Mechanical performance of spider orb webs is tuned for high-speed prey

The design of organisms, and the materials from which they are grown, often incorporates significant safety mechanisms that prevent catastrophic failure. Some safety mechanisms simply consist of using more material to strengthen a structure, such as thickening the bending axis in a plant stem or bone (Vogel, 2003). More complex safety mechanisms include the J-shaped stress–strain curves of many biological materials, such as tendon and spider capture silk, which help to limit the failure probability by recruiting more load-bearing molecules as the load increases (Vogel, 2003). The safety factor is a traditional method of quantifying how closely structures approach failure during performance. For example, the strength of a bone may be several fold higher than the forces typically encountered, but approach failure under extreme events such as falls. The safety factor is quantified as the ratio of the breaking stress of the bone to the typical stress to which it is subjected. During steady-state locomotion, the bones of small mammals have higher safety factors than the bones of large mammals, hinting at the importance of intense, non-steady state activities such as jumping in smaller mammals (Biewener, 1982; Biewener, 2005). Most mammals, including horses, have higher safety factors in more proximal bones, and hence higher breaking probability in distal limb bones (Vaughan and Mason, 1975). Cursorial mammals risk higher breakage probability in these distal bones in order to maintain high speed and high acceleration during locomotion. Finally, at the highest level of complexity, neural mechanisms such as the Golgi tendon reflex mechanism in mammalian muscles detect dangerous levels of tension and lower the muscle force generated, preventing catastrophic tearing (Eccles et al., 1957). Thus, multiple mechanisms including material properties, shape of individual components and the overall design of complex structures interact in determining successful performance.

Spider orb webs are a likely candidate for safety mechanisms operating at multiple levels because webs are complex structures assembled from multiple materials and are exposed to prey that vary enormously in both impact energy and benefit of capture. In particular, ecological data suggest that orb webs maximize spider fitness when capturing rare, but large prey (Blackledge, 2011; Venner and Casas, 2005). Physiologically, growth of ‘giant’ female Nephila depends more on the consumption of individually large, rare insects at larger instars (Higgins and Goodnight, 2011). Mechanically, the stickiness of spider web glue droplets scales closely with the strength of the underlying axial fibers so that the glue detaches instead of the threads breaking, allowing them to repeatedly adhere to prey (Agnarsson and Blackledge, 2009), but also providing a potential safety release. Both the adhesiveness of individual glue droplets (Sahni et al., 2010) and the toughness of silk threads (Cunniff et al., 1994; Denny, 1976) increase with strain rate. Finally, larger species of spiders also produce webs using higher quality silk (Sensenig et al., 2010).

Spider orb webs are constructed of outer frames and supporting radial spokes spun from stiff major ampullate silk, and capture spirals of highly compliant flagelliform silk covered in adhesive aggregate glue (Vollrath, 1988). The components of the spider orb web – radial silk, spiral silk and glue droplets – work together first to intercept, then to stop and finally to retain prey (Blackledge and Eliason, 2007; Blackledge et al., 2011). Thus, orb webs do not function as simple sieves, and variation in the geometric arrangement of these silks, and in their mechanical performance, can favor the capture of specific types of insect prey. Orb spiders depend on particularly large insects for most of their nutrition, even though such prey are only rarely captured (i.e. the large but rare prey hypothesis for spider orb webs) (Blackledge, 2011; Venner and Casas, 2005). Despite their abundance and ease of capture, smaller, slower flying insects simply do not provide as much biomass as these rare ‘bonanzas’. Yet, large prey are heavier and, more importantly, fly significantly faster so that they impact webs with much greater kinetic energy. Targeting large prey is a risky strategy that substantially increases the probability of webs failing without providing benefit to the spiders, but also provides a big payout when the webs function successfully.

Here, we examine the hypothesis that the design of orb webs favors the capture of larger and faster flying prey. We develop three models (fixed, improvement and safety release) for how energy absorption may scale with prey speed (Fig. 1), and apply these models to prey in both low and high kinetic energy regimes. The differences in the models hinge on the sign, rather than the magnitude, of the slope of energy absorption versus prey speed (e.g. zero, positive or negative). Orb webs may function with a fixed capacity to dissipate prey energy. Insects whose kinetic energy exceeds that capacity would always escape, while insects below that threshold would occasionally escape depending on the vagaries of precisely how they contact threads in the orb web. Alternatively, orb webs may improve energy absorbance when struck by faster prey. This pattern would support the strong importance of the rare, large prey hypothesis for the evolution of spider orb webs (Blackledge, 2011; Venner and Casas, 2005). Improved performance could be caused by strain-rate-dependent properties of silk (Gosline et al., 1999) and/or emergent properties of whole web architectures (Cranford et al., 2012). Finally, orb webs may exhibit a safety release mechanism that makes it easier for larger and faster flying insects, which exceed the performance threshold, to break through webs with minimal damage (Denny, 1976). A safety release would better preserve web function for capture of future insects with lower kinetic energy, and hence higher probability of capture. While these three models predict differences in maximum web performance across all prey speeds (Fig. 1), real differences can only be observed when the speed (or size) of prey is high enough that the insect's kinetic energy exceeds the stopping potential of silk in the orb web. Furthermore, successful captures of prey do not directly measure the maximum kinetic energy that an orb web can resist, when prey are slow or small (left side of black line in Fig. 1). The three models therefore predict observable differences in the capture success of webs under a set of intermediate speeds that are difficult to determine and quantifiable differences in the kinetic energy removed from prey that routinely break through orb webs at higher speeds.

