substrate diameter and compliance affect the gripping...

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INTRODUCTIONThe locomotor performance of animals can affect critically importantabilities, such as acquiring food resources, competing for mates andavoiding mortal harm (Turchin, 1998; Nathan et al., 2008), andarboreal habitats pose many functional challenges for locomotionas a result of their narrow cylindrical surfaces, inclines, anddiscontinuities between branches. Although branch diameters andorientation vary considerably in arboreal habitats, available datasuggest that small diameters (median <0.8cm) and steep inclines(median 67deg) dominate (Mattingly and Jayne, 2004). Narrowsurfaces and steep inclines in the arboreal environment each providea unique set of challenges for locomotion. Small diameter substratesmight interfere with the ability of an organism to balance or fit onthe substrate (Cartmill, 1985), as well as with the ability to applypropulsive or gripping forces. In addition, steep inclines decreasethe proportion of the mass of the organism supported passively bythe substrate and thus are likely to require added muscular effort toprevent slipping.

Of the many attributes of branches that vary, the effects of branchdiameter on locomotion are well studied (e.g. Irschick and Losos,1999; Lammers and Biknevicius, 2004). However, a correlate ofdecreased diameter in natural substrates is an increased compliance,which is defined as the amount of deflection of the substrate whenloaded. Substrate compliance poses additional challenges, such aseffects on locomotor stability and energy damping (Bonser, 1999),which also might affect the mode (Thorpe et al., 2009) and dynamics(McMahon and Greene, 1979; Byrnes et al., 2008) of locomotion.However, no study has explicitly examined the combined effectsof substrate diameter and compliance on animal locomotion.

To successfully climb vertical surfaces without structures thatallow animals to adhere, sufficient friction must be generated byactive gripping to prevent slipping. The ability to grip a substratedepends on the nature of the contact between the animal and thesurface (Cartmill, 1985). For example, grip force in humans reachesa maximum at an intermediate diameter proportionate to thedimensions of the hand, with reduced force at both larger and smallerdiameters (Edgren et al., 2004). The elongate body plan of snakesallows them considerable ability to modulate the extent of wrappingand the number of gripping regions, but extreme branch diametersmight limit the ability of snakes to conform to or grip the branch,which in turn could negatively affect performance (Astley and Jayne,2007).

Snakes climb cylindrical vertical substrates using concertinalocomotion (Astley and Jayne, 2007), characterized by convolutedstatic regions pressed against the substrate while another portion ofthe body extends anteriorly (Gray, 1946; Jayne, 1986). The cyclicalchanges in momentum associated with repeated starting and stoppingmake concertina locomotion (in tunnels) far more costlyenergetically than other modes of locomotion for an animal of agiven mass (Walton et al., 1990), and narrower tunnels appear tobe more demanding than tunnels of a moderate width (Jayne andDavis, 1991). Compared with horizontal locomotion, the energeticcosts of climbing vertical surfaces using concertina locomotionshould increase because of the additional work done against gravity.Thus, climbing narrow and compliant vertical substrates ispresumably a highly demanding task. As a result, studying thisbehavior facilitates our understanding of how environmentalvariation affects locomotion.

The Journal of Experimental Biology 213, 4249-4256© 2010. Published by The Company of Biologists Ltddoi:10.1242/jeb.047225

Substrate diameter and compliance affect the gripping strategies and locomotormode of climbing boa constrictors

Greg Byrnes* and Bruce C. JayneDepartment of Biological Sciences, University of Cincinnati, PO Box 210006, Cincinnati, OH 45221-0006, USA

*Author for correspondence ([email protected])

Accepted 20 September 2010

SUMMARYArboreal habitats pose unique challenges for locomotion as a result of their narrow cylindrical surfaces and discontinuitiesbetween branches. Decreased diameter of branches increases compliance, which can pose additional challenges, includingeffects on stability and energy damping. However, the combined effects of substrate diameter and compliance are poorlyunderstood for any animal. We quantified performance, kinematics and substrate deformation while boa constrictors (Boaconstrictor) climbed vertical ropes with three diameters (3, 6 and 9mm) and four tensions (0.5, 1.0, 1.5 and 2.0 body weights).Mean forward velocity decreased significantly with both decreased diameter and increased compliance. Both diameter andcompliance had numerous effects on locomotor kinematics, but diameter had larger and more pervasive effects than compliance.Locomotion on the largest diameter had a larger forward excursion per cycle, and the locomotor mode and gripping strategydiffered from that on the smaller diameters. On larger diameters, snakes primarily applied opposing forces at the same locationon the rope to grip. By contrast, on smaller diameters forces were applied in opposite directions at different locations along therope, resulting in increased rope deformation. Although energy is likely to be lost during deformation, snakes might use increasedsurface deformation as a strategy to enhance their ability to grip.

