Detection of energetic equivalence depends on food web architecture and estimators of energy use

Domain: biology
Published: 2025-12-19
Editorial outcome: major_revision

Abstract
Ecologists have long debated the universality of the energetic equivalence rule, which posits that population energy use should be invariant with average body size due to negative size–density scaling. We explore size–density and size–energy use scaling across 183 geographically–distributed soil invertebrate food webs (comprising 55,054 individual soil invertebrates) to investigate the universality of these fundamental energetic equivalence rule assumptions across trophic levels and varying food web structure. Additionally, we compare two measures of energy use to investigate size–energy use relationships: population metabolism and energy fluxes. We find that size–density scaling does not support energetic equivalence in soil communities. Furthermore, evidence of energetic equivalence is dependent on the estimate of energy use applied, the trophic level of consumers, and food web properties. Our study demonstrates a need to integrate food web energetics and trophic structure to better understand how energetic constraints shape the body size structure of terrestrial ecosystems.

Introduction
The scaling of body size with organism metabolism and abundance are underlying expectations and ecological properties on the scaling of some of the most widely observed, studied, and debated biological organism body size and population energy use estimates, despite early relationships. Yet, there is persisting discord around the generality of the energetic equivalence rule (EER) across ecosystems. This partly stems from variation in the underlying biological assumptions of the EER, differences in approaches used to estimate community body size–energy use relationships, and limited consideration of how EER scaling depends on organism trophic position and food web architecture. To date, few studies have quantified the influence of these advancements in size–density scaling to understand energetic constraints of food webs over two decades ago.

Assessing the EER is fundamentally reliant on determining the scaling relationship between population body size and energy use. The EER is a central expectation of the Metabolic Theory of Ecology (MTE), which predicts that population energy use (hereafter, En, the total energy consumption required to support population (density) n biomass) should be invariant with respect to population–average body size, that is, En ∝ Mn 0. This is based on the underlying assumptions that 1) individual organism energy use i (Ei) scales with whole–organism body size Mi with a positive ¾ (Ei ∝ Mi 0.75) exponent, and 2) the abundance (i.e., density) N of individuals scales with population body size M with a negative ¾ (N∝M–0.75) exponent. A zero exponent of body size–energy use scaling of populations in a given community (i.e., En ∝ Mn 0) should only be met if whole organism body size–energy use (i.e., Ei ∝ Mi) and size–density (N∝Mb) inverse relationships have opposite exponent values (e.g., Ei ∝ Mi 0.75 and N∝M–0.75). Numerous studies have found a –0.75 size–density scaling exponent (N∝M–0.75) among populations within communities, though many others have found this varies considerably across taxa. These observed deviations likely arise from taxonomic variation in the allometric exponent of basal metabolic rates and varying energetic constraints across trophic levels, life history traits, environmental conditions, and spatial scale. Nevertheless, an expectation of a –0.75 size–density exponent is still widely employed at both local and macro–ecological scales. Despite the fundamental assumptions of the EER, few studies have analysed both size–density and size–energy use relationships to detect energetic equivalence, and most assume energetic equivalence based only on size–density (N∝M–0.75) or whole–organism body size–energy use (Ei ∝ Mi 0.75) scaling. Furthermore, describing size–energy use scaling relationships poses the challenge of assessing population energy use, which is typically achieved by quantifying population metabolism. This approach, however, does not consider additional energetic expenditure due to the inefficiency of trophic energy transfer, losses to predation from higher trophic levels, and other trophic–level–dependent variation in energy loss. Although the EER is derived from macro–scale patterns (the GSDR), we should still expect this rule to apply for communities at carrying capacity, which would theoretically be evident from a size–density scaling relationship exponent of –0.75. Arguably, however, a more robust test of the EER at the local community scale would be to examine the population energy use–body size relationship, as this accounts for differences in energy use due to factors like taxonomic composition and trophic structure.

