and toe pads in geckos. Rough substrates that may provide limited surface area for setal attachment do allow mechanical purchase for claws. When substrates permit attachment of both claws and toe pads, that may increase clinging performance, even though there is limited surface area available for the setal fields by themselves. On the other hand, certain fine-grained substrates do not permit secure attachment of claws or setal fields, leading to diminished clinging performance (Naylor & Higham, 2019). These combined processes may lead to a trend in which smooth substrates (permitting maximal engagement of setal fields) allow generation of great clinging performance, whereas, on certain coarse substrates, an intermediate proportion of the setal field can engage in conjunction with mechanical interlocking of claws. Further, the lowest performance presumably occurs on substrates of intermediate roughness, which provide poor purchase for both claws and setal fields ( Figure 1b). Thus, surfaces with intermediate roughness may permit only partial contact, producing a nonlinear performance curve, if performance is plotted against peak-to-valley height, or roughness (Huber et al., 2007). In addition, some studies at very small scales suggest that surfaces with very low and quite high levels of roughness will permit increased contact between spatulae and the surface compared to surfaces with intermediate roughness (Huber et al., 2007), which would also give rise to a nonlinear graph of shear forces in relation to roughness.
Thus, we suggest there are multiple ways in which the adhesive apparatus of geckos could interact with substrates, which may give rise to different relationships between substrate roughness and shear forces generated. We predicted one of two possible trends in gecko attachment when examined on substrates with varying roughness (glass, fine sandpaper, and coarse sandpa-  Figure 1b). We quantified shear forces produced by two gecko species with different morphology, body size, and habitats, along a roughness gradient. We aimed to investigate the shape of the response, as shear force generated versus peak-to-valley height of each surface.

| Study species
This study was conducted between August 2017 and December 2018. Two Diplodactylid gecko species (the northern spotted velvet gecko, Oedura coggeri, and the giant tree gecko, Pseudothecadactylus australis) were used to determine whether clinging ability imparted by geckos would decline monotonically with roughness or vary nonlinearly across substrates. Ten adult individuals (three males and seven females) of O. coggeri, a saxicolous species, were collected exclusively from rocky microhabitats around Paluma Range National Park, Queensland, Australia (GPS coordinates: −18.982772, 146.038974; datum = WGS84; 10 km radius), and housed at the James Cook University, Townsville Campus. Similarly, ten adult individuals (six males and four females) of P. australis, an arboreal species, were collected from tree bark and bamboo in Iron Range National Park, Queensland, Australia (GPS coordinates: −18.054768, 143.322002; 10 km radius), and were tested at a field station prior to release at their site of capture.

| Ecological relevance of substrates
To select test substrates offering similar ecological challenges (at least in terms of peak-to-valley heights) to those faced by O. coggeri and P. australis in nature, we measured the peak-to-valley heights of natural substrates used by geckos (rock, tree bark, and bamboo samples collected at gecko capture sites). To quantify gecko clinging ability on surfaces at least partially representative of natural surfaces, we used F I G U R E 1 Conceptual model in which substrates are ordered by decreasing roughness (coarse sandpaper, fine sandpaper, and glass), suggesting (a) declining shear force with increasing roughness or (b) a nonlinear performance curve in relation to roughness. Points are joined to illustrate the expected shape of trends coarse (P40) and fine (P400) sandpaper with similar peak-to-valley heights as test surfaces in this study ( Figure 2). Additionally, glass was used as a test substrate as it is a smooth substrate, commonly used in gecko performance studies. Average peak-to-valley heights were measured using a surface profile gauge (Landtek Srt-6223 Surface Profile Gauge, accuracy: ±5 µm; resolution: 0.1 µm/1 µm; range: 0-800 µm).
Peak-to-valley heights were measured at 10 random points, within 10 cm of each other, in the laboratory for coarse and fine sandpaper, and from collected samples of rocks used by O. coggeri. Bamboo and bark substrates used by P. australis were measured in the field, using similar methodology. The surface profile gauge was calibrated prior to each measure using supplied standard glass exhibiting peak-to-valley heights of 0 µm. Differences in mean peak-to-valley heights (μm) among the substrate types were quantified using a Kruskal-Wallis test followed by a pairwise Wilcoxon post hoc analysis.

