Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a carrying capacity that switches either randomly or periodically between states of abundance and scarcity. The population dynamics is characterized by demographic noise (birth and death events) coupled to the fluctuating population size. By combining analytical and simulation methods, we elucidate the similarities and differences of evolving subject to stochastic and periodic switching. We show that the population size distribution is  broader under intermediate and fast random switching than under periodic variations, with periodic changes leading to an abrupt transition from slow to fast switching regimes. The fixation probability under intermediate/fast random and periodic switching can hence vary significantly, with markedly different asymptotic behaviors . We also determine the  conditions under which the fixation probability of the slow strain is optimal when the dynamics is driven by asymmetric switching .
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a carrying capacity switching either randomly or periodically between states of abundance and scarcity. The population dynamics is characterized by demographic noise (birth and death events) coupled to a varying environment. We elucidate the similarities and differences of the evolution subject to a stochastically- and periodically-varying environment. Importantly, the population size distribution is generally found to be broader under intermediate and fast random switching than under periodic variations, which results in markedly different asymptotic behaviors between the fixation probability of random and periodic switching . We also determine the detailed conditions under which the fixation probability of the slow strain is maximal .
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that switches
switching
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the fluctuating population size. By combining analytical and simulation methods, we
a varying environment. We
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evolving subject to stochastic and periodic switching. We show that
the evolution subject to a stochastically- and periodically-varying environment. Importantly,
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generally found to be
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with periodic changes leading to an abrupt transition from slow to fast switching regimes. The fixation probability under intermediate/fast
which results in markedly different asymptotic behaviors between the fixation probability of
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can hence vary significantly, with markedly different asymptotic behaviors
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detailed
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optimal when the dynamics is driven by asymmetric switching
maximal