To test these three models of spider orb web performance, we fired wooden pellets and ping pong balls into orb webs at varying speeds and filmed the impacts using high-speed video. We first measured how the capture success of orb webs changes with prey speed. We then tested whether orb webs dissipate more energy from faster moving prey by comparing the energy dissipated from prey that do escape webs across a range of speeds.

We collected penultimate and adult female spiders at the University of Akron's Field Station at the Bath Nature Reserve, OH, and nearby localities. Spiders were housed in either 40×40×10 cm or 80×80×20 cm screen cages with removable plexiglass sides. Spiders were misted with tap water regularly and humidifiers were used to keep humidity above 60%. Some of the spider webs were examined the next day, while other spiders were allowed to build a series of webs before sampling. We used 84 webs of 10 species in the orb weaver clade Araneoidea (Table 1) in order to generalize our findings to this speciose and economically important spider group.

For nine high-energy trials, we used only Larinioides cornutus. The webs of these spiders were spun on thin balsa wood frames to facilitate imaging (1×0.5 cm cross-section wood, 20×20 cm frame). The spiders and frames were isolated in a covered pool of water in the laboratory to encourage web construction on the frames.

Webs were placed in the natural vertical position used by these spider species. Rectangular balsa wood blocks were launched at the web at velocities between 1.3 and 5.5 m s⁻¹ (Fig. 2) using a custom-made spring-loaded plastic cannon. The flying projectile kinetic energies were typical of insects that have been observed in webs (30–1500 μJ) (Blackledge and Zevenbergen, 2006). Projectiles with masses of 30 mg (6×6×6 mm; N=79), 100 mg (10×7×10 mm; N=75) and 300 mg (30×7×10 mm; N=70) were analyzed (Table 1). No one species' web was hit by particularly large or particularly fast balsa wood blocks, so that the effect of speed on capture dynamics was not confounded with taxa (Fig. 2). Individual webs were used for increasingly larger balsa projectile impacts until they were significantly damaged, which was defined as >1 broken radii or >30 broken spirals.

For very high energy intra-web comparisons (Fig. 3), we dropped a standard ping pong ball into nine different horizontal orb webs of L. cornutus. The mass of the ping pong ball dropped into the webs was 2609 mg and frontal surface area of the ball was 11.33 cm², several times the surface area of the 300 mg balsa blocks. The speed and energy of the ball was varied by changing the height of the drop, with zero initial speed possible by placing the ball in direct contact with the web and then releasing the ball. The ping-pong ball always broke through the webs, even at zero initial speed. The ping pong ball was aimed at a point halfway between the hub and the outer edge of the capture area, usually hitting just one radius. The order of drops for a particular web was randomized, so that some fresh webs were hit by a low energy ball while others were hit with a high energy ball as the first impact. Each web was used between two and five times depending on the size of the web and the damage from previous impacts, for a total of 42 impact events (Table 1). We confirmed the independence of drop order and impact speed with both a parametric regression of drop order versus speed (F_1,1,38=0.54, P=0.46) and a Spearman rank order test (P=0.17). Models also suggest that the performance of undamaged portions of orb webs are remarkably robust (Cranford et al., 2012).

Images were captured with a single Fastech Troubleshooter 1268×1024 pixel camera (Fastec Imaging Corporation, San Diego, CA, USA) at 500 frames s⁻¹. ProAnalyst Motion Analysis software (Xcitex, Cambridge, MA, USA) was used to digitize the projectile in each frame. Perspective calibration within ProAnalyst was used to calibrate the plane of motion of the projectile. A planar grid with 3 cm squares served as the calibration object, and was placed to within 1 cm of the trajectory plane of the projectile.

Black dots were marked on the white ping pong ball to facilitate automatic tracking by ProAnalyst, and to monitor rotation of the ball. Balls were dropped with minimal initial rotation, and possessed sufficiently high rotational inertia that rotation during impact was almost undetectable. At the highest speeds, the ball traversed approximately 15 pixels s⁻¹. Digitization accuracy for ball position was approximately 2 pixels, resulting in speed uncertainty of 0.25 m s⁻¹ at the highest speeds.