Size–density and size–energy use scaling relationships have been shown to vary systematically across trophic levels. While some studies have explored body size scaling relationships within a food web context, they lack further synthesis into the comparison between these size–density scaling exponents on their resulting size–energy use scaling. Energy availability decreases with increasing trophic level and body size, due to inefficient energy transfer from resources to consumers. Therefore, the scaling of size–density and size–energy use should be N∝M<–0.75 and En ∝ Mn <0, respectively, across all trophic levels, compared with N∝M–0.75 and En ∝ Mn 0 within single trophic levels that share the same energy pool. However, secondary consumers typically span multiple trophic levels that do not directly access basal resources and tend to prefer larger prey, so they should have the steepest size–density and size–energy use scaling exponents due to greater energetic constraints (although there are documented exceptions across aquatic versus terrestrial systems). Systematic deviations from expected scaling exponents related to trophic positioning of species question the theoretical foundation of the EER and call for a food web approach that discriminates among trophic levels, as information on energetic constraints could be obscured by ignoring trophic differentiation.

Whilst there has been research into environmental drivers of size–density scaling relationships underlying the EER, how variation in food web architecture and estimators of energy use affect these relationships remains unexplored (but see Loeuille & Loreau which examines how body size affects species interactions). Alternative measures of energy use, such as trophic energy flux, account for total transfer of energy in and out of a population and can therefore describe total energetic losses (and thus expenditure) due to metabolism, assimilation efficiency, and consumption by higher trophic levels (i.e., predation). These losses must be balanced by energetic gains and are therefore directly related to population energy use. Thus, despite uncertainty that is inherently introduced by modelling energy fluxes based on published input parameters, measures of total energy consumption (i.e., influx of energy into a given food web node before assimilation) should provide more precise estimates of population energy use that can be integrated into analyses of size–energy use scaling relationships in food webs.

Here we analyse size–density (N∝Mb) and size–energy use (En ∝ Mn b) scaling using a comprehensive dataset of individual body sizes (body mass in mg) in soil invertebrate food webs (i.e., local communities) across four geographic locations (i.e., 183 food webs comprising 55,054 individual invertebrates). We investigate the universality of size–density scaling relationships (based on individual size distributions as opposed to population–level size–density scaling relationships) and their likelihood of indicating energetic equivalence in soil communities of primary and secondary consumers. We compare two different estimates of energy use to investigate differences in size–energy use relationships, population metabolism (In ∝ Mn) and energy fluxes (Fn ∝ Mn), and investigate whether these scaling exponents are reflected by size–density relationships. Additionally, we investigate the marginal effects of node richness (i.e., number of nodes within each food web, where a node is defined as organism taxonomic order), trophic similarity (i.e., mean similarity between nodes per food web), and omnivory (i.e., trophic level omnivory of secondary consumers) on the deviation of food webs from predicted size–metabolism or size–energy flux exponents. We hypothesise that (1) N∝Mb and En ∝ Mn b scaling across all trophic levels (i.e., entire food webs) and for secondary consumers will be more negative than the MTE expectations of scaling exponents (i.e., N∝M<–0.75 and En ∝ Mn <0) due to attenuating trophic transfer efficiency at higher trophic levels. However, we acknowledge that increasing energetic constraints at higher trophic positions may also be partially relaxed by increasing prey richness, available energy sources, and spatial scale of movement of larger–bodied consumers. In contrast, we hypothesise that (2) primary consumers will exhibit N∝M–0.75 and En ∝ Mn 0 scaling because individuals within their trophic guilds feed from and compete over the same basal resource base. We also hypothesise that (3) En ∝ Mn b scaling using metabolism I as an estimate of energy use will be less likely to produce scaling exponents that meet expectations compared to energy flux F, as metabolism does not account for additional energetic expenditure due to assimilation (in)efficiency and losses to predation by higher trophic level consumers. Finally, we hypothesise that (4) deviations from EER expectations of En ∝ Mn 0 scaling will be smaller in food webs with higher node richness and trophic similarity due to greater resource competition imposing proportionately stronger energetic constraints on larger–bodied consumers. Conversely, we expect increasing deviations from En ∝ Mn 0 scaling with omnivory as energetic constraints may be relaxed when consumers feed across more energy sources, leading to En ∝ Mn 0 scaling exponents > 0. However, we also assume these effects of food web properties on deviations from EER expectations will vary across trophic levels due to differences discussed above.

