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


  • Corresponding Editor: A. M. Ellison.


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 without suitable food web models for predicting the absolute density of the herbivore biomass in physical units. Here, I present a parameterized mathematical food web model describing three-trophic-level systems that can predict the biomass density of herbivores h (kg protein/m3) and carnivores c from factors such as nutritive values of plants (np, kg protein/m3), herbivores (nh), and carnivores (nc), searching efficiency (volume) of carnivores (S, m3·m−3·d−1 = d−1), eating efficiency (speed) of herbivores (eh) and carnivores (ec; m3·m−3·d−1 = d−1), respiratory decreases in biomasses (dh and dc, kg·kg−1·d−1 = d−1), absorption efficiencies αh and αc (ratios), and probabilities of carnivores preying on herbivores or carnivores, Phc and Pcc (ratios). 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 exists but is rarer than interguild predation (Phc > Pcc > 0); plants are less nutritive than animals (np < nh, nc); and carnivore searches huge volume daily while eating speed of herbivore is limited (S _ eh). These conditions are well-realized in aboveground terrestrial ecosystems where plant-rich “green worlds” are common, vs. animal-rich belowground and aquatic ecosystems where some conditions are not realized. The h and c calculated from our model agreed well with those from empirical observations in forest ecosystems, where both h and c are within an order of magnitude of 100 mg (fresh biomass/m2 forest), and in savannah ecosystems. The model predicts that plant nutritive value np, digestibility of plants by herbivores αh, and herbivore eating speed eh are positively correlated with h and the intensity of herbivory, which theoretically explains the outdoor defensive effects of plant anti-nutritive or quantitative defenses (e.g., tannins, protease inhibitors), and predicts that c and the carnivore/herbivore ratio c/h are positively correlated with the relative growth rate of herbivores Gh. The present model introduced parameterized realities into food web theory that previous models lack.