Given the need to be able to work with 2D cuts through soils, e.g., by impregnating soils with resin and cutting through the resulting blocks in one way or another, to carry out measurements of (bio)chemical characteristics, it should come as no surprise that dynamical measurements at the microscale have been so far, and may remain for some time, impossible to achieve (Blaser et al., 2016). Of course, dynamical measurements of properties as they emerge at the macroscopic scale can be achieved relatively easily, for example breakthrough curves in column experiments serving as evidence of chemical transport. To some extent and for specific purposes, such macroscopic properties may suffice, but experience has shown time and again that in an of themselves, these macroscopic observations are not adequate to assess the soundness of microscale models of (bio)chemical dynamics.

Much of the energy, nutrient and information (signal molecules) flows in soil occur in aqueous phase. A broad range of organic and inorganic molecular forms are released into solution, taken up and metabolized, transformed by enzymes or immobilized on surfaces continuously. These constitute the most dynamic portion of the microbial environment. Although much research has been carried out on the soluble OM of soil (e.g., Rousk and Jones, 2010; Lerch et al., 2011), the scale at which the measurements have been made is inappropriate for understanding how the flows of energy, nutrients and information vary throughout the soil pore network; only an average value is obtained. Furthermore, extraction methods tend to introduce biases related to the choice of extractant and the disruption of the physical architecture of soil may release molecules not previously in solution (Inselsbacher et al., 2014). The use of miniaturized sampling devices (millimeter scale) such as microdialysis probes or micro-suction-cups offer the possibility of detecting gradients in the soil solution at scales that are getting closer to those relevant to microbial communities (Inselsbacher et al., 2014; Oburger and Schmidt, 2016), particularly in the rhizosphere where gradients are stronger. With microdialysis the soil solution is sampled by passive diffusion and is therefore likely to better reflect the soluble environment perceived by microbial communities. Recent research has shown that there are significant differences in the size and composition of soluble organic and inorganic N pools measured by microdialysis and those measured by the traditional extraction methods (Inselsbacher et al., 2014). The small size of the probes makes it possible to locate them precisely in soil samples using micro-CT imaging and to map diffusive fluxes in real time (Brackin et al., 2017).

## Numerical Modeling

Over the last decade, a very significant amount of work has been devoted by geochemists and environmental engineers to the development of computer models able to describe the fate of a number of chemical species of interest in porous and fractured media (Tartakovsky et al., 2007; Valocchi, 2012; Steefel et al., 2013; Yoon et al., 2015). These models typically combine a transport component with a chemical speciation algorithm. Chemical transport is described using a variety of approaches, including the Lattice-Boltzmann method, smooth particle hydrodynamics (Tartakovsky et al., 2007), hybrid Lattice-Boltzmann-direct numerical simulation (DNS) (Yoon et al., 2012), and pore network models (Li et al., 2006). In terms of the chemical reactions that the speciation algorithms describe, as Iliev et al. (2017) accurately point out, many models focus on chemical reactions occurring in solution, with only a few models dealing with reactions controlled by the reactivity of the surfaces, like the dissolution of mineral phases. This bias makes sense for the type of systems researchers have been trying to describe, namely aquifer materials, calcareous formations, sandstones, or simply laboratory set-ups filled with glass beads. In that general context, one of the key predictions of these models has been that under a wide range of situations, macroscopic-scale descriptions with "effective" (i.e., volume-averaged) parameters do not account adequately for model predictions when nonlinear reactive transport processes are associated with highly localized chemical reactions and incomplete mixing within the porous medium (Li et al., 2007a,b,c; Battiato et al., 2011; Steefel et al., 2013).

The different features of current microscale geochemical models of reactive transport probably explain to a large extent why none of them has been used so far to describe soil processes at the microscale. Given the extremely high specific surface area, and the significant surface reactivity of many soils, in addition to the fact that the reactions that take place in soils are complicated by the presence of very heterogeneous OM, the speciation portion of typical microscale geochemical models would have to be entirely overhauled before it could be applied to soils. Nobody, as far as we are aware, seems to have launched into this work yet. In addition, even if someone had done that work, model predictions could not at the moment be compared with actual microscale measurements at this stage, as discussed in detail in the previous two subsections.

### Visual Summary of the Status of the (Bio)chemical Front

If we try to summarize graphically the state-of-the-art of the (bio)chemical characterization and modeling of soils at the microscale, it is clear that work in this area is far less advanced than on the physical front (**Figure 5**). Measurements of static features or of the dynamics of (bio)chemical species are still very limited. Some of this scarcity of data can, however, be addressed. There is indeed a great potential to generate many static, 2D data, using a wide array of experimental methods, and to extrapolate them to three dimensions. Modeling frameworks are available to describe the transport of reactive chemical species in porous or fractured media, but they would need to be modified substantially before they could be applied to soils, and that significant effort has not taken place yet.

### THE MICROBIOLOGICAL SCENE

### 3D Microscale Distribution of Microorganisms: Absence of Direct Data

To complement the 3D data related to the geometry and topology of soil pores, as well as 3D data about the (bio)chemical properties of soils, generated by interpolation among 2D pictures, it would be ideal if detailed 3D information could be obtained about the distribution of microorganisms in soils. Such information can be readily obtained in the case of wood, at least for fungi (Van den Bulcke et al., 2009). But unfortunately, for exactly the same reasons that hinder the direct 3D determination of the distribution of OM in soils, it has proven impossible so far to quantify the spatial heterogeneity of the distribution of microorganisms in actual soils.

When direct 3D measurements of biomass distribution in porous media have been obtained, it has so far always been under conditions that bear little similarity to real soils. Lilje et al. (2013) describe the development of a culture system and staining protocol they have used to obtain 3D quantitative data of filamentous and zoosporic soil fungi in an artificial matrix that was "developed to simulate the particulate nature of soil." This artificial matrix consists of 500–900 µm diameter X-ray translucent polystyrene beads, which might be morphologically similar, to some extent, to coarse sand particles, but would likely have very different surface and hydration properties than typically highly heterogeneous soils. In many ways, the same comment pertains to the use of nuclear resonance imaging to detect "biofilms" in systems composed of polystyrene beads (Vogt et al., 2013). Sanderlin et al. (2013) pioneered the use of a very promising low-field magnetic resonance system to visualize the 3D distribution of biofilms in glass beads and sand particles, whereas a number of other authors used X-ray tomography to assess the distribution of biofilms in systems of glass beads (Davit et al., 2011; Iltis et al., 2011; Peszynska et al., 2016) or 2.5 mm-diameter Nafion pellets (Carrel et al., 2017). In all these cases, the properties and geometry of the systems investigated are drastically different from those of actual soils, which are generally characterized by a spatially dispersed- rather than concentrated biomass, and it is not clear at all at this stage how the transition from artificial media to actual soils will be made.

Since direct methods are lacking to quantify the 3D microscale distribution of bacteria in whole soil samples in one go, a number of authors have developed sampling techniques to obtain 3D information in other ways. Dechesne et al. (2003) developed such a technique and tested it in repacked soil columns. Their approach consists of a number of steps. The soil is first microsampled within several small subunit volumes of roughly the same volume (minimum sample side: length of 50 µm) within the columns, and these microsamples are subsequently tested for the presence or absence of targeted microorganisms, which in the original study were two bacterial strains but could equally easily have been archaea or fungi. A subsequent statistical analysis involves a comparison of experimental sampling data with data expected from limited sampling of numerous theoretical spatial distributions. Since the exact spatial location of the microsamples was not determined by Dechesne et al. (2003), they could identify only which statistical distributions of patches occupied by bacteria were possible within their sample. However, now that with CT, it might be possible to geolocalize small subsamples within soil columns, a similar approach could now be used to determine spatial distributions of various microorganisms as well, albeit at a relatively low resolution. An implementation of this approach is reported by Kravchenko et al. (2014b). In that work, ≈5 mm-sized soil fragments (referred to as macro-aggregates) were subjected to CT scanning, which provided information on pore architecture. Scanning was followed by cutting the macro-aggregates into geolocalized subsections, that is, the position of each subsection on the CT images was determined. Then, microbial community analyses of each geolocalized subsection via 16S rRNA pyrosequencing was conducted, enabling exploration of associations between presence of certain groups of microorganisms and abundances of soil pores of different sizes.

### Scarce Data on 2D Microscale Distribution of Microorganisms

Given the technical difficulties associated with 3D measurements, it is natural that researchers attempted to find out what information could be obtained from 2D cuts through soils.

Alexander and Jackson (1954, 1955) were apparently the first to suggest that thin sections of resin impregnated soil samples could be useful to observe algae, fungal hyphae, and bacteria, using either light or phase-contrast microscopy. They indicated that staining the soil before impregnation enhances the detection of hyaline mycelia and bacteria. Nevertheless, as soon as transmission and scanning electron microscope became available, microbiologists turned to the machines to obtain information about soil microorganisms. Consistently, they confirmed Clark's (1951) observations. Bacteria, often coated by clay platelets, were generally present, not as "biofilms," but as small colonies of a few cells, with many bacterial cells being dispersed in the rest of the soil as individual cells (Foster, 1988). As enlightening as these and other similar observations have been and still are5 , a drawback with TEM and SEM is the fact that at least until recently they could provide only qualitative information. To obtain quantitative data about the distribution of microorganisms, researchers found it necessary to return to staining cells in thin sections that could be georeferenced easily and viewed in their entirety (e.g., Jones and Griffiths, 1964; White et al., 1994; Nunan et al., 2001, 2002, 2003; Li et al., 2003, 2004). Aside from non-specific stains like calcofluor white M2R applied before impregnation (Postma and Altemuller, 1990), or basic fuchsin and methylene blue applied after impregnation (Tippkötter et al., 1986), researchers also have been interested in selective staining techniques of specific cells, e.g., using fluorescence-conjugated antibody techniques (Postma and Altemuller, 1990), to observe the distribution of bacteria and fungal hyphae in soils. In some cases, problem arose because of the crystallization of the stains when in contact with

soils (Harris et al., 2002, 2003). Nevertheless, after these slight technical issues got resolved, images of soil thin sections obtained with these various staining techniques showed clearly that for fungal hyphae, given their size, it is relatively straightforward to identify them (**Figure 8A**). But for bacteria and archaea, as clearly indicated in **Figure 8B**, a tremendous amount of skill (or faith, or both) is required to be able to identify a cell conclusively. Experience shows that part of the problem is related to the difficulty, with traditional light microscopes to focus precisely on a specific depth. It is possible, but tricky, to focus on the top surface of a thin section, hoping that one would then have a sharp image of the first 1 or 2 µm at the surface (Nunan et al., 2001). An easier solution consists of using a confocal laser microscope (e.g., Caldwell et al., 1992; DeLeo et al., 1997; Li et al., 2004), which can produce sharp 2D images at selected shallow depths within a soil thin section. With special software, 3D images can be reconstructed from a set of z-dependent 2D images. In principle, an extension of Hapca et al.'s (2015) statistical interpolation technique, described earlier, should make it possible to assemble these very thin 3D images into a full 3D picture of microbial microscale distribution in soil columns.

A more difficult problem to resolve with traditional stains is related to their non-specific binding to OM or other soil constituents. As a result, many microbial cells may be undetectable against a very bright background of fluorescing soil constituents (**Figure 8B**). Luckily, that stumbling block too has found a solution in recent years, with the development of very reliable fluorescence in situ hybridization (FISH) techniques, which use fluorescent-labeled oligonucleotide probes (Pickup, 1995; Mcnaughton et al., 1996; Li et al., 2004; Eickhorst and Tippkötter, 2008a). Eickhorst and Tippkötter (2008b) have shown that when FISH is combined with tyramide

FIGURE 8 | Examples of experimentally determined microbial distribution in soils: (A) microscopic image of hyphae of the fungus Rhizoctonia solani growing in the pore space of a sandy loam. Scale bar 20 µm (Harris et al., 2002. Reproduced with permission of the British Mycological Society). (B) Micrograph of ethidium bromide-stained thin sections of a silt loam soil after inoculation by Escherichia coli. Image obtained using an epifluorescence microscope with blue excitation (Modified from Li et al., 2004. Reprinted with permission). (C) CARD-FISH stained Bacillus subtilis cells in soil filter sections under double excitation filter 643 (465–505 and 564–892 nm) (Modified from Juyal et al., 2018).

5Anyone who is planning to simulate soils by using glass beads should have a long look at some of the images in Foster (1988) and in later work that has followed on his footsteps!

signal amplification, in what is referred to as Catalyzed reporter deposition (CARD)-FISH, one typically obtains higher signal intensity and reduced interference of the background fluorescence of the soil. This methodology, or variants of it, have been used by a few researchers in the past decade to assess the distribution of bacteria in soils (Schmidt et al., 2012a,b, 2015; Schmidt and Eickhorst, 2014). The combination of CARD-FISH, or one of its variants, with confocal laser microscopy, affords a very powerful tool to visualize and quantify the distribution of microorganisms in soils, with a satisfactory depthresolution.