Results
Testing the energetic equivalence rule without trophic differentiation
Scaling exponents of soil invertebrate consumers across all trophic levels in soil food webs were, on average, more positive than expected for size–density (i.e., N∝M>–0.75, mean=–0.174, median=–0.152, σ2=0.05), size–metabolism (i.e., In ∝ Mn >0, mean=0.134, median = 0.164, σ2=0.07), and size–energy flux (i.e., Fn ∝ Mn >0, mean=0.204, median=0.195, σ2=0.09) relationships. Nevertheless, scaling exponents derived from both measures of energy use (In ∝ Mn and Fn ∝ Mn) appeared to have a similar central tendency (kurtosis=4, and In ∝ Mn σ2=0.07, Fn ∝ Mn σ2=0.09) around values expected by the MTE, within the confidence interval of exponent estimates. At the whole food web level, metabolism as an estimate of energy use appeared to better fit EER expectations compared to energy flux, as 50.3% of all soil food webs met scaling expectations for size–metabolism relationships compared to 41.5% for size–energy flux relationships. There was a significant positive and negative effect of node richness on the deviation of food webs from the hypothesised size–metabolism and size–energy flux exponent (p<0.01), respectively. We also found a significant negative effect of trophic similarity (i.e., the mean similarity among all nodes in the trophic level (primary consumers or predators) on the deviation of whole food webs from both the hypothesised size–metabolism (In ∝ Mn 0) and size–energy flux (Fn ∝ Mn 0) exponents (p<0.01).

Variation in energetic scaling patterns across trophic levels and food web structure
Similar to the trends in EER scaling relationships observed for whole food webs, primary consumers produced scaling exponents that were, on average, more positive than expected for size–density (N∝M>–0.75, mean=–0.191, median=–0.109, σ2=0.16), size–metabolism (In ∝ Mn >0, mean=0.261, median=0.268, σ2=0.12), and size–energy flux (Fn ∝ Mn >0 mean = 0.761, median = 0.646, σ2=0.51) relationships. Secondary consumer scaling exponents were, on average, more positive than expected for size–density (N∝M>–0.75, mean=–0.218, median = –0.201, σ2=0.06) relationships. However, as we predicted, they were more negative for size–metabolism (In ∝ Mn <0, mean=–0.039, median=–0.003, σ2=0.14) and size–energy flux (Fn ∝ Mn <0, mean=–0.394, median = –0.524, σ2=0.57) relationships. Out of 173 primary consumer communities, 1.1% met scaling expectations for size–density (N∝M–0.75), 42.9% met size–metabolism (In ∝ Mn 0) expectations, and 46.3% met size–energy flux (Fn ∝ Mn 0) scaling expectations of the MTE. Comparatively, out of 180 secondary consumer communities, 2.8% met scaling expectations for size–density, 41.4% met size–metabolism scaling expectations, and 54.1% met size–energy flux scaling expectations of the MTE. We also found less variation (i.e., higher kurtosis and variance of the respective density functions for scaling exponent estimates) around the mean and median exponents for the scaling of body size with energy fluxes (Fn ∝ Mn) compared to metabolism (In ∝ Mn) for secondary consumers, though the opposite was true for primary consumer kurtosis values. These observed differences between measures of energy use were further corroborated by significant differences in the probability distributions of estimated metabolism versus energy flux exponents for both primary (Kolmogorov-Smirnov test D=0.411, p<0.01) and secondary consumers (Kolmogorov-Smirnov test D=0.406, p<0.01). Contrary to our hypothesis, we found that mean and median exponent values for In ∝ Mn and Fn ∝ Mn relationships were closer to zero for secondary consumers than for primary consumers. To ensure that our results were not notably biased by differences among datasets in the measurement of environmental temperature, we calculated metabolic rates and energy fluxes with temperatures extracted from WorldClim and re–ran analyses to test for the sensitivity of EER scaling results to variations in environmental temperature, which yielded no qualitative changes in our results.

We only found a significant positive effect of trophic similarity within secondary consumer food webs on the deviation from size–metabolism scaling expectations (In ∝ Mn 0). In contrast, for size–energy use scaling based on energy fluxes, we found a significant positive effect of node richness and negative effects of trophic similarity and omnivory on the deviation from size–energy flux scaling expectations for secondary consumers (Fn ∝ Mn 0, p<0.01). However, we found no significant effects of node richness or trophic similarity on deviations from the size–metabolism or size–energy flux exponents expected by the EER for primary consumers (p<0.05).

