PMC:1044833 / 23142-50446 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/1044833","sourcedb":"PMC","sourceid":"1044833","source_url":"https://www.ncbi.nlm.nih.gov/pmc/1044833","text":"This study couples an individual-based population growth and sulfide uptake model [12] to a diagenetic diffusion/advection model to compare the relative magnitude of sulfide supply and uptake for long-lived tubeworm aggregations. A series of 1,000 iterations of the model under three different initial conditions (known sources of sulfate, known sources plus root sulfate supply, and known sources with elevated seepage rates) were carried out. The rhizosphere (volume of sediment encompassed by the root system of an aggregation) is modeled as an inverted dome beneath the sediment with a radius equal to the average root length of the population (Figure 3). The rhizosphere was approximated by a series of two-dimensional discs at 2-cm intervals in order to reduce the complexity of a three-dimensional solution for a sphere of changing size. Sulfate (SO4 2−), methane (CH4), sulfide (HS−), bicarbonate (HCO3 −), and hydrogen ion (H+) fluxes across the rhizosphere boundary are determined. Sulfate reduction rates using methane, larger chain hydrocarbons, and buried organic matter as electron donors are modeled in order to estimate the sulfide available to tubeworm aggregations as they change in size over the course of 250 y.\nFigure 3 Model Construction\nPopulation model includes individual size-specific growth and mortality rates, and population size-specific recruitment rate. Growth rate was determined by in situ staining of tubeworm aggregations using a blue chitin stain (in situ photograph of stained aggregation demonstrating annual growth shown here) and collection after 12–14 mo. Diagenetic model included advection and diffusion of sulfate, sulfide, methane, bicarbonate, and hydrogen ions as well as organic carbon content of sediments. Fluxes across the rhizosphere (root system) boundary were compared to sulfide uptake rates for simulated aggregations to determine whether sulfide supply could match the required uptake rates of aggregations (for specific methodology see methods). HC, C6+ hydrocarbons; orgC, organic carbon; ox, oxidation reaction; red, reduction reaction.\n\nPopulation growth model\nThe population growth model follows the methodology presented in [12] and includes population growth, mortality rate, individual growth rate, and sulfide uptake rate. The parameters underlying the population growth model were refined using growth data from an additional 615 individuals and population data from an additional 11 aggregations comprising 4,908 individuals. The model presented here includes data from a total of 23 tubeworm aggregations from three nearby sites (Green Canyon oil lease blocks 184, 232, and 234) collected over a period of 7 y on the ULS to arrive at generalized population growth parameters.\nL. luymesi individuals are dioecious, with males releasing sperm into the water column. Fertilization is believed to be external [30], though sperm has been found within the oviducts of females of the hydrothermal vent tubeworm R. pachyptila [31]. Eggs and embryos are positively buoyant and develop into a swimming trochophore-like larval stage within 3 d of fertilization [32]. Larvae are lecithotrophic and may remain in the water column for several weeks [32]. They require hard substrata for settlement, and acquire symbionts from their environment after metamorphosis [33,34]. Settlement is initially rapid, and continues until the available substrate is occupied [12,23,35]. Population sizes of aggregations collected with existing sampling devices typically vary between 100 and 1,500 individuals ([12,23]; this study), though far larger aggregations covering tens to hundreds of square meters are common at the sites sampled. Previous studies have shown that L. luymesi has an average longevity of 135 y [12], and requires an average of 210 y to reach 2 m in length [26], a size not uncommon among collected animals. Mortality events are exceedingly rare, dropping below 1% annual mortality probability for animals over 30 cm [12]. The expanded datasets of growth and mortality rates included here extend the longevity estimate for L. luymesi to an average of 176 y and the estimated age of a 2-m-long animal to 216 y.