A general parameterized mathematical food web model that predicts a stable green world in the terrestrial ecosystem

Terrestrial ecosystems are generally green with vegetation and only a small part (<10%) of the total plant matter is consumed by herbivores annually, which means herbivore density is consistently low and stable. Nonetheless, the mechanism underlying this pattern has been unclear due to the lack of suitable food-web models for predicting the absolute density of the herbivore biomass in physical units. Here, I present a simple parameterized mathematical food-web model describing three trophic level systems that can predict the biomass density of herbivores h (kg protein/m 3) and carnivores c from ecological factors such as the nutritive values of plants n p (kg protein/m 3), herbivores n h , and carnivores n c , searching efficiency (volume) of carnivores S (m 3 /m 3 day=/day), eating efficiency (speed) of herbivores e h (m 3 /m 3 day=/day) and carnivores e c , respiratory decrease in herbivore and carnivore biomasses, d h (kg/kg day=/day) and d c , absorption efficiency of herbivores and carnivores  h (ratio) and  c , and probabilities of carnivores preying on herbivores or carnivores, P hc (ratio) and P cc. The model predicts a stable equilibrium with low herbivore biomass h sufficient to keep the world green provided the food-web consists of the three trophic levels, plants, herbivores and carnivores; intraguild predation of carnivores exists; n p >e h ; and P hc >P cc >0. These conditions are well-realized in above-ground terrestrial ecosystems where plant-rich " green world " is common, versus animal-rich belowground and aquatic ecosystems where some conditions are not realized. The h and c calculated from our model showed surprisingly good agreement with those from empirical observations in forest ecosystems, where both h and c are order of magnitude of ca. 100 mg (fresh biomass/m 2 forest), and in savannah ecosystems. The model predicts that the nutritive values of plants n p , digestibility of plants by herbivores  h , and herbivore eating speed e h are positively correlated with h and the intensity of herbivory, which theoretically explains the outdoor defensive effects of the anti-nutritive or quantitative defenses (e.g., tannins, protease inhibitors) of plants, and predicts that c and the carnivore/herbivore ratio c/h are positively correlated with the relative growth rate of herbivores G h. The present model introduced parameterized realities into food-web theory, which were missing in previous models.