We use a modified rough surface patch model  to represent the top millimetres to centimetres of soil where most biocrusts develop (see Fig. 2a). For the physical domain, we consider a vertical cross section of a biocrust that considers rough soil grains and the gas pathways between grains (described in 2-D but in a simplified fashion including 3-D features in a spatial element). Geometrically explicit features of the rough surface (pyramid-shaped depressions of different sizes) are averaged according to a probability distribution of the pore sizes (representing the roughness decorating soil grains). For the size distribution, we assign three parameters: local porosity ϕ, surface roughness porosity Φ, and fractal dimension D . This abstract representation of the physical domain permits a physically based calculation of the amount of water held within the rough surface for a given matric potential (our standard hydration metric). The water films then determine the diffusion rates and pathways of nutrients, microbial dispersion rates and ranges, connectivity, and the complementary spaces for gas diffusion. While the representation of microbial life is assigned to the 2-D rough surface, the inference of the gas phase within the cross section is applied to the model by considering two rough surfaces facing each other (see Fig. 2a). This approach allows us to extend the surface model to the vertical cross-sectional model and to include gas diffusion and mass transfer between the liquid and gas phases as a function of matric potential by using effective film thickness (Fig. 2c) without the complexity of 3-D modelling of the pore space in the biocrust .

We represent a section through the biocrust by using a spatially distributed soil properties and assigning key parameters {ϕ,Φ,D} to individual patches (representing soil grains or small aggregates). This domain represents strong heterogeneity in the soil structure, including regions with low or high porosities. For simplicity, we assume in this study that the matric potential is constant for the entire biocrust. Hence, the water distribution in the model biocrust, including phase connectivity and related properties, was predetermined for a simulation. Although evaporation or drainage processes following (rare) rainfall events can generate hydraulic gradients across the biocrust, these effects can be neglected given the small domain size (< 10 mm).

The model includes three essential environmental variables that shape microbial communities in desert soil: water, light, and temperature. For simplicity, we prescribe the hydration status of the biocrust; this status determines the configurations of the liquid and gas phases (that in turn determine the respective diffusion coefficients). The extension to dynamic hydration conditions is relatively simple considering infiltration, redistribution, and soil evaporation (these processes are functions of the crust properties and are representable analytically or numerically). Temperature and light are applied as time-dependent boundary conditions to the top of the crust domain to mimic diel cycles.

The chemical environment of soil is strongly influenced by its microbial activity (especially at the main biocrust region). For example, the pH of biocrust is altered diurnally due to microbial respiration (release of protons and bicarbonates) and photosynthesis, with CO2 removal significantly modifying porewater pH. These, in turn, affect nutrient availability and mobility, CO2 dissolution rates, and the solubilisation of soil minerals . The model includes certain essential chemical processes: diffusion, gas–liquid-phase partitioning, and acid–base dissociation that affect microbial activity within typical biocrusts.

Advances in molecular taxonomic techniques and DNA sequencing have greatly expanded our knowledge on microbial community structure and diversity in biocrusts. These data generally delineate the interplay between multilevel trophic interactions  and surrounding environmental conditions . Biocrusts host a complex community of diverse autotrophs and heterotrophs (hundreds of species including about 20 generic or subgeneric taxa of Cyanobacteria) . Considering biocrusts as independent and self-sufficient ecosystems, the intrinsic diversity found in this system should not come as a surprise. The incorporation of the natural microbial diversity found in biocrusts is beyond the present capabilities of most models. Hence, we opted for a representation of the main microbial actors for modelling the associated biogeochemical cycles in a cyanobacterial crust.

The importance of EPSs for microbial life in natural environments has been discussed in many review articles . Especially in arid or semi-arid environments, the role of EPSs secreted by Cyanobacteria is crucial for microbial communities surviving within (and below) biocrusts . The synthesis of EPSs contributes to the stability of soil structure and hydrated microenvironments in soil, making it a key ingredient of biocrust formation. EPSs also function as nutrient storage by immobilising nutrients (dust trapping or glycosidic bonds) and as a protective shield from adverse environments, such as UV radiation, antibiotic substances, and invading viruses. In this work, we focus on two key aspects of EPSs in biocrusts: modification of the diffusion process of substrates and its role as a nutrient reservoir (increase in soil C) . The complete range of EPS effects on soil hydrology, such as the swelling of hydrated gel owing to its chemical composition and physical structure, are not considered in this study.