| Clinging ability
We used three artificial surfaces (instead of using the natural surfaces used by the geckos) to ensure that the roughness characteristics and surface chemistry of the rougher surfaces were uniform. This approach allowed meaningful comparisons between species and surfaces, while providing measurements on substrates with peak-to-valley heights similar to those of natural substrates.
Prior to recording clinging ability, mass was measured once for each individual, using a digital scale (resolution: 0.01 g). To measure the surface area of toe pads, the ventral aspect of the hands and feet of all individuals was photographed through glass against a uniform dark background with a scale in each image. Lightroom CC (Adobe Systems Incorporated, 2019) was used to adjust the contrast of images to ensure that the emphasis was on the toe pads only.
The thresholding feature in ImageJ (version 1.52a; Schneider, Rasband, & Eliceiri, 2012) was then used to select these toe pads by saturation, as they contrasted highly with the rest of the image. Measurements were calibrated using the scale incorporated in every image. We calculated the attachment area for each gecko on all five toes on the right hand (manus) and right foot (pes) of all geckos and doubled these measures to calculate the total attachment area for each individual. Each toe was measured once.
To record the clinging ability of geckos when attached to a surface, we attached a force gauge (Extech 475040; resolution: 0.01 Newtons; maximum: 49 N ± 0.4% accuracy, Extech Equipment Pty Ltd) to the inguinal region of the gecko using a harness (Niewiarowski, Lopez, Ge, Hagan, & Dhinojwala, 2008) of fishing line (13.61 kg breaking strength; 0.5 mm diameter). Each gecko was permitted to take one step with each of its four feet on the testing substrate (P40, or P400 grit sandpaper, or glass), thereby ensuring that the natural adhesive system of the gecko was engaged (Collins, Russell, & Higham, 2015;Niewiarowski et al., 2008;Stark et al., 2015). Geckos were then pulled horizontally backward at an angle of 0° relative to the tabletop, using a constant velocity (~0.5 cm/s, calibrated using a 30-cm ruler and stopwatch; Crandell, Herrel, Sasa, Losos, & Autumn, 2014;Irschick et al., 2005;Tulli, Abdala, & Cruz, 2011;Zani, 2000). Each individual lizard was tested three times on each surface (three measures per individual: Cole et al., 2005;McKnight et al., 2019;Tulli, Cruz, Herrel, Vanhooydonck, & Abdala, 2009) using all 10 individuals of each species. Order of testing on each surface type was randomized; therefore, we minimized the likelihood of damage caused to the adhesive apparatus by one substrate negatively influencing performance on another substrate. To reduce variation, the "toe pad engagement" of geckos was scored based on their level of attachment from a scale of 1-3 (highest to lowest attachment), and trials with scores higher than 3 were not included in this study (e.g., if a gecko tried to escape, or it did not appear to actively adhere the substrate, it received a higher score and the trial was excluded; Figure 3). Only one investigator (RP) conducted clinging ability trials to ensure consistency (Tulli et al., 2011). One measure of performance by P. australis on glass substrates was identified as an outlier (much >3 standard deviations from the mean) and was excluded from all further analysis.
Linear mixed-effects models were used to quantify the differences in shear force exerted by both species on coarse and fine sandpaper and glass, in the R package lme4 (Bates, Maechler, Bolker, & Walker, 2015). We constructed nine candidate models with three measures per individual on each substrate as our response variable. To account for intraindividual variation, all models included individual gecko IDs as random effects. Toe pad area is positively correlated with body size (mass; Collette, 1962;Irschick et al., 1996), and larger toe pads are more likely to have a larger setal field area, producing increased shear forces, which increase clinging ability (Irschick et al., 1996;Russell & Johnson, 2014;Webster, Johnson, & Russell, 2009).
Hence, the attachment force generated by the adhesive system on a substrate increases proportionally with an increase in toe pad area and F I G U R E 2 Lateral view of surface microtopography of sandpaper with peak-to-valley heights similar to natural substrates used to measure clinging ability in our study. (a) Cross section of coarse sandpaper (P40; 40× magnification); (b) cross section of fine sandpaper (P400; 150× magnification)

