Results/Discussion

L. luymesi Sulfate Release Allows Persistence of Aggregations
The model predicts that inputs from known sources, including diffusion and advection of deep sulfide along with reduced seawater sulfate, will support a moderately-sized aggregation of 1,000 individuals for an average of 39 y (range, 22 to 78 y) (Figure 1). A smaller aggregation of 200 individuals could be maintained with these sources for an average of 64.1 y (standard deviation, 10.6 y). In this model configuration, the duration of adequate sulfide flux is not congruent with the known sizes of aggregations and existing age estimates of L. luymesi individuals and aggregations. Adding sulfate release by tubeworm roots to the model results in sulfide generation and flux at rates that match the demands of large aggregations, allowing the tubeworms to survive for over 250 y (Figure 1). This additional source of sulfate results in a two-orders-of-magnitude increase in sulfate flux in older (>100 y) aggregations, accounting for over 90% of sulfate available after only 24 y. The sulfate released by the tubeworms would be used for anaerobic methane oxidation and hydrocarbon degradation. The nature of the relationship between symbiotic tubeworms and microbial consortia that we are proposing is a coupling of the sulfur cycle only, and not carbon. Light dissolved inorganic carbon (DIC) resulting from the oxidation of hydrocarbons is apparently not taken up by tubeworms as the carbon stable isotope signatures of L. luymesi are heavier than would be expected from a methane-derived DIC source [20,21]. In addition, the well-studied hydrothermal vent tubeworm, Riftia pachyptila, obtains carbon in the form of CO2 across its plume [22]. However, this does not necessarily exclude the passive diffusion of DIC across the root surface, which could account for some of the variability observed in L. luymesi carbon stable isotope signatures [20,21]. By augmenting the sulfate supply to microbial consortia for sulfate reduction, large aggregations of tubeworms may survive for hundreds of years in the model, mirroring the population sizes and individual lengths regularly observed and collected at seeps on the ULS [23].
Figure 1  Ratio of Sulfide Supply to Sulfide Uptake Rate of L. luymesi Aggregations
Equilibrium line (1:1 ratio) and average, maximum, and minimum values for 1,000 iterations presented. Supply rate based on known sources without sulfate release by tubeworm roots shown in blue. Sulfide supply declines below demand after approximately 40 y. Supply rate including sulfate release from tubeworm roots shown in red, with sulfate release constrained by tubeworm symbionts' sulfide oxidation rate. Sulfide supply exceeds demand for the duration of the model.

Model Results Are Robust to Parameter Variation
An alternate hypothesis to explain the discordance between estimated sulfide supply and uptake rates is the presence of locally elevated seepage rates. Sensitivity analyses were carried out to determine the potential effects of uncertainty in seepage rate on supply estimated for aggregations without root sulfate release. A 10% increase in seepage rate resulted in a 5.6% increase in sulfide supply to aggregations 200 y old and older. This corresponds to only 16.4% of the sulfide required, which does not serve to extend aggregation survivorship (average, 39 y; range, 21 to 79 y) beyond that determined for lower flow rates. To supply the sulfide flux required by older aggregations, seepage rate would have to be at least 363 mm · y−1. This is over ten times greater than the rate used in the model (32 mm · y−1), which is the highest region-wide estimate for the Gulf of Mexico [24]. A rate of over 300 mm · y−1 approaches rates reported for active venting of fluids (Table 1). Active venting would result in the visual manifestation of seepage in the form of methane bubbles and oil droplets, which are generally restricted to mussel (Bathymodiolus childressi) beds at these sites [25]. In addition, larger, and therefore older [26], aggregations have lower epibenthic sulfide concentrations [8,9,25] suggesting that seepage becomes less vigorous over time and is not in the form of active venting in larger tubeworm aggregations. While difficult to obtain, in situ measures of advection rate of fluids at Gulf of Mexico seeps could be used to test these assumptions and may lend insight into the relationship between variability in tubeworm growth rate and sulfide availability.
Table 1  Reported Seepage Rates for Hydrocarbon and Methane Seeps The high degree of variability in growth rate and recruitment rate could also affect the ratio of supply and demand in the model. In an aggregation exhibiting anomalously low recruitment, the size of the rhizosphere would increase more rapidly than the biomass of the aggregation. This would lead to high rates of sulfide delivery and generation and low rates of sulfide uptake by tubeworm roots. When initial recruitment rate (a in equations 1 and 2) is decreased by 10%, the length of time that supply exceeds demand increases by 3.7%. This effect appears to be linear, with a 20% decrease in initial recruitment rate resulting in a 7.4% increase in persistence. If growth rate is increased, thereby increasing the rate of rhizosphere growth in terms of surface area for diffusion and advection, there appears to be little effect of the ratio of supply to demand (20% increase in growth—0% change in persistence time). In fact, increasing growth to the upper limits of the error term (equation 5) lowers the amount of time that the aggregation can be supported since biomass and sulfide demand increase more rapidly than increases in supply resulting from additional surface area. By decreasing growth rate, aggregations may be supported for longer periods of time, with a 20% decrease leading to a 6.3% increase in persistence time and a decrease of 88% leading to persistence for over 250 y. While an 88% lower growth rate lies outside of the range of existing growth data, this could be accomplished by ceasing growth for extended periods of time in a quiescent stage. This possibility remains to be investigated in L. luymesi. By utilizing a variable recruitment rate in the model, both between realized aggregations and between years within a model run, along with a growth error term encompassing the full range of observed growth data, the model is capable of generating aggregations within the range of the 10%–20% variability tested in this analysis. Even these outlying aggregations (presented as maxima and minima in Figure 1) support the qualitative conclusions drawn from model results.