Microbial activity and resource consumption are expressed as a set of diffusion reaction equations within the biocrust domain. ∂Cj(r,t)∂t=∇⋅Dj(r,t)∇Cj(r,t)-1Vw(r,t)∑i=1N(r)μi(r)Ynetjibi(t)+Sj(r,t), where Cj(r,t) is the local concentration of substrate j, Dj(r,t) is the local diffusion coefficient (including modification by EPSs), and Vw(r,t) is the amount of water in a given patch at position r and time t. The second term on the right-hand side is the reaction term to calculate the total substrate consumption and production in the patch. N(r) is the total number of individual cells at r, Ynetji is the net yield of species i on substrate j, bi(t) is the biomass, and μi(r) is the growth rate described in Eq. (20). The last term Sj(r,t) is the source or sink term of substrate j with respect to the mass transfer between the gas and liquid phases and the charge compensation from the principles of solution equilibrium and charge neutrality. These chemical processes are very fast compared to microbial reaction and diffusion processes. Thus, we implemented these terms as dynamic boundary conditions (keeping gaseous element solubility and local charge neutrality during one time step). For individual cells, the growth dynamics is written as dbi(t)dt=μi(r,t)-mibi(t), where μi(r,t) is the growth rate from Eq. (20) and mi is the maintenance rate of cell i. Cell growth, division, locomotion, and death are described using individual-based modelling .

A pioneering study on microbial communities within desert biocrusts  has suggested a vertical stratification of microbial community members in which abundance (biomass) and composition (functional groups) vary with the depth of the biocrust. Observations by  demonstrated the stratification as a result of vertical gradients in physico-chemical conditions such as light, oxygen, pH, and other nutrients. The vertical profiles of N2 fixation and the potential NH4+ oxidation rates  and chemical profiles (total ammonium, nitrate) of soil solutions within active biocrusts , as well as the profiling of oxygen concentration after wetting , have been investigated as well. Recently, the effect of physical conditions on cyanobacterial activity was examined using X-ray microtomography . These experimental data on microprofiles within biocrusts can be used for a comparison between the measurements and numerical simulations of chemical and biological components within saturated crusts. For the comparisons in a spatial context, the DBM quantifies the biological activity as a product of local growth rate, μi, and biomass, bi, of cells with a unit of µgcellgsoil-1h-1: Ai(r,t)=μi(r,t)bi(r,t). This activity measure is suitable to indicate the active pathways for the upregulation of functional genes (i.e. the spatial distribution of gene activity). From this activity distribution, it is possible to calculate the rates of microbial processes, such as carbon fixation, ammonia oxidation, and denitrification by simply multiplying the yields from the stoichiometry of each species.

In contrast to the generally dry state of biocrust, most of the detailed studies reported above were conducted using saturated biocrusts (a state that rarely occurs in the field). Data on unsaturated biocrusts are hindered due to the technical difficulty of using microsensors  and molecular analysis of microbial activity . Consequently, we are left with the undesired option of using detailed data from saturated biocrusts for model evaluation. The primary aim of this study is to establish confidence in the DBM for these rare conditions and extend the predictions to the more common case of unsaturated biocrusts.

The DBM was evaluated with respect to diurnal dynamics and the results are compared to experimental studies that measured certain traits (e.g. gaseous efflux), such as the following studies: . In this work, we focus on carbon dioxide efflux under fully saturated conditions . Although the gaseous fluxes are usually considered direct indicators of microbial activity, quantitatively speaking these macroscopic measures emerged from all possible biological, chemical, and physical interactions combined.

For a prescribed matric potential (constant hydration conditions), the corresponding water film thickness, aqueous habitat connectivity, diffusion properties, and specific surface area are obtained locally on a patch scale (about 100 µm) from the pre-assigned surface properties and local porosity of each patch (a spatial element that determines local patch property). We selected parameters that mimic the property of loamy sand (ϕ‾=0.4, Φ‾=0.6, D=2.65). By applying m×n patches, the domain describes a thin strip of biocrust with periodic boundary conditions in the horizontal direction.

For boundary conditions of chemical substances, gaseous elements and dissolved elements are treated differently. Oxygen, carbon dioxide, ammonia, nitrous oxide, and nitrous acid in the gas phase are assigned based on the atmospheric composition from the literature (see Table S1 in Sect. S2). The mixing ratios of atmospheric components are kept constant at the top of the domain during simulations assuming zero diffusive boundary layer and maximised gas exchange between atmosphere and biocrusts. These gaseous compounds are transferred to the liquid phase by their own solubility based on Henry's law . DIC, ammonia, and nitrous acid are partitioned with the principle of local charge neutrality at obtained pH values.

