An integrated modeling framework was developed to assess physical, biological and chemical processes in the sediment and at the sediment–water interface. Special focus is laid on the description of different functional groups of bacteria as defined according to their metabolic pathways, including fermentation, methanogenesis and oxidation of high and low molecular mass dissolved organic carbon, ammonium as well as other reduced compounds. The model is subjected to a new validation method which allows for an appropriate representation of remaining uncertainties. It is also able to reproduce two-dimensional gradients in all state variables induced by a pore-water velocity field typical for permeable sediments. Another improvement with respect to many classical models follows from the simulation of adaptive changes in dormancy and motility strategies. Within an extensive analysis stage, the evolutionary stability of these strategies is investigated under a variable hydrodynamical regime. The results show that optimal behavior in terms of adhesion and readiness to dormancy shifts differ between functional groups. This pattern is compared to recent empirical findings and discussed in relation to the confidence limits of the overall methodology. In the numerical experiments, also the effect of variable microbial strategies on the total carbon mineralization of the sediment is determined.
In the last decade, a series of new techniques have increased our knowledge of the functioning of microorganisms at the cell or molecular level [1,2]. However, one of the challenges in aquatic microbial ecology remains to link the vast array of microscale properties to macroscale descriptions of biogeochemical cycles . It is often unclear, which net effect microbial processes may have in a specified environment. This is in particular true for near-shore habitats where fluctuating conditions lead to complicated spatio-temporal patterns of biochemical variables and microbes exhibit non-equivocal strategies.
In this work a frame is presented as a first step to assess the control of subsurface material fluxes in coastal marine environments by microbial properties. As the latter may be only qualitatively or partially documented by empirical studies, the framework will rely an a modeling approach. With the aim to quantify the relative effects of single strategies, the model has to provide a whole system description and, thereby, will be as complete and highly resolved as possible. Such a approach obviously has major drawbacks like many uncertainties regarding the model structure and parameterization. Another difficulty is met when these uncertainties have to be translated to confidence limits of model outcomes. The latter also comprise model analysis results that reflect sensitivities of the (biogeochemical) variables of interest on particular model processes. Confronting all these items, the framework will be evolved within three stages.
First, an integrated sediment model (ISM) has to be constructed based on existing models and selected outcomes of recent publications. The ISM will be the prerequisite for studying mutual relationships between physical, geochemical and biological factors and mechanisms.
Secondly, the model has to be validated such that few existing literature data are integrated as effectively as possible. A main new element of this stage will be the notion of model ensembles. Instead of running model simulations with a single parameter set, ensembles of trained sets will be gathered and then used throughout the study.
In the third stage of the study, the ISM will be used for numerical experiments where the role of single microbial properties for the total carbon remineralization of the system is investigated. Additional questions of interest are whether these properties correspond to evolutionary stable strategies of the populations and what advantages the different functional groups will take. The selected processes under consideration comprise two major topics in aquatic microbial ecology, i.e. subsurface transportation of cells and adaptive regulation of bacterial metabolism.
By attaching to subsurface grains or trapped organic particles, bacteria can have a better access to nutrients or substrates [4,5]. Adhesion also alters the spatial distribution of cells in the sediment column by changing their passive transportation, with biogeochemical as well as ecological implications at a millimeter to decimeter scale. Although adhesion has already been included in few modeling studies , these impacts have never been assessed by a more systematic approach.
A second focus of this study will be laid on dormancy. By down-regulating metabolic activity, bacteria can successfully deal with unstable environments . However, many aspects of this strategy deserve further research like the adaptive significance of lag times. It will, thus, be investigated in this study, whether fastest response always turns out best in terms of biogeochemical functioning or cell energy budget.
2Materials and methods
It is hardly possible to give a complete derivation of the ISM within a single paper. The documentation is, hence, divided into several works currently in progress.