\nAt the beginning of each iteration, population growth parameters are chosen for the following population growth model:\nwhere N is population size, t is time (in years), K is carrying capacity (set to 1,000 individuals for all simulations presented here), a describes the initial slope of the line, b defines the degree of density dependence, and c is a shape parameter. The first parameter (a) was generated using the following function:\nwhere ɛ[N(0,1)] is a normally distributed random deviate with an average of zero and a standard deviation of one. This allows the initial recruitment rate to vary within the range of all recruitment trajectories that have been observed [12]. The other parameters were not normally distributed; therefore, the log-transformed distributions were used to define the distribution of the random numbers generated. As the three parameters in the model were significantly correlated (ln(a) and ln(b), r = −0.853, p \u003c 0.001; ln(a) and ln (c), r = −0.461, p = 0.036), values of b and c were chosen from their relationship with a:\nThe value of a was allowed to vary each year according to the pooled standard error associated with the estimates of a from the empirical data (standard error, 0.105). Once population size equaled or exceeded carrying capacity, recruitment was ceased, representing the lack of additional substrate or sulfide available in the water column.\nOnce recruitment was determined for that year, the individual-based portion of the model began. Each individual was traced through time with respect to its length, root length, mass, mortality probability, mass-specific sulfide uptake rate, sulfate excretion rate, and hydrogen ion elimination rate. Growth rates of tubeworms were determined by staining tubes in situ (Figure 3) and collection 12 to 14 mo later ([26]; this study). Individual growth rate was determined from the following function (Figure 4):\nFigure 4 L. luymesi Growth Rate\nSize-specific growth of L. luymesi determined from stained tubeworms. Different colors indicate growth data from different aggregations. Blue points labeled “2000” are all from Bergquist et al. [26]. Other colored points refer to submersible dive numbers from 2003 when stained aggregations were collected.\n(A) Growth function and 95% confidence interval for size-specific growth.\n(B) Error function fitted to the residuals of the model. Length (l) is defined here as the distance from the anterior end of the tube to an outer tube diameter of 2 mm following the methodology of [26]. All growth rates were standardized to 365 d. The error term is an additional function fitted to the residuals of the first regression function (Figure 4B), resulting in a variable growth rate. This error term was used rather than varying growth within the 95% confidence interval of the regression of length and growth rate because of the high degree of variability in growth among individuals. It should also be noted that there is a certain degree of variability in growth rate between aggregations (Figure 4). This may be attributable to spatial or temporal variability in seepage rate or sulfide concentration between aggregations. Aggregations may be subject to persistently differing conditions on a small (meter) scale, or may encounter periodic fluctuations in habitat characteristics. Because we are uncertain whether this variation is persistent on the temporal scales that we are simulating, between-aggregation variability is not explicitly modeled, though by chance certain realized aggregations deviated from mean growth rate.\nThe ratio of root length to tube length was determined from individual length using the following function:\nAnnual mortality rate was approximated as the size-specific frequency of empty tubes in collected aggregations [12] with an overall annual mortality rate of 0.569%. This approximation is conservative and likely overestimates yearly mortality, as available data indicate that empty tubes should persist longer than 1 y [12,36]. Mortality probability was determined for each 10-cm size class using the following function:\nwhere m is mortality probability and l is length. Individuals were considered dead if their probability of mortality exceeded a uniform random number between zero and one.