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\begin{document}

\title{Energy transfer efficiency rather than productivity determines trophic
cascades}



\author[1]{Libin Zhou}%
\author[1]{Mingyu Luo}%
\author[1]{Pubin Hong}%
\author[2]{Shawn Leroux}%
\author[3]{Feizhou Chen}%
\author[1]{Shaopeng Wang}%
\affil[1]{Peking University}%
\affil[2]{Memorial University}%
\affil[3]{Nanjing Institute of Geography and Limnology Chinese Academy of Sciences}%


\vspace{-1em}



  
  \date{May 16, 2024}


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\selectlanguage{english}
\begin{abstract}
Trophic cascades are important determinants of food web dynamics and
functioning, yet mechanisms explaining variations in trophic cascade
strength remain elusive. Here we combine a mesocosm experiment
(phytoplankton-zooplankton-shrimp) and theoretical models to disentangle
the relative importance of two processes driving trophic cascade:
primary productivity (productivity hypothesis) and energy transfer
efficiency (energy transfer hypothesis). Our experimental systems showed
consistently positive effects of trophic cascade across mesocosms with
different nutrient inputs and zooplankton communities. Moreover, the
strength of trophic cascade increased with the energy transfer
efficiency between herbivores and predators, but did not change with the
primary productivity. These findings are further corroborated by our
analyses of food chain models in more general settings. Combined, our
results support the energy transfer hypothesis but falsify the
productivity hypothesis. Our study contributes an integrative
perspective to reconcile energetic and population dynamics in food webs,
which has useful implications for ecosystem management.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Trophic cascades characterize the top-down effects of predators
propagating down trophic levels, which represent one of the most classic
paradigms in community ecology and have stimulated tremendous amount of
experimental and theoretical studies (Carpenter \& Kitchell 1988;
Polis\emph{et al.} 2000; Carpenter 2010; Ripple \emph{et al.} 2016).
Mounting evidence have demonstrated the prevalence of trophic cascades
in nature (Pace \emph{et al.} 1999; Shurin \& Seabloom 2005) and their
far-reaching impacts on ecosystem functioning and services (Estes
\emph{et al.} 2011; Strickland\emph{et al.} 2013; Walsh \emph{et al.}
2016; Stock \emph{et al.} 2017). Despite many previous studies to reveal
various biotic and abiotic factors that potentially influence the
strength of trophic cascades (Schmitz \emph{et al.} 2004; Borer \emph{et
al.} 2005; Bruno \& O'Connor 2005; Otto \emph{et al.} 2008), the
inconsistent outcomes, for example the idiosyncratic effects of predator
diversity (Bruno \& O'Connor 2005; Otto \emph{et al.} 2008), suggest a
continued uncertainty of its ultimate mechanisms.

One long recognized potential explanation is the productivity
hypothesis, which predicts that the strength of trophic cascades
increases with primary productivity (Fig. 1a). Primary productivity
provides the essential energy and elements for upper trophic levels
within a food web. Such bottom-up processes determine not only the
trophic position of the apex predator, i.e., food chain length (Post
2002), but also the accumulation of its biomass (Moore \& De Ruiter
2012; Barbier \& Loreau 2019). By supporting higher biomass of apex
predators, a higher primary productivity can potentially trigger a
stronger trophic cascade. This hypothesis, historically illustrated as
the ecosystem exploitation hypothesis (EEH) (Oksanen\emph{et al.} 1981),
has been supported by positive relationships between primary
productivity and trophic cascade strength found across various studies
(Wootton \& Power 1993; Su \emph{et al.} 2021). However, evidence that
does not support the relationship between primary productivity and the
strength of trophic cascades was also reported in other studies (Borer
\emph{et al.} 2005). These contrasting findings are striking as they
have been found even within the same realm, e.g., freshwaters (Borer
\emph{et al.} 2005; Su \emph{et al.} 2021).