Methods
Soilinvertebratecommunitysampling
Soilinvertebratecommunitydatawascollectedfromfourlocations(AotearoaNewZealand,Indonesia,Canada,andU.S.A)throughsamplingeffortsofthreelarge–scaleprojects. (1) The Aotearoa New Zealand plots (People Cities & Nature programme) were established in forest patches within nine cities spanning ~9o of latitude. These were part of a 60–year–old planted and primary old–growth urban forest chronosequence (n=73). (2) The Indonesian (EFForTS project) study plots (n=30) were established in remnant tropical rainforest, jungle rubber agroforest systems, rubber monocultures, and oil palm monocultures across two landscapes surrounding Bukit Duabelas and Harapan rainforest reserves in the Jambi Province, Sumatra, Indonesia. The ECOWORM project study plots (n=80) in (3) the United States (St John’s forest, Minnesota) and (4) Canada (Barrier Lake North, Barrier Lake South, and Bull Creek Hills in the Canadian Rocky Mountains, Kananaskis Valley, Alberta) were established in maple and aspen forest sites, respectively, whereby each of these forests contained a low–invasion and a high–invasion exotic earthworm area–per forest (10 plots in low– and 10 plots in high–invasion areas).

Soilinvertebratecommunitydatacollectionandpreparation
Aotearoa New Zealand soil invertebrates were sampled between November 2019–February 2020 (austral summer) from three 50 × 50 cm subplots by taking one macrofauna soil core (22 cm diameter, 10 cm deep from the mineral soil layers) and one mesofauna soil core (5 cm diameter, 10 cm deep mineral soil layers) per subplot. Macro– and mesofauna were extracted from the soil cores using heat extraction and identified in the laboratory to family or order level (i.e., node). Individual body length (mm) was converted to fresh body size (mg) using length–size scaling relationships according to different invertebrate phylogenetic groups from published literature. Soil invertebrate collection from all other geographic regions followed similar procedures, whereby mesofauna were collected either from small cores (5 cm diameter, 10 cm deep) or 16×16 cm quadrats (5 cm deep), and macrofauna were collected from large soil cores (20 cm diameter, 10 cm deep), leaf litter sieving (0.5 m2 ECOWORM and 1 m2 EFFForTS), and mustard extraction for earthworms (0.25 m2). Invertebrate body size ranged from 4.82×10–5 mg – 5290 mg. For more detailed methods see Antunes.

To analyse size–energy use relationships, we took a size–binning (rather than populations of competing organisms) approach by taking the natural logarithm of all body sizes, across all taxonomic groups, and grouped them into 0.25 ln(mg) size class bins (following Reuman). This size binning approach was used for two reasons. Firstly, population-level information (i.e., species level taxonomic resolution) was not always available for our data, though individual body sizes were. Secondly, these methods have both yielded similar size–density scaling relationships within many food webs studied, so we can assume this consistency also applies to tests of size–energy use scaling relationships. We took the median of the natural logarithm of body size of each size class bin per plot, across all taxonomic groups. Abundance was then calculated as the number of individuals in each size class bin (and per node type for analysing within trophic levels) per plot and scaled to 1 m2. For analysing size–density relationships, the counts of soil invertebrate fresh body sizes (mg) across and within trophic levels were scaled up to 1 m2. We calculated individual metabolic rates I (J hr–1) for invertebrates within each taxonomic group (see Table S3 for regressions applied to each taxon) using the following equation from Ehnes et al.

I=exp(ln(io)+α×ln(M)−E/(k×T)) (1)

Where k is Boltzmann’s constant (8.62×10–5), T is environmental temperature in Kelvin, E the activation energy, io the taxa specific normalisation constant and, α is the allometric exponent. Plot–level mean soil temperature from a three–month period preceding soil sampling was collected using data loggers for the Aotearoa New Zealand. Local area–level annual soil temperature (over a one year period) for the ECOWORM plots was collected from online weather databases (National Oceanic and Atmospheric Administration n.d.). Plot–level mean soil temperature was collected over a 2.5 month period using data loggers for the EFFForTS data. We took the natural logarithm of individual invertebrate metabolic rates, summed per size class bin per plot, and scaled to 1 m2.

