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. One of the likely environment fluctuations happens in nature is the repeated cycle of substrate-rich conditions and starvation, called  "feast-famine cycle". It is not trivial how bacteria can cope with the feast-famine cycle and evolve under such situation, since in the feast period faster growth is beneficial in competition, but faster growth will shorten the feast period. Furthermore, in the famine period  the tolerance to the starvation is needed, which may be negatively correlate with the faster growth. We here study possible outcomes of population dynamics and evolution under the feast-famine cycle by a simple stochastic model. 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. By allowing the model bacteria to evolve growth rate in the feast period with a trade-off with the death rate in the famine period , the bacterial population tends to increase the growth rate and the death rate , even though that tends to decrease the total population size. Under a certain condition, bacterial population eventually go extinct as evolutionary consequence .
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. One of the likely environmental fluctuations that happen in nature is the repeated cycle of substrate-rich conditions and starvation, called the "feast-famine cycle". It is not trivial how bacteria can cope with the feast-famine cycle and evolve under such a situation since in the feast period faster growth is beneficial in competition, but faster growth will shorten the feast period. Furthermore, in the famine period , the tolerance to the starvation is needed, which may be negatively correlated with faster growth. We here study possible outcomes of population dynamics and evolution under the feast-famine cycle by a simple stochastic model. In the model, the feast period is led by a stochastic substrate addition event, while the famine period is evoked because bacteria use the supplied substrate. By allowing the model bacteria to evolve growth rate in the feast period with a trade-off with the growth yield and the death rate , the bacterial population tends to increase the growth rate by changing the counterpart of the trade-off , even though that tends to decrease the total population size. Analysis showed that, under the repeated feast-famine cycles, the ratio between the growth rate and the death rate becomes the effective fitness of the population. Hence, when there is a trade-off between the growth and the death rate, the functional form of the trade-off determines if the bacterial population eventually go extinct . We then show that the increase of the added substrate in the feast period can drive the extinction faster .
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environment fluctuations happens
environmental fluctuations that happen
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the
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situation,
a situation
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,
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correlate with the
correlated with
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(substrate-rich)
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(starvation)
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death rate in the famine period
growth yield and the death rate
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and the death rate
by changing the counterpart of the trade-off
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Under a certain condition,
Analysis showed that, under the repeated feast-famine cycles, the ratio between the growth rate and the death rate becomes the effective fitness of the population. Hence, when there is a trade-off between the growth and the death rate, the functional form of the trade-off determines if the
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as evolutionary consequence
. We then show that the increase of the added substrate in the feast period can drive the extinction faster