Supplementary material available online at http://jeb.biologists.org/cgi/content/full/213/24/4249/DC1

Key words: arboreal, locomotion, performance, kinematics, Boa constrictor, concertina, gait, posture, prehensile, substrate deformation.

THE JOURNAL OF EXPERIMENTAL BIOLOGY

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We studied juvenile boa constrictors; boa constrictors are oftenfound in trees particularly when they are juveniles (Greene, 1983),as indicated in part by the large proportion of passerine birds(>40%) in their diet (Quick et al., 2005). Although many speciesof arboreal colubrid (Lillywhite and Henderson, 1993) and boidsnakes (Pizzatto et al., 2007) have relatively slender bodies, boaconstrictors are rather heavy bodied. Greater weight mightexacerbate some of the challenges of arboreal locomotion, such assupporting body weight by gripping, the risk of toppling when themass is not centered above a branch, and the likelihood ofdeforming thin vegetation. However, just as the large numbers ofvertebrae and the short axial muscle segments of boids are likelyto enhance their ability to wrap around and grip prey duringconstriction (Ruben, 1977; Jayne, 1982), these traits could alsoenhance their ability to grip arboreal surfaces.

The goal of the present study was to determine how the combinedinfluence of diameter and compliance of substrates in arborealhabitats affects locomotor mode and performance. Very narrowsubstrates might limit the ability of animals to produce the necessarynormal forces to grip. Therefore, to produce sufficient force snakesmight use a greater extent of their bodies to grip these substrates.This could have a negative effect on locomotor performance bylimiting the extent of the body free to move anteriorly during eachcycle. In addition, we expected performance to decrease on morecompliant substrates, as some of the muscular force produced togrip or propel the animal forward would be lost to deformation ofthe substrate. Using flexible substrates also allowed us to measuresubstrate deformation and to resolve some of the forces requiredfor locomotion, which could not otherwise be determined for smalldiameters.

MATERIALS AND METHODSExperimental subjects

We used six captive-born juvenile boa constrictors (Boa constrictor;Linnaeus 1758). All animals had prior experience climbing rigidcylindrical surfaces as part of a previous experiment. The snakeswere individually housed in terraria (52�26�31cm), with anincandescent bulb overhead establishing a temperature gradient of27–33°C. The snakes had similar snout-vent length (SVL; meanSVL68.8cm, range66–70cm), total length (TL; meanTL77.1cm, range74–79cm) and mass (mean175.8g,range158–192g). We performed all experiments on post-absorptiveanimals (>7days after feeding) to minimize possible postprandialeffects on locomotor performance (Garland and Arnold, 1983) andmetabolism (Secor et al., 2000).

Experimental protocolWe used vertically oriented, braided nylon ropes (The Lehigh Group,Macungle, PA, USA) with three diameters (3, 6 and 9mm; 13–39%of mid-body diameter of the snakes) encompassing the mediandiameter (0.8cm) of branches in the arboreal environment (Mattinglyand Jayne, 2004) and of perch diameters used in the wild by otherboid snakes (Henderson and Winstel, 1995; Henderson et al., 1998).Preliminary tests revealed that 3mm was the smallest diameter theexperimental subjects would reliably climb and that a gait changeoccurred across this range of diameters. To test the effects ofsubstrate compliance, we increased the tension in the rope to reducecompliance. We used four rope tensions, that were scaled to 0.5, 1,1.5 or 2 body weights. To measure tension (±0.003N) in the ropewe used a linear load cell (Honeywell Sensotec Model 31, 5 lb.,Columbus, OH, USA). The rope was passed through a pulley andattached, via a spring (k46Nm–1), to the load cell fixed to an

adjustable mounting block (Fig.1). To increase the tension, themounting block was moved farther from the pulley, stretching thespring.

