Fig. 1. Logic of the individual-based model.

A Possible genotypes and evolutionary relationships among them emerging from reductive evolution when starting with an autonomous genotype that performs three essential public functions. Note that in this three-function model, some genotypes, i.e., Two-function loss genotypes and cheaters, might evolve from different mother genotypes. B Interaction patterns that could possibly be established in the spatially structured communities. C Schematic of the individual-based simulations. A 100 × 100 array initialization with all autonomous phenotypic individuals (left) was conducted with a long-term stepwise iteration to investigate if diverse interaction patterns could form (right). At each time step, calculations were done from the level of individual grids (top) to whole lattice (bottom). Within each grid box, Monod equation modified by basic assumptions of the Black Queen Hypothesis was used to calculate the microbial growth, while minimum and maximum thresholds of biomass were defined to decide the division and death of individuals (top middle). Microbial individuals were allowed to randomly mutate to lose functions (top middle). Classical discretization of the diffusion equation gave local rules for updating the concentrations of public goods and nutrients in each box (middle). State changes at the individual level lead to the evolutionary dynamics of the communities, which may give rise to the formation of diverse interaction patterns (bottom).