\nBy using generalized population growth parameters in the model presented here, we attempt to encompass the range of empirical data from sampled aggregations in our examination of sulfide uptake and supply rates. Taken together, the population growth model including recruitment, growth, and mortality provides a good qualitative if not quantitative fit for any individual aggregation, reflecting the size frequency of tubeworms within sampled aggregations [12]. It should be noted that the modeling of specific aggregations was not the aim of this study; rather, an attempt has been made to encompass the variability observed in the various populations of tubeworms that have been sampled. To examine the effect of uncertainty in the population growth parameters, sensitivity analyses were carried out. The initial slope of the recruitment rate (a in equation 1) was varied while individual size-specific growth rate was held constant (no error term in equation 5). Growth rate was then varied while holding the initial rate of population growth constant (no error term in equation 2). The effect of a 10% change in each parameter was determined, and then changes of greater magnitude were examined to determine the fastest rate of population or individual growth that could be supported by the sulfide available to the aggregation in the absence of sulfate release.\nIndividual sulfide uptake was allowed to vary within the range of laboratory-determined sulfide uptake rates according to that individual's growth rate for that year:\nwhere u is uptake rate (in micromoles per gram per hour), m is mass (in grams), and g is growth rate (in centimeters per year). Growth rate was divided by the maximum growth rate (10 cm · y−1) such that highest growth rates resulted in highest uptake rates. By scaling uptake rate with growth, we approximate metabolic scaling, resulting in a decline in uptake rate by a factor of 3.7 over the range of tubeworm sizes in this study [12]. The amount of sulfate that could be excreted by each individual was determined from the amount generated by sulfide oxidation carried out by the internal chemoautotrophic symbionts assuming constant internal sulfate concentration, thereby accounting for changes in body volume. We do not account for the binding of sulfur by free amino acids, as this is believed to relatively minor compared the flux rates of sulfate and sulfide, and is reversible [37]. Hydrogen ions are also generated in the oxidation of sulfide by the tubeworm symbionts. Hydrogen ion elimination rate was determined in the model in the same fashion as sulfide uptake, with growth rate determining the variability in this metabolic flux according to laboratory-measured ion fluxes (mean, 10.96 μmol · g−1 · h−1; standard deviation, 1.88 μmol · g−1 · h−1) [38]. Simple diffusion of hydrogen ions across the root surface was included in the model, though the exact mode of proton flux has not yet been determined experimentally for L. luymesi [38]. As diffusion across the roots accounts for a relatively small proportion of total proton flux (less than 10% in large individuals), additional pathways are likely and require further investigation.\n\nGeochemical setting\nKnown sources of sulfide available to L. luymesi aggregations are sulfide transported with seeping fluids [10] and sulfide generated via reduction of seawater sulfate [39,40]. The majority of the sulfide present at ULS sites is believed to be related to sulfate reduction coupled to anaerobic hydrocarbon oxidation [14,39]. Other potential sources of sulfide associated with seepage include anaerobic oxidation of deeply buried organic material [10], “sour” hydrocarbons containing a proportion of sulfur [41], and hydrocarbon interactions with sulfur-bearing minerals such as gypsum and anhydrite found in the salt dome cap rocks of the ULS [8,42,43].\nConcentrations of all chemical species in the sediments surrounding the rhizosphere were derived from the dataset included in Arvidson et al. [13] and Morse et al. [28]. Only those sediment cores taken around the “drip line” of tubeworm aggregations that contained detectable sulfide concentrations were used. Due to the vagaries of sampling with a submersible in sediments heavily impacted by carbonate and roots, those cores with detectable sulfide are believed to more accurately represent conditions around the periphery of the rhizosphere.\nDissolved organic carbon (DOC) concentration was used as an estimate of methane concentration. While other forms of DOC make up this total concentration, methane accounts for 90%–95% of the hydrocarbon gasses dissolved in pore waters [28]. In seep sediments, the majority of DOC is likely to be in the form of hydrocarbon gasses. Because estimates of organic acid concentrations were not available, they could not be explicitly modeled. This would not affect the overall concentration of electron donors in the model, but could affect the sulfate reduction rate. Since sulfate reduction rate estimates for methane seeps in the Gulf of Mexico are among the highest recorded [14,39], any differences in DOC composition (e.g., higher relative concentrations of dissolved organic acids) would serve to lower the overall sulfate reduction rate and sulfide availability. Sulfide supply estimates presented are likely overestimated most by the model without root sulfate release owing to the greater reliance on anaerobic methane oxidation in this form of the model. Simulations including sulfate release by tubeworms are affected to a lesser extent as the concentration of electron donors is not limiting in this model configuration.