The (few) measurements that have been carried out in thin sections have shed some light on the spatial pattern of microbial distribution in soils, but many questions remain. Based on the analysis of 744 images of observed bacterial distributions in soil thin sections taken at different depths, Raynaud and Nunan (2014) found that the distance between neighboring bacterial cells was, on average 12.46 µm and that these intercell distances were shorter near the soil surface (10.38 µm) than at depth (>18 µm), due to changes in cell densities. These authors' analyses suggest that despite the very high number of cells and species in soil, bacteria only interact with a few other individuals. For example, at bacterial densities commonly found in bulk soil (108 cells per gram of soil), the number of neighbors a single bacterium has within an interaction distance of ca. 20 µm is relatively limited (120 cells on average). This analysis is based on calculations of Euclidean distances, which as Raynaud and Nunan (2014) acknowledge do not take into account the presence of solids, nor the tortuosity of the pore space.

A slightly different perspective on the distribution of bacteria is obtained when one proceeds to a simple back-of the-envelope calculation focused on the surfaces of soil pores, which may indicate somewhat better than Euclidean distances the degree of separation among bacterial cells. The specific surface area of soils varies between a low of 0.1 m2 per gram, for coarse sand, to a high of 800 m2 for a smectite clay, with most soils falling in between these extremes (Pennell, 2016). In a soil with a relatively low specific surface area of 10 m2 per gram, a population of 108 bacteria, each having on average a 1 µm2 cross section, would occupy a mere 0.0001 m2 per gram of soil, i.e., about 1/100,000th of the specific surface area. Even if one assumes bacterial cells to be much bigger, with a longitudinal cross-sectional area of 4 µm2 , they would still cover only 1/25,000th of the specific surface. In other words, in either case, it is as if on the surface of soil solids, each cell would sit in the middle of an exclusion zone with an average radius of 178 µm. These numbers, in line with earlier estimates (Postma and van Veen, 1990; Grundmann, 2004; Young and Crawford, 2004; O'Donnell et al., 2007; Vos et al., 2013; Kuzyakov and Blagodatskaya, 2015) suggest a very lonely existence indeed, but of course, they are very crude estimates at best, ignoring any tendency cells may have to aggregate. Nevertheless, as more micrographs like that of **Figure 8C** become available in the coming years, and are combined with detailed information about the geometry of the pore space, it will become possible to refine our understanding of the patterns of spatial distribution not only of bacterial cells, but also of archaea, fungi, and bacteriophages.

### Background: Dominant Paradigm and Slow Shift to a New One

The relatively low number of articles dealing with the distribution of microorganisms in soils may surprise, especially given the tools that have been at our disposal for at least a decade (CARD-FISH) or even two (confocal laser microscopes). To understand why that has been the case, and especially to try to change this unfortunate state of affairs, it is useful to describe briefly in what context this work has been carried out. This background is of course familiar to soil microbiologists, but researchers in other disciplines may not necessarily be aware of it.

In the mid-1960s, contrary to the views that had prevailed earlier, a number of researchers, seeking to make their life easier, decided to start viewing the soil microbial biomass as a blackbox, which meant ignoring entirely both the diversity of microorganisms present in soils and their relation to their immediate physico-chemical environment (Baveye, 2018). This approach became dominant for a few years, but in the 1980s and 1990s, a slew of molecular methods were developed to characterize DNA or RNA extracted from soils (Maron et al., 2011; Mendes et al., 2015). Microbiologists in growing numbers jumped on these methods enthusiastically, with the hope that they would give them the opportunity to get information about the diversity of soil microorganisms, i.e., would allow them access inside the blackbox of soil biomass, but still with the convenience of not having to worry about where exactly microorganisms are located. Indeed, in what became known as "metagenomic" and, more recently, "high throughput sequencing" methods, all that was needed to carry out the analysis of a given soil was to extract its microbial DNA or RNA. Indeed, virtually all researchers adopting this approach have entirely ignored the geometry of the pore space in soils or the characteristics of microenvironments (e.g., Nannipieri et al., 2003). Even the so-called "high-resolution" metagenomics (Kalyuzhnaya et al., 2008) ignores the physicochemical environment of microorganisms. The claim was also made initially, at least by some, that metagenomic methods would enable researchers to avoid having to culture microorganisms in the laboratory, a process that for an estimated 98% of soil microbes, had proven impossible until then (Vogel et al., 2009).

In terms of actual benefits of work carried out along those lines, one should mention the fact that knowledge of the diversity of nucleic acids present in soils paved the way for the design of oligonucleotide probes used in FISH. In itself, this is an important outcome, but in most other ways, experience over the years has demonstrated that many if not all of the initial claims made by proponents of metagenomics were unrealistically optimistic. Scores of researchers have shown that the extraction of DNA or RNA from soils in many cases manages to get at only a fraction of the total amount present (Terrat et al., 2012; Knauth et al., 2013; Dlott et al., 2015; Wagner et al., 2015), that some of this DNA or RNA material is associated with dead or dormant cells, or is extracellular (Carini et al.,

2016), and finally, that the information yielded by DNA or RNA analysis provides a picture of the genetic potential of microorganisms in a soil, not at all of what microorganisms actually do (Prosser et al., 2007; Blazewicz et al., 2013). Furthermore, it has become obvious that, far from alleviating the need to culture microorganisms, the metagenomic approach has increased the urgency of finding ways to identify and characterize vastly more organisms than is the case at the moment (Oremland et al., 2005; Baveye, 2009a,b; Pham and Kim, 2012; Puspita et al., 2012; Prakash et al., 2013). In spite of all these false hopes, limitations, and biases (Lombard et al., 2011; Prosser, 2015), it is fair to say that, at the moment, bulk "meta"-something-"omics" approaches (metagenomics, metatranscriptomics, metaproteomics, metabolomics) capture virtually all the funding dedicated to soil microbial diversity, and their use seems to be crucial to insure microbiologists' career advancement. Year after year, articles praising the merits of metagenomics to uncover the secrets of soils (e.g., van Elsas et al., 2008; Vogel et al., 2009; Delmont et al., 2011; Fierer, 2017; Popescu and Cao, 2018) still make headlines6 and attract record numbers of citations.

But things may be changing. Roughly 12 years ago, partly in response to the inability of metagenomics to link functions to species and also because information needed to make sense of metagenomics data is lacking for a multitude of still uncultured microorganisms (Su et al., 2012; Shi et al., 2015), researchers started investigating ways to isolate and sequence the DNA and RNAs of individual cells. A number of articles (e.g., Wang and Bodovitz, 2010; Lasken, 2012, 2013; Pamp et al., 2012; Stepanauskas, 2012, 2015; Yilmaz and Singh, 2012; Blainey, 2013; Woyke et al., 2017) have recently retraced some of the key breakthroughs that have enabled what could probably be viewed as a fundamental revolution, in particular in the application of molecular biology techniques to environmental systems (Ishoey et al., 2008). The onset of that revolution is generally considered to be Raghunathan et al.'s (2005) proof-ofprinciple demonstration that it is possible to use the multiple displacement amplification (MDA) reaction to amplify genomic DNA from a single bacterium several billion fold, with a recovery of about 30% of the genome in the process. Marcy et al. (2007), Podar et al. (2007), and Kvist et al. (2007) applied MDA to environmental cells and established the feasibility of single-cell genome sequencing from uncultivated targets. Woyke et al. (2010) showed that it is possible to produce a completely closed genome from an individual cell. Progress has been very rapid since (**Supplementary Figure S1**), including in RNA sequencing (e.g., Pan et al., 2013; Svensson et al., 2017), singlecell transcriptomics (e.g., Kang et al., 2011), and single-cell metabolomics (e.g., Heinemann and Zenobi, 2011).

All these single-cell techniques offer tremendous potential for the study of soil microorganisms as various researchers have already pointed out (e.g., Ishii et al., 2010; Pedersen et al., 2015), provided two key challenges can be overcome. The first is related to the fact that FISH, the technique that seems most promising at the moment to locate bacteria and archaea in 2D cuts through soils, has been documented to interfere with single-cell genome recovery (Woyke et al., 2017). This problem may be partly avoided by complementing FISH with other methods to detect and characterize microorganisms, like Raman spectroscopy (see below). The second challenge is related to isolating individual cells from their microenvironments in soils. In the past, various researchers have used micromanipulators of different types over the years, to extract hyphae fragments from soils (Söderström and Erland, 1986) or to sample bacteria on soil surfaces (Dennis et al., 2008). Ashida et al. (2010) and Nishizawa et al. (2012) adopted a micromanipulator originally developed by Fröhlich and König (1999, 2000) and Ishøy et al. (2006), and consisting of a microcapillary (with an outside tip diameter of 60–100 µm), to extract individual, artificially elongated bacteria from a rice paddy soil sample, and subsequently proceed to 16S rRNA gene analysis. More recently, Ringeisen et al. (2015) have used a laser printing technique, called BioLP, to isolate viable microorganisms from a thin layer of soil spread over a titanium-coated quartz plate. For both the micromanipulator and laser printing technologies, the technological challenge at this point is to design a sampling method that would have a far smaller footprint than is currently achievable, to make it possible to zero in on a single cell or a very small group of cells in a soil microhabitat. Since intracellular capillary microsensors with tip diameters less than 1 µm have been used by microbiologists for at least 60 years (Draper and Weidmann, 1951) and the technology of "optical tweezers" has evolved tremendously in the last 2 decades (e.g., Fröhlich and König, 2006; Whitley et al., 2017), it may not be foolish to imagine that we could come up with a way to extract single bacterial cells from soils in a very efficient manner in the not too distant future.

An argument that could be put forth to downplay the interest of this type of single-cell analysis is that such a detailed description of microbial communities is an unnecessary luxury for understanding a large number of microbial functions in soil. It is widely accepted that microbial communities are characterized by a functional redundancy with respect to a range of functions, such as organic C mineralization (e.g., Wertz et al., 2006, 2007; Allison and Martiny, 2008), meaning that the loss of a large number of species does not have a significant effect on functions of interest. Where functional redundancy is apparent, it is possible that viewing microbial communities in soil as a distribution of active sites rather than a distribution of species might suffice. Further research is needed to determine under what conditions information about individual microbial cells is crucial and when it is superfluous.

### Dynamical Picture: Are Micromodels a Way Forward?

Given the need to impregnate soils with resin and to cut through the resulting block in one way or another to obtain information about the distribution of microorganisms and the (bio)chemical features of the microenvironments where they reside, it is clear that it is not possible at this stage to monitor in real time, at the

6As an example of this type of repeated headlines, Charles (2018), on the National Public Radio website in the United States, describes the "Earth Microbiome Project," an initiative started a decade earlier, as a "new approach" to opening up the soil microbial blackbox.

microscale, the dynamics of microbial processes in actual soils. And, to be realistic in our expectations, for bacteria, archaea, and definitely viruses, it may be that we shall never be able to monitor their activity directly in soils.

We might be able, however, to observe the dynamics of these organisms or viruses in 2-dimensional, manufactured soil-like structures, generally referred to as micromodels or "microfluidic" devices. The development of these micromodels has been the object of significant research over the last 20 years (Karadimitriou and Hassanizadeh, 2012; Stanley et al., 2014, 2016; Stanley and van der Heijden, 2017; Aleklett et al., 2018). Early generations of micromodels, still in use to some extent (e.g., Dupin and McCarty, 1999; Stewart and Fogler, 2001; Lanning and Ford, 2002; Coyte et al., 2017; Borer et al., 2018) had idealized geometric properties, being basically two-dimensional networks of straight cylindrical segments, etched in glass or plexiglass. But as technology matured, second- and third-generation structures have become progressively closer to what one would find in a typical fine- to medium sandy soil. Of course, the material these micromodels are made of, often polydimethylsiloxane (PDMS), does not have the same surface properties as sand or silt particles. For some microbial processes this may be an issue, and it makes it impossible to reproduce surface chemical properties of soils, but at least the geometry of the pore space is realistic. With such a soil-like micromodel, Deng et al. (2015) have been able to observe the effect of extracellular polymeric substances (EPS), released by bacteria, on the drying kinetics of the pore space, whereas Rubinstein et al. (2015) have used it to demonstrate the effect a protist, the ciliate Colpoda sp., can have on the transport of nanoparticles through soils.