Aiming to address the biogeochemical dynamics in near-shore sediments, the ISM has to refine state-of-the-art models since these have been developed for relatively stable environments. Most effective improvements are made with respect to (i) an array of transport processes resolved in two spatial dimensions, (ii) microbially controlled reaction rates, and (iii) microbial kinetics and adaptations. In the presented work, a brief overview over the geochemical part serves as a basis for the more detailed description of the microbial model part. Its linkage to the transport modules is made clear as far as necessary for understanding the subsequent analysis.
The geochemical submodel extends few models documented in the literature [8–10]. It includes four different arrays of reactions, degradation of particulate organic carbon (POC), fermentation and oxidation of high molecular dissolved organic carbon (HM-DOC) and oxidation of the low molecular classes (LM-DOC), re-oxidation of reduced substances and mineral precipitation. In this study, the global POC, HM-DOC and LM-DOC pools are divided into three fractions, each with specific turnover rates, similar to the decomposition model of Boudreau .
Hydrolysis of POC may be enhanced by the presence of aerobes as these are capable of producing extracellular enzymes which accelerate dissolution. HM-DOC pools are simultaneously subjected to oxidation and fermentation activity. Following classical theory, the oxidation reaction is split into six biogeochemical pathways (PR-1 to PR-6 in Table 1).
Table 1. Diagenetic reactions resolved within the model
Organic material is chemically represented by carbohydrate CH2O.
Primary redox reactions and ammonium adsorption
Secondary redox reactions
Monosulfide precipitation, re-oxidation and pyrite formation
Nitrogen dynamics is coupled to the carbon cycle through nitrification, denitrification, nitrous oxide production and ammonification. For the latter, the model uses an array of C:N ratios such that the observed correlation between organic matter degradability and nitrogen content is preserved [12,13]. The resulting NH4+ is exclusively oxidized by the most powerful electron acceptors. These are O2, NO3− and MnO2 as formulated in the chemical reactions NH-1 to NH-3 within Table 1.
Re-oxidation of reduced substances is described by the ISM analogously to DOC oxidation. Currently, a set of 10 chemical pathways are resolved (SR-31 to SR-65). For the existence and stoichiometry of each reaction, references can be found in the literature [14,15,8].
2.2Microbial control of geochemistry
A central element of the ISM is to take into account that nearly all reactions in Table 1 are mediated by microbes. Exceptions are ammonium adsorption, the precipitation of monosulfides and their re-oxidation.
At least for sulfate reduction, measurements sustain a strong correlation between specific activity and abundance of active sulfate reducing bacteria (SRB) . Hence, all reaction rates Rn (n=PR-1…PR-6,NH-1…SR-65, see enumeration in Table 1) are supposed to be linear functions of the active microbial biomass Xact,n.
Furthermore, reaction rates are controlled by (i) a term Ln representing limiting effects due to low nutrient concentration or substrate quality, (ii) a non-linear temperature dependence θ(T) and (iii) a global rate constant r:
From a modeling point of view, the dependency on biomass of (active) microorganisms extends the more static picture used by several diagenesis models where energetically less favorable pathways are directly inhibited by the ones which yield more free energy [9,17]. In contrast, the ISM regulates the partitioning of chemical pathways through increasing and decreasing population densities Xact and not by direct product inhibition (cf. ).
2.3Population dynamics and activity
Following standard model descriptions for competing groups of bacteria as, for example, proposed in [19,20], biomass dynamics is determined by a growth and a loss term. The first should be proportional to the gross rate Rn of the reaction catalyzed by the group n, times a yield factor y. This way, the model links cell energetics to reaction kinetics, considering the finding that bacterial yield increases with higher free energy release :
σn denotes a specific growth coefficient as explained later and Xcap a capacity which is here meant as a measure for habitat space. At X=Xcap the limiting effect due to spatial bounds reaches one half. The value of Xcap is the same for all functional groups and, thereby, scales all biomasses.
The temperature dependent loss term ρ(T) comprises removal of individuals, i.e. mortality and bacterivory, as well as maintenance respiration. It is assumed that dormant cells (with biomass Xdorm,n) respire at a lower rate δρ compared to active organisms.
