Conclusion
In this study, the effect size of fish abundance was greatest when our linear model was applied to the ponds, indicating that abundance of herbivores relative to that of primary producers depends highly on abundance of carnivores as classically and repeatedly pointed out since Hairston et al. (1960). We also found that stoichiometry, defense traits, and production rate of producers play substantial roles in regulating the H/P biomass ratio. Thus, this study revealed that herbivore biomass relative to producer biomass was regulated simultaneously by the abundance of carnivores, stoichiometric nutrient content and defense traits of producers, and primary production rate in natural ecosystems. In this study, we considered the size and phosphorus content of phytoplankton as the defense trait and nutritional quality of primary producers, respectively. However, it is also possible to consider effects of other chemical and physical defenses such as toxins and thorns, and nutritional substances such as protein and fatty acid contents in eq. (4). Since our theoretical framework (eq. (4) and (9)) can incorporates multiple factors, application of the model to various terrestrial and aquatic communities is possible and thus would serve to generalize the relative importance among production rate, defense traits and stoichiometric nutrient content of producers, and predation rate by carnivores in various ecosystems.