The use of micromodels opens up a number of very interesting avenues for further research, which may provide useful insight. For example, micromodels would seem to be ideal systems to instrument with optodes (Pedersen et al., 2015; Rubol et al., 2016), in order to access some of the physico-chemical parameters (pH, redox potential) that at the moment we cannot measure in soils at the microscale. The use of micromodels might also allow us to better understand how the moisture content of soils influences the activity of bacteria, archaea, and fungi. There is macroscopic evidence that these organisms react very differently to high or low moisture contents (e.g., Otten et al., 1999; Otten and Gilligan, 2006; Kaisermann et al., 2015; Baveye et al., 2016b), as do their predators, which we should not forget (Stefana et al., 2014), and it would be very useful to obtain direct evidence of this at the pore scale.

However, it is likely that for micromodels to give us valuable insight about actual soils, at least two significant challenges will have to be addressed and resolved. The first concerns the connectivity of the pore space. In nature, microorganisms evolve in a 3-dimensional space, which is significantly more connected than is achievable in 2D (e.g., discussion in Hapca et al., 2011). It will therefore be crucial to find a way to relate 2D observation made in micromodels with the more complex situation found in soils. The second challenge is related to what was referred to as "sub-resolution" pores in CT images. The issue, still very much an object of debate, is whether these pores are important to understand microbial activities in soils, and therefore whether they should be present in micromodels. A body of literature, published over the last few decades, argues that pores in the 30 to 150 µm size range are particularly crucial to understand microbial activity (e.g., Kravchenko and Guber, 2017). Specifically, pores of this size group were found to harbor greater abundance of a number of bacteria groups, such as copiotrophic actinobacteria, firmicutes, and proteobacteria (Kravchenko et al., 2014b) and presence of such pores was associated with greater microbial activity and greater OM decomposition (Killham et al., 1993; Chenu et al., 2001; Strong et al., 2004; Ruamps et al., 2011, 2013), in spite of a higher predation pressure in larger pores, compared to small ones (e.g., Wright et al., 1995). Recently, it was also found that dissolved OM contained within such pores is more labile, having less lignin and tannin-like compounds, than that in small (<6 µm) pores (Bailey et al., 2017; Smith et al., 2017). One perspective on these data is that pores of this size range offer better micro-environmental conditions, e.g., O2 and water supply, while providing enough space not only for individual organisms but for formation of microbial colonies, which then generate these sizeable experimentally detectable activities and changes in soil characteristics.

Based on this evidence, one would be temped to conclude that when constructing micromodels, one could safely ignore small pores, which would undoubtedly make everyone's life simpler. However, the much lower connectivity of the pore space that would result from that may prevent us from describing correctly some of the processes occurring in soils, both in terms of microbial movement and metabolism. To resist predation, it may be vital for bacteria and archaea to be able to find refuge in smaller pores in which amoebae and particularly ciliates are not able to penetrate. One expects motile bacterial and archaeal cells, sometimes as small as 0.3 µm in diameter or width in soils, to be able to move relatively easily in and out of 2–3 µm-wide pores filled with water. But, as the experiments of Männik et al. (2009) with micro-fabricated channels show, some bacterial cells (of Escherichia coli, but not of Bacillus subtilis), can penetrate pores smaller than themselves. Although organisms constricted in narrow channels had no mobility and were squeezed, they could still penetrate the channel by growth and division (Hallett et al., 2013). Perhaps more important still is the fact that, given their even smaller size, exoenzymes that bacteria and archaea, as well as fungal hyphae, release into the soil solution can move in and out of tiny pores. Likewise, solutes present in the soil solution can diffuse in and out of the smaller pores, including the very narrow 1.8 nm-wide spaces between clay particles (Dumestre et al., 2000, 2006). In particular, dissolved components of the OM that is located, and possibly to some extent is physically protected, in small pores can also diffuse out into wider pores, where they can be taken up by microorganisms or be transported with the percolating water. Results obtained by Michelson et al. (2017) using a microfluidic device also suggest that members of the Geobacteraceae family produce nanowires that are able to penetrate in pore spaces too small for cell passage and, there, up to 15 µm away from cell bodies, reduce Mn(IV) and Fe(III) oxides via long-range extracellular electron transport. Finally, the (so far virtually ignored) bacteriophages

swarming in the pore space of soils in huge numbers (Ashelford et al., 2003), with sizes sometimes as small as a few tens of nanometers, are likely to diffuse through tiny pores as well, and it may turn out that to understand the dynamics of phages in soils, a topic of increasing interest at the moment, it will be necessary to deal with sub-resolution pores in one way or another.

For all these reasons, inclusion of sub-micron pores in micromodels is a technological challenge that may need to be met if we want to use micromodels to gain knowledge about a range of soil processes, but in the meantime, a number of interesting processes, which are not or are only marginally influenced by sub-resolution pores, can still be studied with existing soil-like micromodels, such as the proliferation of fungal hyphae (as long as the release of exoenzymes is not the key mechanism by which fungi metabolize food sources), or the effect of bacterial activity on water or particle retention and movement in larger pores (e.g., Deng et al., 2015; Rubinstein et al., 2015).

### Modeling of Microbial Spread and Activity in Soil Pores

Contrary to what has happened on the (bio)chemical scene, the least one can say is that the lack of experimental data about the spatial distribution and activity of microorganisms in soils has not discouraged at all a number of researchers from developing increasingly more sophisticated biokinetic models. On the contrary, work in this area, overwhelmingly carried out by soil physicists, mathematicians, and computer scientists, has been extensive over the last decade (e.g., Thullner and Baveye, 2008; Heße et al., 2009; Gras et al., 2010, 2011; Wang and Or, 2010; Gharasoo et al., 2012; Ebrahimi and Or, 2014, 2015, 2016, 2017; Vogel et al., 2015; Tecon and Or, 2017a,b; Wilmoth et al., 2018; Vogel H.J. et al., 2018; Vogel L.E. et al., 2018). Some of this research has consisted at first of a relatively straightforward extension to the microscale of macroscopic modeling approaches originally developed for saturated porous media, with the biomass consisting exclusively of bacteria, attached to surfaces and growing in response to the influx of a substrate, according to Monod's equation in its simplest formulation (e.g., Widdowson et al., 1988; Baveye and Valocchi, 1989; Loehle and Johnson, 1994; Vandevivere et al., 1995). Over the years, in addition to being extended to the microscale in variably saturated porous media, the original biokinetic model has also been greatly improved (e.g., Hron et al., 2015). Description of bacterial growth has included an explicit account of endogenous metabolism. Bacteria have been allowed to move via chemotaxis, in response to substrate concentration gradients (Olson et al., 2004; Ebrahimi and Or, 2014; Son et al., 2015), and to become dormant (Gras et al., 2011; Resat et al., 2012; Joergensen and Wichern, 2018), under a range of conditions. Instead of simply relying on population-level kinetic equations like Monod's, researchers have progressively turned to individual- or agent-based models, recognizing that locally in soils, the number of bacterial cells tends to be very small, and therefore the large-number assumption embodied in Monod's equation is no longer met (Hellweger et al., 2016). In all these respects, progress in the development of the models over the last decade has been very significant, although from a strictly bacteriological perspective, the models currently available still fail to include a number of processes that might be very significant in soils, like conjugation, quorum sensing, siderophore production, exopolymer and exoenzyme production, filamentous growth of some bacterial strains, or the release of antibiotics to compete with other bacteria or archea (Wolf et al., 2013; Abrudan et al., 2015; DeAngelis, 2016).

In parallel with this modeling effort related to bacteria, various researchers have endeavored to develop computer models to describe the 3-dimensional proliferation of fungi in various types of environments (Otten et al., 2001; Falconer et al., 2005, 2007, 2012, 2015; Boswell and Hopkins, 2008; Jeger et al., 2008; Pajor et al., 2010; Kravchenko A. et al., 2011; Kravchenko A.N. et al., 2011; Hopkins and Boswell, 2012; Cazelles et al., 2013; de Ulzurrun et al., 2017). These models include a number of processes, which for soils might be very relevant, like biomass recycling and the release of exo-enzymes. In applications of some of these models to soils, thresholded CT images can be used to establish the boundaries of the geometric domain in which fungal growth occurs.

Since most soils simultaneously harbor bacteria, archaea, and fungi (among many other organisms), one would expect that the two families of models developed so far to describe specifically the activity of these organisms would have been combined at some stage. This would seem to make a lot of sense, especially as far as bacteria are concerned. One might argue that, under a number of circumstances (e.g., discrete POM serving as exclusive carbon source to fungi), the presence or not of bacteria in the pore space is in general pretty much irrelevant for the proliferation of fungal hyphae. Exceptions occur when bacteria have fungicidal activity (Stanley et al., 2014), and influence the propagation of hyphae. But it is more common for fungi to exert an influence on the behavior and spread of bacteria. Over the last few years, evidence has accumulated that bacteria, "Hitchhikers on the fungal highway" as Warmink et al. (2011) put it, can hop on, or at least be passively carried by, fungal hyphae as they propagate through the pore space (Kohlmeier et al., 2005; Warmink et al., 2011; Ellegaard-Jensen et al., 2014; Stanley et al., 2014), with the consequence that mycelia may be having a very significant role in gene transfer in soils (Berthold et al., 2016; Nazir et al., 2017). Recent ToF- and NanoSIMS measurements carried out by Worrich et al. (2017) also demonstrate that fungal or fungal-like (oomycete) mycelia can reduce water and nutrient stresses experienced by bacteria in otherwise dry and nutrientpoor microhabitats. All these recent observations seem to run counter to previous research suggesting that the high biodiversity of bacterial populations in soils, as well as their community structure, could be accounted for by the low connectivity of the water-filled pore space (e.g., Tiedje et al., 2001; Fierer et al., 2003; Treves et al., 2003; Carson et al., 2010; Ebrahimi and Or, 2015).

Therefore, it would seem important for models describing the activity of microorganisms in soils to simultaneously involve bacteria, archaea, and fungi, and in particular describe the transport of bacterial or archaeal cells by fungal hyphae or the transfer of water and nutrients by mycelia in the pore

space. Unfortunately, this is far easier said than done, because of the difference in scale at which these various groups of organisms operate. In order to describe the activity of fungi realistically, one needs to model a volume of soil in which typically very large numbers of bacterial or archaeal cells would be located, making the prediction of microbial activity extremely CPU intensive, especially when using individual-based models. Within the context of this type of model, there is a possibility to deal with groups of cells, or "super-individuals," as if they were single individuals, to save computing time (e.g., Scheffer et al., 1995) but the approach does not appear to have been used yet to describe bacterial or archeal populations in soils, and it remains to be seen whether it really makes sense.

This hurdle we need to resolve, somehow, about including both bacteria and fungi in the same simulations, raises a broader question of how many other similar hurdles we need to face. How much biodiversity needs to be included in models, in order to have meaningful insights into what is occurring in soils, and in order for the label of "microbial" used abusively in the title of many articles dealing only with bacteria (e.g., Or, 2002; Ebrahimi and Or, 2015), is really justified? In principle, there is no problem in developing models that involve only one type of microorganism, as long as the conclusions reached are restricted to the organism(s) involved, under the conditions assumed in the modeling, and are not considered generally applicable to soils, which contain a multitude of other organisms beside the targeted one(s) (this point is discussed in detail in Baveye et al., 2016b). Clearly, however, such limited models, from which crucial components are missing, are not likely at all to be very useful in the long run in the context of the program defined in **Figure 1**. To make real progress, we need a model that includes as many as possible of the organisms that are relevant to the goal that is being pursued. In general, bacteria, archaea, fungi probably all need to be included, but so do their predators (e.g., DeLeo and Baveye, 1997; Ronn et al., 2012), as well as bacterial and archaeal phages that are present in the soil in large numbers and are more and more suspected to have a very significant, yet still largely misunderstood, influence on microbial dynamics (Williamson et al., 2017; Pratama and van Elsas, 2018). Likewise, the too often ignored aspects of mesofaunal and macrofaunal activity in soils (Briones, 2014), which directly relate to the growth and metabolism of microorganisms, probably also ought to be accounted for, somehow. Depending on the specific questions we try to address, it may be that, in addition to microorganisms, phages and the mesofauna all need to be taken into account in our description of soils, in which case individual-based techniques might not be workable, or only some organisms need to be involved explicitly. Further research is needed to enlighten us in this respect.

As we navigate among all these additional components that may, or may not, need to be added to current microbial models to make them encompass more of the known biodiversity of soils, it soon becomes apparent that progress vitally requires being able to compare model predictions with actual measurements, which at this point, as was discussed in previous sections, are sadly lacking. . . Over the years, various soil scientists have reacted strongly, sometimes eloquently (Thomas, 1992), sometimes caustically (Philip, 1991), against modeling efforts that are not systematically backed by sound experimental support. A well-known philosopher and writer, David Henry Thoreau, offered a long time ago a more positive take on a similar situation (in a different context), when he wrote: "If you have built castles in the air, your work need not be lost; that is where they should be. Now put the foundations under them." (Thoreau, 1854). Clearly, in the case of models of microbial activity in the hugely complicated environment that soils constitute for microorganisms, it seems essential to heed this advice, and to obtain relatively quickly the type of experimental data that would enable us to establish our modeling efforts on a much stronger foundation.