An implicit assumption underlying the productivity hypothesis is
unimpeded vertical energy fluxes, where energy fixed by primary
producers can reach higher trophic levels efficiently. This assumption,
nevertheless, rarely holds in nature (Lindeman 1942; DeBruyn \emph{et
al.} 2007). In natural ecosystems, only a small proportion of energy
from low trophic levels can be converted into biomass of high trophic
levels, due to inefficiencies in food ingestion, assimilation, and
biomass production (Barneche \& Allen 2018; Eddy \emph{et al.} 2021).
For instance, food webs often involve many less edible plants (Oksanen
\& Oksanen 2000) or anti-predative herbivores (Degerman \emph{et al.}
2018), which can significantly hamper vertical energy flow to apex
predators (Stibor\emph{et al.} 2004). Inefficiency in energy transfer
can significantly influence the biomass distribution of food webs (de
Ruiter \emph{et al.}1995; McCauley \emph{et al.} 2018; Barbier \& Loreau
2019) and thereby alter the strength of trophic cascades (Heath \emph{et
al.} 2014; Galiana \emph{et al.} 2021). In particular, too low energy
transfer may decouple biomass production at higher trophic levels from
primary production, violating assumptions underlying the productivity
hypothesis (Brett \& Goldman 1997; Davis \emph{et al.}2010). In such
cases, the strength of trophic cascade depends mainly on the efficiency
of energy transfer (energy transfer hypothesis; Fig. 1b), rather than
the amount of energy supply characterized by the primary productivity.
While the transfer efficiency hypothesis has been formulated in
mathematical models (DeBruyn \emph{et al.} 2007), it has not been tested
explicitly.

In this study, we conduct a field mesocosm experiment, combined with
mathematical models, to test the aforementioned two hypotheses
underlying trophic cascades (i.e., the productivity hypothesis and
energy transfer hypothesis; Figure 1). We constructed mesocosms hosting
a three-level food chain and quantified the strength of trophic cascade
by simulating loss of top predator. We simultaneously manipulated
nutrient supply and zooplankton community composition to generate
variation in primary productivity and energy transfer efficiencies,
respectively. Because both primary productivity and energy transfer
processes are necessary for maintaining higher biomass of apex
predators, we expected a weakened relationship between primary
productivity (resp. energy transfer efficiency) and trophic cascade
strength when energy transfer efficiency (resp. primary productivity) is
impeded (Fig. 1). We end our discussion with scientific and practical
implications of our results.

\textbf{Methods}

Mesocosm experiment

The mesocosm experiment was conducted to simulate three-level food
chains (algae-zooplankton-shrimp) at the Taihu Laboratory for Lake
Ecosystem Research, located at the eastern side of Taihu Lake (31[?]03'N,
120[?]42'E). Lake seston was used as basal resources to allow a regional
assortment of phytoplankton species representative of local water
bodies. We implemented a factorial design by crossing three levels of
nutrient supply (HP, total phosphorus at 0.08 mg L\textsuperscript{-1};
MP, total phosphorus at 0.058 mg L\textsuperscript{-1}; LP, total
phosphorus at 0.028 mg L\textsuperscript{-1}, Fig. S1) with three types
of zooplankton communities (\emph{Daphnia magna} + \emph{Daphnia
brachyurum} ,\emph{Sinocalanus dorrii} + \emph{D. brachyurum} , and
\emph{D. magna} +\emph{S. dorrii} + \emph{D. brachyurum} ). Nutrient
manipulation was achieved by adding
K\textsubscript{2}HPO\textsubscript{4} solutions (0.5 mol
L\textsuperscript{-1}) to 150 L tanks that contained mixtures of lake
water and aerated tap water (at the proportion of 1:1). Tanks receiving
no P additions represents the LP treatments with total phosphorus
concentration at 0.028 mg L\textsuperscript{-1} (Fig. S1c). In addition,
KNO\textsubscript{3} solutions were added to all tanks to compensate for
the dilution effects of tap water (Fig. S1d-f). Zooplankton communities
were manipulated by manually adding pre-cultured zooplankton species
(\emph{see details in SI Appendix 1} ) to each tank at a total density
of around 30 ind. L\textsuperscript{-1}. Among these species, \emph{D.
magna} possesses larger body size, slower locomotion (thus lower
anti-predation ability), and higher nutrient concentrations than the
other two species (Sterner \emph{et al.} 1992). We therefore expected
\emph{D. magna} to be higher-quality food for predators. The inclusion
of \emph{D. brachyurum} in all treatments was to prevent the extinction
of zooplankton communities due to predator exploitation. Before filling
the tanks, animals originally contained in lake water were eliminated
via repeatedly screening through a 15 \selectlanguage{greek}µ\selectlanguage{english}m mesh. For each of the nine
treatments (3 nutrient levels\selectlanguage{ngerman}×3 zooplankton communities), we created six
mesocosms, half with and the other half without predators (i.e., two
individuals of juvenile shrimp \emph{Exopalaemon Modestus} ) in order to
quantify the strength of trophic cascades (He \emph{et al.}2021).
Therefore, a total of 54 experimental units (i.e., 3 nutrient levels × 3
zooplankton community compositions × 2 predator treatments × 3
replicates) were created. All the mesocosms were fixed in a pond to
ensure a relatively constant ambient temperature and checked three times
a day to remove unexpected allochthonous materials. The experiment
lasted for 6 weeks from 14 July to 25 August, 2021.