Notably, the regulative shift in the metabolism of single species like from aerobic oxidation to denitrification and vice versa is implicitly followed by the ISM as competition between functional groups. The validity, however, of this approach depends on whether the velocity of adaptive metabolic shifts occur within the same time scales as structural changes in the modeled community.
The dominance sequence of primary redox reactions [22,23] is here translated to gradients in specific growth coefficients σn. Measurements comparing two pathways indeed reveal a decrease in bacterial growth rates along the theoretical free energy sequence [24–28]. From those studies, at least ranges for σn and limitation terms Ln can be guessed. The real picture might not be that simple. For example, Kristensen et al.  suggested that limitation by the initial hydrolysis stage and not different utilization of DOC components may be responsible for distinct degradation kinetics.
While all reaction rates are related to the biomass of the active population Xact,n, Eq. 2 applies to the total biomass Xn (also within the rate function Rn). Then the actual biomass of active cells is a function of Xn and Xdorm,n:
The division between active (Xact) and dormant cells (Xdorm) rudimentarily follows theoretical considerations made in . Other recently proposed modeling approaches even allow for a full and dynamic treatment of an array of metabolic stages . In this study, however, a simpler and numerically more efficient solution has been found, by which the fraction of dormant cells is switched between two states according to current growth conditions:
The coefficient β describes the flexibility of the switch between the active and dormant state. Considering a high flexibility (β=1), one has a relatively large value of Xdorm as soon as the relative growth rate (RGRn=(dXn/dt)/Xn) becomes negative. Thus, respiration of the population is diminished. Vice versa, more cells turn to higher activity under favorable conditions, giving rise to a rapid recuperation of high biomass levels. This relationship is converted to the opposite for a value of β at one half so that up- and down-regulation takes more time.
The background value (Xstat) of non-active biomass is estimated on the basis of the steady state value of X. The latter can be derived from Eq. 2 using Xdorm≪Xact, Ln∼0.1 and θ(T)=1:
With this formulation, typical adaptation times of microbial communities after sudden environmental changes [24,30,31,10] can be reproduced. It is furthermore possible to simulate high amounts of dormant cells as found in several field studies [32,30].
2.42D transport and microbial adhesion
The sediment system is subjected to a high spatial and temporal variability in external forces, mediated through a set of transport processes like bioirrigation, diffusion and hydrodynamically induced advection in sediments [33,34]. These processes act on three different phases. First, one has dissolved chemical species in the pore-water, whereas solid mineral species and particulate organic material can either be in a suspended state or be integral part of the sediment matrix. The relative amount of suspended versus fixed particulate material, s, is calculated in a submodel which uses the pore-water velocity field, a critical resuspension velocity and a specific stickiness parameter. Diffusion only affects the pore-water phase, whereas advection acts on suspended and dissolved material. Exchange with seawater by bioirrigation works independently of the phase. Bacteria may in addition regulate their transportation in the sediments by attaching to sand grains or trapped particles. After introducing the coefficient α for the relative amount of adhering cells, the advection rates become functions of α and s. Considering a horizontally (x) and a vertically (z) explicit flow field (ux,uz), the temporal biomass evolution due to advection reads like:
In the model setup used in this study, the velocity field ux(x,z) and uz(x,z) is analytically calculated on the basis of a pressure gradient which in turn is generated by an overlaying water flow above a sand ripple [35,36].
The sediment column is represented by an array of finite boxes, increasing in size going to deeper layers. This non-uniform resolution has been proven to be well adapted to the gradients in the velocity field (ux,uz) while keeping the numerical effort during integration of the model equations reasonably low.
In order to resolve frequencies of external forces as realistically as possible, also a dry phase during ebb tide is resolved, simulating vanishing exchange rates for most chemical species for a site specific period of time.
2.5Boundary conditions and reference data
Most data used in this work derive from the large Wadden Sea ecosystem project ELAWAT . Measurements were taken out in the backbarrier reef of the Spiekeroog island located in the southern German Bight. The model employed time series for the period 1995–1996. Physical parameters comprise water temperature and wind velocity. Simulated pore-water flow velocity was correlated to measured wind velocities if these exceeded a threshold representing normal situations.
