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).