Environmental 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.

中文翻译：

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人口对环境波动的反应的决定因素。

环境的波动，例如条件的变化和养分供应的变化，是几乎所有人口动态中不可避免的组成部分。它们以通常难以预测的方式影响人口，有时甚至导致自相矛盾的结果。在这里，我们提出了一种通用的分析方法，以检验人口对波动的反应。我们表明存在一般的明确条件，这些条件可以确定波动在多大程度上传播到响应的可变性以及它们如何改变系统的行为，包括它们是否促进增殖或死亡，以及它们是否促进竞争物种的共存或排斥。这些条件取决于增长率的线性和非线性项以及波动的特征时间。我们通过计算实验验证了随机波动和混沌波动以及多种类型系统的通用方法。从应用的角度来看，我们的结果为通过波动以及仅通过平均属性来精确控制人口行为提供了一条途径。