Model evaluation is based on the following components: we first present the steady-state distribution of geochemical variables within the biocrust domain. Next, we present the quasi-steady distribution of microbial functional groups within the biocrust under field capacity (relatively wet conditions). We then compare the model results for the saturated conditions under which sample experimental data are available.

The abiotic exchanges that affect local distributions of geochemical environments and traits are evaluated first. A steady state of a chemical domain is calculated in the absence of biological activity. We consider a biocrust following wetting at field capacity (corresponding to water saturation 0.6 for the entire domain) assuming that this condition describes wetted crusts after drainage (in contrast to a fully saturated crust with saturation degree 1). We focus on traits such as diffusion, gas–liquid partitioning, and acid–base calculation without microbial activity. The spatial variations in phase distributions within the simulation domain (vertical cross section of biocrust) and related attributes are depicted in Fig. 4. The results suggest that these relatively wet conditions may disrupt gas-phase connectivity to the atmosphere. Gas diffusion through the biocrust is determined by the connectedness of the gas phase according to percolation theory. For certain values of local gas content (below 0.2), the gas phase becomes disconnected, affecting O2 distribution. This implies that gas volumes not connected to the atmosphere may exist in isolated pockets within the soil domain. Thus, the local concentration of dissolved oxygen varies according to this atmospheric source and spatial heterogeneity (Fig. 4c). This also shows a correlation between the gas-phase configuration and the spatial heterogeneity of porewater pH; the higher the local gas content, the lower the pH values (activity of protons). This indicates that a higher mass transfer rate from the gas to the aqueous phase yields acidity since the dissolution of CO2 is very fast in unsaturated soils (large surface areas and thin water films). On the other hand, patches with high water content and limited gas-phase penetration show higher pH (around 8–9) as the model mimics alkaline soils with high cation content (about 10 µgg-1 calcium and the same amount of other non-reactive cations, as shown in ). This implies that volume-averaged pH may not be representative of local soil porewater or water film pH in unsaturated soil, thereby affecting microbial activity locally and giving rise to processes not definable by average values.

The four microbial groups are introduced into the simulation domain (representing a cross section in desert biocrust) and allowed the system to stabilise under diurnal cycles. Phototrophs were initially inoculated in the domain in an exponentially decaying manner over the biocrust depth to reflect a natural organisation under light penetration, while other groups were inoculated uniformly in the domain. Only phototrophs were inoculated differently to reduce the computational time as phototrophs only thrive up to the depth at which light penetrates. This well-mixed inoculation pattern ensures that the spatial organisation of microbial populations within the crust was not affected by initial conditions. The initial population sizes were the same for all functional groups, about 4000 cells for the entire domain. After about five consecutive days (diurnal cycles), the total population and spatial distribution of microbial groups reached a quasi-steady state.

Noticeable changes in the resulting chemical environments occurred due to microbial activities even though the physical environments and hydration conditions were assumed to be constant (held at relatively wet conditions corresponding to field capacity). Figure 5 depicts four spatially distributed chemical attributes, namely dissolved oxygen, pH, total ammonia nitrogen, and nitrate, for midday (top panels) and midnight (bottom panels). The chemical profiles delineate the diurnal cycles of microbial activity across the soil domain. For instance, the alkalisation of top crust (2 mm) was clearly shown together with the production of ammonium. This implies that phototrophic activity fixes inorganic carbon and produces ammonium to fix N2 using heterocysts. However, the oxygen profile was relatively stable compared to other chemical substances although photosynthesis and dark respiration could introduce changes in the local concentration of dissolved oxygen. This is due to the unsaturated conditions on the top crust where gas transfer rates override the net reaction rate of oxygen within the profile. In addition, the nitrate profile exhibits the tendency of cumulation below 4–5 mm, implying that inhibited denitrification occurred under unsaturated conditions. The diurnal patterns of nitrate were not clear, unlike the profile under saturated biocrusts (see Fig. S4 in Sect. S6). In general, regardless of differences among various chemical species and diurnal cycles, the strong spatial heterogeneity was still significant within the domain shaped by gas–liquid configuration.