Foodwebreconstructionandconsumerenergyintakecalculation
To reconstruct soil food webs, nodes were defined according to organism taxonomic order (or family level for Hymenoptera and Coleoptera) for which information on their general feeding preferences was obtained. We constructed a meta–matrix of binary consumer–resource interactions, where feeding links were assigned based on feeding preferences obtained from literature. Energy influx in J day–1 into each consumer node within a local food web (i.e., plot) was calculated using the food–web energetics approach as described by Barnes and Gauzens to quantify the energy intake of organisms across the 183 local food webs. To calculate energy fluxes, we assumed that losses in energy from consumer nodes (via metabolism and predation) were balanced by intake of energy through resource consumption. Energy flux values were calculated taking into account the assimilation efficiency of energy by consumers based on the resources they feed on (i.e., primary versus secondary consumers).

Using the fluxing function from the fluxweb package in R, the influx of energy to consumer (j) was calculated as:

Σi(Wij×eij×Fij)=Ij+Σj(Wij×Fj) (2)

where eij is the assimilation efficiency by which a consumer (j) converts energy consumed from its resource (i) into energy for metabolism and biomass production. To determine the assimilation efficiency of energy by consumers based on the resources they feed on, eij was set to 0.906 for animals (e.g., as resources of predators), 0.545 for plants, 0.158 for detritus, 0.6 for bacteria, and 0.5 for fungi. Metabolic rate Ij for all animal consumers was equal to the summed individual metabolic rates per node, per plot. Ij was set to 1 for all basal resources (bacteria, detritus, plants, and fungi). Fij=Wij×Fj is the flux of energy to a consumer where Fj is the sum of fluxes into a node and Wij is the proportion of Fj obtained by the node according to scaled consumer preferences (wij) to the biomasses of different available prey as:

Wij=wij×Bi / Σj×wij×Bj (3)

where Bi and Bj are the resource and consumer biomasses, respectively. Bi for all animal resources and Bj for all animal consumers were equal to the summed fresh body masses (mg) of all individuals per node type, per plot. All basal resource biomasses were set to be equal to the average biomass of all consumer node types per plot to set near–equal preferences of omnivores between predatory links and basal resources. This was done to reduce extreme preferences of omnivores towards basal resources, such as plants and detritus that typically have much higher biomasses compared to soil invertebrate prey, but are less preferred by them as they are lower in nutritional value. Studies have tested whether the assignment of feeding preferences of omnivores between basal resources (in this case, just plants) and animals could affect energy fluxes by altering feeding preferences for plants between 0.2 to 0.9 and found no significant change in the outcome of their analysis; therefore, we set equal preferences between basal resources and animal prey in our food webs. Additionally, to reduce the amount of energy predators consume from their own biomass pool and unrealistic feeding preferences toward cannibalism, we set the feeding preferences of any cannibalistic links to 0.1.

Because body size was grouped into size class bins (irrespective of food web node) per plot to analyse size–energy relationships and energy flux was calculated per food web node per plot (Fnode), to attribute the proportion of ingoing energy flux from each food web node to each size class bin per plot (Fsizeclass), we calculated proportional energy flux according to the summed metabolism of each size class (Isizeclass) and energy intake of that node as:

Fsizeclass= f(Isizeclass,node =Inode)×Fnode (4)

Where Inode represents the total metabolism of a node. Energy fluxes were then natural logarithm–transformed and scaled to 1 m2.

To obtain food web metrics that could explain variation in expectations of size–density scaling and energetic equivalence of soil food webs, we quantified mean trophic similarity among nodes (for the whole food web, and within primary and secondary consumers) by calculating the average Jaccard similarity among consumer nodes based on their feeding links with resource nodes. Specifically, trophic similarity TSij between consumer i and j represents the similarity in their diets, estimated with a Jaccard index:

TSij=|Pi∩Pj|/|Pi∪Pj| (5)

Pi represents the set of prey of consumer i and |Pi ∩ Pj| is the cardinality of the intersection of Pi and Pj (i.e., the number of prey common to consumer i and j). High trophic similarity indicates a large average overlap among consumers, which can occur in the absence of omnivory, e.g. if many specialists feed on a shared resource. We calculated observed node richness as the number of nodes within each food web (total nodes in the food web, and the number of primary and secondary consumer nodes). Furthermore, we calculated trophic level omnivory of secondary consumer i (Oi) as the variance of the trophic levels of its prey:

Oi=1/ni Σj=1...ni(TLj−TLx̄i)2 (6)

Where TLx̄i is the average trophic level of the prey of species i. For each local food web, we further determined the prey–averaged trophic level (TLi) of each node, such that the trophic level was equal to one for basal resources, two for primary consumers, and >2 for secondary consumers as:

TLi=1/ni Σj=1...niTLj (7)

Where ni is the number of prey of species i, and j are prey of species i.