### Visual Summary of the Status of the Microbiological Front

In terms of measurements, the situation on the microbiological front is very similar to that found on the (bio)chemical one (**Figure 5**). Quantitative measurements of microbial distribution or dynamics are extremely limited and related only to a very small portion of the biodiversity found in soils. Unlike on the (bio)chemical front, however, efforts to model the activity of microorganisms in soils have been extensive, especially regarding bacteria, and have produced some interesting predictions. Nevertheless, this effort has so far been entirely focused on selected bacteria and just a few species of non-sporulating fungi, and in the absence of actual measurements, it is not clear at all how close to reality model predictions are.

#### INTEGRATION AND MODELING OF MULTIPLE SCENARIOS

The next step in the program of **Figure 1** consists of integrating disciplinary insights into a coherent integrated picture of microbial processes in soils. This integration should take place at both the static and dynamic experimental levels, and in terms of modeling, with the understanding that what is needed eventually, going into the next step, is a comprehensive, thoroughly tested microscale model of microbial activity. Right from the onset, one should expect this integration to pose significant challenges. Besides the usual institutional impediments to any kind of interdisciplinary research (see, e.g., Baveye, 2013b, 2014; Baveye et al., 2014), this integration is complicated by the fact that separate measurements that need to be made on the same soil samples often require heavy pieces of equipment that are not commonly found in a single location, causing logistic issues.

At the experimental level, one would expect that since data are still scanty on the (bio)chemical and microbiological scenes, very little integration would have taken place. And yet, encouragingly, some countries have set up a framework for efforts along these lines (e.g., Kögel-Knabner et al., 2008) and there have already been several attempts at integrating various types of experimental approaches. A case in point is the

very interesting article by Rawlins et al. (2016). These authors attempt to determine how soil heterotrophic respiration (SHR) is related to the accessibility of OM to microbes in aggregates of a soil from the United Kingdom. They use a combination of synchrotron X-ray CT, osmium staining, and total organic carbon (TOC) content measurements to quantify the 3D distribution of OM, pore space, and mineral phases, and eventually find a weak correlation (r = 0,12) between SHR and a measure of accessibility of OM, which they define as the probability that a given voxel, "filled" with OM be adjacent to a pore voxel. More recently, Yu et al. (2017) combine synchrotronbased 3D X-ray micro-computed tomography with scanning electron microscopy of 2D slices of two different soils, coupled with an energy –dispersive X-ray spectrometer (SEM-EDX) to establish the relation between pore architecture and cementing substances (iron oxide, carbon) in soil aggregates. In an even more recent article, Vidal et al. (2018) combine Nano-SIMS to FIB-SEM to gain information about the distribution of minerals and biomass in the vicinity of roots. They show in particular that bacteria near roots are surrounded by iron oxides, and that some microaggregates are intimately associated with the surface of fungal hyphae.

In terms of the integration of models, some limited work has been carried out as well. Falconer et al. (2012) focus on combining predictions of water retention in a soil, using a LB approach, with a model of the growth of fungal hyphae. Simulation results, based on X-ray CT images of three different soils, show that the water distribution in the soils is affected more by the pore size distribution than by the total porosity of the soils. The presence of water decreases the colonization efficiency of the fungi, as evinced by a decline in the magnitude of all fungal biomass functional measures, in all three samples. The architecture of the soils and water distribution have an effect on the general morphology of the hyphal network, with a "looped" configuration in one soil, due to growing around water droplets. These morphologic differences are satisfactorily discriminated by Minkowski functionals, applied to the fungal biomass.

Two other articles, also combining different models, demonstrate the large benefits that can be derived from the availability of models. Once an X-ray CT image of a soil have been obtained, one can artificially create all kinds of "whatif " scenarios, in which one can imagine that the OM or the microorganisms are distributed in the soil in a multitude of different manners, and one can determine the effect that these relative distributions have on some macroscopic outcome, like the amount of CO2 evolved from a given soil sample. Of course, such "what-if " scenarios do not alleviate the need to secure actual measurements, of microbial and OM distribution, as well as of any macroscopic outcome one is interested in, but the scenarios can definitely complement and expand the experimental data set in very advantageous ways, if only for the purposes of testing statistically various types of novel metrics of microscale heterogeneity (discussed later on). For example, Falconer et al. (2015) obtain strikingly different predictions of evolved CO2 and fungal biomass production in soils, depending on how an identical amount of POM is distributed spatially in the pore space (**Figure 9**). When POM is present in relatively

interfaces. Individual samples differ in the way POM is distributed in the pore

space (Modified from Falconer et al., 2015).

large chunks (>200 µm in diameter, in scenarios 1 and 4), results in terms of both CO2 evolution and biomass C produced show a large variability and in some cases a high level of production. On the contrary, when an identical amount of POM is more finely dispersed in the soil sample (scenarios 2 and 3), CO2 evolution and biomass C production both vanish. This result may surprise, but as discussed by Falconer et al. (2015), it is entirely consistent with the foraging pattern of fungi. In another article also published just a few years ago, Vogel et al. (2015) analyze numerically the role of meso- and macropore topology on the biodegradation of a soluble carbon substrate in variably saturated and pure diffusion conditions. The simulations involve the coupling of a LB model to describe the retention of water in the pore space, and a simplified compartmental biodegradation model that does not allow bacterial motility. Not unexpectedly, Vogel et al. (2015) show that under these conditions, the biodegradation of the solute is strongly dependent on the separation distance between bacteria and solute, and is influenced by the moisture content of the soil.

#### Visual Summary of Integration

To summarize this inevitably quick overview of the work done so far on the integration of disciplinary perspectives on soils at the microscale (**Figure 5**), it seems fair to say that very little progress has been achieved, in large part because very few research projects have so far focused on integration. Such an integration is already largely feasible, for example by measuring in the same soil samples, both the characteristics of the pore space and the spatial heterogeneity of physico-chemical parameters, or either one of these parameters and the spatial distribution of microorganisms. And yet, at the time of the writing of this review article, very little integration at all has occurred at the experimental level. The tiny bit of work that has been carried out is encouraging, but a whole lot of research remains to be done. This is even more so in the case of upscaling, which remains a virtual terra incognita.

### UPSCALING, HOW?

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#### Representativeness of Observations and the Imperative of Upscaling

To achieve a high resolution when scanning soil samples, it is necessary to restrict the size of the samples. Typically, with tabletop scanners, samples cannot have a volume larger than 100 cm3 to obtain micrometer resolution, and they have to be significantly less than that if one wants to reach the highest resolution (of about 0.3 µm) that is advertised by manufacturers. Meanwhile, the modeling of soil samples with lattice Boltzmann models is often limited at the moment to handling images of at most 500 × 500 × 500 voxels, which at a resolution of say, 20 µm, corresponds to a physical volume of only 1 cm3 .

This small size of soil samples has occasionally raised questions in terms of the "representativeness" of measurements or simulations carried out with these samples (e.g., Al-Raoush and Willson, 2005; Costanza-Robinson et al., 2011; Gao et al., 2014; Rab et al., 2014). These questions stem from the concept of Representative Elementary Volume (REV), which has served over the last few decades as a conceptual foundation for much of the description of transport processes in soils (Fowler, 1997; Vogel and Ippisch, 2008; Hemes et al., 2015; Tracy et al., 2015; Daly et al., 2016; Liu et al., 2016; Cooper et al., 2017; Gonzalez et al., 2018). From that standpoint, soil samples scanned via X-ray CT or simulated via LB, which are of a much smaller size than the REV, would not be sufficiently representative, and one should therefore try to work with larger samples, be it physically, or virtually by aggregating together, mosaic-style, images obtained on a number of small juxtaposed samples. The difficulty with this approach is that in general one has no idea how big an REV is in any particular situation or whether an REV indeed exists (Baveye and Sposito, 1984, 1985; Vogel et al., 2002; Koestel, 2017). One can try computationally to consider sequentially larger volumes of soil in CT images to ascertain that a given property, e.g., porosity or bulk density, tends to become constant as the volume grows, as was done by various authors (Baveye et al., 2002; Vogel et al., 2002). However, there is no guarantee that the REV associated with a particular soil property applies to any other parameter of interest, so that the volume-growing procedure has to be repeated in principle for every single parameter needed to fully describe soil dynamics. Therefore, what at first appears to be a sound physically based constraint on the size of soil samples turns out often not to be operationally meaningful, and the best one can do, as suggested by Baveye and Sposito (1984), is to carefully reference any observation that is made on a soil sample to the volume and shape of this sample.

Nevertheless, regardless of how one feels concerning the need to invoke the notion of REV, it is clear that observations made on cm3 -sized soil samples are not directly relevant to answering the questions raised by soil management, all of which relate to significantly larger spatial scales. Even the root zone of individual crop plants at maturation often encompasses several m3 (Baveye and Laba, 2015) and many societal concerns at the moment relate to the kilometric cells of typical climate and general circulation models used to predict global environmental change, or even to the much larger scales of watersheds and continents. Therefore, there is a definite need to upscale the observations made on small soil samples to the much larger scales at which answers are needed. In the words of Wachinger et al. (2000), "a path for translating small-scale understanding into large-scale phenomenology is required." At the moment, no solution is available for this upscaling, which turns out to be an extremely challenging step, but different options have been suggested, some of which can be eliminated right off the bat.

### Are Increasing Sample Sizes or Volume Averaging Feasible Options?

One of the approaches that could be considered as an upscaling option consists of the process of mosaicking images obtained on small-sized soil samples, so as to obtain a virtual sample of much larger size. If this procedure results in soil samples of decimetric dimensions, one could be led to assume that the microscopic information and description relevant to the soil samples has been somehow "upscaled" to the macroscopic scale. However, even though the final sample considered may indeed be macroscopic in extent, the information one gets about it essentially remains microscopic in nature and does not necessarily provide the type of simplified description of reality that is sought in **Figure 1** and that corresponds to the notion of emergence.

Another option, which has been used by numerous authors over the last two decades, consists of averaging microscopic descriptions of porous media, over either a Representative Elementary Volume or an arbitrary volume (e.g., associated with a measuring instrument), in order to obtain macroscopic variables (Ayub and Bentsen, 1999; Lichtner and Kang, 2007a,b; Golfier et al., 2009; Valdes-Parada et al., 2009; Wood, 2009, 2010; Davit et al., 2010; Baveye, 2013a; Lugo-Mendez et al., 2015). Davit et al. (2013) have shown that in terms of outcome, this approach is equivalent to another popular upscaling method involving homogenization through multiscale asymptotics (e.g., Roose et al., 2016). In the classical literature on scales in hydrology, both methods are closely associated with what is often referred to as "coarse-graining," in analogy to a common practice in image analysis (Kitanidis, 2015). When applied to the type of soil processes we are interested in, the upshot of volume averaging, however, one looks at it, is a massive loss of information (Baveye, 2010), which takes us several steps backward in our understanding of emerging microbial processes. Indeed, if in a given soil, we perform a simple volume averaging of the concentration of a carbon source and, separately, of the biomass density, and if in so doing we ignore all the microscopicscale information about the relative distributions of both, we are back to a situation we used to be in, with macroscopic parameters that have no causal relationship any more, and do not allow us to describe emerging processes accurately. Even if, as envisaged, e.g., by Wood (2010) and Porta et al. (2016), one goes beyond simple volume averaging, and somehow takes into account spatial fluctuations or variance within the volume in which averages are computed, leading to non-local integrodifferential equations, the results still miss some of the key ingredients that we recognize intuitively that an upscaled description of emerging microbial processes should have, in particular a quantification of the disconnect between microorganisms and their carbon/energy sources.

### Deep Learning?

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Occasionally, in discussions, the suggestion is made that the very popular "machine" or "deep" learning techniques (LeCun et al., 2015; Willcock et al., 2018) could perhaps provide a way to upscale microscale modeling of soils to the macroscopic scale (Veres et al., 2015). Machine learning explores the study and construction of algorithms that can learn from data and make data-driven predictions. Machine learning algorithms have started to be employed in soil science, in particular for pattern analysis and image classification to predict material classes in single channel X-ray CT images (Chauhan et al., 2016) and multi-channel nanoSIMS images (Steffens et al., 2017; Schweizer et al., 2018). Deep learning is a class of machine learning algorithms that use a cascade of multiple layers of non-linear processing units for feature extraction and transformation; learn in supervised and/or unsupervised (e.g., pattern analysis) manners; learn multiple levels of representations that correspond to different levels of abstraction; and use some form of gradient descent for training via back-propagation.

