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The representativeness of steady state characterizations of biological systems strongly depends on the interplay between the time scales of the external perturbations altering their state and their intrinsic time scales, dictating their speed of adaptation. In this talk, I will delve into two examples in which such interplay yields complex transient behaviors challenging well-established results in different fields such as population genetics and mathematical epidemiology. First, I will adress the evolution of genetic diversity of species under cyclic habitat changes considering a Wright Fisher model with time-varying population sizes. I will show how, despite the loss in population, genetic diversity might increase during range contractions for species out of genetic equilibrium. Second, I will present a minimal eco-evolutionary framework to study the persistence of rapidly evolving viruses in population. There, I will show that evolution in transmissibility during the first epidemic waves crucially alters the features of those viruses more prone to become endemic. I will finish the talk by showing that evolutionary dynamics yields a potential trade-off between the short-term benefits and long-term consequences of non-pharmacaeutical interventions to manage epidemics.