Practice question

Exponential growth requires the per-capita rate of increase to remain approximately constant as population density rises. That condition is approached in an ideal, effectively unlimited environment where food, space, nutrients, and other essential resources do not constrain reproduction or survival. Predation, infectious disease, and resource scarcity usually introduce density-dependent mortality or reduced fecundity, causing per-capita growth to fall and the trajectory to depart from an exponential curve. Under ideal conditions, dN/dt = rN and a positive r causes abundance to increase by a constant proportion per unit time. Absolute increments consequently become larger as the population grows. Such conditions rarely persist indefinitely in nature because organisms eventually modify or exhaust their environment. Nevertheless, brief exponential phases occur when microbes enter fresh medium, a species colonizes vacant habitat, or a population rebounds from low density. The model is therefore a useful null expectation and a description of potential growth, not a claim that resources are literally infinite. Once limiting feedback becomes important, logistic or more detailed density-dependent models are more appropriate.