To break a coralline: mechanical constraints on the size and survival of a wave-swept seaweed

The intertidal zone of rocky shores is a hydrodynamically stressful environment, where breaking waves can generate water velocities greater than 25 m s^–1 (e.g. Denny et al., 2003) and impose great forces on intertidal inhabitants(Koehl, 1984; Koehl, 1986; Carrington, 1990; Gaylord et al., 1994; Denny, 1995; Gaylord et al., 2001; Helmuth and Denny, 2003). The severity of wave-induced forces has been hypothesized to limit the maximum size to which intertidal organisms can grow (e.g. Denny et al., 1985; Gaylord et al., 1994; Denny, 1999). For example,unlike whales and giant kelps that live in deeper water, intertidal flora and fauna rarely exceed 0.5 m in any dimension(Denny et al., 1985). Blanchette found that intertidal algae transplanted from sheltered to wave-exposed locations `tattered' back to a smaller size(Blanchette, 1997). Such damage is likely to be the result of drag, the primary wave-induced force applied to intertidal macroalgae (Denny and Gaylord,2002).

Several studies have measured drag on seaweeds in an attempt to predict the size to which various species can grow in the intertidal zone(Carrington, 1990; Dudgeon and Johnson, 1992; Gaylord et al., 1994; Wolcott, 2007) but have had mixed success. This may be due in part to the characterization of drag at slow speeds (<3 m s^–1) in re-circulating water flumes and the need to extrapolate from these data to environmentally relevant water velocities (20–30 m s^–1). Such long-range extrapolations can be misleading (Vogel,1994; Bell, 1999). In particular, drag coefficient (C_d) decreases as flexible macroalgae bend and reconfigure with increasing water velocity(Bell, 1999; Boller and Carrington, 2006a),but the extent of this reconfiguration and its effect on C_d have never been characterized at the high velocities found on wave-swept shores. Here, we introduce a gravity-accelerated water flume, capable of generating jets of water (meant to mimic crashing waves) up to 10 m s^–1. Thus, for the first time, it is possible to measure drag and re-configuration of seaweeds at high velocities, reducing the need for extrapolation.

The articulated coralline alga Calliarthron cheilosporioides Manza thrives in wave-swept intertidal habitats along the California coast(Abbott and Hollenberg, 1976). Unlike fleshy algae, which are flexible along their entire length, Calliarthron thalli are firmly calcified but have flexible joints(genicula) that allow fronds to bend when struck by breaking waves. Flexible genicula also define breakage points along calcified thalli(Martone, 2006) and are hypothesized to be especially susceptible to bending stresses, as segmented bending may locally amplify stress within genicula [see accompanying paper(Martone and Denny, 2008)]. Nevertheless, Calliarthron fronds can grow to a length of 25 cm,including more than 100 genicula, and can dominate the most wave-exposed habitats.

When struck by incoming waves, erect articulated fronds bend in the direction of flow parallel to the substratum. Most genicula are stretched in tension by each passing wave, but basal genicula, which are farthest from the free end of any frond, experience the greatest bending moments (see Martone and Denny, 2008) and are hypothesized to be the most prone to breakage(Martone, 2006). Morphological characteristics of bending genicula are significantly different from those of tensile genicula [see table 3of the accompanying paper (Martone and Denny, 2008)], helping them increase flexibility and decrease stress amplification [see figure 7 of accompanying paper(Martone and Denny, 2008)],and bending angles may be constrained by the close proximity of neighboring fronds, further mitigating the amplification of stress within bending genicula. The mechanical advantages of such traits may be limited, however, if tensile genicula ultimately break first.

In this study, we compared breaking forces of genicula and drag forces on articulated fronds to explore physical constraints on the size and survival of this ecologically successful intertidal seaweed. We used empirical and modeling techniques to quantify forces to break bending genicula, with and without neighbors, and compared them with forces sufficient to break tensile genicula. These data allowed us to evaluate the mechanical limits of bending genicula and to estimate the average drag force required to break fronds in the field. Drag on articulated fronds was measured in the lab, and the size to which fronds can grow without breaking in a given water velocity was predicted. We tested laboratory predictions by measuring maximum water velocities and frond sizes in the field and propose that, although articulated fronds are remarkably well adapted to resisting wave-induced drag, breaking waves may, indeed, be sufficient to constrain the size of intertidal Calliarthron.