Measurement

During the course of the experiment, phytoplankton biomass (measured as
Chl-a concentration) was quantified at a weekly basis to track
phytoplankton response and calculate the trophic cascade strength. We
also measured the net production at each trophic level for estimating
energy transfer efficiencies. Specifically, primary production
(\(P_{\text{phy}}\)) was measured via the light-dark bottles method at
the end of the experiment (Devlin \emph{et al.} 2016). Zooplankton
production (\(P_{\text{zoo}}\)) was estimated based on changes in the
body size and egg production for each taxon from the third week onwards.
Predator production (\(P_{\text{shr}}\)) was estimated as the increase
rate of shrimp biomass throughout the experiment (Dickman \emph{et
al.}2008). Production at all trophic levels were measured in the unit of
C L\textsuperscript{-1} day \textsuperscript{-1} (\emph{see details in
SI Appendix 1} ).

Total nitrogen (TN) and total phosphorus (TP) concentrations in waters
were monitored weekly, and elemental composition of each trophic level
were also measured at the end of the experiment to assess the
stochiometric responses of food webs. Due to practical reasons, however,
for zooplankton species we only measured elemental composition of
species \emph{D. magna} and \emph{S. dorrii} (\emph{see details in SI
Appendix 1} ).

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.,\(E_{\text{pre}}\)=\(P_{\text{shr}}\)/\(P_{\text{zoo}}\)
(Dickman\emph{et 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 \emph{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 \emph{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.

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).

Theoretical models

To better understand the mechanisms underlying trophic cascades in our
experiment and extend them to more general settings, we also used food
chain models to investigate the relationship between trophic cascade,
predator efficiency and primary production. The model is described as
follows:

\begin{equation}
\left\{\begin{matrix}\frac{\text{dC}}{\text{dt}}=e_{C}F_{C}-d_{C}C\\
\frac{\text{dH}}{\text{dt}}=e_{H}F_{H}-F_{C}-d_{H}H\\
\frac{\text{dR}}{\text{dt}}=rR\left(1-\frac{R}{K}\right)-F_{H}\\
\end{matrix}\right.\ \nonumber \\
 \end{equation}

where \emph{R} , \emph{H} , and \emph{C} are the biomasses of the basal,
herbivore, and predator species, respectively (as in Fig. 1),
\(r\) and K are the intrinsic growth rate and carrying
capacity of the basal species, respectively. \(F_{H}\) and
\(F_{C}\) are the foraging rates of the herbivore and predator
species, respectively, for which we consider three types of functional
responses. For the type I functional response,\(F_{H}=a_{H}\text{RH}\) and
\(F_{C}=a_{C}\text{HC}\). For the type II functional
response,\(F_{H}=\frac{a_{H}\text{RH}}{1+a_{H}h_{H}R}\) and\(F_{C}=\frac{a_{C}\text{HC}}{1+a_{C}h_{C}H}\). For the type III
functional response, \(F_{H}=\frac{a_{H}R^{2}H}{1+a_{H}h_{H}R^{2}}\)and \(F_{C}=\frac{a_{C}H^{2}C}{1+a_{C}h_{C}H^{2}}\). In these
formulas, \(a_{H}\) and \(a_{C}\) are attack rates,
\(h_{H}\) and\(h_{C}\) are handling times,
\(e_{H}\) and \(e_{C}\) are assimilation
efficiencies, and \(d_{H}\) and \(d_{C}\) are
mortality rates of the herbivore and predator species, respectively.

