Introduction
The biomass ratio of herbivores (H ) to primary producers (P ) reflects the structure of a community. Because of its fundamental importance, a large number of studies have empirically and theoretically examined the H/P biomass ratio and showed that factors related with either bottom-up or top-down forces play crucial roles in determining it. These factors are production rate (Coe et al. 1976; Power 1992; Word et al. 2015), defense traits (Coley et al. 1985; Wolfe et al. 1997; Poelman et al. 2008; Moony et al. 2010) and nutrient contents of producers (Sterner & Elser 2002; Cebrian et al. 2009), and predation rate by carnivores including food-chain length (Hairston et al. 1960; Hanley & La Pierre, 2015; Carpenter et al. 1985). However, the relative importance of these factors across natural communities is elusive, since few studies have considered a theoretical framework for explicitly examining the relative importance of these effects on community structure.
The top-down forces are determined by the feeding rate and the abundance of consumers at higher trophic levels (Shurin et al. 2002; Vanni et al. 1990), while the bottom-up forces are determined by the primary production rate regulated by supplies of nutrients (Schindler 1974; Smith & Schindler 2009) and light (Karlsson et al. 2009). In addition, both in terrestrial and aquatic producers including vascular plants and algae, chemical and physical defense traits are well documented as factors limiting herbivory (Wolfe et al. 1997, Agrawal & Fishbein 2006; Pančić & Kiørboe 2018), indicating that edibility or defense traits of primary producers to consumers are crucial factors in determining the biomass ratio (Coley et al. 1985; Moony et al. 2010). The nutrient content of producers is also viewed as a prime factor in regulatingH/P mass ratio (Cebrian 1999; Sterner & Elser 2002; Cebrian et al. 2009; Konno 2016). Depending on supply rates of light and nutrients, contents of biologically important elements such as nitrogen and phosphorus relative to carbon vary widely among primary producers (Sterner & Elser 2002). Since herbivore growth depends highly on the elemental content of primary producers (Frost et al. 2006; Urabe et al. 2018), the stoichiometric mismatch in carbon to phosphorus or nitrogen ratios between primary producers and herbivores likely results in decreasing the H/P ratio (Cebrian 1999; Sterner & Elser, 2002Cebrian 2009). However, no study has yet formulated how these different factors affect simultaneously the H/P biomass ratio.
In this study, therefore, we constructed a framework for assessing the relative importance of primary production rate, defense traits and nutrient contents of producers, and predation rate on the H/Pratio in natural communities based on the classic Lotka-Volterra equations. Then, by fitting biomass data from planktonic producers and herbivores in experimental ponds to the model, we tested a hypothesis if these factors simultaneously affect the H/P ratio and examined the relative contributions of these factors to the biomass ratio. In experimental ponds, we manipulated light input by shading, and top-down force was assessed by regularly monitoring abundance of planktivorous fishes. We show that top-down forces and stoichiometry of primary producers played pivotal roles in determining the H/P ratio, followed by defense traits and primary production in the plankton communities.