Time series of pelagic POC, NH4, NO3, O2 were included as biochemical driving forces. Since data are available only in a 1–4 week resolution, linear interpolations were made each simulation day. Missing values for POC in 1996 were estimated using phytoplankton biomass data from [37,38]. As reference values for the model calibration, four to six profiles for benthic TOC, DOC, SO4, H2S, and total pools of extractable sulfur (TS) and iron (TFe) were used. The profiles derive from the reference line of an experiment documented in . Measurements for one occasion in 1996 presented in the publication were completed by unpublished data covering the whole period.
Microbiological data originate from monthly measurements from March 1995 to September 1996 along a nearby transect within the backbarrier reef [40,]. Within the transect a sand flat location showed highest correspondence to the experimental site chosen by Rusch and colleagues. The dataset contains, among others, total cell counts (most probable number, MPN) and colony forming units (CFU) of anaerobes as well as aerobes. Given that profile data are partially incomplete, we selected only the continuously available measurements for the upper 1 cm of the sediment.
Despite their relatedness to microbial biomass, CFU and MPN do not allow for a direct comparison with the model variable X. Both quantities are based on analysis methods that cover only particular aspects of bacterial abundance . To average out some of the peculiarities, an aggregated number was built: the microbial biomass index (MBI) denotes the sum over CFU and MPN after normalization with respect to their 2 year averages in the dataset:
Model MBI is simply defined as the sum of all active biomasses, divided by a typical mean value which should be proportional to the capacity measure. It is found that Xact,n/8Xcap gives a reasonably scaled index.
2.6Validation under uncertainty
A complete validation of the ISM evidently poses a non-tractable problem. On the one side, in situ measurements are rare and confined to few observables, while, on the other side, the model employs 55 state variables and 68 parameters. Nevertheless, one can try to reduce model uncertainty by performing automatic model tuning . After an initial sensitivity study based on the methodology described in , 19 most sensitive parameters were selected for the automatic calibration. This was performed using Monte Carlo techniques so that parameter values were set to random numbers within meaningful limits.
For each of the random parameters set, the error in the model dynamics was calculated with respect to the data described in Section 2.5. Integrating minimal deviations over all data points yielded final errors of each simulation which then were ordered. This way, from a large number of 105 random sets an ensemble of 40 best fitting parameterizations has been filtered out.
In a second numerical experiment, the model is repeatedly run over a period of 8 days with typical external forcing and an intense storm with increased pore-water flow during the third day, leading to a short term down-penetration of the oxic and suboxic zone to about 12 cm depth. The model dynamics always reached a limit cycle after 16 days independently of the parameterization.
Using these fixed boundary conditions, the adhesion coefficient α is varied from 0 to 1 and the dormancy flexibility β from 0.5 to 1. Other parameters or boundary conditions remained unchanged.
Considering exclusively best fitting parameter sets, each variation is computed 40 times. Resulting RGR of functional groups and CO2 production are averaged over the last 8 days of the simulation, over the sediment column and finally over the ensemble of simulations based on different parameterizations. Standard deviations are retrieved using the ensemble values only.
3Results and discussion
After the training phase, the ISM was able to generate seasonally varying profiles in acceptable correspondence with the data. This is shown for the state variables H2S in Fig. 1 using the best fitting parameterizations, but other members of the trained ensemble induce nearby trajectories.
Similarly, the seasonality of MBI in the upper 1 cm of the sediment is well redrawn (Fig. 2). The statistical distribution of parameter values within the trained ensemble can be distinguished into three cases. Few parameters were confined to narrow ranges. Few others parameters follow a multi-modal distribution while approximately half of the calibrated coefficients were still dispersed along relatively large intervals.