While the model was based on empirical data to the greatest degree possible, estimates of many of the parameters necessary to resolve the model were not available or are extremely difficult to measure in deep water with existing technology. Uptake rates were measured in the laboratory [8] for relatively small individuals (<50 cm). While we attempted to approximate metabolic scaling by covarying uptake and growth rates, it is possible that large individuals require even lower sulfide flux. Model predictions are not overly sensitive to variability in this parameter. A reduction by 10% of the overall sulfide uptake rate results in a 5.2% increase in persistence time. To maintain an aggregation for over 250 y, mass-specific uptake rate would have to be reduced 6-fold. While this could also be accomplished by entering a period of quiescence as mentioned before, there is no existing evidence for this ability in vestimentiferans.
The second version of the model is based on the assumption that L. luymesi is capable of releasing sulfate through its roots. It should be noted that in the model, sulfate release is constrained by the rate of sulfate generation by the tubeworm's sulfide-oxidizing symbionts, resulting in the near 1:1 ratio of supply and demand in Figure 1. Though modeled sulfate flux across the roots into the rhizosphere may exceed 20 mmol · h−1 in older aggregations, the roots provide an ample respiratory surface such that rates of sulfate flux per unit root surface area do not exceed 0.4 μmol · h−1· cm−2 in the model. It remains possible that a proportion of the sulfate could be released through the plume of the tubeworms, though the energy required to pump sulfate against a concentration gradient (seawater [SO4] = 29 mM) [13] suggests that it would be more energetically favorable for the sulfate to passively diffuse out of the roots. It is also possible that sulfate flux could be increased by active bioirrigation delivering seawater to deeper sediment layers through the tubeworm tubes. This could allow the sulfide-oxidizing symbionts to store some of the oxidized sulfide as elemental sulfur rather than releasing it as sulfate, while maintaining sufficient sulfate flux to deeper sediment layers for sulfide generation. These mechanisms remain hypothetical and require further experimental investigations to evaluate their potential role in this system.

Tubeworms Impact Seep Biogeochemistry
Tubeworm sulfate release, in conjunction with high sulfide uptake rates, could contribute to the observation of declining advection rate in older aggregations. By increasing sulfate flux to deeper sediments, L. luymesi increases integrated rates of anaerobic methane oxidation and hydrocarbon degradation, which would enhance authigenic calcium carbonate precipitation within the rhizosphere. Under the conditions of root sulfate release in the model, calcium carbonate precipitation is rapid (0.109 to 0.316 μmol · l−1 · sec−1) in the first 53 y, with rates declining exponentially thereafter. By creating a barrier to fluid advection [4], this could result in the observed decrease in epibenthic sulfide concentration in older aggregations [8,9] and the predicted cessation of tubeworm recruitment around this time [12,23].
In order to prevent the precipitation of carbonate directly on the root surface, L. luymesi individuals may release hydrogen ions as well as sulfate through their roots. While hydrogen ion flux through the roots has not yet been empirically demonstrated, none of the nearly 5,000 tubeworms examined as part of this study were observed to have carbonate formed directly on their roots, suggesting that this form of precipitation is inhibited in some manner. In the model, diffusion of hydrogen ions across the root surface (the only form of release explicitly modeled) accounts for less than 40% of ion generation when carbonate precipitation is most vigorous. We speculate that L. luymesi may utilize the excess hydrogen ions generated by their sulfide-oxidizing symbionts to periodically raise the rate of hydrogen ion flux from their roots. This would not only supply additional hydrogen ions to sulfate-reducing bacteria, but could inhibit carbonate precipitation on the tubes and subsequent reduction of the root area utilizable as a respiratory surface. Further pH reduction could dissolve existing carbonate in sediments beneath the rhizosphere, thereby opening seepage pathways and allowing further root growth. This possibility is corroborated by the observation of young tubeworms that had apparently bored through bivalve shells in an experimental system (R. Carney, personal communication). Empirical measurements of hydrogen ion flux across the root tissue of L. luymesi are required to test these hypothetical mechanisms.
