Abstract: We present a theoretical analysis of the temporal variation of a population subject to a variable environment. This is achieved by treating the carrying capacity, a proxy for the environment as a state-variable. This enables us to describe the population and environment interaction via a set of nonlinear coupled differential equations. Importantly, we discuss the effect of a delay in the environmental response to changes in population density. The existence of a Hopf bifurcation is established as well as the minimum time delay required for the onset of sustained periodic fluctuations in the population. Finally, we discuss the ecological management implications imputed by the model.