The effects of projectile speed on energy absorbed were tested separately for each projectile size using general linear models (GLMs) (Figs 2, 3) in STATISTICA (version 9, StatSoft, Tulsa, OK, USA), with initial impact speed and spider body mass as predictors of energy absorbed during breaking impacts. The effects of projectile speed on capture probability was tested separately for each projectile size using logistic regression in STATISTICA. A successful capture event was assigned a 1, and failure to capture was assigned a 0 value. This binomial distribution was regressed against projectile speed using the logit link function. To graph the data, bin widths of 0.33 m s⁻¹ speed increments were chosen. Error bars for the capture probability within these bins (Fig. 4) representing 95% confidence intervals were calculated using the Wilson interval (Wilson, 1927) as recommended by Brown et al. (Brown et al., 2001).

Two criteria must be met in order to test the effect of projectile speed on energy dissipation. First, the speed of projectiles impacting webs must be normally distributed across spider species and body masses. Heavier spiders generally spin thicker silk threads, producing webs that would absorb more energy (Sensenig et al., 2010). A normal distribution of projectile energies across spider body size ensures that potentially higher energy webs were not hit disproportionately by higher energy projectiles. The GLM controls for the effect of body mass, even if the impacts are not normally distributed. Second, spatial calibration error must be sufficiently low, as a positive bias in the length scale would increase velocity, kinetic energy and potential energy. This would produce a positive correlation of speed and energy from calibration error alone. We found that the calibration error was on the order of 10% of the difference in energy between high- and low-speed trials, and therefore calibration error did not significantly impact the observed trends. Digitization uncertainty also produced error on the order of 10% of the observed differences.

We assessed the energy absorbed by webs when broken by projectiles, i.e. using only the escape events. The balsa wood projectiles comprised a lower energy regime, similar to real insects, because of lower mass. In contrast, the ping pong balls represented a very high energy regime that was unrealistic of typical prey but ideal for separating the three models of orb web performance. The energy absorption increased with the speed of the projectile for all escaping projectile sizes (30 mg, F=14.9, P<0.001; 100 mg, F=30.5, P<0.001; 300 mg, F=10.4, P=0.002; ping pong, F=8.42, P=0.006; Figs 2, 3). To verify that this trend was not caused by higher-speed projectiles hitting tougher webs, we verified using the same GLM that body mass (surrogate for web toughness) had no effect on energy absorption for any projectile size (30 mg, F=0.09, P=0.77; 100 mg, F=0.07, P=0.79; 300 mg, F=0.73, P=0.40; ping pong, F=3.9, P=0.06). The speed of the ping pong ball did not affect the distance to which webs extended at failure (four out of nine webs had positively sloped regression lines, χ²=0.111, P=0.74; Fig. 5), suggesting that the increased energy absorption was due to increased breaking stress at higher speeds and not due to webs maintaining contact with the ping pong balls for longer distances.

For the lower energy regime (balsa wood projectiles), we assessed probability of capture separately for the three different sizes of projectiles (Fig. 4). Capture probability decreased significantly as a function of speed only for the smallest projectiles (30 mg, Wald statistic=5.81, P=0.016; 100 mg, Wald statistic=1.98, P=0.15; 300 mg, Wald statistic=2.32, P=0.13).

Energy absorption of capture events is generally higher than for escape events at a given speed because not all of the kinetic energy is removed for escape events, and because capture events can include a significant change in gravitational potential energy as the projectile comes to hang in the web. Our data place upper limits on energy absorption for given sizes of prey. Specifically, we measured the highest capture energies of 200, 800 and 2200 μJ for the increasing sizes of wooden projectiles (Fig. 2). Breaking energy increased with projectile size, rising as high as 5000 μJ for ping ball balls. The fastest projectiles always broke the web for each size category, with webs never catching any projectile faster than 3.5 m s⁻¹. The trivial squared dependence between energy and speed of captured projectiles is plotted (Fig. 2), because this illustrates the upper limit to energy potentially absorbable for breaking events occurring at the same speed.

Our study shows that spider silk in the orb web forms a structure that exhibits improved performance with strain rate, with energy-absorbing performance improving by up to sixfold over the range of speeds applicable to flying insect prey (Fig. 3). The results from both the low energy regime (potentially stoppable prey) and the high energy regime (unstoppably heavy ping pong balls) support the improvement model in that the energy absorbed by the webs from the escaping projectiles increased with projectile speed. We failed to find evidence for the release mechanism model and the fixed performance model (Fig. 1). Larger insects generally fly faster than smaller insects. Therefore, from a kinetic energy perspective, orb webs appear to function as traps that maximize the probability of stopping the largest possible prey.