The dynamics of the biocrust chemical environments are not only due to general microbial activity, but specifically due to trophic interactions within the biocrust community (due to different substrate use by microbial groups). A typical simulation result of the DBM is given in Fig. 6 to represent the activities and interactions among biocrust microbiota under two distinctive phases: (1) during daytime with active photosynthesis (a–d) and (2) during nighttime with dark respiration (e–h). The results show the emergence of vertical stratification of each microbial process within the thin biocrust (10 mm). The biocrust community is highly active above 4 mm and only some aerobic activities appeared very sparse and low below 4 mm. The spatial pattern is driven by trophic interactions among groups, by the chemical environments, and by the resource gradient since the non-phototrophic cells were uniformly inoculated over the entire domain. We note that while activity and growth rates were in diel cycles, the spatial patterns become relatively steady and migration is not observed although cell motility is enabled (each population reached its local carrying capacity). The patterns can be analysed as follows: the phototrophs as primary producers (green in Fig. 6) perform intense photosynthesis at the biocrust top following the distribution of light. The produced oxygen and carbohydrates combined with N2 fixation benefit aerobic heterotrophs (yellow in Fig. 6) that exhibit high activity 2 mm below the surface. This strong cooperation between phototrophs and aerobic heterotrophs supports a high population on the top of the crust. Although close proximity (mixing) between phototrophs and aerobes is expected, their activities are segregated due to the strong alkalisation during photosynthesis and intense competition over ammonium with AOB (marked in dark blue). Weak activity of anaerobic bacteria is also found together with aerobes at a similar depth due to the need for organic carbon for their activity. Local anoxic conditions support their growth in certain regions (purple in Fig. 6a and e) due to the consumption of oxygen by other organisms, heterotrophs, and nitrifiers. Below 3 mm, anaerobic activity is not found because the oxygen consumption by aerobic organisms is too low to create local anoxic conditions. Chemoautotrophs appear sparse over the depth, and AOB and NOB (light blue) stay in proximity as they are in a mutualistic relation. AOB shows high activity within 2 mm during daytime, benefiting from the ammonium fixed by the heterocysts of phototrophs and the inorganic carbon produced by heterotrophs. Its growth is mainly limited by inorganic carbon used during photosynthesis. The activity of NOB is also high at the top crust due to nitrite production by AOB.

Generally during daytime, the activity of phototrophs enhances other microbial activity by fixing inorganic carbon and nitrogen (Fig. 6d). During nighttime, phototrophs switch their activity to dark respiration. Dark respiration by phototrophs drives intense competition for organic carbon and ammonium among individuals at the top of the domain. As the input of fixed carbon and nitrogen is absent, the depletion of ammonium at the top crust lowers the activity of most organisms (Fig. 6g). However, NOB shows slightly higher activity during the night below 3 mm, suggesting that during daytime they are outcompeted by other organisms owing to their high yield and low growth rate.

Despite the focus of the desert biocrust model (DBM) on unsaturated conditions in desert systems, we had to rely on definitive experimental data from saturated biocrusts to evaluate the details of model performance . The simulation domain was saturated by simply applying near-zero matric potential and filling up all surface pores with water. Using the fully saturated domain with stable microbial community distribution, the model biocrust was then exposed to diurnal cycles of radiation and temperature.

The spatial distribution of microbial activity within a fully saturated biocrust is given in Fig. 7. Ten independent simulations were averaged to obtain the possible distribution of microbial processes. The potential activity of anaerobes peaks below 2 mm (in contrast to other aerobic organisms) due to the formation of an anoxic region (Fig. S4 in Sect. S6). At the top, microbial distribution is clearly stratified in the following order: phototrophs, nitrifiers, aerobic heterotrophs, denitrifiers. Unlike unsaturated biocrusts, the vertical stratification is accentuated largely because of a strong oxygen gradient profile driven by photosynthesis.

The spatio-temporal behaviour of the oxygen and pH profiles predicted by the model are compared with available datasets in Fig. 8. The simulation results are in quantitative agreement with reported data from experiments on various types of cyanobacterial crusts (e.g. light crusts and dark crusts) from several locations . A common finding with respect to the oxygen profile is its supersaturation within the top few millimetres and the formation of an anoxic region below. While the model was able to capture the dynamics of dissolved oxygen, pH dynamics showed large deviations between the model and the data, especially during nighttime. The chemical environments of other substrates during daytime and nighttime are given in the Supplement: Fig. S4 in Sect. S6.