To determine the amount of force required to deform each of thethree ropes, we applied known horizontal forces at each tension (0.5,1, 1.5, 2 mean body weights) using a setup that allowed unopposedforces similar to those the snakes produce (Fig.1, inset). Twoidentical masses, ranging from 0–120g in 10g increments, weresuspended over brass pivots using silk sutures attached to the rope15cm apart, and we measured the resulting rope deformations usingthe load cell.

Preliminary experiments revealed that using a small section ofpipe covered at one end to create a dark refuge near the top of therope was the best method to motivate snakes to climb vertically.The snakes performed three trials for each experimental condition(3 diameters � 4 tensions). Each snake was rested for at least twohours between experimental conditions and the snakes performedno more than two experimental conditions per day. We randomizedthe order in which diameter and tension were presented to snakesto reduce potential effects of experience on performance. The bodytemperatures of the snakes were approximately 30°C during all trials,which is within the range of reported field-active body temperaturesfor this species (McGinnis and Moore, 1969; Montgomery and Rand,1978).

We recorded each trial at 30framess–1 using two synchronizeddigital video cameras (Panasonic PV-GS320, Secaucus, NJ, USA)positioned orthogonal to the long axis of the rope. We used AdobePremiere Pro v7 (Adobe Systems, San Jose, CA, USA) to convertthe video to AVI files that were imported into MaxTRAQ v2.19software (Innovision Systems, Columbiaville, MI, USA) forkinematic analysis. Because the snakes were able to wrap aroundthe substrate in any orientation relative to the two cameras, the widestportion of the head was the most practical landmark to use forfollowing the forward progress of each snake. We used the verticalline connecting the ends of the rope in the video frame as the x-axis of our coordinate system.

G. Byrnes and B. C. Jayne

1.8 m

To amp and computer

Fig.1. Schematic illustration of the experimental setup to measuresubstrate deformation by snakes climbing compliant perches. Snakes werefree to climb a 1.8m rope that passed through the pulley and was coupledto the linear load cell via a spring. Inset shows the experimental setup fordetermining the normal force required for observed substrate deformations.Equal masses were passed over pivots at a distance similar to thewavelength between gripping regions of the snake.


4251Diameter and compliance affect climbing snakes

The force and video data were synchronized using a square wavevoltage to illuminate LEDs that were visible in both cameras. Theanalog signal from the load cell was amplified using HoneywellSensotec Model UV in line amplifier and acquired digitally at 1kHzand low-pass filtered with a cutoff frequency of 25Hz using aPowerlab 8 SP system and Chart 5 software (ADInstruments, CastleHill, NSW, Australia).

To determine the coefficient of static friction (s), we placed eachsnake in a natural extended posture on a board (28�120cm) coveredin 3mm nylon rope, such that the long axis of the snake was parallelto the orientation of the rope and the long axis of the board. Oneend of the board was elevated until the snake began to slidedownwards. Boa constrictors began to slide at an average angle of12.7deg, corresponding to a s of 0.225±0.003. Given this measureds, a total normal force of approximately 7.6N (4.4 body weights)is required to the support the body weight of the snake.

Kinematic and kinetic measurementsWe analyzed five variables describing the whole-body kinematics

and force over each cycle. The cycle duration (tcycle) was the totaltime from the start of static contact until the end of subsequent slidingcontact. The percentage of time in static contact (%stat) was theamount of time during a cycle in which a given point along thebody was in static contact with the substrate divided by tcycle. Thetotal height climbed per cycle was Dx. The mean forward velocity(vx) was Dx divided by tcycle. The maximum change in tension(DTmax) within each cycle, representing the amount of substratedeformation, was also calculated from the force data.

Six additional variables quantified the posture and movementsassociated with the snake gripping the substrate and extending thebody forward within each cycle. We determined the maximum andminimum vertical (x) length (lmax and lmin) of the body and tail alongthe rope. We also determined the maximum and minimum numberof simultaneous crossing regions per cycle (Ncr.max and Ncr.min),which represent the number of potential gripping regions, and thedifference between them (DNcr). For each cycle, we also calculatedthe mean angle of the midline of the body at each crossing regionrelative to x at the time of the greatest longitudinal extent of staticcontact (acr) for locations that were nearly parallel to the plane offocus of the camera.