Prey capture is a complex process in orb spiders where webs first intercept insects, then stop their flight, and finally retain the insects for some period of time (Blackledge, 2012; Blackledge, 2013; Blackledge et al., 2011; Harmer et al., 2011). The struggle by kicking and flapping prey and surface structure of the prey (e.g. silk entangling setae or Lepidoptera scale-shedding reducing silk adhesion) of the prey introduce new variables not accounted for in our simple kinetic energy model (e.g. Blackledge and Zevenbergen, 2006; Opell and Schwend, 2007). Also, if the prey oscillates in the web, our model presumes that the stickiness of the web is sufficient to hold the prey on each rebound. However, we feel that our analysis of the middle phase of capture – stopping prey kinetic energy – is a crucial step with important implications for spider fitness. The study of rare, but fitness-defining prey capture events is a challenge to spider web ecologists because rare massive prey captures are by their nature difficult to document (Blackledge, 2011; Venner and Casas, 2005). In particular, the impact of rare prey capture events for spider fitness may be determined less by how often they occur (determined in part by changes in how orb webs intercept prey) than by how effectively webs capitalize upon those events when they do occur (determined by successfully stopping and retaining prey).

Why didn't we find evidence for a safety release mechanism in orb webs that limits damage under catastrophic prey impacts? Some crucial ecological differences between spider orb webs and other foraging systems may explain our results. Many foraging decisions by animals involve cost–benefit analysis, where pursuit of prey is aborted if the prey is deemed too costly or risky (Bowen et al., 2002; Caro, 1995; Griffiths, 1980). For orb spiders, a crucial foraging step is performed by the web, substantially reducing risk to the spider itself. A web represents only approximately 0.2% of a spider's body mass (Blackledge, 1998; Gosline et al., 1986), and much of that investment can be recovered when the orb spider consumes the web and recycles the silk (Townley and Tillinghast, 1988; Townley et al., 2006). In other words, greater risks can be taken with resources that are utilized outside the organism, and that hence pose no direct mortality risk. However, spider orb webs are structurally robust to damage, with pristine regions of the web surface maintaining functionality after individual sectors are torn (Cranford et al., 2012). This suggests a ‘generic’ type of safety release mechanism that functions independent of prey speed or energy per se.

We suggest that the performance improvement in spider orb webs with strain rate is due in part to intrinsic silk material properties, although an additional role for web architecture remains to be explored. Specifically, the energy absorption increased with strain rate for both a rather small projectile size (100 mg), which usually hit only one or two threads, thereby limiting the complexity of the structure involved, and a large projectile hitting approximately seven different inter-connected threads (e.g. ping pong ball). Direct tensile tests of the material properties of individual silk threads are typically limited to relatively slow strain rates of <10% s⁻¹ (Sensenig et al., 2010; Swanson et al., 2006). Higher strain rates are derived from dropping weights onto threads. Over a 100,000-fold change in strain rate (0.05 to 5000% s⁻¹), the toughness of Araneus single MA threads increased by approximately 10-fold (Denny, 1976; Gosline et al., 1999). Here, we generated strain rates from quasi-stationary up to 300% s⁻¹, and measured at most a sixfold increase in total energy absorbed by the web. Some studies have suggested that spider silk could increase work by slightly increasing total extension at high strain rates (Gosline et al., 1999; Laible, 1980), but we found no evidence of higher extension of silk measured at the whole-web level (Fig. 5). At a given length, silk must therefore be stiffer at higher strain rates. We suggest that faster extension of silk threads inhibits the entropy-driven collapse of the alpha helices, an effect not measured previously because of the low extension rates used in previous studies. Limited ballistic tests (strain ~50,000% s⁻¹) of pads made of spider silk show that energy absorption is similar to quasi-static tests, although it is not clear whether the ballistic impacts consist primarily of extension or compression of the material (Cunniff et al., 1994).

In summary, our findings suggest that natural selection acted upon spider orb webs to enhance capture of large, fast-flying insects. Orb webs respond to faster prey with better performance through a complex interplay of web architecture and silk material properties. We conclude that spider orb webs (particularly the individual sectors of the web) are unlikely to exhibit safety release mechanisms because the web is a ‘disposable’ structure optimized for a one-time impact, contrasting with many mechanical systems that are intrinsic to organisms. Instead, spider orb webs function more like human technology such as helmets and bullet-resistant armor that are designed for single impacts. Future engineering improvements to these technologies may find inspiration in the structure of spider orb webs, which have evolved for similar function at least since the early Cretaceous (Peñalver et al., 2006).

This is publication no. 33 of the University of Akron Field Station and was conducted under permit 2005-004.