Scaling of the extended phenotype: convergent energetics from diverse spider web geometries

1. Introduction

All living organisms rely on energy to fuel the processes of maintenance, growth and reproduction. Across metazoans, these processes typically scale allometrically (i.e. not a 1 : 1 relationship) with body mass (M) in remarkably similar ways [1]. Per-unit-mass maintenance metabolic rates scale as M^−1/3 or M^−1/4, whereas rates of growth and reproduction scale as M^−1/4 [1–3]. Because all organisms exchange energy and materials with their environment, they must capture energy to meet these basic energetic requirements while balancing environmental losses and undergoing their developmental program. To do so, organisms rely on phenotypic traits. Such phenotypic traits are well-defined behavioural, physiological or morphological properties of organisms that impact survival and reproduction [4–6]. To capture energy, some organisms have evolved traits that exist outside of their bodies, referred to as extended phenotypes [7,8].

Extended phenotypes, in the form of shells, burrows, nests, mucous houses and webs, exist in a diversity of organisms, including both vertebrates and invertebrates [8,9]. In organisms such as spiders, net-spinning caddisfly larvae, mucous-net-feeding zooplankton (larvaceans) and antlions, extended phenotypes have evolved to capture resources. The role of extended phenotypes in resource capture and their ability to be studied as a trait with a high degree of separation from the organisms that build them makes them a useful tool for understanding processes such as energy budgeting, trait evolution and community assembly. Despite this, relatively few studies have described the scaling of these traits within a general context of energy and metabolism (e.g. [10,11]). Here, we do so through the lens of perhaps the best-known example of an extended phenotype: spider webs.

Spider webs are external constructions produced by a spider’s genetically endowed behaviours [12]. Web-building spiders represent approximately one-quarter of all spider diversity, largely due to their success as insect predators [13,14]. Spiders typically intercept prey as a function of the surface area of their webs [15], which may have vastly different taxon-specific shapes [16–20]. We refer to the shape and dimensionality of a web as a web’s geometry. Web geometries tend to be constrained taxonomically at the family level—two-dimensional (2D) orbs are built by tetragnathids, uloborids and araneids, whereas tridimensional (3D) tangles and sheet-and-tangles are built, among others, by theridiids and linyphiids, respectively [13] (see figure 1 for examples of web geometries). Spider webs represent an ideal system to investigate whether and to what extent extended phenotypes are adjusted to meet the energetic demands of the organisms that build them and to test predictions based on metabolic theory.

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Given that spider webs are built to capture energy from the environment and that sessile terrestrial metazoans are expected to require less energy per unit mass as they increase in size [1–3], the surface area of spider webs need not scale isometrically (i.e. slope equal to 1.0) with body size. Instead, the surface area of spider webs may scale hypometrically (i.e. slope < 1.0) with body size to match the energetic requirements of the spiders building them. The precise scaling, however, may depend on a web’s geometry and other properties of the webs such as energetic cost and silk stickiness. However, the question of how the geometry of a web impacts its scaling within the context of its multiple properties is yet to be addressed [16,20–22]. In a sample of approximately 300 web-building spiders from 10 genera and 5 families, we assessed how the prey capture surface area of a spider’s web and how much energy they consume scale as a function of spider body size. Our findings illustrate how these extended phenotypes have been shaped by natural selection and physical laws to meet the energetic demands of the spiders building them, converging in a common relationship for the amount of energy per unit mass they consume despite disparate geometries. We also discovered a property of certain types of sheet-and-tangle webs that allows them to avoid the increased cost of maintaining a roughly constant per unit mass prey capture surface area of their webs as they grow in size.

2. Material and methods

We conducted our study at Pacific Spirit Regional Park (PSP), in Vancouver, British Columbia (49.2533° N, 123.2156° W) from July to September 2020. We used the available diversity of web-building spiders to compare across body sizes and web geometries. We selected spiders to accommodate roughly two-and-a-half orders of magnitude in body size. To maximize the range of body sizes available for our study, we conducted observations on adult females, subadults and late-stage juvenile spiders.

