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Antimicrobial resistance to drugs (AMR), a global threat to human and animal health, is often regarded as resulting from a cooperative behaviour. Moreover, microbes generally evolve in volatile environments that, together with demographic fluctuations (birth and death events), drastically alter population size and strain survival. 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 …