Statistical analysesWe analyzed each variable for the four fastest cycles for eachindividual in each experimental treatment (N12) using a three-waymixed-model ANOVA (total N288). Diameter (N3) and tension(N4) were considered fixed, crossed factors, whereas the individualsnake used (N6) was considered a random, crossed factor. We alsoperformed a principal component analysis (PCA) on eight kinematicvariables to evaluate whether distinct locomotor patterns occurred.We used a mixed-model ANOVA (as above) to test whether thefirst two principal component scores differed significantly withdiameter or tension. All statistics were performed using the StatisticsToolbox in Matlab v7.4 (MathWorks, Natick, MA, USA), andP<0.05 was used as the criterion for significance.

RESULTSPerformance

All snakes successfully climbed all combinations of substratediameter and compliance, but all climbing velocities were extremelyslow (~0.5–1.0cms–1), and seldom greater than 2% SVL s–1

(Fig.2A). Backwards slipping was common on the smallestdiameter, especially with higher substrate compliance (Fig.3A).

Substrate diameter and compliance significantly affected vx (Table1;Fig.2A). Velocities increased approximately twofold from thesmallest to the largest diameter, as well as having nearly a 1.4-foldincrease with increased rope tension for a given diameter (Fig.2A).

Locomotor modeAll snakes used a variant of concertina locomotion with periodicstarting and stopping along the length of the body, and at no timewas the entire length of the body moving simultaneously (Fig.3).Regardless of diameter or compliance, the snakes climbed usingalternating curves to the left and the right, gripping the substrateusing medially directed normal forces in regions where the bodycrossed the rope (Fig.3). Occasionally, snakes made full helicalwraps around the rope, with their tails. On the smaller diameters,the dorsal, lateral and ventral surfaces often contacted the rope,whereas on the largest diameter greater ventral flexion resulted in

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Fig.2. Mean values (±s.e.m.) of whole-cycle variables on the threesubstrate diameters, 3, 6 and 9mm, and four tensions. (A)Maximal forwardvelocity, vx. (B)Cycle duration, tcycle. (C)Distance traveled per cycle, �x.(D)Percentage of cycle spent in static contact with substrate, %stat.


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predominantly ventral scale contact and gripping. On the twosmallest diameters, each point on the snake followed nearly the samepath along the rope as the snake moved forward (Fig.3A,C). Bycontrast, on larger diameters, snakes used a form of concertinalocomotion in which extensive portions of the body, correspondingto multiple adjacent gripping loops, were progressively extendedanteriorly and did not follow a similar path.

Kinematics and substrate deformationDiameter significantly affected more kinematic variables than didsubstrate compliance (11 vs 5 of 11) (Table1). During climbing,both tcycle (Fig.2B) and �x (Fig.2C) increased with increasingdiameter, whereas %stat decreased significantly with increaseddiameter (Fig.2D; Table1). On larger diameters, the potentialbenefits of the large increase in �x and the decrease in %stat onvelocity were partially offset by longer cycle durations, resulting inonly a modest increase in velocity.

Several kinematic variables describing the ability of snakes toboth grip the substrate and extend the body anteriorly also changedsignificantly with both diameter and compliance. The maximum(lmax) and minimum (lmin) longitudinal extent of the snake along therope decreased significantly as diameter increased and as substratecompliance decreased (Table1; Fig.4A). As diameter increased, bothNcr.max (Fig.4B) and Ncr.min decreased significantly, whereas �Ncr

(Fig.4C) increased significantly (Table1). However, none of thesevariables describing the number of crossing regions changedsignificantly with substrate compliance. Both increased diameterand decreased compliance significantly increased acr (Table1;Fig.4D).