Before beginning prey capture observations, we classified webs according to their geometry as either 2D orbs or 3D tangles or sheet-and-tangles [16,20] (figure 1, electronic supplementary material, table S1). We then measured the size of each spider and its web. Web measurements were web-geometry specific. For orbs, we measured the length of the longest axis and width and for tangles, the length of the longest horizontal axis, width and height. The sheet-and-tangles at our field site belonged mostly to the family Linyphiidae (electronic supplementary material, table S1), whose webs typically contain a horizontal sheet shaped as a dome (Neriene litigiosa), basket (Neriene digna) (figure 1c) or a slightly depressed hammock (Microlinyphia), all with mostly hollow space within. For this web type, we measured the length, width and height of this structure and the height of the prey capture threads above or also below it. We then calculated the prey capture surface area and volume of webs given their geometrical shape [23]. For orbs, we assumed the shape of an ellipse and a triangle for spiders in the genus Hyptiotes. For tangles, we assumed the shape of a cylinder. We included the bottom surface area of the cylinder because tangles also use sticky lines that contact the substrate below the web to capture prey [15]. For sheet-and-tangles, we assumed the shape of one or two separate cones depending on whether the prey capture portion of their webs was at the top, bottom, or both above and below the dome or basket. As elongation is a mechanism to preserve surface area to volume ratios (SA : V) as objects increase in size [24], we tested whether larger 3D webs became more elongated along either their horizontal or vertical dimension (electronic supplementary material, table S4). For sheet-and-tangle webs, we additionally analysed the volume of the hollow space inside the dome or basket of the webs against spider mass (electronic supplementary material, table S5), as hollowing may preserve SA : V ratios [24] without, in this case, incurring the cost of filling the additional space with silk. After observations were completed, we collected the silk of all webs to test whether hollowing reduced the weight of silk per unit volume in sheet-and-tangle webs (electronic supplementary material, table S5) and to assess the relationship between total silk content and spider size for all web types (electronic supplementary material, table S6 and figure S2). After removing any debris attached to the silk, we used a Mettler Toledo MX5 microbalance to estimate the total web weight in milligrams.

We carried out prey capture observations on each spider for 6–16 h depending on whether the spider remained or not in its web. We marked all spiders with non-invasive UV dust prior to conducting observations to track individuals over the 2 day observation period [22,25]. We visited each spider every 2 h from approximately 8 a.m. to 3 p.m. or 12 p.m. to 6 p.m. each day. A 2 h window was selected to ensure that spiders would not fully consume prey before we had the opportunity to re-visit their webs [20,23]. During the first visit to a web, we noted all the prey present, which set the baseline for the following visits. On each subsequent visit, we visually inspected the spider’s web and noted if any new prey items had been captured and whether the spider was present. We identified each prey item to order and estimated its length to the nearest millimetre using a ruler [20,23]. We counted prey as captured if they were either completely immobilized (i.e. not moving or wrapped in silk) or were being fed upon by the spider. To estimate consumption rates, we calculated each prey’s dry consumable biomass from its length using taxon-specific equations for insects [26] and translated these into joules using a biomass conversion factor for insects [27]. After completing two consecutive days of prey capture observations for each web, we collected the spiders and measured them using a microscope equipped with a measurement device. We then used a regression of field and lab-measured body size to correct field estimates for spiders we were unable to collect (electronic supplementary material, figure S3). We converted estimates of spider body length into dry mass using a general regression equation derived for temperate spiders by Pennell et al. [28]; this equation, which according to its authors can be applied to spiders of similar climatic zones, included the same web geometries as in our study.

