  Bacterial populations in natural conditions are expected to experience
stochastic environmental fluctuations, and in addition, environments are
affected by bacterial activities since they consume substrates and excrete
various chemicals. We here study possible outcomes of population dynamics and
evolution under the repeated cycle of substrate-rich conditions and starvation,
called the "feast-famine cycle", by a simple stochastic model with the
trade-off relationship between the growth rate and the growth yield or the
death rate. In the model, the feast (substrate-rich) period is led by a
stochastic substrate addition event, while the famine (starvation) period is
evoked because bacteria use the supplied substrate. Under the repeated
feast-famine cycle, the bacterial population tends to increase the growth rate,
even though that tends to decrease the total population size due to the
trade-off. Analysis of the model shows that the ratio between the growth rate
and the death rate becomes the effective fitness of the population. Hence, the
functional form of the trade-off between the growth and death rate determines
if the bacterial population eventually goes extinct as an evolutionary
consequence. We then show that the increase of the added substrate in the feast
period can drive the extinction faster. Overall, the model sheds light on
non-trivial possible outcomes under repeated feast-famine cycles.