The release of sulfate by tubeworm roots potentially explains the frequent observation of highly degraded hydrocarbons in the vicinity of large tubeworm aggregations [27]. The majority of sulfate supplied by tubeworm roots is utilized for microbial hydrocarbon degradation in the model (Figure2). This process alone accounts for over 60% of the sulfide available to aggregations after approximately 80 y. In the absence of liquid and solid phase hydrocarbons, methane flux would have to be approximately four times the rate in the model in order to fuel sufficient sulfate reduction to support an aggregation for over 200 y. This could occur in sediments overlying rapidly sublimating gas hydrates, and hydrate abundance has been previously suggested as a potential factor influencing the distribution of chemosynthetic communities in the Gulf of Mexico [10]. However, model results indicate that large chain hydrocarbons are the most significant energy source for sulfate reduction in tubeworm-dominated sediments. Increased integrated rates of hydrocarbon degradation would lead to highly biologically altered hydrocarbon pools among the roots of tubeworm aggregations. Hydrocarbon oxidation has been implicated as one of the dominant processes in the carbon cycle at ULS seeps, accounting for over 90% of the carbon in carbonates collected in the vicinity of tubeworm aggregations [19]. Model analysis indicates that the minimum amount of organic carbon (including hydrocarbons as well as buried organic material) in sediments required to supply sulfide at rates matching aggregation demand (1:1 supply:uptake ratio) is 1.03% by weight, remarkably close to the lowest value found in any of the seep sediment core samples (1.2%) [13,28], and greater than that found in ULS sediments away from seeps (0.71%) [29]. Determination of organic carbon concentration in sediments beneath tubeworm aggregations is necessary to test the prediction that elevated carbon content at seeps, primarily resulting from oil seepage, provides the energy source required to generate sufficient sulfide for tubeworm aggregations.
Figure 2  Sources of Sulfide Available to Tubeworm Aggregations over Time in the Model
Sources of sulfide include advection and diffusion of sulfide from deep sources (yellow) or sulfate reduction using methane (blue), buried organic carbon (green), or C6+ hydrocarbons (dark grey) as electron donors. Sulfate is provided by diffusion from sediments surrounding the rhizosphere, diffusion at the sediment–water interface, and release from tubeworm roots. Additional sulfate flux from tubeworm roots could also explain the high apparent sulfate diffusion coefficients determined for tubeworm-impacted sediments [13]. Anomalous sulfate fluxes have been proposed to be a result of bioturbation and bioirrigation by macrofauna [3,5], and recycling by microbial mats [13]. The results of the model presented here provide evidence for macrofaunal sulfur recycling, an additional component to be considered in future investigations of cold seep biogeochemistry. The hypothesized release of sulfate by tubeworm roots potentially explains numerous, apparently disparate observations, hinting at the great impact that L. luymesi aggregations may have on their abiotic environment.
While the proposed interactions between symbiotic tubeworms and sulfate-reducing bacteria are essential for the persistence of L. luymesi aggregations in the model, we suggest that there are significant effects on the microbial community as well. This syntrophy will increase the abundance of sulfate-reducing bacteria and therefore increase the rates of anaerobic methane oxidation and hydrocarbon degradation carried out by microbial consortia that rely on sulfate as an oxidant. Tubeworm-generated sulfate supplies a more energetically favorable electron acceptor below the normal depth of sulfate penetration at seeps, relaxing the limitation on anaerobic oxidative processes at these sediment depths. Deeper sediment layers then become habitable to sulfate reducers, significantly altering the microbial community structure within the rhizosphere. Model configurations neglect the potential role of bioirrigation of seawater sulfate through L. luymesi tubes, which could further increase sulfate supply to deeper sediment layers. The possible role of tubeworm roots as substrata for the growth of microbial consortia, analogous to the habitat afforded mycorrhizal symbionts of higher plants, remains another possible benefit for the microbes. These predictions may be tested by determination of the relative abundance of microbial consortia at different depths of sediments both impacted by and isolated from tubeworms. Localization of the microbes on the root surface would provide evidence for a more intricate relationship. It is our hope that the results of this model may provide the impetus for future rigorous experimental tests of these ideas.

Summary
The model results presented here are consistent with the hypothesis that L. luymesi releases sulfate into hydrocarbon-rich sediments to fuel sulfide generation, allowing for the persistence of the longest-lived animal known. The importance of this process to sulfide generation in the modeled rhizosphere implies a complex relationship between an animal with bacterial endosymbionts and external sulfate-reducing bacteria, often in consortia with methane-oxidizing or hydrocarbon-degrading microbes. This positive interspecific relationship, including members of all three domains, would benefit both the tubeworms and the microbial consortia involved. This expands our existing concept of the potential for complexity in mutualisms and the benefits they may confer. Further complex relationships are likely to be discovered through continued research into the role of positive species interactions at the individual and community levels.