Results
The standing biomasses at all trophic levels were strongly affected by experimental treatments (Fig. 2). The biomass of the predator E. modestus was significantly lower in the LP (i.e., low phosphorous concentration) treatment compared with those in HP (i.e., high phosphorous) and MP (i.e., medium phosphorous) treatments, and lower in mesocosms consisting of S. dorrii and D. brachyurum than those consisting of D. magna and D. brachyurum (Fig. 2a, Table S2). Zooplankton biomass was influenced by the presence of predators (F1,36 = 114.36; P < 0.001), nutrient supply (F2,36 = 235.87; P < 0.001), zooplankton community composition (F2,36 = 40.3;P < 0.001), as well as their interactions (Fig. 2b-c and Table S1). Specifically, zooplankton biomass was significantly suppressed by the presence of predators, while strongly promoted by nutrient enrichment (Fig. 2b-c). In the presence of predators, zooplankton communities consisting of all three species had the highest biomass across all nutrient treatments (Fig. 2b). In the absence of predators, zooplankton communities consisting of D. magna andD. brachyurum had higher biomass than those consisting of all three species in HP and MP treatments (Fig. 2d), due to higher biomass of D. magna in the former case (Fig. S2e-f). In the LP treatment, however, the inverse pattern was observed (Figs. 2c, S3a-b).Throughout the experiment, phytoplankton communities were dominated by green algae (Fig. S4). Nutrient enrichment and the presence of predators strongly boost phytoplankton biomass (P < 0 .001 for both factors; Fig. 2d-e and Table S1). Our analyses also showed significant interactive effects between predators and zooplankton community composition on phytoplankton biomass (F2,36 = 3.9, P = 0.03) and nutrient supply (F2,36 = 10.8, P < 0.001). At all trophic levels, the responses of biomass production rates to experimental treatments were similar to those of standing biomass (Fig. S2, Table S1).
Nutrient supply not only altered the standing biomass and production rates at different trophic levels, but also their stoichiometric characteristics. Phytoplankton molar C:P ratios decreased with increased ambient P concentrations (F2,36 = 253.7; P< 0.001; Fig. S4c; Table S1) and were higher in the presence of predators (F1,36 = 5.4, P = 0.026). By altering the stoichiometry of phytoplankton, nutrient supply also had carry-over effects on the stoichiometry of higher trophic levels. Specifically, an increase in ambient P concentration decreased the molar C:P ratios of zooplankton D. magna and S. dorrii (Fig. S4a-b), leading further to a lower body molar C:P ratios of predatorE. modestus (Fig. S4d).
The energy transfer efficiency between producers and herbivores (hereafter herbivore efficiency) was strongly modulated by the presence of predators (F1,36 = 16.4, P < 0.001) and zooplankton community composition (F2,36 = 8.4,P = 0.001, Table S1). The presence of predators significantly decreased herbivore efficiency, especially in mesocosms with zooplankton communities of D. magna and D. brachyurum (Fig. 3a). Similarly, the energy transfer efficiency between herbivores and predators (hereafter predator efficiency) was higher in mesocosms with zooplankton community D. magna and D. brachyurum , compared with those containing other zooplankton communities (Fig. 3c). While nutrient supply had no significant effects on herbivore efficiency and only marginally significant effects on predator efficiency (Fig. 3b-c, Table S1-2), it significantly affected the overall energy transfer efficiency from producers to predators (hereafter food chain efficiency). That is, the food chain efficiency was significantly higher in MP treatments compared with those in HP and LP treatments (F2,18 = 7.68; P = 0.001; Table S2; Fig. 3d).
The top-down effects of predators on zooplankton biomass and their cascading effects on phytoplankton biomass both differed significantly among mesocosms with different zooplankton community compositions (F2,18 = 49.51, P < 0.001 for zooplankton biomass; F2,18 = 75, P < 0.001 for phytoplankton biomass), but not with nutrient conditions (F2,18 = 0.23, P = 0.796 for zooplankton biomass; F2,18 = 0.084, P = 0.920 for phytoplankton biomass) (Figs. 4, S6, Table S2). Mesocosms with zooplankton communities of D. magna and D. brachyurum showed the strongest cascading effects (on average 107.8% increase in phytoplankton biomass in the presence of predators across three nutrient levels), followed by those consisting of all three zooplankton species (57.3%) and those consisting of S. dorrii and D. brachyurum (41.5%) (Fig. 4). To further disentangle the drivers of trophic cascades, we conducted stepwise regression analyses and found that the strength of trophic cascades was best explained by variation in predator efficiency (Fig. 5b; Table S3-4). In food chains with higher predator efficiencies, the strengths of trophic cascade were stronger (Fig. 5b). In comparison, neither primary productivity nor its interaction with energy transfer efficiencies had significant impacts on the cascading effects (Fig. 5a, Table S1).
Using food chain models with the type I functional response, we derived analytical relationships between trophic cascade strength (STC) and energy transfer efficiencies, i.e.,
\begin{equation} STC=\frac{e_{C}}{e_{C}-E_{\text{pre}}}\nonumber \\ \end{equation}
and between trophic cascade strength and primary productivity\(P_{\text{pro}}\):
\begin{equation} STC=\frac{e_{1}a_{1}}{rd_{1}}P_{\text{pro}}\nonumber \\ \end{equation}
These solutions suggest that the relationship between STC and\(E_{\text{pre}}\) involves only one covariate, while that betweenSTC and \(P_{\text{pro}}\) involves multiple covariates and thus may be more variable. This expectation was confirmed by numerical simulation in general settings. Across simulated food chains with varying parameters, the trophic cascade strength is strongly related with predation efficiency, but relatively weakly related with primary production and herbivore efficiency (Figs. 5c-d, S7-12). Similar results were found in more complex food web models with two herbivore species (Figs. S13, S14). Overall, our mathematical models support the mechanistic link between energy transfer efficiency and the strength of trophic cascades observed in our mesocosm experiment.