Does dormancy increase fitness of bacterial populations in time-varying environments?

*(English)*Zbl 1142.92045Summary: A simple family of models of a bacterial population in a time varying environment in which cells can transit between dormant and active states is constructed. It consists of a linear system of ordinary differential equations for active and dormant cells with time-dependent coefficients reflecting an environment which may be periodic or random, with alternate periods of low and high resource levels. The focus is on computing/estimating the dominant Lyapunov exponent, the fitness, and determining its dependence on various parameters and the two strategies, responsive and stochastic, by which organisms switch between dormant and active states. A responsive switcher responds to good and bad times by making timely and appropriate transitions while a stochastic switcher switches continuously without regard to the environmental state.

The fitness of a responsive switcher is examined and compared with the fitness of a stochastic switcher, and with the fitness of a dormancy-incapable organism. Analytical methods show that both switching strategists have higher fitness than a dormancy-incapable organism when good times are rare and that a responsive switcher has higher fitness than a stochastic switcher when good times are either rare or common. Numerical calculations show that stochastic switchers can be most fit when good times are neither too rare or too common.

The fitness of a responsive switcher is examined and compared with the fitness of a stochastic switcher, and with the fitness of a dormancy-incapable organism. Analytical methods show that both switching strategists have higher fitness than a dormancy-incapable organism when good times are rare and that a responsive switcher has higher fitness than a stochastic switcher when good times are either rare or common. Numerical calculations show that stochastic switchers can be most fit when good times are neither too rare or too common.

##### MSC:

92D40 | Ecology |

92D15 | Problems related to evolution |

92C37 | Cell biology |

37N25 | Dynamical systems in biology |

93A30 | Mathematical modelling of systems (MSC2010) |

##### Keywords:

quiescence; Lyapunov exponent; Floquet multipliers; random Perron-Frobenius theorem; fitness
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\textit{T. Malik} and \textit{H. L. Smith}, Bull. Math. Biol. 70, No. 4, 1140--1162 (2008; Zbl 1142.92045)

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