Statistical analysis
We used ANOVAs to assess the responses of biomass, production, and
energy transfer efficiencies to experimental manipulations.
Specifically, we used three-way ANOVAs to test the responses of biomass
and production of phytoplankton and zooplankton, as well as the energy
transfer efficiency between these two trophic levels (i.e.,\(E_{\text{her}}\)), to manipulations in nutrient supply, zooplankton
community composition, and the presence of predators. Similarly, two-way
ANOVAs were applied to test the responses of predator biomass and
production, and energy transfer efficiency between zooplankton and
predator (i.e.,\(E_{\text{pre}}\)) and food chain efficiency (i.e.,
FCE), to manipulations in nutrient supply and zooplankton community
composition. We also applied two-way ANOVAs to explore how nutrient
supply and zooplankton community composition influence strengths of
top-down control and trophic cascades. In addition, we also explored
responses of TP and TN, as well as elemental composition at each trophic
level to experimental manipulations using a three-way ANOVA. For all
these analyses, Tukey post hoc tests were performed for pairwise
comparisons.
To further test the productivity hypothesis (hypothesis I in Fig. 1a)
and energy transfer hypothesis (hypothesis II in Fig. 1b), we applied
stepwise regression models with trophic cascade strength as response
variable and energy transfer efficiencies (\(E_{\text{her}}\),\(E_{\text{pre}}\), and FCE), primary productivity, and their
interactions as explanatory variables. We performed bidirectional model
selection by iteratively adding variables to an intercept model and
reducing variables from a full model, and selected models with the
lowest Akaike Information Criterion (AIC) values. Similarly, we also
performed stepwise regression models to test the effects of primary
productivity and energy transfer efficiencies on the strength of
top-down control on zooplankton biomass. Multivariate regression was
performed to assess the contributions of selected variables. All the
statistics were performed in R (R Core Team, 2019).