\nSolid and liquid phase organic carbon was separated into hydrocarbons and buried organic material according to their relative concentrations in hydrocarbon seep and surrounding Gulf of Mexico sediments. Background sediments on the ULS contain 0.71% organic carbon by weight [29]. At hydrocarbon seeps on the ULS, organic carbon accounts for 4.47% of total weight. This was assumed to be the sum of background organic input plus carbon in the form of C6+ hydrocarbons. It is possible that the higher biomass located at ULS seeps in the form of non-living macrofaunal and microbial materials may also contribute to the increased organic carbon concentration, but without empirical estimates, this could not be accounted for in the model. Hydrocarbons may consist of between 50% and 95% labile materials [44,45,46]. Based on existing data on degradation rates and residual hydrocarbons subjected to degradation [42,47], a value of 50% labile material was used here. These assumptions of hydrocarbon concentration and degradation potential are therefore believed to be conservative.\nThe following functions were fitted to the sulfide, sulfate, and methane concentration profiles (Figure 5) to determine the boundary conditions at any given depth:\nFigure 5 Concentration Profiles of Sulfate, Sulfide, and DOC\nPoints represent average concentration at a given depth from 13 sediment cores taken around the periphery of tubeworm aggregations (see Materials and Methods and original data in [13,28]). Best-fitted line based on least squares fit of equation 9. where C 0 is initial concentration, C∞ is concentration at infinite distance, and Ci is concentration at depth d. As there were no existing data for sediments below 30 cm, concentrations at infinite depth (C∞) were used (SO4 2− = 0 mmol · l−1, HS− = 12 mmol · l−1, DOC = 11 mmol · l−1, DIC = 20 mmol · l−1, pH = 7.78). The first derivatives of the sulfide and methane profiles were used for the calculation of advective flux from depth. The first derivative of the sulfate profile was used for diffusive flux across the water–sediment interface of the rhizosphere, with advection rate subtracted from diffusive flux of sulfate across this surface. Advection (seepage) rate varied with time according to the following function:\nwhere t is simulation time in years and sed is sedimentation rate (6 cm · 1,000 y−1) [29]. Early seepage rate approximated the highest flux rates measured or estimated for methane seeps and declined with time in the model to the highest estimates for persistent, region-wide seepage in the Gulf of Mexico (Table 1). This follows a pattern of hydrocarbon seep development, with the highest seepage rates early in the evolution of the local seepage source followed by occlusion of fluid migration pathways by carbonate precipitation, hydrate formation, and possibly tubeworm root growth. By using the highest rate estimated (32 mm · y−1 = 0.000365 cm · h−1 in equation 10) as the basal seepage rate, we are testing the possibility that tubeworm aggregations could survive under the most favorable conditions possible in the absence of tubeworm sulfate supply.\nFor sediments encompassed by the rhizosphere, sulfide, sulfate, methane, DOC, and hydrogen ion concentration profiles were determined iteratively prior to model implementation using a central difference scheme:\nwhere C i(t) is concentration in cell i at time t, D is the diffusion coefficient, k is the maximum reaction rate, and Ks is the half-saturation constant for the reaction (Table 2). Reactions included anaerobic methane oxidation (equation 17), tubeworm sulfide uptake rate (equation 8), and carbonate precipitation rate (equation 22). The concentration in each 2 × 2 cm cell was calculated at 1 h time steps. At the end of each year, diffusion distance increased. The number of cells (total diffusion distance) was determined by the average root length of L. luymesi populations as realized in independent runs of the population growth model described above, and included here as model input only. A separate function was fitted to each of the