The role of mathematical modelling in understanding prokaryotic predation

With increasing levels of antimicrobial resistance impacting both human and animal health, novel means of treating resistant infections are urgently needed. Bacteriophages and predatory bacteria such as Bdellovibrio bacteriovorus have been proposed as suitable candidates for this role. Microbes also play a key environmental role as producers or recyclers of nutrients such as carbon and nitrogen, and predators have the capacity to be keystone species within microbial communities. To date, many studies have looked at the mechanisms of action of prokaryotic predators, their safety in in vivo models and their role and effectiveness under specific conditions. Mathematical models however allow researchers to investigate a wider range of scenarios, including aspects of predation that would be difficult, expensive, or time-consuming to investigate experimentally. We review here a history of modelling in prokaryote predation, from simple Lotka-Volterra models, through increasing levels of complexity, including multiple prey and predator species, and environmental and spatial factors. We consider how models have helped address questions around the mechanisms of action of predators and have allowed researchers to make predictions of the dynamics of predator-prey systems. We examine what models can tell us about qualitative and quantitative commonalities or differences between bacterial predators and bacteriophage or protists. We also highlight how models can address real-world situations such as the likely effectiveness of predators in removing prey species and their potential effects in shaping ecosystems. Finally, we look at research questions that are still to be addressed where models could be of benefit.