Abstract
Mathematical modelling of bacterial communities has capital importance in ecology, as it provides of means to characterize such comunities, identify key species and establish in silico predictions. In reference to human microbiota, a proper model would allow, not only to determine certain diseases' e_ect on microbiota composition, but also to predict the impact of perturbations such as antibiotics or diet and reconduct an unhealthy microbiota to a healthy one. The aim of this work is to characterize the e_ect of the environment (host) on the viability of bacterial communities. Two types of models are being used by the scienti_c community to include the environment in the study of ecosystems: traditionally, the environment is assumed to be static, but lately the study of a changing environment is growing. In this work two models will be used: one based on Lotka-Volterra generalized model, and a second one based on evolutionary games theory. Communities of two and three species will be considered. This work also proposes the use of the term viability to refer to the equilibrium point of an ecosystem. This term includes both the considerations of feasibility and stability, given that, in order to have a biological meaning, an equilibrium point is required to meet both conditions. Following the Lotka-Volterra approach, random 2x2 and 3x3 matrices were modi_ed by the environment, having their viability studied before and after. We studied the parameter space of matrices that were made viable, as well as that of their corresponding environments. Our results show that an environment that promotes viability strengthens intraspeci_c competition, that is to say, reduces the species' growth rate, as well as reduces interspeci_c interactions, whether introducing spatial structure or functional redundancies. On the other hand, the evolutionary game model was based on that proposed by Tilman et al (2020), in which two payo_ matrices are de_ned for minimum and maximum values of a resource, which is produced by the host and consumed by the community. We studied the viability of the bacterial community both without and within the environment, as well as the games played in each case. We found that the resource is able to turn into viable all kind of games, as well as allows coordination games in the equilibrium to be viable. The resource in the equilibrium will lean towards the game that provides a larger viability, which are snowdrift followed by coordination. Moreover, we found that this model enables the viability of species coexistence with a much larger frequency, suggesting that this evolutionary approach may be a more accurate way to model the relationship between a bacterial community and its environment. Our results show that the co-evolution of environment and community results in a more stabilising environment.