The application of machine or deep learning techniques to soils might consist of feeding a computer with detailed information about a multitude of scenarios, like those depicted in **Figure 1**, as well as results of simulations carried out for each scenario with the integrated model. With this supply of "big data," deep learning algorithms would in principle search for patterns through all the simulations. Based on these patterns, it would then become feasible to predict the macroscopic behavior of a soil sample on the basis of microscopic data, without having to go through the likely time-consuming effort of rerunning the integrated model. This type of outcome might conceivably be useful under specific circumstances, but it clearly does not correspond to what is expected of an upscaled model in **Figure 1**, namely the ability to predict the macroscopic behavior of soil samples based on macroscopic data. In other words, deep learning in itself does not automatically result in true upscaling. Nevertheless, deep learning algorithms might still be useful if somehow the patterns they identify in the data could (1) be revealed explicitly, (2) be related to specific macroscopic features of the soils, and (3) help in the development of appropriate macroscopic measurement techniques. At this point, further research is needed to determine whether any one of these different conditions can be met.

### Disconnect Is the Key, but How Do We Measure It in Practice?

The research carried out to date, and in particular some of the scenario modeling alluded to earlier, point to a "disconnect" between microorganisms and their carbon/energy sources as being one of the keys to a proper understanding of emergent microbial processes in soils. In principle, this disconnect could be quantified in a number of ways. The Euclidean distance between microorganisms and OM might be a logical candidate, but it does not suffice, since closeness does not guarantee that OM be accessible either directly to a microorganism or indirectly to its extracellular enzymes (see illustration in **Supplementary Figure S2**). To convey the degree of direct or indirect accessibility of OM to microorganisms, a possibility is to consider the length of the most direct path through the pore space that connects a given bacterial cell or segment of fungal hyphae to a blob of OM, if pore connectivity allows such a path to exist at all. This shortest path, generally referred to as the "geodesic" distance, can be computed easily for individual pairs of points, using a number of algorithms developed in graph theory. In principle, a statistical mean of all relevant geodesic distances can then be generated within a specific soil sample. Within a range of CT image resolutions (which influence the apparent connectivity of soils, and therefore the calculation of shortest paths), the mean geodesic distance may prove to have merit, in particular if its use to characterize soil samples in investigations on the effect of temperature and precipitation on carbon mineralization manages to reduce the unexplained experimental variability observed so far.

Unfortunately, the geodesic distance in itself does not provide a complete answer. One issue with it is the fact that it does not take into account the geometry of the pore space along the shortest path, with which it is associated. In practice, this geometry matters tremendously. If a given geodesic path such as the one in **Supplementary Figure S2** goes through a tiny constriction (which used to be referred to as a "pore neck") between two adjacent voids in a soil, not only might bacterial cells or fungal hyphae have great difficulties passing through it, but chemical species (dissolved OM, exoenzymes, byproducts of enzymatic reactions) diffusing randomly through the pore space might also have a reduced likelihood of crossing over. From this perspective, instead of computing the geodesic distance, it might make more sense to quantify the average length of the path taken by molecules diffusing through the pore space. Even though conceptually, the geodesic and diffusion distances are very different, computationally they are not as distinct. Indeed, in order to compute the geodesic distance, algorithms typically track the diffusion paths of large number of random walkers, from which they eventually retain the shortest path. Therefore, the computation of an average diffusion distance between two points does not take a lot more time than the estimation of the geodesic distance.

Computer simulations, using the models under development at the moment and with a wide range of scenarios, could help determine under what conditions metrics like the mean geodesic distance, the mean diffusion distance, or some refinement of them, could be useful. The challenge at that point, then, will be to find a way to relate the metric that eventually turns out to be most suitable, to actual macroscopic measurements that make sense operationally. This is clearly a formidable challenge, whose practical importance cannot be downplayed. The end result of the program of **Figure 1** absolutely cannot require

extensive microbiological, chemical, and physical measurements at the microscopic scale. To be useful, the research needs to come up with simple measurement techniques, which can be used routinely, in a fully automated mode. It is far too early to have even a vague idea of what these routine measurements might be, but they need to remain front and center on our radar screen.

One way to perceive the overall message conveyed by the visual assessment of **Figure 5** is that we are not very far along the way, and that a tremendous amount of work remains to be done. One could easily argue that this "half-empty glass" perspective is more than warranted. There is indeed a lot of work left, and a long way to go. From a more optimistic, "half-full glass" viewpoint, one could contend that, given the incredible complexity of soils and the fact that suitable technologies to deal with the various components of this complexity have been available for only a little over a decade, the progress achieved to date is remarkable.

Regardless of how one feels about the current state of affairs, it seems clear what the next steps in the research should be. The first step needs to address the clear imbalance that exists among the three core disciplines in the level of effort made to secure measurements in soils at the microscale. The current uneven level of knowledge, with some aspects of the research program that are far more advanced than others, if it is not alleviated in some way, is likely to dramatically hinder the credibility of any effort to make the basic disciplinary outlooks converge into a fully integrated microscopic model. At the moment, some integration of models has taken place, but one cannot actually assess how reliable the integrated descriptions are in practice, because in most situations, relevant microbiological observations are utterly lacking. Therefore, it seems fair to say that one of the key priorities of the research in this field will be to come up with the kind of microscale observations of the distribution and activity of microorganisms that are needed, whether that work be carried out by soil microbiologists or, as it has often happened in the last few decades, by non-microbiologists who have managed to gain the required expertise. When more precise information about the location and activity of microorganisms in soils becomes available, it will be useful to try to characterize as accurately as possible the physical and (bio)chemical nature of their microenvironments, and to determine how these microenvironments co-evolve with microorganisms over time.

A second step, which should be initiated now already, without waiting for the first step to be completed, consists of running multiple analyses on the same soil samples, in order to obtain an integrated view of the different parameters that control their functioning at the microscale. Some timid efforts have been made in this respect, but we have to shift to higher speed. In most cases, given the fact that the heavy equipment (e.g., scanners, NanoSIMS) used for some of these analyses are not located in the same institutions, this integration will require soil samples and possibly also researchers to travel from one institution to another. For some time, it has become well accepted that to run synchrotron-based analysis of soils (e.g., µXRF, XANES, or NEXAFS), one had to take soil samples to one of the handful of synchrotrons around the world. But now, this same attitude will have to be generalized to a much wider range of investigations, including microbiological analyses.

The next activity we should delve into at this point, much more forcefully than has been the case so far, is to use the existing microscale models of soils to run multiple "what-if " scenarios, and thereby try to understand how, for example, a spatial disconnect between microorganisms and the POM in soils affects the mineralization of this POM. Little by little, as more and more scenarios are run, it is likely that we will progressively get a sharper idea of the features that control the emergent properties of microbial activity in heterogeneous soil microenvironments, and eventually guide us in terms of the still somewhat fuzzy (but crucial) upscaling to the macroscopic scale.

These steps should keep us busy over the next 5 years. Besides funding, several factors will determine how fast we can make progress. In particular, much could depend on how quickly we can take advantage of a number of tremendous technological advances that should become readily available to researchers in the next few years.

#### FORESEEABLE HELP FROM NOVEL TECHNOLOGIES?

As the preceding sections have documented in some detail, research on microscale aspects of emergent soil properties has been greatly stimulated by a number of major technological breakthroughs achieved at the turn of the century, especially in terms of X-ray CT but also with respect to other measurement techniques (e.g., CARD-FISH). The literature published in the last few years suggests that research is currently paving the way for another wave of phenomenal technological advances, which in several ways can be expected to be even more revolutionary than the previous one. Several of the new technologies are still at the development stage, such as zerofield nuclear magnetic resonance (Ledbetter and Budker, 2013) or quantum microscopes using molecular-scale MRI sensors built from diamonds (Reardon, 2017), but others have already become commercially available and could conceivably cause a huge leap in our ability to visualize and quantify processes in soils.

Years of efforts have been devoted to the development of near-synchrotron quality X-ray sources in facilities that are much smaller than the football stadium size of synchrotrons, and cost significantly less than the billions of euros a typical synchrotron does. Some of these efforts have resulted in 2015 in the installation in Munich (Germany) of the first commercially available mini particle accelerator, or "compact light source" (Eggl et al., 2016). With a very small 5 by 3 m footprint, it produces X-rays through Compton scattering, resulting from the interaction of low energy electrons and a high-powered laser pulse. The X-rays have highbrightness, intermediate between that of X-ray tube sources, used in table-top CT scanners, and large-scale synchrotrons. Another machine based on a similar principle, the ThomX compact light

source is currently under completion at Orsay (France). It has an 18 m long storage ring, and will produce photons with energies up to 90 keV with a maximum flux of 1013 photons per second, i.e., with a brightness similar to that of synchrotrons. Undoubtedly, this type of machine will become widely available in years to come, and will eventually afford soil scientists far more access to nearly monochromatic, tunable X-ray beams than is currently the case.

X-ray beams produced using a very different approach may prove to be of even greater interest to soil scientists, because of the very small footprint and, potentially, cost, of the technology. The principle of laser-wakefield accelerators (LWFAs) was proposed more than three decades ago, and technological advances are progressively bringing them closer and closer to practical applications. In a LWFA, not much larger than a shoebox, where an intense laser pulse focused onto a plasma forms an electromagnetic wave in its wake, electrons can be trapped and are now routinely accelerated to GeV energies. Betatron motion, Compton scattering, and undulators produce tunable x-rays or gamma-rays by oscillating relativistic electrons in the wakefield behind the laser pulse, a counter-propagating laser field, or a magnetic undulator (Malka et al., 2008; Ben-Ismail et al., 2011; Mourou et al., 2013; Albert et al., 2014; Cole et al., 2015a,b; Albert and Thomas, 2016). LWFAs still need to be improved, and in particular their brightness needs to increase significantly to the level of synchrotron sources. Nevertheless, progress has been very rapid in recent years, so much so that a number of researchers have been able to use the technology for microtomography of bones, insects, and small mammals (Cole et al., 2015a,b; Wenz et al., 2015; Döpp et al., 2018). It may not be very long before LWFAs are commercialized and become viable options to image soils.

Perhaps as a result of the appearance of novel sources of X-rays, there has also been an upsurge of interest in developing a variety of novel X-ray detectors (Gruner, 2012), such as the photon-counting silicon-strip detector allowing energy-resolved CT (Persson et al., 2014). Various research groups have also been keen to look beyond simply taking advantage of X-ray attenuation to produce 3D images of materials, including soils. Phase-contrast is a very good candidate in this respect (Bhreasail et al., 2012). Techniques that have received attention recently are edge-illumination phase-contrast tomography (Zamir et al., 2017), dark-field scatter tomography (Bech et al., 2010) and ptychographic X-ray computed tomography. In the latter, phasecontrast information can be used to generate high-contrast 3D electron density maps without having to invoke the usual assumptions of a weak phase object or negligible adsorption (Chapman, 2010; Dierolf et al., 2010). To our knowledge, even though they have been mentioned in the literature on natural porous media, these techniques have not yet been applied to soil samples, but this is bound to happen in the not too distant future, at which point it will be possible to determine exactly how much promise they hold.

A possible danger with these tremendous technological advances that are now on the not-very-distant horizon is that they will allow major progress to be made chiefly in the quantification of the physical aspects of soils, thereby widening the already large gap that exists relative to the (bio)chemical and microbiological aspects. But that does not need to be the case. High-brightness, monochromatic, tunable X-ray and gamma-ray beams, possible with LWFAs, could prove extremely useful to visualize water and OM in soils. Also, it may turn out that some of the alternative X-ray techniques, like phase-contrast or dark-field imaging, may offer great advantages to visualize OM or even fungal hyphae in soils. Techniques like 3D micro-XRF or micro-XANES (Silversmit et al., 2010), whose application to characterize the (bio)chemical make-up of soils is currently handicapped by the limited access to synchrotron facilities, may also benefit greatly from the widespread availability of much cheaper, versatile X-ray sources.

Progress is being achieved not only in terms of X-ray or gamma-ray. One area where progress has been tremendous, and that, clearly, holds a lot of promise to assess the distribution of microorganisms in soil thin sections is related to fluorescence microscopy. Light microscopy, including fluorescence microscopy, has experienced phenomenal advances in the last decade. Until about 40 years ago (Cremer and Cremer, 1978), the resolution achievable with light microscopy was strictly constrained by the diffraction of light. Over time, increasing numbers of "super-resolution" microscopes have been developed, relying either on deterministic super-resolution techniques, like the stimulated emission depletion (STED) and saturated structured illumination microscopy (SSIM), or on stochastic functional techniques, like the super-resolution optical fluctuation imaging (SOFI) and the omnipresent localization microscopy (OLM) (Min et al., 2011; Cremer and Masters, 2013; Duwé and Dedecker, 2017; Ji, 2017; Power and Huisken, 2017; Yang and Yuste, 2017). Again, most of these techniques have yet to be applied to soil samples. With more and more of this super-resolution equipment becoming commercially available, there is little doubt that this application to soils will occur in the near future. When super-resolution images become available, we might be surprised (or not) to find out that the individual spots of light in images like those of **Figure 8**, which at the moment are identified as single bacterial or archaeal cells, are in fact small groups of cells.

