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Quiescence refers to a reversible state in which cells exhibit low metabolic activity, do not divide, and enjoy a lower death rate. Certain microbial populations exercise this capability to survive stress such as lack of resource, extreme temperature, and antibiotic regime. In this monograph, fitness of a quiescence-capable population is quantified using some linear systems of ordinary differential equations, and compared with that of a quiescence-incapable population, in order to examine the benefit of quiescence in a time-varying environment. Nonlinear deterministic models based on ordinary differential equations are constructed and thoroughly analyzed to study the impact of essential nutrients, low levels of which induce quiescence, on the adaptive dynamics of microbial populations. Resource competition among quiescence-capable populations is also studied.