Statistical analyses
We used mean values from June 10 to August 27 for all variables in the
following statistical analyses (Table S1). Relationships among
phytoplankton and zooplankton biomasses, specific production rate and
fish abundance were examined by correlation analysis. To test
differences in phytoplankton and zooplankton community composition among
the treatments and between the two ponds, permutational multivariate
analysis of variance (PERMANOVA) was performed by the adonis() function
in R package “vegan” (Oksanen et al. 2018). In this test, we used 999
permutations and the Euclidean distance both for phytoplankton and
zooplankton communities as an index of dissimilarity in the community.
We applied mean phytoplankton carbon biomass, zooplankton carbon
biomass, fish abundance, specific production rate and fraction of edible
phytoplankton for P , H , θ , μ , andαedi in eq. (9), respectively. Forαnut , we focused on phosphorus since freshwater
limnetic ecosystems are primarily phosphorus limited (Schindler 1974;
Smith a& Schindler 2009) and since growth of zooplankton is affected by
relative phosphorus in algae (Frost et al. 2006, Urabe et al. 2018).
Specifically, we used the carbon to phosphorus ratio of seston as a
surrogate for αnut because this ratio has been
generally used in theories of ecological stoichiometry (Sterner & Elser
2002). Thus, we expected lower H/P ratios at larger values of
seston carbon to phosphorus ratio. To examine effects of these
explanatory variables on the H/P ratio, a simple regression
analyses was performed. Then, after checking multicollinearity among the
explanatory variables by variance inflation factors (Kennedy 2008), we
fitted these data to eq. (9) using a lm function of R 3.2.1 (R core
team, 2018) with the examination of Akaike’s information criterion. In
this analysis, 95% confidence intervals of the regression coefficients
were estimated using bootstrapping with a residual resampling procedure
(Moulton & Zeger 1991) and 1999 replicates. Since eq. (9) indicates ana priori effect direction of a given variable, we estimated upper
or lower one-tailed 95% confidence intervals (100 and 5 percentiles)
for the explanatory variables according to negative or positive effects
predicted by eq. (9). Effect sizes of these explanatory variables were
assessed using standardized regression coefficients of the multiple
regression. Finally, to examine whether effects of explanatory variables
on the H/P mass ratio were independent of each other and
significant, we performed partial regression analysis with residual
leverage plot according to Sall (1990) using leveragePlots() in R
package “car” (Fox &bWeisberg 2011).