Authors: Lluís Hernández-Navarro, Matthew Asker, Mauro Mobilia
Abstract: Antimicrobial resistance to drugs (AMR), a global threat to human and animal health, is often regarded as resulting from a cooperative behaviour, leading to the coexistence of drug-resistant and drug-sensitive cells in large communities and static environments. However, microbial populations generally evolve in volatile environments, yielding sudden changes in the available amount of nutrients and toxins. These, together with demographic fluctuations (birth and death events), have been recognised to drastically alter the population size and strain coexistence, as well as the ability of one strain to fixate and take over the entire population. Motivated by the need to better understand the evolution of AMR, we study a population of time-varying size consisting of two competing strains, one drug-resistant and one drug-sensitive, subject to demographic and environmental variability. This is modelled by a binary carrying capacity randomly switching between mild and harsh environmental conditions, and driving the fluctuating volume (total amount of nutrients and antimicrobials at fixed concentration), and thus the size of the community (number of resistant and sensitive cells). We assume that AMR is a shared public good when the concentration of resistant cells exceeds a fixed “concentration cooperation threshold”, above which the sensitive strain has a growth advantage, whereas resistant cells dominate below it. Using computational means, and devising an analytical treatment (built on suitable quenched and annealed averaging procedures), we fully characterise the influence of fluctuations on the eco-evolutionary dynamics of AMR, and notably obtain specific strain fixation and long-lasting coexistence probabilities as a function of the environmental variation rate and cooperation threshold.