Substrate deformation is the result of forces applied to the ropeby the snake in opposite directions at different points along the lengthof the rope, analogous to a moment couple. We will refer to theseforces as ‘unopposed forces’. Both increased diameter and increasedrope tension decreased the amount of rope deformation, as indicated


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Max. gripPush

Pull

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Fig.3. Video images of movement (A,C,E,G) and thecorresponding force profiles (B,D,F,H) for fourcombinations of substrate diameter and tension: (A,B)3mm, 0.5 body weights (BW); (C,D) 3mm, 2.0 BW; (E,F)9mm, 0.5 BW; and (G,H) 9mm, 2.0 BW. For A, C, E andG, frames were taken at equal time intervals within acycle. Frames 2–6 correspond to a complete cycle andframe 1 is an equal time interval prior to the start of thecycle. Time intervals in between successive frames were2.7, 1.2, 3.0 and 2.8s, respectively, for A, C, E and G.Shaded regions represent areas along the snake in staticcontact with the substrate. Numbers in B, D, F and Hcorrespond to individual frames in A, C, E and G,respectively. ‘Pull’ refers to the uphill movement of theposterior body towards a more anterior region of gripping,‘Push’ refers to the anterior extension of the anterior bodyand ‘Max. grip’ refers to the maximum longitudinal extentof gripping along the substrate. Videos of boa constrictorlocomotion on narrow substrates are available in thesupplementary material (Movies 1–4).



by �Tmax, within the locomotor cycle (Table1; Fig.3; Fig.5A).Snakes produced the largest substrate deformations in two ways:increasing the number of gripping regions (Ncr.max), which effectivelyincreased the number of unopposed forces applied to the rope, andrapidly extending the anterior body (Fig.3B,D,F). However, at thecombination of highest diameter and lowest compliance, little or nodeformation occurred (Fig.3H).

The first two principal components (PC1 and PC2) accountedfor 52% and 16% of the observed variation in the data, respectively.Higher values of PC1 represent greater �x and acr, and smaller lmax

and lmin, whereas higher values of PC2 represent larger values oftcycle, Ncr.max and Ncr.min (Table2). The PCA effectively distinguishedthe largest and smallest diameters into distinct clusters in the PCspace, but both had significant overlap with the intermediatediameter; conversely, different tensions were not easily distinguished(Fig.6). However, in the mixed-model ANOVA, both diameter(F160.6, P<0.0001; d.f.2,10) and tension (F7.7, P0.002,d.f.3,15) significantly affected PC1. By contrast, PC2 only changedsignificantly with diameter (F8.8, P0.006, d.f.2,10).

DISCUSSIONUnderstanding variation in locomotor gait or mode provides insightsinto how motor output changes with changes in environmentaldemands or speed (Biknevicius and Reilly, 2006). Historically,locomotor gaits or modes have been defined by a variety ofcontinuous kinematic parameters, including duty factor and limbphase (Hildebrand, 1965; Hildebrand, 1968), or by discrete changes,such as in locomotor mechanics (Cavagna et al., 1977; Hedrick etal., 2002) or appendage use (Webb, 1982). Although the definitionsof locomotor modes obtained using these different criteria do notalways correspond perfectly to one another (Biknevicius and Reilly,2006), both of these types of information prove useful for identifyingnovel locomotor modes. In this study, a combination of changes incontinuous kinematic variables and a change in the gripping strategyused by boa constrictors suggest that two locomotor modes occurredwith varying environmental conditions.

Locomotor mode and performanceNo previous study has examined the combined effects of substratediameter and compliance, and for the snakes in our study both ofthese salient features of arboreal habitats significantly affected theirlocomotion. Snakes commonly alter locomotor mode in responseto variations in environmental structure (e.g. Gray, 1946; Jayne,

1986), whereas many gait transitions of animals with appendagesare associated with changing speed.

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Table 1. Effects of diameter and tension on performance, kinematics and force

Effect

Variable Diameter (d.f.2,10) Tension (d.f.3,15) Diameter � tension (d.f.6,30)

vx 44.4 (<0.001) 11.1 (<0.001) 0.5 (0.629)tcycle 20.5 (<0.001) 2.0 (0.160) 0.4 (0.691)Dx 57.5 (<0.001) 2.2 (0.134) 1.5 (0.205)%stat 22.59 (<0.001) 1.31 (0.308) 0.7 (0.644)lmax 31.9 (<0.001) 3.9 (0.030) 0.7 (0.651)lmin 62.8 (<0.001) 9.8 (<0.001) 1.3 (0.307)Ncr.max 49.1 (<0.001) 1.6 (0.227) 1.1 (0.361)Ncr.min 80.1 (<0.001) 2.6 (0.087) 0.7 (0.652)DNcr 6.2 (0.017) 0.9 (0.479) 0.4 (0.871)acr 76.3 (<0.001) 4.4 (0.021) 3.0 (0.022)DTmax 32.2 (<0.001) 51.1 (<0.001) 4.6 (0.002)