Let \((R_{3}^{*},\ H_{3}^{*},\ C_{3}^{*})\ \)denote the equilibrium biomasses of the three
species in the presence of the top predator and\((R_{2}^{*},\ H_{2}^{*})\) the
equilibrium biomasses of the basal and herbivore species in the absence
of top predator. Similar to our empirical analyses, we quantified the
strength of trophic cascade as:

\begin{equation}
STC=\ln\left(R_{3}^{*}/R_{2}^{*}\right)\nonumber \\
 \end{equation}

and the predator efficiency as:

\begin{equation}
E_{\text{pre}}=\frac{e_{C}F_{3C}^{*}}{e_{H}F_{3H}^{*}}\nonumber \\
 \end{equation}

where \(F_{3C}^{*}\) and \(F_{3H}^{*}\) represent the
equilibrium foraging rates of the predator and herbivore, respectively,
in three-species food chain models. In addition, primary productivity is
given by (Loreau 2010):

\begin{equation}
P_{\text{pro}}=rR_{3}^{*}\nonumber \\
 \end{equation}

We then performed analytical investigations and simulations to
understand the relationships between \emph{STC} , \(E_{\text{pre}}\)
and\(P_{\text{pro}}\). For the type I functional response model, we
derived analytic solutions for the relationship between trophic cascade
strength\emph{STC} and predator efficiency \(E_{\text{pre}}\) (see
\emph{SI Appendix 2} ). For all types of functional responses, we also
performed numerical simulations to investigate the relationships
betweenSTC, \(E_{\text{pre}}\), and
\(P_{\text{pro}}\). In our simulations, we fixed two intrinsic
parameters for the plant or predator (both fixed in our experiment),
i.e., \(r=0.8\) and \(d_{C}=0.5\), but changed other
parameters to capture variation in the herbivore species
\(H\) and the nutrient supply level, as in our experiment.
Specifically, we randomly draw
parameters\(K\sim U\left[2,5\right]\),\(a_{H},a_{C}\sim U\left[0.2,0.8\right]\),\(h_{H},h_{C}\sim U\left[0.01,0.3\right]\),\(d_{H}\sim U\left[0.1,0.5\right]\),
where\(U\left[x,y\right]\) denotes the uniform distribution over the
interval \(\left[a,b\right]\). For assimilation efficiencies, we used
both fixed values (Yodzis \& Innes 1992), i.e.,\(e_{H}\)= 0.45
and \(e_{C}\)= 0.85, and varying values,
i.e.,\(e_{H}\sim U\left[0.3,0.6\right]\ \text{and\ }e_{C}\sim U\left[0.5,0.9\right]\). For each type of functional response, we
retained 1000 replicates of simulated food chains where all three
species can stably persist, for which we recorded the strength of
trophic cascades, predator efficiency and primary productivity
(\emph{see details in} \emph{SI Appendix 2} ).

To test the robustness of our results to model complexity, we further
considered a four-species model that includes one plant, two herbivores,
and one predator (McCann 2011). Because our simulations of three-species
food chains showed highly consistent results across different types of
functional responses, we considered only the type II functional response
for the four-species model (\emph{see details in SI Appendix 2} ).
Overall, all models (with different functional responses or herbivore
richness) showed similar patterns, so in the main text we presented only
results based on the three-species food chain model with type II
functional response. Results from other models were presented in\emph{SI
Appendix 2} .

\textbf{Results}

The standing biomasses at all trophic levels were strongly affected by
experimental treatments (Fig. 2). The biomass of the predator \emph{E.
modestus} was significantly lower in the LP (i.e., low phosphorous
concentration) treatment compared with those in HP (i.e., high
phosphorous) and MP (i.e., medium phosphorous) treatments, and lower in
mesocosms consisting of \emph{S. dorrii} and \emph{D. brachyurum} than
those consisting of \emph{D. magna} and \emph{D. brachyurum} (Fig. 2a,
Table S2). Zooplankton biomass was influenced by the presence of
predators (F\textsubscript{1,36} = 114.36; \emph{P} \textless{} 0.001),
nutrient supply (F\textsubscript{2,36} = 235.87; \emph{P} \textless{}
0.001), zooplankton community composition (F\textsubscript{2,36} =
40.3;\emph{P} \textless{} 0.001), as well as their interactions (Fig.
2b-c and Table S1). Specifically, zooplankton biomass was significantly
suppressed by the presence of predators, while strongly promoted by
nutrient enrichment (Fig. 2b-c). In the presence of predators,
zooplankton communities consisting of all three species had the highest
biomass across all nutrient treatments (Fig. 2b). In the absence of
predators, zooplankton communities consisting of \emph{D. magna}
and\emph{D. brachyurum} had higher biomass than those consisting of all
three species in HP and MP treatments (Fig. 2d), due to higher biomass
of \emph{D. magna} in the former case (Fig. S2e-f). In the LP treatment,
however, the inverse pattern was observed (Figs. 2c,
S3a-b)\emph{.}Throughout the experiment, phytoplankton communities were
dominated by green algae (Fig. S4). Nutrient enrichment and the presence
of predators strongly boost phytoplankton biomass (\emph{P} \textless{}
0 .001 for both factors; Fig. 2d-e and Table S1). Our analyses also
showed significant interactive effects between predators and zooplankton
community composition on phytoplankton biomass (F\textsubscript{2,36} =
3.9, \emph{P} = 0.03) and nutrient supply (F\textsubscript{2,36} = 10.8,
\emph{P} \textless{} 0.001). At all trophic levels, the responses of
biomass production rates to experimental treatments were similar to
those of standing biomass (Fig. S2, Table S1).

