  Antimicrobial resistance to drugs (AMR), a global threat to human and animal
health, is often regarded as resulting from 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 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. We find
that microbial strains tend to coexistence, but demographic fluctuations
eventually lead to the extinction of resistant or sensitive cells for small or
large values of the concentration cooperation threshold, respectively. This
also holds for dynamic environments, whose specific properties determine the
extinction timescale.
