### Definition of Antagonistic Interaction

The computer modelling framework used in this work has proven to be very useful in studying the spatial and temporal behaviour of various biological phenomena (Ermentrout and Edelstein-Keshet, 1993; Alber et al., 2003; Rohde, 2005). Therefore, we decided to use it to test the hypothesis that macroscopic community spots can occur as a result of microscopic individual interaction in a homogeneous environment. Our results not only confirm the feasibility of such a hypothesis, but also show that these patches allow bacteria to minimize conflicts while preserving biodiversity. To test how system dynamics depend on the architecture of the antagonism interaction network, we constructed alternative antagonism matrices (and used them to repeat the analysis of system dynamics) that follow two different strategies: Microbial ecosystems have proven to be excellent frameworks for understanding ecological systems (Prosser et al., 2007). New ecological theories have emerged from microbial ecology because of its simplicity, controllability, reproducibility and experimentally required time (Jessup et al., 2004). Remarkably, much of this progress has been achieved through simplified theoretical models (Momeni et al., 2011). Most of these models take into account the interaction of only a few microbial populations. This is an advantage because simple models can be more easily studied both numerically and analytically, but also a limitation because such models oversimplify biological reality. Today, thanks to the rapid increase in computing power, it is possible to study the dynamics of larger groups of interacting populations (Costello et al., 2012). On the other hand, it should be emphasized that the rules underlying the calculation algorithm implemented are associated with bacteria with low motility that grow in a homogeneous surface and interact through pair-local interactions. These limits are consistent with the environmental conditions observed in Cuatro Cienegas ponds (Johannesson et al., 2004), where consistent oligotrophic conditions have allowed a wide variety of bacteria to exploit all components of surrounding environments (Escalante et al., 2008; Cerritos et al., 2011) and compete with direct neighbours (Pérez-Gutiérrez et al., 2013; Aguirre-von Wobeser et al., 2014). However, we wondered to what extent low-motility bacteria are a necessary prerequisite for the conservation of biological diversity. To test this, we repeated our simulations, but included a periodic and random mixing of grid cells.

Since we have observed, without exception, that all susceptible strains disappear, we conclude that a slowly changing environment is essential for biodiversity conservation when highly antagonistic, neutral and highly sensitive strains share the ecosystem. In summary, the interaction network architecture plays a very important role in creating the community patch structure. In particular, the trait that seems essential seems to be that bacterial strains can be divided into three distinct classes: aggressive (highly antagonistic and resistant to other strains), neutral (barely antagonistic and resistant to aggressive strains) and sensitive (non-antagonistic and sensitive to aggressive strains). In 2013, Pérez-Gutiérrez et al. (2013) we hypothesized that microscopic microbial antagonist interactions may be responsible for the formation of bacterial communities at the macroscopic level, and that this may be sufficient to explain the observations listed above. The present work aims to prove the feasibility of such a hypothesis from the point of view of mathematical modelling. To this end, we decided to model the pond as a square grid, each of whose cells represents a small area that can be colonized by at most one bacterial strain. The dynamics of grid cells are then modeled as a set of rules derived from the antagonism matrix experimentally determined in Pérez-Gutiérrez et al.

(2013). We chose to apply this modelling strategy because it is appropriate given the available experimental data and because it has been used to demonstrate how local interactions can lead to complex global models as observed in natural systems (Gardner, 1970; Hogeweg, 1988; Iwasa et al., 1998; Sarkar, 2000; Wootton, 2001; Wolfram, 2002; German and Dormann, 2005). To our knowledge, this is the first study to address such a problem with an antagonistic network involving a large number of interacting strains. When we repeated the simulations with experimental interaction matrices, we were able to retrieve all the results described above with and without mixing. Nevertheless, simulations with random interaction matrices yielded completely different results. Community spots can still be observed in simulations without mixing, but the final size of the bacterial population is less dispersed than in simulations performed with experimentally obtained or experimental antagonism matrices. In addition, most bacterial strains disappear in brewing simulations and no correlation between AI and stationary population size is observed (see Additional Material). In this work, we use the interaction network of a set of 78 bacterial strains isolated and studied by Pérez-Gutiérrez et al.

(2013). The strains of this set were isolated from 5 different samples taken from the surface sediments of the Churince Pond in Cuatro Cienegas, Mexico. Since the insulation methodology consisted of exposing the samples to thermal shock, all isolated strains were found to be thermostable and most of them belong to the genus Bacillus. The 78 × 78 pairs of bacterial strains were grown in petri dishes to test antagonistic interactions. The resulting antagonism matrix is reported in Pérez-Gutiérrez et al. (2013) and reproduced in Figure 1.1. In this figure, bacterial strains are organized in descending order according to their aggressiveness index (number of other strains antagonistic by a particular strain, minus the number of other strains that contradict it). The identification numbers given to all strains in this work, the labels used by Pérez-Gutiérrez et al. (2013) and the corresponding aggressiveness indices are presented in Table 11. To answer the question of whether the results discussed in the previous subsections depend on the architecture of the antagonist interaction network (determined by the antagonism matrix), we generated random and experimental interaction matrices (see section 2). Experimental-type interaction matrices have the same number of antagonist strains at high, medium, and low levels, and the distribution of antagonism and received antagonism compounds exerted is very similar to that of the experimentally obtained matrix.

On the other hand, random antagonism matrices were constructed by connecting pairs of randomly selected bacterial strains via antagonism interactions (avoidance of self-antagonism). The number of antagonism compounds in random matrices obtained experimentally is always the same. Experiments with different combinations show that binary mixtures of phenols can lead to a synergistic antioxidant effect or an antagonistic effect. [7] Figure 22 shows the results for a single simulation. We performed several simulations and obtained equivalent results in all cases. After a few iteration steps, a spatial arrangement emerges from the bacterial communities in the patches extends over the grid, and finally a steady state is reached in which the patches no longer change (see Figure 2B).2B). We note that the formation of plots coincides with the fact that different strains were isolated from different samples (Pérez-Gutiérrez et al., 2013), despite the homogeneity of the habitat. In addition, we can see in this particular simulation, but it is a consistent observation that the spots of susceptible strains are always surrounded by spots of other strains and protected from the most aggressive strains, which are resistant to both aggressive bacteria and not antagonistic to sensitive bacteria. This result suggests a survival mechanism for low-antagonistic and sensitive bacteria, but also provides a plausible explanation for the observation that antagonistic interactions within a sampling site are, on average, rarer than interactions between sites (Pérez-Gutiérrez et al., 2013). Various biotic interactions have been described experimentally in nature, and others have been hypothetically described from mathematical modelling results (Evans et al., 2013). At the microbial level, an exceptional range of interaction mechanisms have been observed (Prasad et al., 2011) that promote competition rather than cooperation (Foster and Bell, 2012). Antagonistic interactions (also known as interference competition) were studied by Czárán et al.