Quantification of energy transfer efficiency and trophic cascade
The energy transfer efficiency between phytoplankton and zooplankton communities (\(E_{\text{her}}\), herbivore efficiency for short) was defined as the ratio of zooplankton production to phytoplankton production, i.e.,\(E_{\text{her}}\)=\(P_{\text{zoo}}\)/\(P_{\text{shr}}\), and that between zooplankton and top predator (\(E_{\text{pre}}\), predator efficiency for short) was defined as the ratio of predator production and zooplankton production, i.e.,\(E_{\text{pre}}\)=\(P_{\text{shr}}\)/\(P_{\text{zoo}}\) (Dickmanet al. 2008). Food chain efficiency (FCE) was calculated as the geometric average of herbivore efficiency and predator efficiency: FCE =\(\sqrt{E_{\text{her}}\bullet E_{\text{pre}}}=\sqrt{P_{\text{shr}}/P_{\text{phy}}}\)(Heymans et al. 2014).
The strength of trophic cascade was measured as the natural log ratios of phytoplankton biomass between treatments with (\(R_{3}\)) and without (\(R_{2}\)) predators (Borer et al. 2005):
\begin{equation} STC=\ln\frac{R_{3}}{R_{2}}\nonumber \\ \end{equation}
Similarly, the strength of top-down control on zooplankton biomass was measured as the natural log ratio of zooplankton biomass between treatments with and without predators.