Herbivores enable plant survival under nutrient limited conditions in a model grazing system

We make a theoretical study of nitrogen cycling in a model of a grazing system with five compartments. The rates of uptake of nutrient by plants and herbivores are allowed nonlinear forms which involve no a priori assumptions about whether the system is subject to top-down or bottom-up control. We derive a method of piecewise linear approximation which allows analytical study of the system. We then use this method to investigate the properties of the equilibrium states of the system, and in particular whether the system favours donor- or recipient-control, the grazing optimization problem, and the potential benefits of herbivory to plant growth. We are able to generalise our results to all uptake functions of the same qualitative class as those considered, and to show that in general the system will tend to a stable equilibrium state of donor-controlled herbivory. In this model, the presence of the ‘right’ class of herbivore is not only beneficial to plant growth in certain circumstances, but can be essential to their survival, allowing plants to co-exist with herbivores under conditions in which they would be unable to survive alone.