Grazing optimization and nutrient cycling: when do herbivores enhance plant production?

In a general theoretical ecosystem model, we investigate the conditions under which herbivores increase primary production and lead to grazing optimization through recycling of a limiting nutrient. Analytical and simulation studies of the model lead to several general results. Grazing optimization requires that (1) the proportion of nutrient lost along the herbivore pathway be sufficiently smaller than the proportion of nutrient lost throughout the rest of the ecosystem; and that (2) inputs of nutrient into the system be greater than a threshold value, which depends on the sensitivity of plant uptake rate to an increase in soil mineral nutrient. An increase in nutrient turnover rate is not sufficient to explain grazing optimization in the long term. When a nutrient is the single limiting factor, plant biomass and productivity at equilibrium are determined only by the balance of ecosystem inputs and outputs of nutrient. Processes that do not have an impact on these inputs or outputs have no effect on primary producers. On the other hand, turnover rates are important for the transient dynamics of the system, and the equilibrium analysis is relevant only if it can be reached in a reasonable time scale. The equilibrium is not reached by a compartment with a very slow turnover rate, such as the resistant soil organic matter, before several centuries. On a small time scale, such a compartment can be considered constant, and the trend of the system is predicted with a simplified system. The results at equilibrium are insensitive to the functional form used to describe herbivore consumption: the results obtained for simple, linear, donor-controlled herbivory also apply to most forms of more realistic, recipient-controlled herbivory. We conclude that grazing optimization is most likely to occur in systems with large losses of the limiting nutrient during recycling of plant detritus, or where herbivores bring nutrient from outside the ecosystem considered (which acts to reduce, or even make negative, the fraction of nutrient lost along the herbivore detritus pathway).