The Evolution of Antibiotic Production in a Spatial Model of Bacterial Competition

Abstract

Bacteria occupy a wide range of niches with many different types coexisting. They compete directly, with some capable of producing antibiotics that kill other members of the niche. Despite this, long term survival of these ecosystems is possible. Here, we consider a lattice-based three-component system with antibiotic producers, non-producers (or cheaters), and susceptible cells competing. In our system, there is a metabolic cost tied to production rate, resulting in a decrease in growth rate for the producers. Non-producers behave as cheaters that gain the benefit of an antibiotic without the cost of producing it themselves. The susceptible cells are a faster growing different species. The model behaves in a fashion similar to the game “rock-paper-scissors", because producers beat susceptible cells, non-producers beat producers, and susceptible cells beat non-producers. We consider two spatial lattice models, one in which there is a nearest neighbour interaction between cells, and one in which the long-range diffusion of the antibiotic is explicitly included. We consider the parameter space in which the three cell types can coexist (taking into account cost and production rate), and determine the regions in which production rate is too high or too low to allow coexistence. We determine that antibiotic producers will evolve to an optimal production rate and that low-rate producers can outcompete complete cheaters (non-producers). We finally illustrate that the introduction of a fourth “resistant” cell type allows the system to survive with four members for some parameters. In other cases, addition of the resistant cells causes the extinction of the producers, which eventually favours the susceptible cells.