In addition to comparing processes within the crust (Figs. 7 and 8), we simulated gas efflux from the saturated biocrust and compared it with the measurements of . Figure 9 depicts the efflux of three gas compounds of carbon and nitrogen, namely CO2, NH3, and N2O. We represent uptake as negative gas efflux and positive for emissions. The diel cycles of CO2 efflux are plotted together with experimental data tracking the net carbon exchange between the biocrust and the atmosphere (Fig. 9a). Within the biocrust, carbon fixation and respiration occur simultaneously; the net CO2 efflux indicates a balance between respiration (release) and photosynthesis (uptake). The simulation results are in qualitative agreement with experimental data, except the steep transitions after sunrise and gradual changes after sunset that are not captured properly. We attribute this to the simplified model (using Monod functions) of the onset of photosynthesis and dark respiration. Next we evaluate the daily patterns of ammonia volatilisation to represent nitrogen abiotic losses. The results in Fig. 9b show that ammonia volatilisation occurs mainly during daytime as the top of the biocrust turns alkaline (pH above 10). The total ammonia loss due to volatilisation was estimated to be about 500 nmolm-2day-1, similar to reported values of 540 ∼ 1000 nmolm-2day-1 from intact biocrusts on the Colorado Plateau . We then evaluate N2O release from the biocrust (indicative of denitrification); the results in Fig. 9c show that immediately after wetting N2O flux is high. We attribute this rapid release to the accumulation of NO3- during unsaturated conditions. After 2 days, nitrate is exhausted and denitrification relies on the activity of NOB. Finally, we also considered the potential release of NO2- from the soil solution in the form of nitrous acid HONO. However, the results show no such release in agreement with the observations of , which are not presented in this paper.

Soil pH has been recognised as a significant predictor of microbial community composition and diversity . Furthermore, for alkaline or saline soils (typical desert soils), abiotic contributions to gaseous efflux may account for up to 40 % of total CO2 emissions . Thus, to separate biotic and abiotic contributions for gaseous efflux, reliable estimates of pH are needed. It is especially crucial when the main producer of the system, phototrophic microorganisms, depends on the accessibility of inorganic C and N. The proposed desert biocrust model (DBM) offers a distinct advantage in this respect, namely the localised (pore scale) representation of pH that integrates physico-chemical interactions and microbial activity. The simulated pH profile dynamics within wet biocrusts presented above (Fig. 8) have confirmed that the activity of photoautotrophs alters local pH by depleting DIC during a diel cycle (consistent with observations).

The results of the DBM suggest strong spatial variations in local pH within the unsaturated biocrust although the overall (spatially averaged) soil pH indicates an alkaline soil (Fig. 4). In practice, however, the spatial distribution of local soil pH is difficult to measure and often requires the use of microelectrodes . Moreover, it has been argued that the use of microsensors is limited to near-saturated soils . The modelled spatial variations in local acidity are consistent with the uptake kinetics of nitrous acid in the gas phase on a wetted wall film . The model results suggest that pH in thin water films may be lower than in bulk liquid due to the resistance of mass transfer from the gas to the bulk liquid phase (we use the term “bulk” to represent large water-filled pores within the biocrust). As liquid surface on the wall corresponded to acidity in thin water film in the model, this result may support model predictions and the importance of soil water configuration in shaping local pH within unsaturated soils.

The strong correlation between soil moisture retention and soil pH and their role in defining the microbial community structure  might be attributed to local pH distribution in unsaturated soil. We speculate that the high abundance of Acidobacteria (at phylum level), known to grow well in acidic cultures (pH 3.5–6.5) as aerobic heterotrophs  in most soils , might offer more evidence of the importance of localised acidity in unsaturated soils. We note that such an acidity-related phylum was also found in biocrust communities .

Spatial segregation along vertical gradients is a well-known feature of microbial communities in aquatic biofilms, microbial mats, and endolithic communities . Similar to the Winogradsky column, these microbial stratifications are driven by the distribution of electron acceptors and donors. Since the most favourable electron acceptor for aerobic organisms is oxygen, the low solubility of oxygen and the limited diffusion of dissolved oxygen play a pivotal role in the emergence of spatial stratification. Stratification within biocrusts is also observed in terms of the biomass of oxygenic phototrophs, aerobic copiotrophs , and community composition analysis based on 16S rRNA sequencing . The simulated results of our biocrust model agree with observations of vertical stratifications in the biocrust community (Figs. 6 and 7).