Values are F (P).vx, average velocity; tcycle, cycle duration; Dx, distance per cycle; %stat, percentage of cycle static; lmax, maximum length along substrate; lmin, minimum length

along substrate; Ncr.max, number of crossing regions at lmax; Ncr.min, number of crossing regions at lmin; DNcr, change in number of crossing regions; acr, meanangle of body with rope; DTmax, maximum change in tension.

Fig.4. Mean values (±s.e.m.) of postural variables on the three substratediameters, 3, 6 and 9mm, and four substrate tensions. (A)Minimumlongitudinal extent of the snake’s body along the substrate, lmin.(B)Maximum number of crossing regions, Ncr.max. (C)Change in thenumber of crossing regions within a cycle, �Ncr. (D)Angle of the body withrespect to the substrate at the minimum longitudinal extent, acr.


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On narrow vertical substrates, the snakes in this study used formsof concertina locomotion, with some similarities to the forms ofconcertina locomotion used by other species in tunnels (Mosauer,1932; Gray, 1946; Jayne, 1986; Jayne and Davis, 1991) and on rigidcylinders (Astley and Jayne, 2007). On all diameters, movementused alternating curves of the body to the left and the right, periodicstopping, and static contact along some extent of the body. However,climbing on ropes had two differences with tunnel concertinalocomotion. First, forces applied to the substrate were alwaysdirected medially regardless of rope diameter. Second, on thesmallest diameter, the entire body followed nearly the same pathas the crossing region at a specific location along the rope, whichshifted posteriorly within the body of the snake while the animalascended (Fig.3A,C); this is similar to the arboreal concertinalocomotion observed during vertical climbing in Pantherophis(Elaphe) (Astley and Jayne, 2007). By contrast, on the largestdiameter, points along the body did not follow a similar path, moreclosely resembling concertina locomotion in tunnels (Fig.3E,G).This kinematic difference is one line of evidence for the existenceof two distinct variants of arboreal concertina locomotion in B.constrictor in response to changes in diameter.

As in previous studies of snakes (Astley and Jayne, 2007) anddiverse limbed animals (Losos and Sinervo, 1989; Delciellos andVieira, 2009), substrate diameter had profound effects on locomotorperformance. In many lizards (Sinervo, 1991; Losos and Irshick,1996; Irshick and Losos, 1999) and some mammals (Delciellos andVieira, 2009), maximum speed decreases with decreased perchdiameter. By contrast, Astley and Jayne (Astley and Jayne, 2007)found that for North American rat snakes, moving both horizontallyand uphill, speed decreases with increased cylinder diameter. Thedifferent ranges of substrate diameters used in these two studiesprobably explain this discrepancy. We used very small ropediameters (13–39% of the mid-body width of the snake) whencompared with those previously used for adult Pantherophis(76–1000% of mid-body width) (Astley and Jayne, 2007). Thus,for snakes, performance is probably maximized at an intermediatediameter (Herrmann and Jayne, 2010).

Substrate deformation and gripDepending on their body plan and behavior, animals use variousstrategies to closely conform to objects in their environment in orderto effectively apply gripping or propulsive forces. Two contrastingways in which such close contact can be attained are for the animalitself to deform and comply with shapes in the environment or,conversely, to deform the environment so that it complies with theshape of the animal. The snakes in our study successfully employedboth of these mechanisms while climbing compliant substrates.Some of the effects of surface compliance on locomotor performanceare dependent on the amount of environmental deformation and therate of energy return. For example, in terrestrial systems, bothhumans (Ferris et al., 1999) and cockroaches (Spence et al., 2010)can maintain or increase velocity when running on elastic surfaces,whereas, on substrates that yield permanently underfoot, such assand, the mechanical work required for locomotion increases(Lejeune et al., 1998). Similarly, in arboreal systems, terminal branchcompliance increases the costs of leaping across canopy gaps(Alexander, 1991; Demes et al., 1995). However, in rare casesanimals can employ branch compliance to their benefit (Thorpe etal., 2007). In our study, increased rope compliance decreased theperformance of snakes, and the combination of deformations in the