Patchiness in the spatial distribution of biochemical species in near-shore sediments occurs on many scales. Vertical profiles originating from sites at a distance of few decimeters can have very different shapes . A feature of the ISM not discussed into great detail here is to produce similar horizontal gradients in initially homogeneously distributed variables like POC or bacterial biomass just by coupling the reactions to a simulated pore-water flow.
Fig. 3 illustrates a typical advection regime beneath a sand ripple as projected by the ISM. The calculated extent of the washout zone is in good agreement with measurements in sandy sediments , or with the form and intensity of reported flow patterns beneath ripple-like structures [35,36]. Nonetheless, it should be noted that the aim for calculating the advection field is not an accurate description of pore-water fluxes per se, but to give a proxy for a series of mechanisms which are responsible for a dynamic, spatially heterogenic transportation in tidal flat sediments, such as hydraulic drainage or wave induced pore-water advection. Also the structuring function of bioturbation and bioirrigation, yet treated by a horizontally uniform term within the model, is to some extent implicitly captured by the imposed flow field.
It is found that for carrying new organic material together with oxidized iron and manganese into the sediment, subsurface trapping is of great importance. Effective trapping intensity is in turn represented by gradients of the fraction of suspended particulate material (s). Model projected gradients are shown in Fig. 3. Short pathways near the sediment–water interface lead to high contents of floating material and, thus, high values of s. The latter again decreases in deeper layers or decreasing pore-water velocities. In the discharge zone at the lee site of the ripple, previously trapped material is resuspended from the mineral matrix, whereas trapping becomes most effective in the zone with highest spatial differences in s values.
Transport and growth rates both control the subsurface distribution of model bacteria. The mapped concentration of denitrifiers displayed in Fig. 4 demonstrates the capability of the model to produce a complicated, two-dimensional pattern with various niches, each characterized by different biogeochemical regimes and functioning of microbial communities.
3.3Role of adhesive properties
With more bacteria attached to organic or mineral surfaces, a smaller fraction of cells can be removed from their specific habitat. As a consequence, standing biomass is generally, albeit not always, higher for model populations with high adhesion coefficient α, especially in the upper sediment layers. This can be seen from the linear trend between α and the CO2 production as shown in Fig. 5. Changing from zero to maximal adhesion, CO2 production rises for about 40% of the average value of all variation experiments.
Parallel to this result, the losses of cells washed out to the water column is negatively correlated with α. But the growth part of local population dynamics does not follow a general rule (Fig. 6). ORB and NRB grow faster when attachment decreases, FeRB are not significantly affected, whereas SRB grow slightly slower with small but increasing adhesion. At high values of the adhesion coefficient, the sulfate reducers again gain clear advantage of an attaching behavior.
If the washout losses and growth rates are summed to the local net change rate of the population, the problem of defining an appropriate system boundary comes into play. Bacteria lost to the seawater are not necessarily lost to the sediment since they are likely re-introduced to remote subsurface systems. This is in particular the case in tidal flat environments. Alternating life histories are, for example, represented by the ability of many anaerobic bacteria to sustain their viability for several hours under oxic conditions . It makes therefore sense to reduce the relative contribution of transportation losses when calculating the total RGR as the main group specific target function of our analysis. If only one half of the washout losses are considered, total RGR of ORB and NRB reveal no or a negative correlation with their adhesiveness. Thus, these groups may profit from a higher mobility with which occasionally occurring gradients in the spatial distribution of substrates or electron acceptors can be better exploited. Contrarily, functional groups which are located in deeper sediment layers like FeRB and SRB, can be expected to be more inclined to biofilm formation.
Comparable empirical studies on differences in adhesion strategies of (facultative) aerobic and anaerobic bacteria are currently not known to the author. But the high fraction of surface attached SRB with typical values up to 90% as well as the high readiness of aerobes for detaching  seem to be in line with the model based hypothesis.