Calliarthron fronds (N=15) were collected from the low intertidal zone in a moderately wave-exposed surge channel at Hopkins Marine Station (HMS) in Pacific Grove, CA, USA. Stress–strain curves were generated for one geniculum in each frond loaded in tension using a custom-made tensometer and a video dimension analyzer (model V94, Living Systems Instrumentation, Burlington, VT, USA) as described in the accompanying paper (Martone and Denny,2008). Tensile moduli (E_t) were calculated as the slopes of linear stress–strain regressions forced through the origin; breaking strains (ϵ_break) were assumed to be the strain measurements immediately preceding frond breakage during mechanical tests. E_t and ϵ_break were correlated, and a linear regression was fitted to the E_tversusϵ _break data. Residuals were calculated for each datapoint(N=15), and the standard deviation of residuals was calculated.

In the field, Calliarthron fronds often break near the base(Martone, 2006), where bending moments and bending stresses are greatest(Martone and Denny, 2008). To explore breakage in bending, Calliarthron fronds (N=7) were collected from the field site described above. Branches were removed from each frond by cutting below the first dichotomy, and the remaining straight chains of segments were tested as follows. Individual fronds were gripped in clamps by the first few genicula and held horizontal(Fig. 1A). To quantify the force to bend genicula to failure, a second clamp was secured near the tenth genicula (numbered from the clamp) and masses were hung, in 20 g and 50 g increments, from the clamp until fronds broke(Fig. 1B). As bending genicula experienced increasing force, they broke gradually(Fig. 1C). An image analysis revealed that unbroken genicular cells approached, but had not yet exceeded,the average breaking strain (ϵ_break) of genicula loaded in tension (P.T.M. and M.W.D., unpublished data).

Dimensions of broken genicula were quantified as described in figure 1 of the accompanying paper (Martone and Denny,2008). Genicular radii (r₁,r₂) and intergenicular radii (y) were measured with an ocular dial-micrometer. Genicular lengths (ω) and gap lengths(ω–2x) were measured in wet, long-sectioned genicula adjacent to broken genicula and briefly decalcified in HCl. Average length measurements were assumed for broken genicula. Intergenicular lip length (x) of broken genicula was estimated as half the difference between mean ω and mean gap length.

The mathematical model that we present in our other study(Martone and Denny, 2008) was augmented to allow genicula to break gradually in order to estimate the force to bend experimental genicula to failure. The distribution of breaking strains was assumed to be normal with a mean of x̄_ϵ,break and standard deviation of s.d. _ϵ,break, and when tensile moduli(E_t) were plotted against breaking strains(ϵ_break), residuals were assumed to be normally distributed around the linear regression with a mean of 0 and standard deviation of s.d._residual. To generate unique bivariate normal pairs of E_t and ϵ_break for each iteration of the model, a random value was chosen from the ϵ_break distribution and a corresponding E_t was calculated from the normal distribution of values around the regression. As virtual fronds deflected, the model eliminated any portion of the first geniculum whose strain exceededϵ _break (see Appendix). This reduction of tissue was factored into the internal moments and neutral axis positions calculated by the model. In some cases, reduction of genicular cross-section created a positive feedback, increasing bending angles and further increasing strain. Breakage occurred when ϵ >ϵ_break across the entire geniculum. All other components of the original bending model were unchanged (see Martone and Denny, 2008).

To validate the model, forces (means ± s.d.) to break experimentally broken genicula described above (N=7) were estimated mathematically from 1000 model iterations. Observed and predicted breaking forces were compared.

To estimate breakage of fronds in the field, morphological dimensions of 10 fronds were used from our other analysis [see table 3 in Martone and Denny(Martone and Denny, 2008)]. Forces to break first genicula (nearest the base) of these experimental fronds in bending were calculated from 1000 model iterations (means ± s.d.; N=10).

When fronds bend over, most genicula experience drag force in tension [see right panels of figure 4 in Martone and Denny (Martone and Denny,2008)]. Tensile forces required to break tenth genicula in the 10 experimental fronds were estimated using genicular cross-sectional area and breaking stresses sampled from a normalized distribution with x̄_σ,break=25.9 MN m^–2 and s.d._ϵ,break=2.3 MN m^–2 [determined by Martone(Martone, 2006)]. Mean and standard deviation of 1000 breaking force estimates were calculated for each geniculum. Forces to break tenth genicula in tension and to break first genicula in bending were compared, assuming fronds would break at the lesser force. Mean and standard deviation of forces to break fronds were calculated,and these values were used to predict breakage of articulated fronds in the field.