Statisticalanalysis
To analyse size–density relationships (N∝Mb) across whole soil invertebrate food webs and within primary and secondary consumers, we used maximum likelihood estimation (MLE) to estimate the exponent b (i.e., λ+1) derived from individual size distributions (ISD) of all individual body sizes (scaled to 1 m2) within soil invertebrate communities using the sizeSpectra package in R. To check the fit of models against observed body size data (x), rank–frequency plots were produced giving the natural logarithm–rank of the number of observations ≥x against the value of x.

To analyse size–metabolism (In ∝ Mn), and size–energy flux (Fn ∝ Mn) scaling relationships across whole soil invertebrate food webs and within primary and secondary consumers, we used ordinary least squared (OLS) regression using logarithm median body mass data (scaled to 1 m2). MLE and OLS regression models were run across all communities (i.e., plots) within the four geographic regions. The 95% confidence intervals around the exponent values were also calculated, and exponents were considered to meet N∝M–0.75, In ∝ Mn 0, or Fn ∝ Mn 0 expectations if these confidence intervals included the expected exponent value. We excluded all resulting models with less than 10 body size class bins or individuals per food web from our analysis due to insufficient data for estimating reliable model fits. To evaluate the distribution of scaling exponents around the mean and median values of our models, we calculated the kurtosis of their probability density functions using the kurtosis function in R. In this regard, higher kurtosis values indicate greater deviation from a normal distribution, reflecting increased variation around the mean and median exponent values. We also ran a two-sample Kolmogorov-Smirnov test, to determine if our two sample distributions (e.g., metabolism and energy flux exponents) come from the same probability distribution using the ks.test function in R. To analyse size–metabolism (In ∝ Mn), and size–energy flux (Fn ∝ Mn) scaling relationships across whole soil invertebrate food webs and within primary and secondary consumers, we also used ranged major axis (RMA) regression using the lmodel2 package in R to analyse these relationships. RMA regression is used when both x and y variables (e.g., median body size, abundance, metabolism, and energy flux) in the regression equation are random. RMA regression models were run across all communities (i.e., plots) within the four geographic regions. We excluded all resulting models with less than 10 body size class bins or individuals per food web from our analysis due to insufficient data for estimating reliable model fits. As a result, our analyses yielded a total of 183 food webs (i.e., comprising both primary and secondary consumers) and 360 trophic level models (180 models for primary consumers and 180 for secondary consumer food webs). Our analyses yielded a total of 183 food webs (i.e., comprising both primary and secondary consumers) and 355 trophic level models (173 models for primary consumers and 179 for secondary consumer food webs).