Nutrient supply not only altered the standing biomass and production
rates at different trophic levels, but also their stoichiometric
characteristics. Phytoplankton molar C:P ratios decreased with increased
ambient P concentrations (F\textsubscript{2,36} = 253.7;
\emph{P}\textless{} 0.001; Fig. S4c; Table S1) and were higher in the
presence of predators (F\textsubscript{1,36} = 5.4, \emph{P} = 0.026).
By altering the stoichiometry of phytoplankton, nutrient supply also had
carry-over effects on the stoichiometry of higher trophic levels.
Specifically, an increase in ambient P concentration decreased the molar
C:P ratios of zooplankton \emph{D. magna} and \emph{S. dorrii} (Fig.
S4a-b), leading further to a lower body molar C:P ratios of
predator\emph{E. modestus} (Fig. S4d).

The energy transfer efficiency between producers and herbivores
(hereafter herbivore efficiency) was strongly modulated by the presence
of predators (F\textsubscript{1,36} = 16.4, \emph{P} \textless{} 0.001)
and zooplankton community composition (F\textsubscript{2,36} =
8.4,\emph{P} = 0.001, Table S1). The presence of predators significantly
decreased herbivore efficiency, especially in mesocosms with zooplankton
communities of \emph{D. magna} and \emph{D. brachyurum} (Fig. 3a).
Similarly, the energy transfer efficiency between herbivores and
predators (hereafter predator efficiency) was higher in mesocosms with
zooplankton community \emph{D. magna and D. brachyurum} , compared with
those containing other zooplankton communities (Fig. 3c). While nutrient
supply had no significant effects on herbivore efficiency and only
marginally significant effects on predator efficiency (Fig. 3b-c, Table
S1-2), it significantly affected the overall energy transfer efficiency
from producers to predators (hereafter food chain efficiency). That is,
the food chain efficiency was significantly higher in MP treatments
compared with those in HP and LP treatments (F\textsubscript{2,18} =
7.68; \emph{P} = 0.001; Table S2; Fig. 3d).

The top-down effects of predators on zooplankton biomass and their
cascading effects on phytoplankton biomass both differed significantly
among mesocosms with different zooplankton community compositions
(F\textsubscript{2,18} = 49.51, P \textless{} 0.001 for zooplankton
biomass; F\textsubscript{2,18} = 75, \emph{P} \textless{} 0.001 for
phytoplankton biomass), but not with nutrient conditions
(F\textsubscript{2,18} = 0.23, \emph{P} = 0.796 for zooplankton biomass;
F\textsubscript{2,18} = 0.084, \emph{P} = 0.920 for phytoplankton
biomass) (Figs. 4, S6, Table S2). Mesocosms with zooplankton communities
of \emph{D. magna} and \emph{D. brachyurum} showed the strongest
cascading effects (on average 107.8\% increase in phytoplankton biomass
in the presence of predators across three nutrient levels), followed by
those consisting of all three zooplankton species (57.3\%) and those
consisting of \emph{S. dorrii} and \emph{D. brachyurum} (41.5\%) (Fig.
4). To further disentangle the drivers of trophic cascades, we conducted
stepwise regression analyses and found that the strength of trophic
cascades was best explained by variation in predator efficiency (Fig.
5b; Table S3-4). In food chains with higher predator efficiencies, the
strengths of trophic cascade were stronger (Fig. 5b). In comparison,
neither primary productivity nor its interaction with energy transfer
efficiencies had significant impacts on the cascading effects (Fig. 5a,
Table S1).