concentration profiles:\nTable 2 Parameters Involved in Diagenetic Model\naDiffusion coefficients all corrected for temperature, pressure, and salinity according to Stumm and Morgan [51] and Pilson [52]\nbAll disassociation constants corrected for temperature, salinity, and pressure according to Stumm and Morgan [51] and Pilson [52] except: CaOH, no correction; CaHCO3, CaSO4, CaSO4H2O, MgHCO3, temperature only; H2CO3, temperature and salinity only; and HSO4, temperature and pressure only where d is radial distance. The relationship between the parameter a and distance was used to generate concentration profiles for each disc comprising the rhizosphere. Because of the tight linear relationship between diffusion distance and the shape of the curve, concentration profiles could be generated for a disc of any size using the following function:\nwhere α is 1.7344 and β is 1.0104 for HS−, α is 0.2111 and β is 0.3363 for SO4 2−, and α is 0.1626 and β is 0.2518 for CH4. Diffusional fluxes of sulfide, sulfate, and methane were calculated according to the first and second derivatives of the concentration profiles as determined by the diameter of each disc.\n\nModel implementation\nThe model estimates sulfide availability to the aggregation as a whole by summing the fluxes separately determined for each 2-cm disc composing the rhizosphere. Depth-dependant boundary conditions were set for each disc separately based on the sediment profiles (Figure 5). Diffusional fluxes into each disc were calculated from the shape of the concentration profiles according to the following function [48]:\nwhere C is concentration, r is disc radius, and Ds is the diffusion coefficient corrected for porosity by:\nwhere Do is the diffusion coefficient corrected for temperature and pressure, n is the chemical species-specific constant, and φ is porosity. The value of n was set to 2.75 as this was found to be a reasonable fit for all chemical species examined [49]. The ionic states of each species at the average pH value of tubeworm-dominated sediments (7.78) were used for the determination of diffusion coefficients. Porosity was determined from the following function:\nwhere φz is porosity at depth z, φ0 is porosity at the sediment–water interface, and φ∞ is porosity at infinite depth; φ0 was set at 0.841, φ∞ at 0.765, and a at 0.210, as determined from the best fit with the porosity data (Figure 6) from Morse et al. [28].\nFigure 6 Sediment Porosity Values\nPoints represent average porosity at a given depth from 13 sediment cores taken around the periphery of tubeworm aggregations (see Materials and Methods and original data in [13,28]). Best-fitted line based on least squares fit of equation 9. Diffusion across the sediment–water interface of the rhizosphere was also considered as an additional input of sulfate and hydrogen ions. This was included as one-dimensional diffusion across a circular surface (subtracting the area encompassed by the tubeworm tubes) with diffusion distance equal to rhizosphere diameter, and concentration differential from seawater concentration to the average concentration within the rhizosphere. Sulfate and hydrogen ion diffusion across the root surface was then added (if included in the set of model realizations) as simple Fickian diffusion. Concentration differential was the difference between internal concentration and average concentration for each disc of the rhizosphere assuming roots were evenly proportioned according to the volume encompassed by each disc. Internal sulfate concentration and pH (Table 2) represented an average of the values determined for R. pachyptila [22], a hydrothermal vent tubeworm. Internal sulfate concentrations and pH of L. luymesi have not been reported, but these values are generally consistent within taxa [50]. Uptake of sulfide and release of sulfate were summed across the entire tubeworm population, again assuming an even distribution of roots within the rhizosphere. The paucity of empirical data on the location of any individual tubeworm's roots within an aggregation precluded modeling space explicitly; therefore, it is assumed that each individual has equal access to the resources available within the rhizosphere.