We analysed the scaling of the spiders’ webs (cm² prey capture surface area) and the energy they consumed (watts = J s⁻¹) as a function of the spiders’ body size (mg) with either the whole variable or with mass-specific values (i.e. the variable divided by the weight of the spider). We did the former to exercise caution given potential spurious correlations that can arise with ratio variables when there is greater measurement error in the numerator relative to the denominator [29,30]. As the null hypothesis for linear models is a slope of 0.0, but it should be 1.0 in whole-variable models, we used the linear hypothesis function in the Car package (v. 3.1-2) in R for whole-variable model tests. We did this for all whole-variable models except our PGLS model, as the function does not work on this type of model. In this case, we used the 95% confidence interval (CI) to assess whether the slope in the whole-variable PGLS model differed from 1.0. As significance levels were identical for the whole- and mass-specific cases (electronic supplementary material, table S2), we graphed the ratio variables, as the allometry of the scaling exponents can be more easily appreciated by inspecting how much the slope of the regression deviates from a flat line versus a 1 : 1 line when plotting whole response variables. Accordingly, for the most part, we refer to mass-specific scaling when discussing our results. We performed our statistical analyses in R (v. 4.0.2) [31].

With the response variables above, we ran linear mixed-effects models (LME; lme4 package v. 1.1-35.5 in R) with spider mass, web geometry and the interaction between the two as predictors, including temperature as a covariate and spider genus as a random effect. For the latter, we excluded four genera with fewer than three data points to reduce error in our estimates. For spiders whose genus we could not identify, we entered an ‘unknown’ category within their respective families (electronic supplementary material, table S1). Prior to analyses, we log₁₀-transformed each variable and checked for assumptions of over-dispersion and normality. As there was a significant interaction between spider mass and web geometry for prey capture surface area (electronic supplementary material, table S2), for this variable, we followed up with separate models for each web geometry.

For the relationship between energy consumption rate and body mass, we also ran a phylogenetic least squares regression model (PGLS; Caper package (v. 1.0.3) in R) to correct for potential phylogenetic non-independence. In this case, we used genus averages, as the best-resolved spider phylogeny is to genera [32]. Here too, we filtered out genera with fewer than three data points to reduce error in our estimates. We did not include web geometry as a factor in the PGLS models because we lacked the statistical power for a two-predictor model [33]. Due to a similar lack of statistical power, we could not run a PGLS model on the scaling of web prey capture surface area and body size. A lack of statistical power for such analyses appears inevitable in temperate regions where, as in our case, there is a relatively low richness of genera. A phylogenetic test with three predictor variables, as in our LME models, would require the inclusion of at least 30 genera (based on [33]). A sample this large is unfeasible outside of highly diverse tropical habitats, making this a potentially common issue in temperate ecological studies.

3. Results

(a) The scaling of spider webs

Prey capture surface area per unit mass scaled with spider body size with different slopes depending on a web’s geometry (figure 2; electronic supplementary material, table S2). It scaled isometrically with spider body size in sheet-and-tangle webs where the per-unit-mass slope of this variable was not significantly different from 0.0 (−0.25 ± 0.33, 95% CI) (figure 2; electronic supplementary material, tables S2 and S3). At the other end of the spectrum, the prey capture surface area of tangle builders did not increase with spider size, with their per-unit-mass slope being indistinguishable from −1.0 (−0.96 ± 0.45, 95% CI). The per-unit-mass slope of orb webs was intermediate between those of the two other web types (−0.63 ± 0.34, 95% CI) (figure 2; electronic supplementary material, table S3). Rather than scaling with body size, the whole and ratio variable analysis revealed that the surface area of tangle webs was positively correlated with temperature (χ² = 40.41, d.f. = 1, p < 0.01). Neither the tangle nor the sheet-and-tangle webs became more elongated in either dimension as their size increased (electronic supplementary material, table S4 and figure S1). The volume of the hollow space contained within the dome or basket of the three most common species of sheet-and-tangle webs at the field site (N. litigiosa, N. digna and Microlinyphia mandibulata), however, scaled hypermetrically (i.e. slope > 0.0, for the per-unit-mass model or slope > 1.0, for the whole-variable model) with spider mass (per-unit-mass slope ± 95% CI = 0.39 ± 0.17; figure 3a; electronic supplementary material, table S5). As a result, web weight per unit web volume decreased with the size of the webs (slope ± 95% CI = −0.88 ± 0.29; figure 3b; electronic supplementary material, table S5) such that sheet-and-tangle webs increased in volume without increasing the amount of material they contained (and also decreasing web weight per unit spider mass for larger spiders; electronic supplementary material, figure S2, middle).

