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.