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Fig.5. Mean values (±s.e.m.) of force variables on the three substratediameters, 3, 6 and 9mm, and four substrate tensions. (A)Change intension in the substrate due to deformation, �Tmax. (B)Unopposed normalforce required to attain the change in tension (�Tmax) due to the substratedeformations observed from the snakes shown in A.

Table 2. Principal components analysis factor loadings

Variable PC1 PC2

tcycle 0.33 0.42Dx 0.40 0.30DTmax –0.28 –0.28lmax –0.35 0.12lmin –0.44 –0.02Ncr.max –0.26 0.65Ncr.min –0.33 0.46acr 0.41 0.04

Loadings with a magnitude ≥0.35 are marked in bold type.PC1 and PC2, principal components 1 and 2, respectively.See Table 1 for variable definitions.

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Fig.6. Principal component 1 (PC1) versus principal component 2 (PC2)from an analysis of eight kinematic variables on the three substratediameters and four substrate tensions. White, gray and black symbolsrepresent 3, 6 and 9mm diameters, respectively. Minimum polygons aredrawn for 3 and 9mm. Each tension is a given by a different symbol (circle,0.5 BW; triangle,1.0 BW; square, 1.5 BW; star, 2.0 BW). Factor loadingsare given in Table2.



ropes and in the bodies of the snakes seems likely to have someadditional consequences on how the substrate is gripped.

What we observed for the largest diameter rope compared withthe two smaller ones suggests a change in gripping strategy,whereas different compliances of the ropes might explain much ofthe observed variation between the two smallest ropes. Althoughall ropes were of similar material and weave, our deformations ofthe ropes with standard weights revealed that compliance decreasedwith increased rope diameter (see supplementary material Fig.S1).Thus, the nearly identical deformations caused by the snakes on thetwo smaller diameters (Fig.5A) with much higher values ofunopposed normal forces (Freq) are consistent with the decreasedcompliance of the larger rope. By contrast, the unopposed Freq ofthe 9-mm diameter rope decreased substantially when comparedwith that of the 6-mm diameter rope (Fig.5B). Consequently, thenear absence of observable deformation of the largest rope by thesnakes (Fig.5A) seems likely to indicate a reduction in unopposednormal forces and a greater reliance on opposing normal forces toprevent slipping. Positioning the body nearly perpendicular to thelargest rope in the gripping regions and the greater ventral contactwith the rope seem likely to enhance the ability to generate opposingnormal forces while minimizing unopposed normal forces.

This mode of gripping observed on the largest rope created largegripping arcs. Similarly, the opposable thumb of primates facilitatesgripping larger arcs and hence increasing grip force becausefrictional gripping arcs of >180deg cause the normal forces to pushthe substrate towards the animal (Cartmill, 1974; Cartmill, 1979).

The observed change from using predominantly opposing gripson the largest diameter to using both gripping strategies on smalldiameters might result from limits on flexibility or on the abilityto produce sufficient normal forces on small diameter substratesusing opposing grips. The inability to form a small radius ofcurvature (rc) might underlie this change in gripping strategy, andrc could be affected by increased mobility between adjacentvertebrae, increased numbers of vertebrae per unit distance, thestoutness of the body, or the architecture of the axial muscles. Theshorter length of some axial muscle segments in boid species mightenhance their force production at small rc values compared withthat of many colubrid species (Ruben, 1977; Jayne, 1982). Someof the similarities of body posture between the colubridPantherophis on a wide range of diameters (Astley and Jayne, 2007)and the boa constrictors on very small diameters might reflect theneed of Pantherophis to use a gripping strategy that will compensatefor a larger rc, owing to both a smaller body diameter and longeraxial muscle segments.

