Oscillatory depletion models for renewable ecosystems

The usual logistic model of ecology is augmented by multiplying the carrying capacity K by 1 − D(t), where D(t) is a resource depletion fraction that is determined by the time-varying population level N(t) over the last T time units. Two examples are given to show that N(t) and D(t) can oscillate antiphasically. The model is used to explain a boom-and-bust cycle of reindeer on an island in the Bering Sea.