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(b) The scaling of energy consumption rates

There were no differences across web geometries in the slopes of per-unit-mass energy consumption rates, which scaled with body size with a slope of −0.70 ± 0.29 95% CI for all three web types in the LME analyses (figure 4; electronic supplementary material, table S3). The relationship was also allometric in the PGLS model, where the estimated slope was −0.35 ± 0.25 95% CI (figure 4; electronic supplementary material, table S3).

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4. Discussion

Diversity is a solution to the problem of life, which requires a constant flow of energy and resources to fuel the metabolic processes of growth, survival and reproduction. To make use of Earth’s limited resources, natural selection and physical laws have shaped strategies that allow organisms to use resources in unique ways, avoid competition and facilitate the acquisition of the energy needed to sustain life. Our study included spiders of diverse web geometries—2D orbs and 3D tangles and sheet-and-tangles, which characteristically utilize space and capture prey in distinct ways [17,34,35]. Here, we show that these diverse geometries are associated with a different slope for the relationship between a web’s prey capture surface area per unit mass and spider body size (figure 2), with one of the web types—sheet-and-tangle webs—expanding the hollow space within them (figure 3a) to maintain a constant surface area per unit spider mass without increasing the weight of the webs as they increased in size (figure 3). Despite the diversity of these scaling relationships, spiders of all web geometries converged upon a common slope and intercept for the rate of energy consumption per unit mass as a function of body size (figure 4). The latter finding suggests that webs are well-integrated extended phenotypes whose various elements (geometry, internal structure, silk stickiness, etc.) have been shaped by natural selection and physical laws to capture the expected amount of energy per unit mass that spiders require for growth, survival and reproduction in diverse ways.

In addition to spiders, three other groups of organisms build external structures for energy capture [9]: net-spinning caddisfly larvae (Trichoptera: Hydropsychidae), which are sedentary filter feeders that capture flowing food particles in freshwater streams by building 2D silk nets at the entrance of their retreats [36,37]; antlions (Neuroptera: Myrmeleontidae) and wormlions (Diptera: Vermileonidae), whose larvae dig conical pitfall traps in loose sediment to capture wandering arthropods [38–40]; and larvaceans, which are pelagic tunicates (class Appendicularia) that build spherical mucous nets (referred to as ‘houses’) around their tadpole-shaped bodies to concentrate tiny marine food particles [41,42]. Relatively little is known about the scaling properties of these structures. Net-spinning caddisfly larvae have been found to build larger nets with coarser meshes when inhabiting upstream areas of rivers where food particles are coarser; downstream, where temperatures are warmer, they build smaller nets, which they replace less frequently, exhibiting also a broader respiration (metabolism) range [37]. In larvaceans, the need to rebuild their mucous houses when clogged is a major metabolic cost, resulting in species with large houses relative to their body size rebuilding them less often [41]. Lombard et al. [43] detected hypometric metabolic scaling across instars in one such larvacean species, which is unusual for pelagic organisms, which tend to exhibit isometric scaling [44]. The costs, benefits and metabolic consequences of pit construction in antlions have received comparatively greater attention. In a Costa Rican population, Swenson et al. [45] found that the surface area of antlion pitfall traps scaled with mass to the 3/4 power, consistent with metabolic theory predictions for sessile organisms. As sit-and-wait predators, antlions, as well as spiders, have been found to have lower metabolic rates than other poikilotherms [38,46].