Using food chain models with the type I functional response, we derived
analytical relationships between trophic cascade strength (STC) and
energy transfer efficiencies, i.e.,

\begin{equation}
STC=\frac{e_{C}}{e_{C}-E_{\text{pre}}}\nonumber \\
 \end{equation}

and between trophic cascade strength and primary
productivity\(P_{\text{pro}}\):

\begin{equation}
STC=\frac{e_{1}a_{1}}{rd_{1}}P_{\text{pro}}\nonumber \\
 \end{equation}

These solutions suggest that the relationship between STC
and\(E_{\text{pre}}\) involves only one covariate, while that
betweenSTC and \(P_{\text{pro}}\) involves multiple
covariates and thus may be more variable. This expectation was confirmed
by numerical simulation in general settings. Across simulated food
chains with varying parameters, the trophic cascade strength is strongly
related with predation efficiency, but relatively weakly related with
primary production and herbivore efficiency (Figs. 5c-d, S7-12). Similar
results were found in more complex food web models with two herbivore
species (Figs. S13, S14). Overall, our mathematical models support the
mechanistic link between energy transfer efficiency and the strength of
trophic cascades observed in our mesocosm experiment.

\textbf{Discussion}

Despite long-standing interest in food web energetics (after Lindeman
1942) and trophic cascades (after Hairston \emph{et al.} 1960), research
on these two processes have been largely disconnected in the literature.
Energy transfer was considered mainly by ecosystem ecologists as a
diagram to understand ecosystem energetics and functioning
(Chassot\emph{et al.} 2010; Eddy \emph{et al.} 2021), whereas trophic
cascades were widely adopted by community ecologists to understand
population dynamics (Layman \emph{et al.} 2015; Jonsson 2017; Barbier \&
Loreau 2019). These two paradigms, however, address highly related
processes of the same ecosystem, so a unified framework has increasingly
been advocated by theoretical studies (DeBruyn \emph{et al.} 2007;
Barbier \& Loreau 2019). In line with these theoretical advances, our
study proposes to understand trophic cascades from an energetic
perspective and combines mesocosm experiments and food chain models to
disentangle two energetically relevant hypotheses. Our results showed
strong associations between trophic cascade strength and predator
efficiency but not with primary productivity (Fig. 5; Table S3, S4),
supporting the energy transfer hypothesis rather than the productivity
hypothesis. Thus, although primary productivity plays vital roles in
food webs by providing ultimate energy for all trophic species (Oksanen
\& Oksanen 2000; Post 2002), an impeded energy transfer could limit the
biomass of top predators and weaken their cascading effects (Mooney
\emph{et al.}2010; Kersch-Becker \& Thaler 2015). These findings
corroborate a recent study on grassland experiments, where a decreased
energy flow to predatory beetles led to stronger suppressing effects of
arthropod herbivores on plants, i.e., weaker cascading effects (Barnes
\emph{et al.} 2020).

In our experiment, the predator efficiency varies significantly among
mesocosms with different zooplankton community compositions. Mesocosms
dominated by \emph{D. magna} (e.g., those initialized with \emph{D.
magna} and \emph{D. brachyurum} ) showed the highest predator efficiency
(Fig. 3c) and strongest trophic cascades. In comparison, mesocosms
dominated by other zooplankton species (e.g., those initialized
with\emph{S. dorrii} and \emph{D. brachyurum} , or with all three
zooplankton species) showed lower predator efficiency and weaker trophic
cascades in spite of higher total zooplankton biomass (Fig. 2b). This
may be explained by the physical and chemical characteristics of
\emph{D. magna,} making them better food sources for predators (Vincent
\emph{et al.} 2020). Specifically, the lower motility of \emph{D. magna}
can increase the attack rate of predators (Rall \emph{et al.} 2012), and
its high body nutrient concentration can increase the assimilation
efficiency (DeMott \emph{et al.} 1998). Therefore, the lower predator
efficiency may be attributed to the lack of high-quality resources in
mesocosms without \emph{D. magna} , or low amount of high-quality
resources (i.e., lower biomass of \emph{D. magna} ) in mesocosms with
all three zooplankton species (Fig. S3)\emph{.} These results highlight
the roles of species identity (O'Connor \& Crowe 2005), rather than
species richness per se (Duffy 2002), in mediating the strength of
trophic cascades. Similar patterns have been reported for
plant-herbivore interactions, where a higher primary productivity driven
by plant diversity does not propagate to higher trophic levels due to
the presence of inedible or anti-herbivory plant species (Brett \&
Goldman 1997; Davis \emph{et al.} 2010).

