COS 141-7
A general mathematical food web model that predicts a stable green world in the terrestrial ecosystem

Friday, August 14, 2015: 10:10 AM
323, Baltimore Convention Center
Kotaro Konno, Insect-Plant Interaction Research Unit, Division of Insect Sciences, National Institute of Agrobiological Sciences, Tsukuba, Ibaraki, Japan

Terrestrial world is generally green and only a small part (< 10%) of plant matter is consumed by herbivore annually, which means the density of herbivore is consistently low and stable. However, the mechanism that causes this pattern has been unclear because of the lack of the food web model that can predict the absolute biomass density of herbivores accompanied by realistic physical units. Therefore, I attempted to establish a simple mathematical food web model that can predict the biomass density of herbivore (primary consumer) h (kg protein/m3) and carnivore (secondary consumer) c (kg protein/m3) from ecological factors such as nutritive values of plant (plant material, producer) np (kg protein/m3), herbivore nh (kg protein/m3), and carnivore nc (kg protein/m3), searching efficiency (volume) of carnivore S (m3/m3day=/day), eating efficiency (speed) of herbivore eh (m3/m3day=/day) and carnivore ec (/day), daily respiratory decrease of herbivore and carnivore biomass, dh (kg/kg day=/day) and dc (/day), absorption efficiency of herbivore and carnivore αh  (ratio) and αc (ratio), and preying probability of carnivore on herbivore or carnivore, Phc (ratio) and Pcc(ratio).


A new mathematical food web model was established that predicted a stable convergent equilibrium with biomass densities of herbivore h=nc{(1-αc)Pcchehnp–nhdh)+2dcPhc}/2αcPhc2nhS (kg/m3) and carnivore c=nchehnp-nhdh)/PhcnhS (kg/m3). The predicted h is low enough to keep the world green if 1. np<nh,nc, 2. S>>eh, and 3. Phc>Pcc >0. All these conditions are realized in above-ground terrestrial ecosystems, but not in below-ground and aquatic ecosystems, which explains why terrestrial ecosystems (above-ground) are plant-rich while belowground and aquatic ecosystems are animal-rich. The h and c calculated from the model showed surprisingly good agreement with those obtained from empirical observations in forest ecosystems, where both h and c have the order of magnitude of ca. 100 mg (fresh biomass/m2 forest), and also in savannah ecosystems. The model predicts that nutritive values of plant np, digestibility of plant by herbivore ah, and eating speed of herbivore eh positively correlate with h and intensity of herbivory, which theoretically justifies outdoor defensive functions for plant of anti-nutritive or quantitative defenses such as tannins and protease inhibitors, and predicts that c and c/h positively correlate with RGR of herbivore Gh=:(αhehnp-nhdh)/nh. The model further predicts positive correlation between nutrients of litters and their decomposition speeds, conditions of pest outbreaks, etc. Ref.arXiv:1412.5773.