Additionally, we investigated whether the likelihood of size–density and size–energy use relationships to meet EER expectations could be explained by variation in food web structure. To do so, for all food webs, we constructed a normal linear model testing for the response of the absolute logarithm–deviation of observed exponents from expected size–energy use exponents (In ∝ Mn 0 and Fn ∝ Mn 0) to omnivory, node richness, and trophic similarity per food web and per trophic level (i.e., primary and secondary consumers). This produced six linear models in total. All statistical analyses were performed in R version R 4.4.0.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This paper focuses on the Energy Equivalence Rule (EER) that predicts that population energy use is invariant with average body-size. The authors have examined the EER by applying it on a large dataset including 183 soil food webs across the globe, taking into consideration the trophic position of the species under study.\nThe strengths of the study are:\n1. The validity of the EER is a timely question and is subject of debate from theoretical as well as empirical perspectives.\n2. The dataset used is unique given the number of food webs and species under study, as well as the global distribution of the food webs. The food webs are nicely comparable as they are all soil food webs.\n3. The study is scientifically novel, as the application of the EER on the dataset takes into consideration aspects of food web architecture and the trophic positioning of the species.\n4. Also novel is de comparison between measures of population metabolism and total energy flux.\n5. The study is well carried out.\n6. The results are well presented with an adequate number of clarifying figures.\n7. The results are scientifically interesting and relevant, as the soil food webs seem to deviate from the EER in a principal and statistically significant manner. Expectations regarding trophic positioning (primary, secondary, predatory consumers) seem to be confirmed, although not always at the level of statistical significance.\n8. The findings are well discussed but see my remarks below.\nOn the basis of these strengths the study qualifies to be published in a high quality scientific journal.\nBut I have the following concerns regarding the present manuscript.\n1. The introduction could have been clearer regarding the state-of-the-art in this field of research. Then it becomes also clearer what the novelty of the study is and how it stands out from other studies. An important piece of novelty is the consideration of aspects of food web architecture and the trophic position of the species. In the manuscript lines 132 -134 states that variation in food web architecture is unexplored, but this statement should be made more explicit. There is a number of studies in which the EER is applied to datasets including food webs. In one of these studies a large number of soil food webs is analysed (ref 20). And in another study (ref. 1) categories of species are distinguished in part based on their trophic position. It would be helpful when the present study is contrasted to such studies. For example, in terms of what they did and found rather than only mentioning that they have been done.\nIn this context I like to mention a study not referred to in the present manuscript, i.e. Evolution of body size in food webs: does the energetic equivalence rule hold? by Nicolas Loeuille and Michel Loreau in Ecology Letters, (2006) 9: 171–178. In this study the authors model how food web structure evolves from body-size and ecological interactions. The study might be relevant for sharpening the research question.\n2. I am a little uncertain whether I fully understood the results, but what I see is that the soil food webs deviate very strongly from the EER. The size-density index is found to be -0.174 instead of -0.75 (correct?). This is a lot. If the indexes for size-population metabolism and the size-energy flux are 0.134 and 0.204 respectively, then the index for individual size-metabolism should be around 0.5, i.e. smaller than 0.75, but less deviating than the index for size-density. I would emphasize this finding more. This makes the paper more challenging as to me the soil food webs do confirm the EER (at all).\n3. I miss a discussion of how the present results relate to the findings for the soil food webs examined in ref. 20. Also, a comparison with the results given in ref 1. seems relevant.\n4. The results that discriminate between types of consumers are interesting, make sense, and are discussed well. But they might also be viewed in the context of the deviating values for the food webs as a whole.\n5. EER is seen as a rule, but it can also be seen as a hypothesis. The present study formulates hypotheses regarding trophic position, competition and ways to quantify population energy use, so we have hypotheses on top of the EER hypothesis, which makes it sometimes difficult to see what ‘expectations’ mean.\n6. The conclusion drawn in lines 364-368 I find too mild. I don’t think that deviations from the EER is the most promising way to understand population dynamics in soil ecosystems. In the discussion numerous factors and processes are mentioned that influence these dynamics in fundamental ways. And soil populations are known for their large variation in numbers among soils and within soils over time and space. Isn’t it possible to simply reject the EER for soil food webs. We then should not throw away the baby with the washing water of course. The rejection comes from the assumed relationship between body-size and abundance, which to me is the weaker part of the EER (see also ref. 25 and Isaac et al. Global Ecology and Biogeography, 2013, 22, 1–5). The relationship between body-size and individual metabolism though is well based on biological/physiological arguments and has proven to be of value for understanding food web structure and also the structure of soil food webs.