(a) (b)
with mass (Irschick et al., 1996). The species in our study had very different body sizes and toe pad areas (O. coggeri: mean mass = 7.48 g, whole animal mean toe pad area = 55.28 mm 2 ; P. australis: mean mass = 20.21 g, whole animal mean toe pad area = 154.33 mm 2 ); therefore, to account for the influence of mass and toe pad area on absolute force generated, we also included mass and toe pad area as fixed effects in all models, to control for their effects on clinging ability.
Shear force, mass, and toe pad area were log-transformed in all models (Table 1). Model selection was conducted using Akaike's information criterion (AIC) in the R package AICcmodavg (Mazerolle, 2019) to identify the model of best fit (ΔAIC < 2). We conducted post hoc analyses on the best-fit model to identify differences within the fixed effects using the R package emmeans (Lenth, 2019). Results are reported as mean ± 1 standard error. All statistical analyses were conducted in R

| RE SULTS
There was a significant difference in the mean peak-to-valley coarse sandpaper: p < .001; Figure 4).
The best model (ΔAIC < 2) predicting shear force exerted included substrate, mass, and toe pad area as fixed effects, with individual gecko IDs as random effects (conditional R 2 = .59, marginal R 2 = .64; Table 2 and 3). Shear force exerted by both species was significantly greater on

| D ISCUSS I ON
Both P. australis and O. coggeri exerted significantly higher shear forces on glass and coarse sandpaper than on fine sandpaper. Therefore, we did not observe a monotonic decline in performance with increasing peak-to-valley heights, which contrasts with findings of studies in which performance diminished considerably with increasing levels of roughness (Cole et al., 2005;Vanhooydonck et al., 2005). Shear force exerted on coarse substrates was not significantly different from that on glass in either species; thus, our results showed a nonlinear relationship between peak-to-valley heights and  (Collins et al., 2015;Higham & Russell, 2010;Higham et al., 2019;Russell & Delaugerre, 2017).

F I G U R E 3
More comparative studies examining gecko attachment on different substrates are needed to elucidate the potentially context-specific nature of gecko attachment.
The shear force that can be generated by geckos is thought to be impacted by surface topology because topology determines the area available for attachment at the scale of the setal fields and also the degree to which claws can be effective. Natural substrates have microtopographies that are unpredictable and nonuniform compared to glass and other artificially smooth substrates (Russell & Johnson, 2007, highlighting the importance of overall structural considerations of locomotory substrates in gecko adhesion studies . The peak-to-valley heights of the coarse sandpaper we used to measure gecko clinging ability were similar to those of the rock and bark microhabitats used by O. coggeri and P. australis, respectively. Additionally, the fine sandpaper used in our study was similar in peak-to-valley height to bamboo surfaces used by P. australis in nature. There are, however, a range of other characteristics of rough surfaces that may influence attachment, such as variation in amplitude, wavelength , spacing (Zhou, Robinson, Steiner, & Federle, 2014), and microstructuring of surface asperities, which could affect conformity of the adhesive apparatus or the attachment of claws. Additionally, the chemistry of the surfaces could influence interaction strength (Prüm, Bohn, Seidel, Rubach, & Speck, 2013), although we controlled for surface chemistry on both

