Disturbances cause high mortality in populations while simultaneously enhancing population growth by improving habitats. These countervailing effects make it difficult to predict population dynamics following disturbance events. To address this challenge, we derived a novel form of the logistic growth equation that permits time-varying carrying capacity and growth rate. We combined this equation with concepts drawn from disturbance ecology to create a general model for population dynamics in disturbance-prone systems. A river flooding example using three insect species (a fast life-cycle mayfly, a slow life-cycle dragonfly and an ostracod) found optimal tradeoffs between disturbance frequency vs. magnitude and a close fit to empirical data in 62% of cases. A savanna fire analysis identified fire frequencies of 3-4 years that maximised population size of a perennial grass. The model shows promise for predicting population dynamics after multiple disturbance events and for management of river flows and fire regimes.