In terms of the identification of microorganisms, significant progress has also been achieved recently, which could be very helpful in soils. In parallel with single-cell omics methods, a number of other techniques have been developed in the last few years, which allow the less-detailed, but much more rapid, characterization of single microbial cells. For example, Single Cell Raman Spectroscopy (SCRS) allows the direct measurement of intrinsic information about single cells in a non-invasive, label-free, and in vivo manner (Li et al., 2012; Smith et al., 2016). SCRS measures vibrations of biomolecules resulting from the inelastic scattering of incident laser light, producing a Raman spectrum, which is associated with a small physical volume (<1 µm3 ), of about the size of a bacterium. A typical single-cell Raman spectrum contains more than 1000 bands that can be assigned to different cellular compounds such as nucleic acids, protein,

carbohydrates and lipids. With this information, SCRS enables the characterization of different cell types and can show physiological and phenotypic changes in living single cells. At its inception, the SCRS technique was afflicted by weak Raman signal and significant difficulty in the interpretation of the spectral data, however, recent work on multi-laser beams techniques like the Coherent anti-Stokes Raman Spectroscopy (CARS) (Min et al., 2011) and stimulated Raman spectroscopy (SRS) (Freudiger et al., 2011) has allowed a three order of magnitude increase in the strength of the signal, and significant improvements in signal interpretation. Any of these techniques could be routinely used to complement singlecell omics analysis. Prior to carrying out such an analysis on a particular microorganism in a soil thin section, one could ascertain whether its Raman spectrum is similar to one obtained for another organism already analyzed. In the affirmative, there may not be a need to perform a full single-cell omics protocol, resulting in considerable time saving.

### CONCLUSION

The key take-home message of this article is visualized in **Figure 5**. It presents our assessment of progress achieved to date toward what we view as the ultimate objective of the research about emerging soil microbial processes, namely the development of macroscopic measurement techniques that would provide us with the information needed to make reasonably accurate predictions. This **Figure 5** contains good news and bad news. The good news is that we have made significant progress. For forty years after prominent microbiologists argued in the mid 1960s that the quantitative microscale description of soil microbial processes was essential, the lack of suitable measurement techniques prevented the research from advancing at all. As a result, in spite of the publication of numerous articles on soil OM and on microbial processes in soils, very little progress has been achieved since the 1960s on several key questions in these areas. In the past 15 years, major technological breakthroughs have changed all that, with the result that our understanding of soils at the microscale has improved significantly on a number of fronts, experimentally as well as in terms of computer modeling. The bad news is that progress is very uneven. At the extremes of the spectrum, whereas research on the physical characteristics of soils at the microscale is moving full speed ahead, the (arguably more complicated) experimental observation of microbial processes is lagging far behind, casting doubt on the soundness on some of the extensive modeling that has been carried out in this field over the last decade, and hindering the needed integration of physical, (bio)chemical, and microbiological perspectives. Clearly, there is still a long way before reaching the holy grail, with many daunting challenges on the different paths leading to it.

There are reasons to be optimistic, however, and not to be intimidated by these challenges. For one thing, technological breakthroughs did not stop a decade ago. New measuring devices and new technologies in other respects as well (e.g., single-cell "omics") are being developed and, for some of them, even getting commercialized, which should lead to many quantum leaps in our ability to carry out microscale measurements in soils. In addition, one can always hope that as we run more and more experiments to try to understand the emergent microbial properties of soils, someone will come up with an empirical equation that will provide a simple answer to all the questions we have at the moment, a little bit like what Henry Darcy did in his day for water movement in sand filters. Such an empirical description, if and when it becomes available, would completely change the game plan. But in the meantime, we need to keep in mind that we do not really have a choice but to move forward, no matter how challenging that might be. As was mentioned at the beginning of this article, the unresolved questions the research addresses are the object of extreme societal concern and it is not overblown to consider that they need to be answered urgently if we ultimately want humanity to survive. This message is not yet understood by decision makers in most countries, but as time goes by and it becomes more and more urgent to get answers, we should hope that even politicians will realize it will be in everyone's best interest to devote to this research more than the shoe-string budgets that have been allocated to it so far.

## DATA AVAILABILITY

No new data were generated during the writing of this article.

## AUTHOR CONTRIBUTIONS

PCB initiated the writing of this article, based on in-depth conversations he had over an extended period of time with all co-authors, and he revised several successive drafts of the text, after receiving substantial input from everyone (and very helpful suggestions from the associate editor and reviewers). All authors have approved publication of the final version.

## FUNDING

The research described in this article was made possible in part through NPRP grant #9-390-1-088 from the Qatar National Research Fund (Project Simupor), as well as through a grant from the Agence Nationale de la Recherche (ANR, France) to project Soilµ3D. Professor WO acknowledges funding from the National Environment and Research Council (NE/P014208/1). MB-R's contribution was made possible by a postdoctoral fellowship (Programa de axudas á etapa posdoutoral; ED481B 2017/073) awarded by the Consellería de Cultura, Educación e Ordenación Universitaria (Xunta de Galicia, Spain).

## ACKNOWLEDGMENTS

TE acknowledges gratefully the financial support received from the German Research Foundation (DFG; ZK/14/M8-Plus) and German Academic Research Service (DAAD; K/15/464342).

Finally, PCB, SS, TE, and CM acknowledge the financial support by the German Soil Science Society (DBG) for the workshop "Combined analysis of biochemistry and structural complexity of soil via imaging", held at the UFZ in July 2016 and during which many aspects of the topic reviewed in this article were discussed.

#### REFERENCES

#### SUPPLEMENTARY MATERIAL

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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer PN and handling Editor declared their shared affiliation.

Copyright © 2018 Baveye, Otten, Kravchenko, Balseiro-Romero, Beckers, Chalhoub, Darnault, Eickhorst, Garnier, Hapca, Kiranyaz, Monga, Mueller, Nunan, Pot, Schlüter, Schmidt and Vogel. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Microscale Heterogeneity of the Spatial Distribution of Organic Matter Can Promote Bacterial Biodiversity in Soils: Insights From Computer Simulations

Xavier Portell1,2 \*, Valérie Pot2 , Patricia Garnier2 , Wilfred Otten1 and Philippe C. Baveye2

1 School of Water, Energy and Environment, Cranfield University, Cranfield, United Kingdom, 2 UMR ECOSYS, Institut National de la Recherche Agronomique, AgroParisTech, Université Paris-Saclay, Paris, France

#### Edited by:

Tim Daniell, James Hutton Institute, United Kingdom

#### Reviewed by:

Xiaoxian Zhang, Rothamsted Research (BBSRC), United Kingdom Paul Hallett, University of Aberdeen, United Kingdom

\*Correspondence:

Xavier Portell<EMAIL_ADDRESS><EMAIL_ADDRESS>
#### Specialty section:

This article was submitted to Terrestrial Microbiology, a section of the journal Frontiers in Microbiology

Received: 28 March 2018 Accepted: 25 June 2018 Published: 27 July 2018

#### Citation:

Portell X, Pot V, Garnier P, Otten W and Baveye PC (2018) Microscale Heterogeneity of the Spatial Distribution of Organic Matter Can Promote Bacterial Biodiversity in Soils: Insights From Computer Simulations. Front. Microbiol. 9:1583. doi: 10.3389/fmicb.2018.01583 There is still no satisfactory understanding of the factors that enable soil microbial populations to be as highly biodiverse as they are. The present article explores in silico the hypothesis that the heterogeneous distribution of soil organic matter, in addition to the spatial connectivity of the soil moisture, might account for the observed microbial biodiversity in soils. A multi-species, individual-based, pore-scale model is developed and parameterized with data from 3 Arthrobacter sp. strains, known to be, respectively, competitive, versatile, and poorly competitive. In the simulations, bacteria of each strain are distributed in a 3D computed tomography (CT) image of a real soil and three water saturation levels (100, 50, and 25%) and spatial heterogeneity levels (high, intermediate, and low) in the distribution of the soil organic matter are considered. High and intermediate heterogeneity levels assume, respectively, an amount of particulate organic matter (POM) distributed in a single (high heterogeneity) or in four (intermediate heterogeneity) randomly placed fragments. POM is hydrolyzed at a constant rate following a first-order kinetic, and continuously delivers dissolved organic carbon (DOC) into the liquid phase, where it is then taken up by bacteria. The low heterogeneity level assumes that the food source is available from the start as DOC. Unlike the relative abundances of the 3 strains, the total bacterial biomass and respiration are similar under the high and intermediate resource heterogeneity schemes. The key result of the simulations is that spatial heterogeneity in the distribution of organic matter influences the maintenance of bacterial biodiversity. The least competing strain, which does not reach noticeable growth for the low and intermediate spatial heterogeneities of resource distribution, can grow appreciably and even become more abundant than the other strains in the absence of direct competition, if the placement of the resource is favorable. For geodesic distances exceeding 5 mm, microbial colonies cannot grow. These conclusions are conditioned by assumptions made in the model, yet they suggest that microscale factors need to be considered to better understand the root causes of the high biodiversity of soils.

Keywords: soil, pore scale, organic matter, resource allocation, bacteria, biodiversity, agent-based modeling

## INTRODUCTION

fmicb-09-01583 July 30, 2018 Time: 16:47 # 2

During the last decade, soils have become increasingly central to a number of crucial debates on issues of great societal concern (e.g., Baveye et al., 2018). Because soils contain a very large stock of carbon, there is a risk that, with rising ambient temperatures associated with global climate change, soils will release vast amounts of greenhouse gases and thereby accelerate change. Biodiversity losses have also emerged as a major concern in many parts of the world. In this context, it is not surprising that in recent years, there has been a significant surge of interest into the biodiversity of soils, and the effect it has on traditional soil functions (Nannipieri et al., 2003).

Many aspects of the biodiversity of soils have proven very difficult to understand. Soils are highly complex media in which a huge number of bacteria, archaea, and fungi live. In a single gram of soil, it is not exceptional to find as many as 1010 bacterial cells and 5 × 104 species (Roesch et al., 2007), with commensurate numbers found for other microorganisms. To the extent that many microorganisms (an estimated 98.5% in the case of bacteria) have never been isolated or characterized, the measurement of soil biodiversity itself raises a number of fundamental questions (e.g., Nannipieri et al., 2003; Baveye et al., 2016a,b, 2018). Functionally, it is not clear at all to what extent this very large diversity of soil microbial populations is crucial and whether it needs to be preserved at all cost. Experimental results are contradictory in this respect. Whereas, e.g., Philippot et al. (2013) show that the loss of biodiversity in soils decreases denitrification activity and nitrogen cycling, the experimental results of Werts et al. (2006) suggest on the contrary that biogeochemical functions of soil such as carbon mineralization and denitrification are not impacted by a reduction of microbial diversity. Powlson et al. (2017) have recently described as an unresolved 60-year old paradox the fact that CHCl3 fumigation, wiping out 90% of the soil microbial population and modifying drastically its diversity, does not appear to have an effect on soil organic carbon (SOC) mineralization in soils that have a pH above 5.5. SOC mineralization continues at the same rate, after fumigant removal, once the initial decomposition flush is over (Powlson et al., 2017).

A similarly high uncertainty surrounds the features of soils that allow such a large microbial diversity to exist in the first place. Some researchers consider that diversity is mainly caused by biotic interactions between cells (Hanson et al., 2012), but experimental observations increasingly suggest that a high biodiversity is associated with soil spatial heterogeneity (Rainey and Travisano, 1998) and is caused by biotic and abiotic interactions taking place in the soil architecture. Yet the exact mechanisms involved remain elusive. The often advocated explanation that the heterogeneous, disconnected distribution of moisture in unsaturated soils causes distinct groups of microorganisms to be physically isolated from each other (Treves et al., 2003; Long and Or, 2009) is appealing, but it does not apply to fungi or filamentous bacteria (Baveye et al., 2016b) and cannot account by itself for the biodiversity of soils that are periodically saturated after rainfall events. At this point, there is no real, satisfactory explanation of how the spatial heterogeneity of soils might foster the biodiversity of their microbial populations.