The DBM captures the key physico-chemical conditions essential for vertical stratifications. The steep gradient of oxygen on top of the fully saturated biocrust (Figs. 8 and S4) is caused by limited mass transfer from the atmosphere and rapid consumption of oxygen. During nighttime, the depletion of oxygen (below a few millimetres) is expected naturally because of the limited amount of oxygen input. The oxygen produced by phototrophs during daytime is immediately depleted by aerobic organisms in the domain. Clearly, such formation of an anoxic region within the crust benefits anaerobic activity at a few millimetres (Fig. 7). The creation of supersaturation closer to the surface also indicates slower diffusion than net production and consumption of oxygen. Experiments on biocrusts immersed in water indicated effervescing of (presumably) oxygen at the surface . This demonstrates that the net production of oxygen is higher than the diffusion of dissolved oxygen.

The vertical segregation of different microbial groups also indicates organic carbon and nitrogen diffusing from the photoautotrophs and becoming available to other microbial members, especially stratification among aerobic organisms. The dominance of nitrite oxidising bacteria (NOB) at the top 2 mm is largely due to ammonia volatilisation. The alkalisation of the top crust during daytime increases ammonia volatilisation, which is not beneficial for aerobic heterotrophs and ammonia oxidising bacteria (AOB). Therefore, their activity retreats deeper to around 2 mm, allowing NOB to appear at the top surface. Below the location of NOB, we find AOB and aerobic heterotrophs. Although the model has a simple assumption on microbial groups utilising various substrates in a specific trophic landscape assumed for this study (Fig. 6d and h), a similar pattern of segregation is expected within real biocrusts in the field.

For aerated unsaturated biocrusts, the results in Fig. 5a and e show that the high oxygen transfer rate to soil water overrides net reaction, and thus a strong gradient of oxygen is not observed in unsaturated cases (Fig. S4a in Sect. S6). Therefore, the aqueous-phase configuration within unsaturated biocrusts (also possibly extending to general unsaturated soils) shapes microbial activity unlike in aquatic microbial mats and similar saturated systems. This stable oxygen profile of unsaturated biocrusts is due to the mass transfer between gas and liquid, which is assumed to be very rapid in the model (instant equilibration by Henry's law; see Sect. 2.3.2). However, in real biocrusts in natural fields, the exchange of gases with the atmosphere can be constrained even under unsaturated conditions (at a certain range) because of a dense layer of EPSs and a finer soil texture in the uppermost part within biocrusts. These factors can retard mass transfer by decreasing interfacial area under relatively wet conditions (finer soil texture) and by sustaining thick water films owing to the presence of EPSs. The current model allows us to assign a finer soil texture to the biocrust domain by using a low porosity or a high fractal dimension on the uppermost part. For the biocrusts loaded with a dense EPS layer, the model can be improved by relating the local EPS amount with the water film thickness at a given matric potential.

The biocrust community exhibits highly dynamic and complex trophic interactions, such as commensalism surrounding organic carbon utilisation between phototrophs and heterotrophs, competition over nitrogen sources between aerobic heterotrophs and AOB, and cooperation between NOB and anaerobic denitrifiers. Temporally, the diel patterns of trophic interactions (orchestrated by phototrophs) drive the shift in activity distribution of microbial activity as has been shown from Namib Desert soil . Spatially, these complex trophic interactions take place within thin biocrusts and yield emergent spatial distributions of microbial groups as depicted in Fig. 6. The remarkable concentration of such interactions within a few millimetres and the stratification of the activities of the various functional groups highlight the ecological sophistication and versatility of such fine-tuned desert ecosystems. Remarkably, opportunistic life forms are harboured within such biocrusts; for example, the presence of anaerobic heterotrophs at low numbers suggests the presence of local anoxic conditions even under mild unsaturated conditions  and their rapid response to episodic wetting events .

Motivated by the availability of definitive data, the DBM was applied to simulate diurnal changes in gas efflux from saturated biocrusts. The results were in good agreement with measured CO2 efflux (Fig. 9). The model represents the diurnal cycles of other gas fluxes that may be sensitive to pH, such as ammonia volatilisation and HONO emission. Details of the geochemical environment shed light on the important role of local conditions (pH) in soil and biocrust microbial activity. For example, the activity of AOB in alkaline soils can be suppressed during daytime on the top crust as strong alkalisation leads to a loss of nitrogen compounds. On the other hand, NOB in acidic soils should experience the opposite; as the soil becomes more acidic, HONO emission would lead to nitrogen loss.

