Instabilities associated with population growth can be simulated by putting the logistic growth curve in a discrete form. In contrast to the usual derivation of chaos, which can only explain instabilities at the top of the curve, this method can also account for fluctuations during the early phases of the niche-filling process. Precursors, a steep initial rise, and final instabilities can all be interrelated. Industrial examples are given of logistic growth alternating with periods of chaotic fluctuations.