In this general context, the key objective of the present article is to explore the hypothesis that the heterogeneous distribution of the basic nutrient resources used by bacteria in soils can account to some extent for their diversity. The spatial distribution of organic matter in soils is known to be highly heterogeneous. Incorporation of plant residues by tillage results in patchy distribution at the centimeter scale (e.g., Elyeznasni et al., 2012) while at smaller millimeter scales, heterogeneous distribution of soil organic matter has been visualized by Peth et al. (2014) and Kravchenko et al. (2014). On the basis of these microscale observations, the effect of the heterogeneity of the spatial distribution of soil organic matter and of the connectivity of the aqueous phase on bacterial biodiversity was examined in a series of scenarios using a 3D pore-scale carbon dynamics model. Bacterial cells of three strains of the Arthrobacter sp. including highly competitive-, generalist-, and poorly competitive-strains, were randomly placed within the 3D pore space of a small soil sample (of volume size of 314 mm3 ) imaged at a resolution of 68 µm, suitable to visualize meso- and macro-pores.

### MATERIALS AND METHODS

#### Soil Image

Undisturbed soil cores were sampled in the surface horizon of a cultivated soil, a silty loamy (19% clay, 75% silt, 6% sand) Albeluvisol (Vogel et al., 2015). 3D images of the samples were obtained using an X-ray CT scanner (HMX 225, NIKON metrology, Tring, United Kingdom). A global threshold according to Elyeznasni et al. (2012) was used to obtain binary images in which the voxels of the gray CT image were classified either as soil or void voxels. We selected one sub-image (called G6 in Vogel et al., 2015) of 1003 voxels size out of the set of segmented CT images. The voxel-resolution of the image is 68 µm, so that the pore space explored in this study encompasses most of the structural porosity made of meso- and macro-pores. This image corresponds to a volume size of about 314 mm3 , and it has a porosity of 18.82%. This number is undoubtedly smaller than the actual porosity of the soil, because of the fact that sub-resolution pores are ignored (Baveye et al., 2017).

The localization of the fluid and gas voxels corresponding to a given water saturation index, Sw (the proportion of the pore space filled with water), is calculated using a two-phase two-relaxationtimes (TRT) lattice-Boltzmann model (LBM) as described by Genty and Pot (2013) and Pot et al. (2015). Three levels of water saturation of the CT-visible porosity are assumed in the present work, Sw = 1.00, Sw = 0.50, and Sw = 0.25. After a visual inspection of the 3D distribution of the gas phase in the images, we selected a few of the smallest visible pores containing gas and recalculated from the Young-Laplace law a rough estimate of the matric potential for Sw = 0.25 and Sw = 0.50. The matric potentials estimated in this manner are about -0.6 and -0.3 kPa, respectively. Therefore, even though a water saturation level of 0.25 would suggest that the soil is relatively dry, the fact that this number refers only to the CT-visible pore space means that the scenarios reported in the present contribution correspond to wet conditions.

The image offers a tradeoff between resolution and sample size (constrained by X-ray computed tomography). It is a compromise that presents the advantage of reproducing the millimeter-scale variability of the microbial activity, as reported by Vieublé-Gonod et al. (2006), and of enabling us to work with a soil volume that is large enough for carbon mineralization to be measured in practice.

#### Model Description

fmicb-09-01583 July 30, 2018 Time: 16:47 # 3

The description below of the Ib-LBioS-Comp model follows the overview, design concepts, and details (ODD) protocol (Grimm et al., 2006, 2010), which was especially developed to communicate the features of agent and individual-based models.

#### Purpose

Ib-LBioS-Comp, which stands for Individual-based LBM for biodegradation affected by soil structure and competition, is a pore scale modeling approach developed to study the impact of the soil structure or, more appropriately, architecture (see discussion in Baveye et al., 2018), molecular diffusion, spatial heterogeneity of resource distribution, and competition among bacterial species on the biodegradation dynamics of organic matter in the soil.

#### Entities, State Variables, and Scales

Ib-LBioS-Comp combines a lattice-Boltzmann solute diffusion model and an individual-based biological module describing bacterial activity. The model involves single bacterial cells (biotic agents) of up to three different species or strains, dissolved organic carbon or DOC (abiotic lattice-Boltzmann populations), and particulate organic matter (POM, abiotic agents). Bacterial cells and DOC are distributed in the 3D volume of the soil pore volume and POM is distributed in the 3D volume of the soil solid matrix. Enzymatic hydrolysis of POM is assumed to continuously supply DOC to the liquid phase. Then DOC diffuses through the liquid phase toward the microenvironments where it is taken up by bacteria and used as nutrient source. The diffusion and uptake of oxygen are not accounted for explicitly in the model at the moment and are assumed not to limit microbial activity.

The simulated space is divided into a regular 3D grid made of cubic voxels that can be either solid or filled with a fluid (air or water).

A bacterial cell or individual (Ii) is defined by the variables 5i , identifying its position in the domain, its species ji , its mass mi (mg C), its specific uptake rate υDOC,i (tu−1 ), and its mass at reproduction mR,i (mg C). All masses in Ib-LBioS-Comp are expressed in terms of mass of carbon. Letting P = I(t) denote the number of bacteria at time t, one obtains for the state of the population at time t:

$$Pn = \{I\_i \{ \Pi\_i, j\_i, m\_i, \, \upsilon\_{\text{DOC},i}, m\_{\text{R},i} \} \}\_{i=1,2,\ldots,n(t)} \tag{1}$$

where i is the index of individual bacteria and n(t) the total number of cells at time t.

A POM agent (Al ) is defined by a variable indicating its position in the domain, 5l , and its carbon mass, mPOM,l (mg C). Letting A(t) denote the number of POM agents, the POM population state at time t is:

$$POM\_m = \{A\_l \lbrack \Pi\_l, m\_{POM,l} \rbrack \}\_{l=1,2,\ldots,m(l)} \tag{2}$$

where l is the index of the POM agents and m(t) the total number of POM agents at time t.

The DOC solute is simulated by microscopic lattice-Boltzmann populations, fq, that are microscopic solute entities defined in the Q microscopic directions at each liquid node of the 3D grid. The Q directions are defined by the unit microscopic velocity vectors, −→Cq = {Cqα}q=0,...,Q−1;α=1,...,d where d is the dimension of the grid or lattice. We used the model D3Q7.

The DOC concentration in the liquid phase, CDOC (t) (mg C lu−3 ) can be calculated at each liquid node of the grid as the sum of the fq populations:

$$\mathcal{C}\_{DOC} = \frac{1}{\triangle V\_{\chi yz}} \sum\_{q=0}^{Q-1} f\_q \tag{3}$$

with MVxyz the volume of one voxel expressed in lu3 where lu is the spatial unit of the lattice, in our case determined by the scanning resolution so that 1 lu = 68 µm.

The temporal evolution of the system is divided into equal intervals associated with time steps or units (tu) of a time step length dictated by the lattice-Boltzmann submodel. The temporal extent of the simulations was set to 10 days according to previous simulations made by Vogel et al. (2015) in which exponential growth and decline of biomass were observed within this duration. The time step length is 3.44 s (see Sections "Abiotic Processes" and "Model Parameterization").

#### Process Overview and Scheduling

Global simulation comprises three sections (**Figure 1**): (i) the initialization of the simulated system, (ii) the time step loop, which is repeated until the end of the defined time steps, and (iii) the model output section, where the systemlevel (aggregated) and individual-level (non-aggregated) data are saved in files. Initialization of the system includes: reading of model parameters, initialization of the bacterial agents, and initialization of the LBM parameters and DOC populations. The time step loop includes, chronologically: (ii.i) storage of the simulation state in temporary data structures, (ii.ii) the POM agents actions loop, (ii.iii) the bacterial actions loop (**Figure 2**), and (ii.iv) the lattice-Boltzmann actions. Output files of aggregated and state variables are created from the temporary data structures saved previously.

At each time step, bacterial cells perform the following set of actions: uptake, metabolism, reproduction, and mortality. The order in which bacteria act is changed randomly every time step to avoid privileging always the same first-acting bacteria. At each time step, the existing POM agents undergo hydrolysis to produce DOC. The DOC lattice-Boltzmann populations, fq, are then updated through the following set of actions: collision, propagation, and bounce-back when they encounter a solid or a gas neighbor. This last action is motivated by the premise that DOC occurs only in the water phase.

#### Design Concepts

#### **Emergence**

Bacterial processes (uptake, metabolism, reproduction, mortality) are defined at a single-cell level and the population or system level behavior emerges from the interactions among individuals and between the individuals and the media. The main population-level emerging characteristics are the population density (bacteria present in the media), the population biomass, the DOC taken up by the population, the CO2 produced by the population and the bacterial size distribution. Solute diffusion processes (collision, propagation) are defined at the microscopic level of the Q directions of the lattice, and the solute behavior (diffusion) emerges from the interactions among the solute lattice-Boltzmann populations.

#### **Interaction**

Bacteria are considered to be immobile but they compete directly for space through the maximum carrying capacity of a voxel. Therefore, the presence of other bacterial cells in the local space can directly affect the fate of new-born bacteria. Indirect interactions among individual bacteria arises from competition for the DOC available in the local environment.

#### **Stochasticity**

Randomness is considered when the rules are applied to individuals by using probabilistic distributions to deal with or manage individual events. Random processes or events include the assignment of the position of new-born bacteria in the physical domain near the mother when the grid element of the mother reached maximum occupancy, and the occurrence for cell death. The sequence of actions of the simulated bacteria changes randomly at each time step to avoid privileging one over the others. The model can also introduce further stochasticity when setting the mass of the initial individuals, the individual specific uptake rate, and the mass at reproduction of the individual bacteria using folded normal distributions, but this is not considered in the current study.

#### **Observation**

Global and single-cell outputs are recorded at the beginning of the simulation, at regular intervals during the simulation, as well as at the end of the simulation. Global variables calculated at the scale of the entire domain include: mass of DOC, POM, and CO2 produced in the media, and, for each of the three bacterial species, the number of bacteria, and total bacterial biomass. The state of all the individual bacteria is saved at sampling times. These single-cell data include the position within the domain, species, mass, uptake rate, and mass at reproduction of the individuals. The carbon mass and position of all the POM spots (abiotic agents) are also saved at sampling times. The DOC concentration of the liquid voxels holding at least one bacterium is also recorded at sampling times. The final DOC concentration of all the liquid grid cells of the domain is recorded at the end of the simulation.

#### Initialization

The specific uptake rate (vDOC,i), and the reproduction mass (mR,i) of the initial individuals (i = 4, ..., NB0) are assumed to be specific for each jth species. For the individuals of each species j, these properties are set using the model parameters v j DOC and m j t0 , respectively, for the uptake rate and the reproduction mass. No intraspecific variability is considered in the present study. Similarly, the initial mass of the individuals starting the simulations (mi) is initialized according to the model parameters m j t0 .

Since it is generally assumed that bacteria in soil microenvironments tend to be sorbed to, or be at least very near, solid surfaces, the model assumes that bacteria can be located only in liquid voxels having at least one solid neighbor. What defines a neighbor here is the particular lattice-Boltzmann connectivity that is adopted in the calculations (D3Q7 in this case). The initial NB0 bacterial cells are randomly distributed among a number of bacterial spots (NSP0T) that, in turn, are randomly chosen, with replacement, from the liquid voxels having one or more solid neighbors.

The POM agents are situated in the solid matrix of the soil. The initial POM agents are randomly distributed among solid voxels that have at least one liquid neighbor.

An initial amount of dissolved organic carbon, DOC0, is distributed homogeneously among the liquid voxels of the image.

#### Input Data

The model uses soil structural data as described in see Section Soil Image.

#### Biological Processes

Several separate submodels describe quantitatively the uptake, metabolism, reproduction, and mortality, respectively, of individual bacteria.

In the Uptake submodel, the uptake (Ui) of carbon substrate by bacterium i, belonging to the speciesj = ji , is given by the equation depending on the mass mi (t) of the bacterium

$$U\_i(t) = \frac{\nu\_{DOC,i} \ C\_{DOC}^{(t)}}{C\_{DOC}^{(t)} + k\_{DOC}^{j}} m\_i(t) \tag{4}$$

where vDOC,i is the specific uptake rate of the ith bacterium (tu−1 ), and the parameter k j DOC is the half saturation constant (mg C lu−3 ) of the jth species.

In the Metabolism submodel, the mass of carbon taken up is used by the cell to create new biomass. Since catabolic reactions need energy, due to the respiration process, a fraction of the carbon that is taken up is released again to the media in the form of CO2 emissions. Accordingly, the growth of the bacterial cell is modeled using the following equation:

$$m\_i(t+1) = m\_i(t) + U\_i(t) - k\_r^j m\_i(t) \tag{5}$$

where k j r is the respiration rate (tu−1 ) of the species j. Equations (4) and (5) assume that growth respiration (traditionally calculated as a function of substrate during uptake) and maintenance respiration (proportional to the biomass) are not distinguished.