While nutrient supply had no significant impacts on trophic cascades, it
nevertheless imposed strong regulation on other processes of food webs.
In line with previous studies (Teurlincx \emph{et al.} 2017; Zhou \&
Declerck 2019), nutrient manipulations strongly shape the relative
abundance of zooplankton species (Fig. S3) as well as their biomass and
stoichiometry (Figs. 2a, S4). Moreover, the impaired performance of the
predator under LP treatments, e.g., low biomass, production, and body P
content, indicates a carryover effect of phytoplankton P limitation on
top trophic levels (Boersma \emph{et al.} 2008). Interestingly, we found
that food chain efficiency (FCE) exhibited a unimodal pattern along the
gradient of nutrient supply (Fig. 3d). The lower FCE in LP than MP
treatments agrees with previous findings on the negative effects of
nutrient limitation (Dickman \emph{et al.} 2008; Atkinson \emph{et
al.}2021). But with further P enrichment, FCE started to decline, due to
the relatively lower herbivore and predator efficiencies. This result
may suggest a disadvantages of high nutrients for food web efficiency
(Karpowicz \emph{et al.} 2021), due to for example, differences in
responding magnitudes between primary producers and apex consumers to
nutrient enrichment (Fig. S2).

Our results may have useful implications for natural resource
management. In particular, the classic biomanipulation approach for lake
restoration is rooted in the theory of trophic cascades, which assumed
that addition of piscivorous fish suppresses the biomass of
planktivorous fish and releases the herbivorous zooplankton, thus
controlling algal biomass via grazing (Carpenter \emph{et al.} 1995).
The importance of predator efficiency in determining trophic cascades
revealed in the present study suggests that the biomanipulation
approaches are most effective in systems with a higher efficiency of
energy flow into apex predators, whereas eutrophic systems with low
energy transfer efficiency may benefit weakly from the manipulating
practices of piscivores (Langeland 1990; Brett \& Goldman 1996). In
addition, our results also highlight the importance of trophic
interactions as drivers of ecosystem energy budgets, e.g., carbon
related functions (Strickland \emph{et al.} 2013; Schmitz \emph{et
al.}2018; Wyatt et al. 2021). For example, elevated efficiencies of
energy transfer allowed increased biomass accumulation in apex consumers
(McCauley \emph{et al.} 2018) and therefore stronger trophic cascades,
which may turn an ecosystem from carbon source into carbon sink (Schmitz
\& Leroux 2020).

\textbf{Conclusion}

By bridging the bottom-up energetic processes and top-down cascading
effects, our study contributes to reconciling food web studies using
different currencies, e.g., energy and population size. Our findings
advocate an energetic perspective in ecosystem management based on
trophic cascade theory, where strategies should be designed according to
the energetic dynamics of the focal system (Barnes \emph{et al.} 2018).
Our study serves as a benchmark for future research on more complex
ecosystems over larger scales. In particular, in diverse food webs,
energy transfer efficiencies between trophic levels are jointly
determined by herbivore diversity and composition (e.g., in our
experiment), plant (Behl \emph{et al.} 2012; Buzhdygan \emph{et
al.}2020) or predator diversity (Griffin \emph{et al.} 2008), as well as
abiotic factors (Barneche \emph{et al.} 2021; Eddy \emph{et al.} 2021).
Disentangling the influences of these processes is challenging but key
to understanding the feedback between energetic processes and trophic
interactions in natural ecosystems. Moreover, over long timescales,
eco-evolutionary dynamics may alter species properties, e.g.,
anti-predation trait (Vestheim \& Kaartvedt 2006) and thus food web
energetics. Empirical and theoretical studies with respect to these
directions should further contribute to a mechanistic understanding of
the responses of multitrophic communities to environmental changes.

\textbf{Acknowledgements:}

We thank Taihu Laboratory for Lake Ecosystem Research for providing the
ground and facilitations for the mesocosm experiment. This work was
funded by the National Natural Science Foundation of China (31988102,
32101329, 32122053).

\textbf{Competing interests}

The authors declare no competing interests.