To quantify the effect of frond size and growth on drag force, Calliarthron fronds (N=24) were collected from the low intertidal zone at HMS and were tested in re-circulating and gravity-accelerated water flumes. In both flume types, fronds were attached with cyano-acrylate glue to custom-made force transducers. In the re-circulating flume, drag force was measured on fronds (N=8) at 0.23, 0.46, 0.69, 0.92, 2.0 and 3.6 m s^–1. In the gravity-accelerated water flume, drag force was measured as fronds were struck with jets of water (Fig. 3). Flow was fully turbulent as it fell through the 10 cm diameter pipe, and velocity was adjusted by varying the distance through which the water fell. Fronds were tested at 6.8 m s^–1 (N=6) and 10.0 m s^–1 (N=10).

To explore changes in drag force over the lifetime of Calliarthron, fronds were `de-grown' by sequentially removing apical branches, and the resulting effect on drag force was quantified. This method reasonably approximated Calliarthron ontogeny (in reverse), since most growth occurs at the apical meristem(Johansen, 1981) and genicula are approximately the same size in young and old fronds(Martone, 2007). Drag on whole fronds was measured, apical branches of fronds were removed, and drag force was re-measured. Then sub-apical branches of fronds were removed, and drag force was re-measured. This process was repeated until all branches had been removed. Severed branches were digitally photographed and planform areas were measured using an image analysis program (ImageJ, NIH Image, http://rsb.info.nih.gov/ij/). The correlation between frond planform area and drag force was plotted for fronds at all eight water velocities.

To compare the performance of Calliarthron fronds with that of streamlined bodies and fleshy algae in flow, Vogel's E(Vogel, 1984) was calculated as the slope of a linear regression fitted to a log–log plot of speed-specific drag (F_drag/U²) versusvelocity (U).

From November 2003 to November 2006, Calliarthron fronds were collected every few months, totaling eight collections, from the intertidal field site described above. During each collection we searched for the largest available fronds. Collections typically consisted of 10–20 fronds. Fronds were digitally photographed and frond planform areas were measured using image analysis (ImageJ). Maximum frond area was noted on each date over the 3 year span.

From November 2005 to August 2006, maximum water velocities were measured. On 2 November 2005, three dynamometers(Bell and Denny, 1994; Helmuth and Denny, 2003) were installed at mean lower low water approximately 0.75 m apart, spanning the field site. Dynamometers were first checked and reset on 4 November 2005 and were checked and reset during sufficiently low tides (13 times) until 10 August 2006. The maximum water velocity recorded by any dynamometer was noted on each date over the 9 month span.

Field measurements were compared with breakage predictions to determine whether water velocities in the field were sufficient to generate drag forces that would equal forces experimentally determined to break Calliarthron fronds.

Predicted and observed breaking forces were similar(Table 1) and, on average, were not significantly different (P=0.47, Student's paired t-test).

Without neighbors, bending genicula were predicted to break before tensile genicula because, on average, tensile genicula resisted significantly more force (P<0.01, paired t-test; Fig. 5). However, fronds were predicted to resist greater forces in bending when supported by neighboring fronds (Fig. 5). Neighboring fronds were spaced 0.4 mm apart, on average, limiting bending angles to approximately 54 deg. With neighbors, bending genicula and tensile genicula were predicted to resist similar forces(Fig. 5), which, on average,were not significantly different (P=0.30, paired t-test). Mean force to break first genicula in bending with neighbors was 26.3 N, and the mean force to break tenth genicula in tension was 22.7 N(Table 2). Assuming fronds would break at the lesser of the two breaking forces for each frond, mean force to break Calliarthron fronds was 20.0±3.8 N (mean± s.d.; Table 2).

For all water velocities, drag force increased with frond planform area,and fronds of any given area experienced more drag force at greater velocities(Fig. 6). Vogel's Ewas calculated to be –0.68 (R²=0.70; Fig. 7).

The greatest water velocity recorded at the field site was 22.1 m s^–1 (Table 3). On average, the largest frond collected from the field site was 40.9±7.8 cm² (mean ± s.d.), and the largest frond ever collected from the site was 51.9 cm²(Table 4). These field measurements corresponded well to breakage predictions(Fig. 11).

