Delays in nutrient cycling and plant population oscillations

It is well known that delay-differential and delay-difference equations can produce plausible simulations of population oscillations, but many of these equations lack a specific mechanism responsible for the delay. We suggest that delays in release of nitrogen from decomposing litter, caused by microbial uptake, could produce oscillations in populations when the delay in the release of nitrogen is longer than the characteristic time scale of nitrogen uptake. We present a model which captures these dynamics. As the parameter controlling microbial uptake of nitrogen during litter decay increases, the model solutions bifurcate from fixed point equilibria, to periodic orbits (oscillations) which remain bounded for ecologically very long times, and finally to extinction of the plant population because of rapid increases in the amplitude of the oscillations. We suggest that such a mechanism may be especially important for annual plants which do not store nitrogen in perennial tissues to buffer delays. Natural populations of wild rice (Zizania palustris), an annual plant, oscillate with approximately four-year periods. Our model qualitatively mimics the period and shape of population oscillations in wild rice with parameter values in the range of those determined by experiments. The model therefore demonstrates a logical and experimentally plausible link between plant population dynamics and the ecosystem processes delaying the cycling of limiting nutrients.