F I G U R E 4 Peak-to-valley heights of substrates (µm). Substrates include natural surfaces used by Pseudothecadactylus australis
and Oedura coggeri in nature (bark, rock, and bamboo) and test surfaces (coarse and fine sandpaper, and glass) used in this study. The artificial substrates were used to approximate the peak-tovalley heights of natural substrates used by geckos. Rocks used by the northern velvet geckos (O. coggeri) and bark used by giant tree geckos (P. australis) had similar average peak-to-valley height to coarse sandpaper. Bamboo, used by P. australis, had similar average peak-to-valley height to fine sandpaper. TA B L E 2 Models included in selection using Akaike's information criterion, to analyze shear forces exerted by the geckos Pseudothecadactylus australis and Oedura coggeri our rough surfaces by using the same brand of sandpaper, instead of using natural substrates. More research is required to determine the importance of exact topography and chemistry in replicating characteristics of natural substrates and to address the challenges of describing and quantifying surface roughness Persson, Tiwari, Valbahs, Tolpekina, & Persson, 2018). Future research should incorporate carefully described and quantified, realistic surfaces in laboratory studies of attachment Langowski et al., 2018).
We found that shear forces exerted by both P. australis and O. coggeri were greater on glass compared to on fine sandpaper. The gekkotan adhesive system is often characterized as most efficient on smooth substrates (Russell, Baskerville, Gamble, & Higham, 2015).
High performance on glass, observed in our study, was consistent with previous studies that have tested clinging ability on artificial smooth substrates (Autumn et al., 2006(Autumn et al., , 2000Huber et al., 2007;Irschick et al., 1996;Mahendra, 1941;Naylor & Higham, 2019). Smoother surfaces provide an increased area onto which fields of setae can make simultaneous contact, and generate substantial force (Russell & Johnson, 2007 (Song, Dai, Wang, Ji, & Gorb, 2016). In our study, the nonlinear relationship of adhesion with roughness may have occurred because setal fields could maximize contact on smooth surfaces compared to fine-grained substrates. The lower generation of shear forces on fine-grained substrates was possibly because the opportunity for mechanical interlocking of claws was reduced on the finer-grained sandpaper. Fine-grained substrates are less likely to permit claws to attach compared to coarse substrates, producing the lowest generation of shear forces on fine-grained substrates in our study. On coarse surfaces, claws could mechanically interlock, compensating for the lack of effectiveness of setae on such surfaces and increasing overall shear forces. Other studies suggest that rough surfaces provide plenty of purchase for the setal system alone (Russell & Johnson, 2014). For example, the African geckos Rhoptropus cf. biporosus attached well to sandstone substrates, even though they lack tractive claws (Russell & Johnson, 2014). Additionally, Langowski et al. (2019) also report a similar trend in tree frogs, which lack claws entirely.

F I G U R E 5
Clinging ability (log (Newtons)) of the northern spotted velvet gecko (Oedura coggeri) and giant tree gecko (Pseudothecadactylus australis) on glass, coarse sandpaper (P40 grit), and fine sandpaper (P400 grit). Both species performed significantly better on glass and coarse sandpaper than on fine sandpaper, producing a nonlinear trajectory, consistent with the prediction in Figure 1b   Our results show that gecko clinging performance did not decline monotonically with increasing peak-to-valley heights of substrates.
Instead, performance was lowest on the substrate with intermediate peak-to-valley heights and was similar on glass and coarse sandpaper. Our findings demonstrate that gecko attachment forces can be context-dependent and provide a basis for further studies examining the role of substrate and the different elements (claws and setae) in gecko attachment. Further, our study showed: (a) complex mechanisms promoting gecko attachment on multiple substrates with different microtopography, and illustrated that geckos can cling well to rough substrates thought to offer limited accommodation for the adhesive apparatus of geckos (Naylor & Higham, 2019;Russell & Johnson, 2007; and (b) that measuring performance using substrates with ecologically relevant roughness enables the quantification of clinging ability within a range that is biologically and evolutionarily meaningful (Bartholomew, 2005;Hagey et al., 2014;Higham et al., 2019;Langowski et al., 2018;Niewiarowski, Stark, McClung, Chambers, & Sullivan, 2012;Peattie, 2007;Russell & Johnson, 2007. Mukherji for their assistance in fieldwork, husbandry, and monitoring of geckos used in this study. We thank Ross Alford, Lily Leahy, and Kyana Pike for suggestions regarding statistical analysis. We are grateful to Wayne Morris for his guidance in selection and use of the surface profile gauge. We would like to thank three anonymous reviewers for their valuable suggestions in improving the manuscript.

CO N FLI C T O F I NTE R E S T
The authors have no competing interests.

AUTH O R CO NTR I B UTI O N S
RP, EN, JR, and LS conceived the ideas and designed the methodology; RP collected the data; RP, EN, JR, and LS analyzed the data; and RP led the writing of the manuscript. All authors contributed critically to the drafts and gave final approval for publication.