For their further interpretation one has to keep in mind that the effect studied here is solely based on altered spatial patterns of microbes on a centimeter scale (cf. Fig. 4). Microscale or side effects of adhesion as reviewed by Fletcher, , for example, are neglected in the ISM. Bioavailable physical space is reduced when changing from a three-dimensional volume to a surface distribution [48,49]. If such a reduction with higher α would have been included (Xcap(α) instead of Xcap in Eq. 2), the curves included in Figs. 5 and 6 will take a unimodal form, thus critical adhesion values emerge where total CO2 production or RGR again decreases with increasing α (simulations not shown). With the choice to leave such trade-offs aside, it is aimed to disentangle the different ways in which adhesive properties act on sediment biogeochemistry. In addition, a more resolved picture of the microscale benefits of specific groups would be needed by the model, if one employs a Xcap(α) dependency. For example, microbes may be able to compensate spatial limitations while attaching to a favorable substrate.
After varying the specific dormancy flexibility (β) a linear response in the CO2 production is observed for smaller values of β. With increasing flexibility also total mineralization rises by 20% of the average value for all variations (Fig. 7). The faster the model populations switch to lower activity and respiration under starvation, the higher is the total turnover rate of the system.
Like for adhesive strategies, microbial populations in the oxic and suboxic zone behave differently to variations in metabolic adaptiveness compared to strict anaerobic populations. The negative effect of increasing β visible for all functional groups, especially for NRB, can partially be traced back to the differential success of model populations living at the edge of their habitat. When RGR tend to be around zero, it may be more profitable to maintain a suboptimal level of activity if changes are very likely to arrive in near future. Thus, responding after some lag time (β∼1) may improve the fitness in fluctuating areas like the suboxic zone (Fig. 8).
This effect also attributes to the anomaly of reduced CO2 production at high β values displayed in Fig. 7.
Uncertainty deriving from an incomplete validation of the model adds to all outcomes a noise factor which turns out to be quite large for the CO2 production and relatively small for the RGR values. An essential proof for the usefulness of the methodology, however, derives from the fact that all trends presented in this study can be considered as significant in relation to these uncertainties. Of course, further studies have to capture a broader spectrum of boundary conditions since these define an essential source of variability. Then it should be tested whether the presented trends will still exceed the noise levels.
It is well known that the fitness of sediment-bacteria increases due to the facultative shift to dormancy. Here, we found this rule more pronounced for oxic and suboxic populations. Also adhesion strategies seem to affect these functional groups more drastically. Both findings can be understood in terms of the more frequent and intense fluctuations in vicinity of the sediment–surface interface.
More importantly, such sensitivities can now be quantified and compared to sensitivities in other factors or parameters. This capability has to be explored in a series of further studies. But already the first outcomes achieved in the preliminary sensitivity analysis made in this work indicate an intermediate role of microbial properties. By optimizing several metabolic and behavioral strategies, bacteria may change the balance between trapping of organic carbon on the one side and release or burial on the other side by up to approximately 10–20%. Some global transportation coefficients exert a higher control on total carbon mineralization, whereas the variation of single kinetic or geochemical coefficients has a smaller impact on the total CO2 production.
One has always to keep in mind that the ISM does not allow for exact predictions or for a coupling to ecosystem or global biogeochemical models because of its irreducible uncertainties and high numerical effort. An attempt to overcome these limitations through building an aggregated model version is under way. It relies on recently developed, sophisticated upscaling methods .
There are obviously many shortcomings of the ISM itself so that model improvements and further validation has to be made in various directions. Nevertheless, the model captured sufficient complexity for the type of analysis proposed in this work and provides currently the only existing framework for combining microbial physiology and population dynamics, physical transport in subsurface systems and geochemical cycles. Quantitative arguments as pursued by this work offer an alternative route for improving our understanding of the diverse strategies exhibited by bacteria.
I thank many of my colleagues working in the project ‘Biogeochemistry of Tidal Flats’, in particular H.P. Grossart, M. Simon, M. Böttcher and H. Cypionka for their constructive support and discussions. A. Rusch, W.E. Krumbein and B. Albers are acknowledged for the kind permission to use their data. This work was supported by the Deutsche Forschungsgemeinschaft.