The Reproduction submodel adopts a simple bipartition condition (Banitz et al., 2015) according to which the bacterial cell has to attain a specific individual reproduction mass before dividing. Every time step, the mass of a bacterium is compared to mR,i (mg C), the reproduction mass of the ith individual. If mi(t + 1) > mR,i , the mass of the bacterium is halved, and simultaneously a daughter cell of the same mass is created. If the number of bacteria occupying the voxel of the mother cell is less than NVOX, the maximum carrying capacity of a voxel, the cell is created in the current voxel. Otherwise, the simulator chooses randomly a voxel that has not attained the maximum carrying capacity. The searching algorithm looks progressively to neighbors situated at increasing distances (in voxels) from the mother's voxel of origin, until all the tridimensional space is inspected. If all the voxels reach the maximum carrying capacity, the simulation stops. The daughter cell remains active but does not act until the next time step is reached. The specific uptake rate of the new-born individual (vDOC,i) and its mass at reproduction (mR,i) are inherited from the mother.

Finally, the Mortality submodel accounts for bacterial cell death derived from internal and external events (e.g., predation by other organisms). The cell cannot survive anymore due to internal events when the cell size decreases below the minimal cell size characteristic of its species j, m j MIN which can be attained due to a starvation process. Cell death due to external events is accounted by a probability, p j M(dimensionless), independent of the cell state. At every time step, the submodel compares rp with p j M, where rp is a random realization coming from a uniform distribution between 0 and 1. If rp > p j Mthe individual bacterium dies. The cell carbon lyses and creates new DOC in the current voxel.

#### Abiotic Processes

The main abiotic processes simulated by the model are the hydrolysis of POM and the diffusion of DOC in the 3D pore space. No convective movement of DOC was considered in the model. POM agents release DOC, decreasing as a result the mass of the POM agent. The model assumes only one homogeneous fraction of POM with a unique hydrolysis rate. The hydrolysis process is modeled assuming a first order kinetics of constant rate, kPOM. The underlying hypothesis is that exo-enzymes are ubiquitous in soil (Folse and Allison, 2012). Nannipieri et al. (2003) reported that newly produced exo-enzymes by bacterial cells are short-lived molecules because, for instance, proteases can degrade them. Thus, the ubiquitous enzymes are probably those physically protected though their adsorption to clay particles or humic molecules (Burns, 1982). Burns (1982) considers it a likely scenario that these enzymes become active when a POM fragment comes into contact with them. Then, the DOC released by the agent is distributed equally among the liquid voxels neighboring the solid voxels containing the POM agent.

We implemented the TRT lattice-Boltzmann approach of Ginzburg (2005). The evolution equation of the DOC microscopic entities at the liquid nodes (grid cell with k = lq), −−→Vxyz from time t to t+ 1 is given by:

$$\begin{aligned} f\_q(\overrightarrow{V\_{xyz}} + \overrightarrow{c\_q}, t+1) &- f\_q(\overrightarrow{V\_{xyz}}, t) \\ &= \lambda\_c[\overrightarrow{f\_q}^+(\overrightarrow{V\_{xyz}}, t) - \overrightarrow{e\_q}^+(\overrightarrow{V\_{xyz}}, t)] + \lambda\_o[\overrightarrow{f\_q}^-(\overrightarrow{V\_{xyz}}, t) \\ &- e\_q^-(\overrightarrow{V\_{xyz}}, t)] + \mathcal{S}\_q \end{aligned} \tag{6}$$

in which the collision and propagation steps are described, respectively, by the two first terms of right hand side and left hand side of (7), respectively. The sink/source term of DOC, Sq, is calculated from the hydrolysis and bacterial processes. In the TRT scheme, the microscopic entities fq are decomposed into symmetric, f + q and antisymmetric components, f − q along their opposite velocities −→cq = − −→c q (Ginzburg, 2005). During the collision step, the relaxation of moments resulting from the entities' distribution at time t toward an equilibrium state eq = e + q + e − q governs the reorganization of the entities. The relaxation parameter λe is a free parameter and the relaxation parameter λo is related to the molecular diffusion coefficient, D LBM m (lu2 tu−1 ) along:

$$D\_m^{LBM} = \frac{-1}{3} \left( \frac{1}{2} + \frac{1}{\lambda o} \right) \tag{7}$$

Both parameters must be comprised between -2 and 0 for stability. The rescaling of lattice Boltzmann time units (tu) in real time units [T] is made through the relation:

$$T\_R = \frac{D\_m^{LBM} L\_{R^2}}{D\_m^R L\_{LBM}^2} T\_{LBM} \tag{8}$$

where TLBM and LLBM are the space and time in lattice units (respectively, tu and lu) and TR and LR are their corresponding time and space units in real units [respectively (T) and (L)].

#### Model Parameterization

Typical parameters for the three different strains 3R, 7R, and 9R of Arthrobacter sp. (see **Table 1**) were taken from the literature. The specific uptake rate, ν j DOC, the half saturation constant of the uptake rate, k j DOC, and the respiration rate, k j r , of the three species were directly taken from Monga et al. (2014), while the population mortality rate, provided by the same authors, was reinterpreted as probability, P j m, dependent on the duration

Symbol Definition Unit Strain j = 3R j = 9R j = 7R BACTERIAL PARAMETERS ν j DOC Maximal uptake rate d−1 17 9.6 8.0 k j DOC Half saturation constant mg C cm−3 water 5.0 × 10−4 1.0 × 10−3 1.4 × 10−4 k j r Respiration rate d−1 0.2 0.2 0.3 m j R Reproduction mass mg C 1.32 × 10−10 1.32 × 10−10 1.32 × 10−10 P j m Mortality probability – 1.5 0.5 1.0 m j MIN Min bacterial mass mg C 0.1 mR 0.1 mR 0.1 mR m j t0 Initial mass of the bacterial cells mg C 5.39 × 10−11 5.39 × 10−11 5.39 × 10−11 N j B0 Initial bacterial number Cells 230 230 230 Unit Value BIOTIC PARAMETERS NVOX Voxel Max. carrying capacity Cells 751,423 ABIOTIC PARAMETERS kPOM POM decay rate d−1 0.25 DM DOC mol. diff. coeff. cm2. s −1 6.73 × 10−6

TABLE 1 | Model parameters values used in the simulations. See text for an explanation of the computations and the bibliographic references used.

of the time step. These strains have different growth patterns, with 3R expected to be the fastest growing strain and strain 9R the least competitive one due to its highest value of the half saturation constant of the uptake rate. Strain 7R is supposed to be representative of a more generalist strain.

The maximum carrying capacity of a lattice-Boltzmann node, NVOX, was calculated from the volume of a single image voxel (683 µm3 ) and the mean cell volume of a bacterial cell. The mean volume of an Arthrobacter cell was calculated to be 0.418 µmł according to data from Erlebach et al. (2000), assuming a spherical shape for the bacterial cell. We used this mean volume for the three strains of Arthrobacter sp. The mean reproduction diameter (i.e., the diameter attained by the cell before division) was also estimated from Arthrobacter cell size distributions (Erlebach et al., 2000) and assumed to be in the range 1.25 ± 0.15 µm, which includes the biggest diameters of the size distribution measured with a Coulter counter. The central value of 1.25 µm has been used in the present study.

Then, the mean carbon content of a single cell (m j t0 , **Table 1**) and the value for the reproduction mass, m j R , were calculated from the mean cell volume and the mean reproduction volume calculated earlier, assuming a density of 1.1 g/cm3 , a ratio of dry to wet cell weight of 0.25, and a carbon content of 0.47 g C per gram of dry cells (Gras et al., 2011).

The value of the decay rate of the POM agents, kPOM, was set to 0.25 day−1 as reported by Iqbal et al. (2014) for the decomposition rate of maize (Zea mays) stem residues. These authors found "optimal decomposition conditions similar to those obtained with ground material" for fragments of POM of 0.02 cm length. Assuming a density of POM of 0.12 g cm−3 (Iqbal et al., 2013) and a volume of POM residue of about 0.02 cm × 0.02 cm × 0.01 cm, we calculated an initial POM mass of carbon, POM0, of 1.92 10−4 mg C. We translated this fragment of POM into four fragments of parallelepiped shape (1 × 1 × 3 voxels), located at the solid/liquid interface (**Figure 3**). When the POM hydrolyses, the DOC produced is included in the neighboring fluid site.

The molecular diffusion coefficient in lattice-Boltzmann units, D LBM m , is fixed to 0.5 lu2 tu−1 (Vogel et al., 2015, 2018). Since the DOC molecular diffusion coefficient, D R m, is 6.73 10−6 cm2 s −1 (Weast et al., 1986) and 1 lu = 68 µm, the rescaling equation (8) gives 1 tu = 3.44 s.

#### Simulation Scenarios

The scenarios were designed to investigate the effect of the local micro-environments of bacteria on the strains abundance. For all scenarios we randomly placed 230 bacteria of each strain in the medium which resulted in 690 bacterial spots. In one

FIGURE 3 | 2D view of the POM initialization scheme used in the scenarios. In the figure, the POM (red), the DOC (yellow), the soil solid matrix (black), and the pore space (white) are depicted. In (a), POM disaggregated, four parallelepiped POM fragments of 1 × 1 × 3 image voxels, were assumed to be present and connected to the pore space through a single voxel. In (b), POM aggregated, a single 3D POM fragment of 4 × 4 × 3 was assumed to be present and connected to the pore pace through 4 of its voxels.

particular scenario (S4) the three strains systematically co-exist in the same bacterial spot, so that only 230 bacterial spots were generated. The local micro-environments of these bacterial spots were modified by introducing heterogeneity in the placement of the resource (POM and DOC) in the medium. The water content level was also modified. **Table 2** summarizes the characteristics of the different scenarios. Scenarios S1, S2, and S3 test the effect of the spatial distribution of organic matter on the global organic matter degradation and strain abundance. Scenario S4 tests the effect of the direct interspecific bacterial competition on strain abundance, whereas scenarios S5 and S6 are designed to test the effect of the water saturation level on organic matter degradation and strain abundance. Details of these scenarios are given below.

#### Scenario S1

The initial 690 bacteria were distributed among 690 randomly selected liquid voxels neighboring the soil solid matrix. Four POM fragments were randomly distributed in the medium (**Figure 3a**). Ten replicated simulations were performed with the position of POM fragments controlled by a random seed. The positions of the 690 bacterial spots were left unchanged for the ten replicated simulations. The water saturation level, Sw, was 0.50.

#### Scenario S2

The four fragments of POM were gathered in one fragment made of 2 × 2 × 3 voxels with the base 2 × 2 voxels being contiguous solid sites neighboring 2 × 2 fluid sites (**Figure 3b**). Bacteria were located in the same 690 positions as for scenario S1 and the same water saturation level, Sw = 0.50, was adopted. Ten replicated simulations were again performed with the position of POM fragments controlled by a random seed Comparison of scenario 1 and 2 made it possible to assess the effect of the degree of spatial heterogeneity of POM.

#### Scenario S3

We assumed that all the carbon that can, potentially, be hydrolyzed and released to the liquid phase of the soil in the scenarios S1 and S2, was already homogeneously distributed in the liquid phase of the medium at the beginning of the simulations as a DOC. A water saturation index of Sw = 0.50 was also adopted. In ten replicated simulations, a random seed

controlled the position of 690 bacterial spots. This resulted in 9 extra configurations of the 690 bacterial positions tested in S1 and S2. Comparison of S3 with S2 and S1 allowed us to evaluate the impact of homogenously- vs. heterogeneously distributed C within the soil.

#### Scenario S4

This scenario was aimed at the effect of direct interspecific competition on strain abundance. Two simulations (identified as S4a and S4b) involved 3 bacteria, one of each strain, in selected 230 bacterial spots. In S4a, we took one particular repetition of scenario S2 in which the three strains had a noticeable growth (repetition S2r2) and we classified the 690 spots according to the amount of biomass growth of the colony in a descending order. The first 230 bacterial spots were selected and used to place the initial bacteria. In S4b, we took the repetition S2r2 but we just selected the 230 bacterial positions occupied by the less competitive strain (9R). In each of these spots, we placed initially 3 bacteria, one of each strain.

#### Scenarios S5 and S6

These scenarios are identical to scenario S2 except for the water saturation level that was fixed to 1.00 (S5) and 0.25 (S6). Because the positions of the 690 bacterial spots are left unchanged, in scenario S6 there were 165 bacterial spots that were found to be in the gas phase, and thus did not grow. In the 525 spots still placed in water filled grid cells, the three strains were found to be equally distributed as 178 cells of strain 3R, 172 cells of strain 9R and 175 cells of strain 7R.

#### RESULTS AND DISCUSSION

#### Effect of Spatial Distribution of Organic Matter on Global Organic Matter Degradation and Strain Abundance

Simulation scenarios S1 and S2 assume that the soil organic matter is found in a number of POM fragments that are distributed (S1) or aggregated (S2). In the proposed scenarios, the hydrolysis rate of POM is set to a constant value, so that