To realistically describe microbial life within unsaturated biocrusts or dry soils, the inclusion of gas-phase interactions is necessary. Most experiments on biocrusts were conducted under saturated conditions (presumably to induce a significant and measurable response); however, these responses occur during narrow climatic windows with high precipitation . Although we have shown gaseous efflux from saturated soils to compare with experimental results, the DBM is capable of quantifying gaseous efflux from unsaturated biocrusts by tracking gas and water distribution.

The proposed DBM makes numerous simplifications pertaining to the life and functions of a complex microbial community in biocrusts in arid and semi-arid regions. Regarding the key physical processes, we built a physical domain that contains small subregions represented as patches. A patch is a subsection within a small vertical cross section in the biocrust that represents soil surfaces with different properties that retain water films and transport nutrients and gas. This enables the consideration of spatial heterogeneity within a vertical 2-D cross section across a biocrust; however, lateral variations in biocrust properties in space are not considered here.

Key geochemical processes that are dominant in desert soils (and biocrusts) are considered in this model. For simplicity, we consider calcium as a buffer together with other non-diffusing background cations (assuming uniformly distributed non-reactive cations as a set point of pH). The effects of saline soil (also a common property of desert soils) on dissociation constants and its influence on soil pH are not considered. We also did not include the effect of EPSs (as organic matter) on the top of the biocrust. The role of EPSs as a gate for matter flux on desert soil surfaces, the interaction between pH alteration and microbial activity, and changes in the physical properties of soil (relation between EPS swelling ratio and pH) can be the next goals for a mechanistic model of biocrusts. Other important aspects regarding chemical processes include modifying the diffusion equation. In the current model, the possibility of electrokinetic flow is not included. A more detailed description of electromigration can be included by modifying the diffusion equation for ionic particles by using the Nernst Planck equation. However, as the input of carbon dioxide to the thin water film is faster than the aqueous diffusion of ionic particles, the occurrence of local pH variation owing to the configuration of the gas phase is still expected in unsaturated soil.

By far, the most simplified component in this model is the biological one related to microbial processes. The DBM represents a system containing an astonishing level of diversity with a small number of microbial functional groups. The interactions among these community members are regulated by simple stoichiometric relations that control microbial growth. Monod parameters are mostly taken from models for activated sludge (a system far removed from life in desert biocrusts) . Considering that a desert is a water-, carbon-, and nitrogen-limited system with abiotic stresses, the values of these parameters are likely to be different from those governing life in sludge systems. We note, however, that the proposed Monod growth parameters are affected by local environmental conditions, such as temperature, pH, and substrate concentrations. Yet, an understanding of half-saturation constants and ratios between growth rates among different microbial groups would be necessary for establishing quantitative predictions by the DBM for real systems.

The members of the biocrust consortia were selected to focus on C and N cycling and the characteristics of arid environments. Recently, the role of heterotrophic diazotrophs, anaerobic ammonium oxidisers, and nitrate-reducing bacteria within biocrusts has been studied. Including these members might alter some of the expected rates that we presented in this study. Comparisons between crust models with their presence and absence can be one of the future applications. Furthermore, as the model describes a hydrated porous medium, the fully saturated domain is easily applicable to describe the microbial community of sediments or microbial mats. However, when it comes to modelling such systems, other groups, such as anaerobic phototrophs, sulfate- and iron-reducing bacteria, or methanogens, might need to be considered together with the proposed community of C / N cycling. This might be beneficial for a mechanistic understanding of the biogeochemistry of such systems.

The DBM can be further used to predict the gaseous efflux dynamics of wetting–drying cycles and C and N turnover rates during hydration events. As hydration events in arid and semi-arid areas are scarce, a mechanistic understanding of biocrust response to hydration would benefit estimations of its contribution to global biogeochemical cycles. For instance, high N loss via NO3- leaching, NH3 volatilisation, and HONO emissions can be investigated with respect to N cycling in such an environment. Furthermore, short-term perturbations of hydration conditions on biocrusts can be another application of the model, such as short wet-up cycles or rapid evaporation at high temperatures. The physical roles of biocrusts in hydrological processes can also influence C and N cycling in arid areas. For instance, changes in infiltration properties and wind and water erosion are not considered in the current work on microbial communities in biocrust. However, on a larger scale, these physical changes in the domain can be further extended.