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\textbf{Fig. 1} Conceptual illustration of two hypotheses underlying
trophic cascade strengths: the productivity hypothesis \textbf{(a)} and
the energy transfer hypothesis \textbf{(b)} . R (horizontal green bars),
H (horizontal brown bars), and C (horizontal red bars) represent the
biomass of plants, herbivores, and predators, respectively. The upper
arrows between adjacent trophic levels represent energy transfer, where
E\textsubscript{her} (green arrows) and\emph{E\textsubscript{pre}}
(brown bars) represent herbivore and predator efficiency, respectively,
with the thickness of arrows representing the relative magnitude. The
bottom dark-green upper arrows (\emph{P} ) refer to the primary
productivity. The dashed arrows indicate the indirect effects of the
apex predator on plant biomass (i.e., trophic cascades) with their
thickness representing the relative strength. The productivity
hypothesis posits that a higher productivity can increase the biomass of
apex predators and thereby enhance trophic cascades (Fig. 1a, Hypothesis
I). The energy transfer hypothesis posits that a higher efficiency of
energy transfer promotes the biomass accumulation of apex predators and
subsequently strengthens trophic cascades (Fig. 1b, Hypothesis II). The
dashed line with a smaller slope in Fig 1a (resp. Fig. 1b) indicates
weakened production effects (resp. weakened effects of energy transfer)
under a lower energy transfer efficiency (resp. lower production).

\textbf{Fig. 2} Responses of standing biomass at different trophic
levels to experimental manipulations: (a) predator \emph{E.modestus} ,
(b, d) zooplankton herbivores, (c, e) phytoplankton. Different capital
characters indicate significant differences (\emph{P}\textless{} 0.05)
among treatments varying in zooplankton community composition, and
different lowercases indicate significant differences among treatments
varying in nutrient supply. The bars and error bars show the averages
and standard errors across three replicates, respectively.

\textbf{Fig. 3} Responses of energy transfer efficiencies across trophic
levels to experimental manipulations: (a-b) Herbivore efficiency, (b)
predator efficiency, (d) FCE. The red arrows in the illustration schemes
represent the focal energy transfer processes. Different capital
characters indicate significant differences (\emph{P} \textless{} 0.05)
among treatments varying in zooplankton community composition, and
different lowercases indicate significant differences among treatments
varying in nutrient supply. The bars and error bars show the averages
and standard errors across three replicates, respectively.

\textbf{Fig. 4}Responses of trophic cascade strength to experimental
manipulations. Different capital characters indicate significant
differences (\emph{P}\textless{} 0.05) among treatments varying in
zooplankton community composition, and different lowercases indicate
significant differences among treatments varying in nutrient supply. The
bars and error bars show the averages and standard errors across three
replicates, respectively. The horizontal grey lines correspond to no
cascading effect, i.e., no change in phytoplankton biomass following the
removal of the top predator.

\textbf{Fig. 5} Relationships between trophic cascade strength with
primary production (\textbf{a, c} ) and predator efficiency (\textbf{b,
d} ), derived from experimental data (\textbf{a, b} ) and theoretical
models (\textbf{c, d} ). In \textbf{a} and \textbf{b} , each symbol
represents one mesocosm, where circles (SD) represent zooplankton
communities consisting of \emph{S. dorrii} and \emph{D.
brachyurum,}triangles (DD) represent zooplankton communities consisting
of \emph{D. magna} and \emph{D. brachyurum} ; and squares (SDD)
represent zooplankton communities containing all the three species. The
dashed black line in (\textbf{a} ) represents a non-significant
relationship (\emph{P}\textgreater{} 0.05), whereas the solid black line
in (\textbf{b} ) indicates a significant relationship (\emph{P}
\textless{} 0.05). Shaded areas are the error bands and denote 95\%
confidence intervals. In\textbf{c} and \textbf{d} , each point
represents one simulated food webs with randomized assimilation
efficiencies, i.e.,\(e_{H}\sim U\left[0.3,0.6\right]\) and\(e_{C}\sim U\left[0.5,0.9\right]\), where
trophic interactions follow the type II functional response. Other
parameters are specified in Methods. The horizontal grey lines
correspond to no cascading effect.\selectlanguage{english}
\begin{figure}[H]
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\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

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\textbf{Figure 1}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}



\textbf{Figure 2}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5}

\selectlanguage{english}
\FloatBarrier
\end{document}