Despite the amplification of bending stresses within genicular tissue(Martone and Denny, 2008), Calliarthron genicula are clearly well adapted to resist mechanical failure in wave-swept habitats. Even without the support of neighbors, fronds located near the periphery of aggregations are able to bend to 90 deg., and several experimental fronds supported more than 1 kg of weight (>9.8 N) in this position (Table 1). When neighboring fronds are considered, bending angles of central fronds are constrained, allowing first genicula to resist approximately twice the force of fronds near the periphery. Ultimately, fronds growing within dense populations are just as likely to break at tenth genicula in tension as they are to break at first genicula in bending.

These data suggest that genicula are not `over-designed' in an evolutionary sense. The tensile strength of calcified intergenicula in Calliarthron (28.5 MN m<sup>–2</sup>)(Martone, 2006) is similar to that of coral skeleton (25.6 MN m<sup>–2</sup>)(Vosburgh, 1982) and to that of several bivalve and gastropod shells that appear similar to Calliarthron cell walls (`homogeneous' type, 30 MN m^–2; `foliated' type, 38.3 MN m^–2)(Currey, 1980). This suggests an upper limit to the tensile strength of biologically deposited calcium carbonate within Calliarthron cell walls. This mechanical constraint may be biologically linked to genicula, whose tissue is equally strong (25.9 MN m^–2) (Martone,2006). Indeed, genicular tissue is far stronger than other algal tissues (up to an order of magnitude)(Martone, 2006) but may be biologically constrained from growing any stronger. Given this putative maximum tensile strength of genicular tissue, there may not be a selective advantage to adjusting the spatial density of fronds or the dimensions of bending genicula, if tensile genicula would ultimately break first. In other words, growing more densely packed clusters of fronds or decreasing the length of intergenicula (see Martone and Denny,2008) may indeed increase the breaking force of bending genicula,but such fronds would probably break at tensile genicula anyway; and breakage of either bending or tensile genicula near the base is likely to be disadvantageous, resulting in the loss of an entire frond that may have been reproductive and several years old(Johansen and Austin,1970).

Together, these data are consistent with the engineering theory of optimal design [Maxwell's Lemma (see Wainwright et al., 1982)], which states that all components in a mechanically stressed system should be equally strong to avoid wasting resources in their construction. The fact that bending and tensile genicula are morphologically distinct (Martone and Denny,2008) but resist similar drag forces suggests that these structures may have been shaped by selective pressures imposed by breaking waves. Morphological differences among tensile and bending genicula,therefore, may represent adaptations to hydrodynamic stress.

To our knowledge, this is the first study to report drag coefficients for an intertidal seaweed at high, environmentally relevant water velocities. Drag coefficients reported here for Calliarthron are up to an order of magnitude lower than those reported for several other algae at slow water velocities (Carrington, 1990; Dudgeon and Johnson, 1992; Gaylord et al., 1994). Our data suggest that drag coefficient continues to decrease as water velocity increases, at least up to 6 m s^–1(Fig. 8), contrary to the assumption that reconfiguration is solely a low-velocity phenomenon (see Bell, 1999). Vogel's E(–0.68) suggests that the drag coefficient of reconfiguring Calliarthron fronds drops faster than that of a typical streamlined body (–0.50) (Vogel,1984) and faster than those of several branched red algae,including a congeneric species (–0.35±0.13, mean ± s.d., N=7 species), although slower than those of flat bladed algae(–1.11±0.10, N=3 species; Fig. 7) [data compiled from table 4 in Gaylord et al.(Gaylord et al., 1994)]. Without high-speed data for other seaweeds, it is unknown at this time whether such low drag coefficients are a distinct characteristic of Calliarthron or a shared feature of intertidal algae. Our data emphasize the importance of measuring drag at high water velocities to avoid,or at least improve, extrapolation. For example, Gaylord and colleagues extrapolated fivefold beyond their data to generate drag predictions(Gaylord et al., 1994); in contrast, we would need to extrapolate less than twofold beyond our high-speed flume velocities (i.e. a short distance along the logRe_f axis of Fig. 9) to generate the same predictions. The accuracy of past predictions awaits verification in the high-speed flume.

