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Antimicrobial resistance to drugs (AMR), a global threat to human and animalhealth, is often regarded as resulting from a cooperative behaviour, leading tothe coexistence of drug-resistant and drug-sensitive cells in large communitiesand static environments. However, microbial populations generally evolve involatile environments, yielding sudden changes in the available amount ofnutrients and toxins. These, together with demographic fluctuations (birth anddeath events), have been recognised to drastically alter the population sizeand strain coexistence, as well as the ability of one strain to fixate and takeover the entire population. Motivated by the need to better understand theevolution of AMR, we study a population of time-varying size consisting of twocompeting strains, one drug-resistant and one drug-sensitive, subject todemographic and environmental variability. This is modelled by a binarycarrying capacity randomly switching between mild and harsh environmentalconditions, and driving the fluctuating volume (total amount of nutrients andantimicrobials at fixed concentration), and thus the size of the community(number of resistant and sensitive cells). We assume that AMR is a sharedpublic good when the concentration of resistant cells exceeds a fixed"concentration cooperation threshold", above which the sensitive strain has agrowth advantage, whereas resistant cells dominate below it. Usingcomputational means, and devising an analytical treatment (built on suitablequenched and annealed averaging procedures), we fully characterise theinfluence of fluctuations on the eco-evolutionary dynamics of AMR, and notablyobtain specific strain fixation and long-lasting coexistence probabilities as afunction of the environmental variation rate and cooperation threshold.

Eco-evolutionary dynamics of cooperative antimicrobial resistance in a population of fluctuating volume and size