AbstractEnvironmental fluctuations, such as changing conditions and variable nutrient availability, are an unavoidable component of the dynamics of virtually all populations. They affect populations in ways that are often difficult to predict and sometimes lead to paradoxical outcomes. Here, we present a general analytical approach to examine how populations respond to fluctuations. We show that there exist general explicit conditions that determine to what extent fluctuations propagate to the variability of the responses and how they change the behavior of the system, including whether they promote proliferation or death and whether they facilitate coexistence or exclusion of competing species. These conditions depend on linear and nonlinear terms of the growth rate and on the characteristic times of the fluctuations. We validated our general approach through computational experiments for both stochastic and chaotic fluctuations and for multiple types of systems. From an applied point of view, our results provide an avenue for the precise control of the population behavior through fluctuations in addition to just through average properties.