As a result of these probable anatomical constraints on theirgripping ability, snakes could use other methods on smallerdiameters to generate the necessary normal force to both supportbody weight and ascend. Unlike arboreal primates that cope withcompliant branches by increasing the number of discrete hand andfoot holds (Thorpe et al., 2009), the elongate and flexible bodies ofsnakes have an exquisite ability to modulate the size of the grippingregion, thereby providing additional strategies that snakes could useto increase grip force, including deforming the substrate and helicalwrapping.

The frictional force generated can be increased exponentially byincreasing the contact angle (an angular measure of arc length)between a flexible substrate and a cylinder as a result of the capstaneffect (Meriam, 1980). This principle is used in a variety ofmountaineering equipment, creating a convoluted path to retard thesliding of a loaded rope. For snakes on the two thinner ropes, wecommonly observed five crossing regions, each of which bent the

rope approximately one-tenth the circumference of the snake, andthe resulting contact angle of 180deg would create a capstan effectsufficient to support one-half of the weight of the snake. Perhapssnakes applied greater unopposed normal forces at each tension onthe 6mm compared with the 3mm rope to attain a similar amountof deformation (Fig.5) and thus facilitate gripping the substrate.

In addition to increasing the frictional force by substratedeformation, helical wrapping can passively increase the normalforce applied by the snake on the substrate. By using helicalwrapping, twining vines grip their host plant by self-tightening undertension (Silk and Hubbard, 1991; Isnard et al., 2009). Self-tighteningof a helix can produce greater normal force with increases in thecurvature (decreased diameter), the pitch angle and the number ofgyres (Silk and Hubbard, 1991). Many of the changes observed inthe posture and helical wrapping for snakes on smaller diameter areconsistent with enhancing this effect. If snakes produce normal loadssimilar to those of twining plants (Silk and Hubbard, 1991), thispassive mechanism could support the entire weight of the snakewhile at rest.

Although previously undescribed, it is likely that other arborealorganisms use similar mechanisms to supplement their ability togrip. For instance, although the gripping postures of tails have notbeen studied in detail, they seem likely to be subject to similarmechanical demands as those faced by snakes. A common featureof prehensile tails that have evolved convergently in diverse lineagesof reptiles (Zippel et al., 1999) and mammals (McClearn, 1992;Schmitt et al., 2005) is that they have sufficient length, flexibilityand strength to encircle branches and produce normal force.

Despite the likely physical and energetic challenges, the benefitsof the ability to move on narrow and compliant substrates mighthave large ecological implications for animals. Arboreal organismsmust often feed or hunt in the terminal branch niche, which requiresthe ability to move safely on small diameter and compliantsubstrates. Additionally, because of the discontinuous nature ofarboreal habitats, the limits of diameter and compliance on whichan animal can safely move determines the length of a detour ananimal must make around an impassable gap (Thorpe et al., 2009),which is likely to influence foraging patterns, energy expenditureand exposure to predators.

Diverse substrates place similar functional demands on climbingorganisms using frictional grips. These vertical substrates requirethe ability to produce forces normal to the surface using muscularcontraction. However, to climb perches with differing substrateproperties, different strategies are used. In boa constrictors, a shiftin the locomotor mode of animals climbing on smaller diametersubstrates results from both differing kinematics and grippingstrategies. Broad comparisons across species of both grippingbehavior and the underlying motor control could elucidate thepotential mechanisms that underlie these shifts in climbing strategy,and thus could promote a better understanding of the diversity ofarboreal forms.

LIST OF SYMBOLS AND ABBREVIATIONSFreq normal force required to attain observed DTmax

lmax maximum longitudinal extension of body and tail along therope

lmin minimum longitudinal extension of body and tail along therope

Ncr.max number of crossing regions at lmax

Ncr.min number of crossing regions at lmin

rc radius of curvaturetcycle cycle duration in secondsvx average velocity of a cycle


4256

acr mean angle of the body midline with respect to the long axisof the rope at crossing regions during maximal staticcontact

DNcr change in number of crossing regionsDTmax maximum change in tension due to deformation within a cycleDx distance traveled per cycles coefficient of static friction%stat percentage of a cycle in static contact with the substrate

ACKNOWLEDGEMENTSThis work was supported by NSF grant IOS 0843197 to B.C.J. We thank H. Ofori-Sampong for her assistance throughout the project. We also thank twoanonymous reviewers for their comments that have improved the manuscript.

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