Calculating food web energy fluxes
Energy fluxes (joules per year) among all nodes in the local food webs were calculated using the food web energetic approach (Barnes et al. 2018; Gauzens et al. 2018). The method assumes a steady state in which all energetic losses of nodes in the food webs (quantified by metabolism/physiological processes and predation by higher trophic levels) is exactly balanced by energy intake (quantified by consumption of resources, after accounting for efficiency of energy assimilation from ingested resource). The Fij , the flux of energy from resource i to consumer j , was calculated as:
\begin{equation} \sum_{j}{e_{\text{ij}}F_{i}}=X_{j}+\sum_{j}{W_{\text{ij}}F_{j}}\nonumber \\ \end{equation}
Where eij is the efficiency that consumerj converts energy coming from resource i into energy used for its metabolism and biomass production, which can vary with trophic levels (Barnes et al. 2014). This equation represents the balance between energetic gains of consumer j via consumption of resources (the left side of the equation), and energetic losses resulting from metabolism Xj (the sum of individual metabolic rates from fish in nodes j ) and from predation on consumer j by higher trophic levels (the right side of the equation; Gauzens et al. 2018). Energy flux to each consumer in the food web was defined as Fij = WijFj , where Fjis the sum of intake flux to species j, and Wij defines the proportion ofFj that is obtained from species i , which was obtained by scaling consumer preferences wijto the biomasses of different available resources:
\begin{equation} W_{\text{ij}}=\frac{w_{\text{ij}}B_{i}}{\Sigma_{k}w_{\text{kj}}B_{k}}\nonumber \\ \end{equation}
where Bi is the biomass of resource i . There were cannibalistic links in top-carnivorous fish (e.g.,Hoplias argentinensis ), but biomass independent preference for cannibalism was set to 0.1 to strongly down-weight the amount of energy a predator consumed from its own biomass pool. Importantly, despite energy flux being expressed in the flux of energy (joules) per unit of time, energy flux is directly associated with material ingested/consumed by fish consumers in food webs as it describes the chemical energy that is taken up by fish consumers and both converted to biomass and processed and lost as kinetic energy through metabolism (Brown et al. 2004). Furthermore, the material ingested by fish consumers is composed of chemical elements (e.g., C, P, and N) that comprise organic compounds, which harbor chemical energy that is released and transformed through the process of metabolism (Brown et al. 2004). Therefore, energy fluxes are also closely correlated with chemical elemental fluxes in food webs (Barnes et al. 2018).
We calculate the total intake energy flux for each trophic guild representing single functions (carnivory, omnivory, anddetritivory ). We summed the intake energy flux in all trophic compartments representing the entire food-web functioning (i.e.,multitrophic functioning ). Total top-carnivorous flux was calculated as the sum of all outgoing energy flux from mesocarnivores, omnivores, and detritivores. Total mesocarnivorous flux was calculated as the sum of all outgoing energy flux from invertebrates and small fish prey. Total omnivorous flux represents the sum of all outgoing energy flux from algae/plants, detritus, and invertebrates. Total detritivorous flux is the total amount of flux from detritus. We calculated the relative contribution (%) of the different trophic guilds to total energy flux. Energy flux was calculated using the “fluxweb” R package (Gauzens et al. 2018).