Consistent with the expectation for sessile terrestrial metazoans [1,3,47], we found that web-building spiders, regardless of the geometry of their webs, consume less energy per unit mass as they increase in size (figure 4; electronic supplementary material, tables S2 and S3). Similarly, negative allometric scaling of metabolism and body size has been observed in studies that include both web-building and non-web-building spiders [46,48,49]. Although the average slope of energy consumption per unit mass in our LME model was generally steeper than expected from metabolic theory (i.e. M^−2/3 observed in our study versus M^−1/3–M^−1/4 expected from metabolic theory), the slope estimated from our PGLS model (−0.35 ± 0.25; electronic supplementary material, table S3) overlaps with expected values based on metabolic theory and previous empirical results for spiders (electronic supplementary material, table S3).

Mass-specific consumption rates are generally expected to scale in proportion to either (i) the surface used to acquire energy, which is assumed to be proportional to organismal length squared or mass to the 2/3 power [50], producing per-unit-mass consumption rates that scale with body size either to the −1/3 power for a single species or 0 to −1/4 for comparisons across multiple species [51,52]; (ii) metabolic rate under the assumption that energetic supply limits demand such that metabolic rate per unit mass scales to the −1/4 power of body size [52–54]; or (iii) a balance between the scaling of nutrient absorption, which is a surface-driven process, scaling with mass to the 2/3 power, and digestion, which is a volume-driven process (i.e. digestive enzymes operate on a volume of food), scaling isometrically with mass to produce per-unit-mass consumption rates that scale between 0 and −1/4 power of body size [55]. Thus, expectations for the scaling of per-unit-mass consumption rates and body size generally sit between 0 and −1/3 power. Although the 95% CI of our PGLS model overlaps with the range of values predicted in the above theories (electronic supplementary material, table S3), the average slope of our LME model is nonetheless steeper than expected from metabolic theory.

There are several possible explanations for this discrepancy: it may indicate that (i) there is a phylogenetic effect present in our LME model, which is consistent with the shallower slope found in our PGLS model that overlaps with that expected from metabolic theory; (ii) larger spiders may be more efficient at using the resources they ingest to nonetheless reach a metabolic rate per unit mass between 0 and −1/3 power; (iii) we may have missed the consumption of rare but large prey, which is expected to supply adult spiders with the food necessary for reproduction [56]. In other words, as these catches are expected to occur every 20 days or so [56], our 2 day prey capture surveys may be underestimating the energy consumption rates for larger web-building spiders.

Despite the common slope in the relationship between energy consumption rate per unit mass and body size (figure 4), the different web geometries had vastly different slopes for the per-unit-mass prey capture surface area of their webs as a function of body size, being hypometric in orb-weaving spiders, isometric in sheet-and-tangle builders, and strongly hypometric in tangle builders (figure 2). Given the 2D nature of orb webs, it is clear that the hypometric scaling of web surface area per unit mass would translate into a similarly hypometric scaling of energy capture rate with body size (electronic supplementary material, table S3). Prey retention in ecribellate orb weavers is aided by their use of viscid silks, which are characteristic of the Araneoid clade [13,57,58]. Viscid silks are not used, however, by sheet-and-tangle builders in the family Linyphiidae [59], which use instead a knockdown trap of denser silk to ensnare insect prey [15,16]. Straus et al. [20] showed that, for a given spider size, sheet-and-tangle webs contain two orders of magnitude more silk than orbs or tangles, which would explain why these webs are rarely relocated [25]. As a surprising solution to maintaining the web’s surface area without incurring the cost of filling the entire web’s volume with silk, we discovered that sheet-and-tangle webs in the family Linyphiidae disproportionately increased the hollow space contained within their webs in dome- or basket-shaped structures (figure 3a). As a result, they maintained their surface area per unit spider mass as they increased in size without increasing silk content (figure 3b; electronic supplementary material, S2). The alternative solution of elongating the webs to maintain surface area with size [24] did not apply to either sheet-and-tangle or tangle webs (electronic supplementary material, figure S1). As they maintained their shape, tangle webs exhibited a steeply declining web surface area per unit mass with size (figure 2). While independent of spider size, the web surface area of tangle builders was strongly correlated with temperature, suggesting that tangle builders may rely on additional strategies to capture prey, such as throwing silk on wandering prey or using viscid glue on their gum-foot lines [15,58] or elsewhere [60].

