Transients and tradeoffs of phenotypic switching in a fluctuating limited environment

Phenotypic variability in a microorganism population is thought to be advantageous in fluctuating environments, however much remains unknown about the precise conditions for this advantage to hold. In particular competition for a growth-limiting resource and the dynamics of that resource in the environment modify the tradeoff between different effects of variability. Here we investigate theoretically a model system for variable populations under competition for a flowing resource that governs growth (chemostat model) and changes with time. This environment generally induces density-dependent selection among competing sub-populations. We characterize quantitatively the transient dynamics in this system, and find that equilibration between total population density and environment can occur separately and with a distinct timescale from equilibration between competing sub-populations. We analyze quantitatively the two opposing effects of heterogeneity-transient response to change, and fitness at equilibrium-and find the optimal strategy in a fluctuating environment. We characterize the phase diagram of the system in term of its optimal strategy and find it to be strongly dependent on the typical timescale of the environment and weakly dependent on the internal parameters of the population.