The way fluctuations shape the population behavior is an outstanding question of practical importance in ecology, microbiology and epidemiology. We present an analytical framework to examine the effects of external fluctuations in a wide variety of systems. Through this framework, we have obtained explicit conditions that determine to what extent fluctuations propagate to the variability of populations and how they affect fundamental properties of the system, including whether they promote or prevent proliferation and whether they stabilize or destabilize coexistence. The wide-ranging applicability of these general conditions has been extensively validated explicitly through computational experiments of single-species and multispecies dynamics, encompassing the three classical types of functional responses as well as exponential growth, growth with saturation, and logistic growth. We found that, in general, fluctuations can both positively and negatively impact population proliferation and coexistence, depending on their precise interplay with the linear and nonlinear terms of the system. Our results make it possible to informedly target the quantities and the fluctuation properties that best can be used to change the behavior of populations, thus opening an avenue for controlling populations through fluctuations in addition to just through average properties.