\nWithin the rhizosphere, sulfide generation may be limited by sulfate supply, electron donor availability, or sulfate reduction rate. Sulfate supply was determined as the sum of flux across the series of discs approximating the rhizosphere dome, across the sediment–water interface, and from root sulfate (if available). Available sulfate is utilized for anaerobic methane oxidation first (the more energetically favorable process), then hydrocarbon and organic matter degradation. Electron donors included methane, complex hydrocarbons, and buried organic material. Solid and liquid phase hydrocarbons and organic material were assumed to be homogenous within the rhizosphere. Methane supply was determined as the sum of flux across each rhizosphere disc boundary. Hydrocarbon and organic material concentrations were determined as the amounts encompassed within the rhizosphere volume minus that oxidized in previous years. Sulfate reduction rate was determined from the relative amounts of the various electron donors with higher rates (0.71 μmol · ml−1 · h−1) for methane oxidation and lower rates (0.083 μmol · ml−1 · h−1) for organic matter or hydrocarbon degradation [39]. Microbes carrying out these processes are assumed to be evenly distributed within the rhizosphere.\nTotal hydrogen sulfide availability to the aggregation was determined as the sum of sulfide diffusion and advection across each rhizosphere disc and sulfide generated within the rhizosphere from sulfate reduction according to the following reactions:\nSO42− + CH4 → HS− + HCO3− + H2O\nSO42− + 2CH2O → HS− + 2HCO3− + H2O\nSO42− + 1.47CnH2n+2 → HS− + 1.47HCO3− + H2O\nBicarbonate (HCO3 −) is generated at a 1:1 stoichiometry during anaerobic methane oxidation and a 2:1 stoichiometry in the degradation of organic material. As hydrocarbons are degraded forming smaller chain hydrocarbons and organic acids, bicarbonate is generated at different stoichiometries. Because different-sized hydrocarbons and organic acids were not accounted for in the model, a rough average of these stoichiometries (1.47:1) based on toluene, ethylbenzene, xylene, and hexadecane degradation [18] was used to determine the amount of bicarbonate generated per mole of carbon. Hydrogen ions are also used up in a 1:1 stoichiometry with sulfate in the sulfate reduction half reaction as included in reaction 17.\nIn order to account for carbonate precipitation, the model traced DIC concentration, calcium concentration, hydrogen ion concentration, buffer capacity, carbonate saturation, and carbonate precipitation rate. The buffer state of the rhizosphere was calculated to determine changes in pH resulting from hydrogen ion flux. Buffer capacity (β) was calculated using the following function [51]:\nwhere A and B represent the concentrations of the various acids and bases in the buffer system. In addition to hydrogen and hydroxyl ions, the buffer system included carbonate (CO2, H2CO3, HCO3 −, and CO3 2−), sulfide (H2S and HS−), sulfate (HSO4 − and SO4 2−), and borate (B[OH]4 − and B[OH]3) speciation. Current pH was used to determine the ionic state of each species according to temperature-, pressure-, and salinity-corrected disassociation constants when available [51,52] (Table 2). Change in pH was determined from hydrogen ion flux and buffer capacity as follows:\nSaturation state is highly dependent on the degree to which calcium and bicarbonate form complexes with other ions. The “free” calcium was determined as the proportion of calcium that is not associated with complexed bicarbonate (HCO3 −), carbonate (CO3 2−), hydroxyl (OH−), or sulfate (SO4 2−) ions. Free carbonate was determined as the amount not forming complexes with calcium (Ca+) or magnesium (Mg+) ions in solution. Saturation state was then calculated from the product of the concentrations of free calcium and carbonate divided by the solubility product constant. If the saturation state was above one, then carbonate precipitation occurred at a rate determined by:\nwhere k 1 is 0.00597 l · mol−1 · sec−1 and k3 = 0.456 l · mol−1 · sec−1 [51]. Because there is no empirical relationship between weight percent of carbonate and sediment porosity in tubeworm-dominated sediments [28], precipitation did not directly affect porosity. Precipitation was accounted for in the model by subtracting the volume of carbonate precipitate from the total volume encompassed by the rhizosphere.\nAt the end of each annual time step, model output included average length of individuals, population size, sulfide uptake rate, sulfide supply rate, root sulfate flux (if included), root hydrogen ion flux, amount of sulfide supply accounted for by each process (sulfide seepage, anaerobic methane oxidation, organic matter degradation, and hydrocarbon degradation), number of individuals that could be supported by sulfide supply, carbonate precipitation rate, volume of carbonate precipitate, and 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