Our data demonstrate effects of both planform area and water velocity on drag coefficient, suggesting yet another source of error in previous studies that treated drag coefficient strictly as a function of velocity and tested only a narrow size range of fronds (e.g. Carrington, 1990; Dudgeon and Johnson, 1992; Gaylord et al., 1994; Bell, 1999). Flexible algal fronds have lower drag coefficients in faster water because of the increased reconfiguration that occurs as fronds bend. Similarly, larger fronds are likely to have lower drag coefficients because of their capacity to re-arrange their branches and collapse to be more streamlined, unlike smaller fronds whose sparse branches are perhaps less capable of reconfiguration(Fig. 8).

It is important to note that, in this and previous studies of algal reconfiguration, drag coefficient is calculated using frond planform area(i.e. flattened and photographed from above). This methodology assumes a constant area term, allowing the drag coefficient to absorb any change in shape due to reconfiguration; all else being equal, larger fronds will tend to have lower drag coefficients (see Eqn 3). This contrasts sharply with a recent study(Boller and Carrington, 2006a)that calculated drag coefficients using frond projected area (i.e. photographed from upstream in flow) and tracked the independent decline of both projected area and drag coefficient as macroalgae reconfigured with increasing water velocity – a method that had previously been applied to reconfiguring gorgonians (Sponaugle and LaBarbera, 1991). Their data show that as flow increases,projected areas and drag coefficients both decline; fronds with larger projected areas have higher drag coefficients. Unlike our method, theirs generates drag coefficients that are directly comparable to other engineering shapes. However, because projected area cannot be visualized or measured in turbulent water at high speeds (e.g. in the gravity-accelerated water flume or under breaking waves), predictions of projected area, like those for drag coefficient, will inevitably rely upon long-range extrapolations. Thus, even though the drag coefficients presented here cannot be compared with those of standard shapes, our method reduces extrapolation and so seems suited to exploring the maximum size to which wave-swept fronds can grow.

Forces estimated to break Calliarthron fronds in the field are consistent with forces previously measured to break genicula in tension(Martone, 2006). An average Calliarthron frond can resist approximately 20 N of force before breaking – a substantial amount of force. For example, one large experimental frond (30 cm²) experienced only 5 N of drag force at 10 m s^–1 (Fig. 6) – far below the threshold breaking force. This suggests that Calliarthron may be well adapted to resist drag imposed by intertidal water velocities. However, velocities as high as 35 m s^–1 have been recorded at HMS (M.W.D., unpublished data), and articulated fronds may ultimately be size limited when water velocities approach this extreme.

Indeed, data presented here suggest that the size of Calliarthronfronds may be limited by drag forces imposed by intertidal water velocities. According to our breakage model, the maximum water velocity measured at the field site (22.1 m s^–1) closely predicts the mean maximum size (40.9±7.8 cm², mean ± s.d.) of Calliarthron fronds expected to survive there(Fig. 11). These data suggest that the broad range of frond sizes observed at the field site may, at least in part, be a consequence of variation in forces to break genicula. Our simplified breakage model ignores any possible drag-reducing effects of neighboring algae (Boller and Carrington,2006b) and, because intertidal water velocities vary widely in both space and time (Denny and Wethey,2001; Helmuth and Denny,2003; O'Donnell,2005), characterizing years of wave-forces with only a few dynamometer measurements is a broad generalization. For example, if breaking waves during some storm event actually generated 28 m s^–1water velocities at the field site – a distinct possibility – then the size of the largest frond predicted to survive, including 95% model error,would closely match the observed size of the largest frond (51.9 cm²; Fig. 11). The close correlation between maximum velocity and frond size across the field site suggests that, although Calliarthron is well adapted to resisting breakage, growth may ultimately be limited by wave-induced drag forces. Observations of larger fronds growing subtidally (K. A. Miller,personal communication), where drag is lower, support this conclusion but have yet to be properly quantified.

This manuscript benefited from comments made by M. Boller, K. Mach, L. Miller, K. Miklasz, R. Martone, and two anonymous reviewers. Research was supported by the Phycological Society of America, the Earl and Ethyl Myers Oceanographic and Marine Biology Trust, and NSF grant no. IOS-0641068 to M.W.D. This is contribution number 309 from PISCO, the Partnership for Interdisciplinary Studies of Coastal Oceans, funded primarily by the Gordon and Betty Moore Foundation and the David and Lucile Packard Foundation.