A noticeable pattern in our data was the uneven distribution of spider body sizes along the three web geometries (figure 4), with orb weavers reaching the largest sizes, sheet-and-tangle builders being intermediate and tangle builders the smallest, a pattern first noted by Craig [17]. All taxa in our study, except for those in the family Uloboridae (electronic supplementary material, table S1), belong to the spider superfamily Araneoidea, where it has been hypothesized that the orb web may have been lost in some lineages [13,14,61]. Craig [17] suggests that such a loss may have given some taxa access to microhabitats not available to orb spinners. The body size pattern suggests that the novel web geometries may have imposed constraints on body size. The large amount of material required to build a sheet-and-tangle web [20], for instance, may have limited the evolution of larger body sizes in clades with this web geometry. Group living, as in the genus Anelosimus (Theridiidae) [62], may have allowed some spiders with sheet-and-tangle webs to overcome this constraint through web-sharing, which leads to reduced per capita costs via an economy of scale [20]. Similarly, modern orb-weaving spiders may have been able to evolve larger body sizes because of the energetic savings associated with the replacement of costly cribellate silks with adhesive ones [63,64]. Tangle builders’ reliance on leaves to support their webs, on the other hand, may have indirectly placed limits on body size through constraints on the size of the webs. Physical laws, such as surface area to volume laws [65], which place constraints on the size and shape of spider webs, would have further played a role in the coevolution of web geometry and body size in spiders. Finally, several taxa have abandoned the web altogether [13,14,64], which would have had the benefit of eliminating its cost and giving the spiders access to a wandering lifestyle.

It is well established that various energetic variables scale allometrically with body size across diverse organisms [2]. Yet, no studies have systematically shown how the extended phenotypes organisms use to acquire energy mediate these patterns. Although our focus is on the role of extended phenotypes to acquire energy, structures animals build can also serve other purposes, such as shelter and support, as is the case for shells, corallites, burrows and nests [9]. Given their accessibility and presence across life, extended phenotypes can be used to estimate energetic inputs and outputs in a diversity of organisms, making them ideal for testing theories based on energy and metabolism.

Using the extended phenotypes of web-building spiders, we illustrate how the scaling of prey capture surface area per unit mass and body size vary uniquely across a diverse set of spider web geometries (figure 2; electronic supplementary material, table S3). We also show how body size and web geometry covary such that larger web-building spiders consume proportionally less energy per unit mass than smaller ones (figure 4; electronic supplementary material, table S2) with a value, according to our PGLS model, not significantly different from the expected −0.25 for interspecific metabolic scaling [10,52]. We hypothesize that if temperature-corrected generation times scale with body size reciprocally (i.e. +0.35 for web building spiders, based on our PGLS result; figure 4b), as they do with metabolic rate in other organisms across the Tree of Life [10,11,66], smaller spiders would be expected to live proportionally shorter lives than larger ones. This would yield an equivalence paradigm akin to the equal fitness paradigm, which predicts that all organisms reproduce equal amounts of energy per unit mass across their lifetimes [10,11,67]. Similarly, under our hypothesis, all web-building spiders would be expected to consume equal amounts of energy per unit mass across their lifetimes despite the diversity of structures they build to do so, suggesting that widely different spider webs may perform equally well in supplying a unit of spider mass with energy across a lifetime.

Ethics

This project including the collection of specimens was authorized and conducted under PAC_Aviles_2020, which was issued by the Metro Vancouver Park Services.

Data accessibility

Link to a repository access here [68].

Supplementary material is available online [69].

Declaration of AI use

We have not used AI-assisted technologies in creating this article.

Authors’ contributions

G.G.-P.: conceptualization, formal analysis, visualization, writing—original draft, writing—review and editing; S.S.: conceptualization, investigation, methodology, writing—review and editing; R.B.: investigation, resources; L.A.: conceptualization, funding acquisition, investigation, methodology, supervision, writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

Funding for this project comes from a NSERC Canada Discovery Grant (RGPIN-2019-06539) to L.A.