\nHope my comments are helpful in making the positioning of the study somewhat clearer and the implications of the findings somewhat more pronounced.", "reviewer_2": "I truly appreciate the opportunity to read this manuscript. It is well written and provides a significant contribution with a mass of evidence about density-body size and energy use – body size. This is a significant landmark about the empirical support or not for sound ecological rules. The authors analyzed the most comprehensive data set of induvial body size in terrestrial food webs, covering 183 food webs from different geographic regions. The results are not confirmatory, clearly indicating that the increase in density with body size is usually more positive than expected by the main theories and that in most cases energetic use is predominantly associated with body size. This qualitative result was consistent with the estimate of energy use from the expected metabolic rate or with the estimate of energy flux. However, the estimated exponents differed between these estimations. This is a point to highlight because of the lack of support for the general use of metabolic scaling to assess energetic equibalance. In this sense, the focus on the energy flux represents a relevant methodological and conceptual advance that might challenge the accumulated evidence. Differences were detected between scaling patterns in primary and secondary consumers supporting the role of the food web structure in energy use and scaling with body size.\nI have different comments to consider by the authors.\nThere is a methodological point that represents the most important concern. There is evidence that the selected method, binning the data, provides a biased estimation of the true exponent and that Maximum Likelihood estimation based on the individual size distribution must be used (Clauset et al., 2009; Newman, 2005; White et al., 2008). ML estimation on the size distribution provides an unbiased estimation and also requires the finding of the minimum and maximum individual sizes within which the estimation has to be performed (see Fig. 3.3 in Clauset et al., 2009). Note that energetic constraints to density and the effect of body size on energy flow are not expected to operate equally in all body sizes, expecting nonlinear relationships and ranges of different body sizes with different scaling (Arim et al., 2011; Clauset et al., 2009; Newman, 2005).). However, I have to say that I understand the authors´ decision to use a widely used method in ecology (even after the report on its shortcomings) and that the discrepancy of ML on estimation of the scaling in the size distribution with alternative methods is a point of attention. However, so far I know, there is no evidence supporting binning methods over ML on the size distribution, nor is there evidence supporting that binning methods are not biased, particularly for the amount of information available in ecological studies. Regrettably, discrepancies between energy use and density scaling can be affected by the selected method.\nThe rest of my comments do not represent major concerns:\nAlong the introduction, I think that some points could be further highlighted. The density and energy rules were generally supported at large geographic scale, but not in local communities; which is the scale of the present study (White et al., 2007). In addition to the soil studies mentioned by the authors, other studies considered the existence of an effect of local conditions and biotic organization on scaling (e.g. Cyr et al., 1997a; Cyr et al., 1997b).\nI find the discussion to be a bit long and repetitive in some ideas. For example, paragraphs 2-3 focus on the performance of energy flux and similar methodological issues; probably they can be reduced and merged in half of its actual extension. In addition, I found some sections unnecessarily speculative with general comments but not explicit attention to the underlying mechanisms (e.g. the mention to the habitat complexity hypothesis of Pawar et al.; the mechanisms through which richness affect scaling, the potential evaluation of alternative scaling methods, etc.).\nPrevious studies on EER and Damuth in particular highlighted the lack of an energetic advantage associated with body size, and the fact that this difference did not evolve was surprising (Damuth, 2007). However, the present results contradict this view, indicating the need to consider the ecological and evolutionary mechanisms involved in the existence of systematic differences in the use of energy by the population associated with body size. I think this should be a matter of discussion here.\nSpecific Comments\n· contribution, particularly along the discussion section.\nThere are several important results, and in some points the synthesis could be difficult for a first reader, figures help, but I wonder if a synthesis figure resuming results can improve the clarity of the main massage; may be expanding Figure 1?.\n· About the hypotheses. Consumers not only lose available energy at higher trophic position because of the low efficiency in energy flow available energy can also increase by other mechanisms. Attenuation in gape limitation, an increase in the spatial scale of movement of individuals, a larger prey richness, and the access to novel energy source can also compensate for the loss of energy at higher trophic positions (Arim et al., 2010; Rooney et al., 2008). Even along primary consumers, the well-reported increase in prey richness with body size can increase the amount of available energy, by means of the above-mentioned mechanisms (Arim et al. 2010).\nL159 More competition will affect the scaling only if competition changes with body size and/or differentially affect species efficiency or predation at different body sizes (Ritchie, 2010)\nHypotheses about the effect of richness and complementary trophics are also expected for this section.\n- I agree with the use of kurtosis, but it is not clear why not use variance, since a similar kurtosis level can mask different variances.\nFor energy use scaling, I appreciate having a histrogram reporting the R2 values.\nL 88 “population [density] n biomass”.\nL 89 if possible try to add citations in words and not following exponents.\nL 93. Perhaps some references would be added here.\nL157 it is difficult that a whole trophic level is represented by a single guild\nL182 This is the first time that the node richness appears in ms. I think the motivation for considering node richness should be stated in the Introduction. In addition, until this line, I consider that each node was the population of single species, probably some mention to tropho species or node aggregation can also help.\nL184 What is the trophic similarity? Is it estimated within or between nodes?\nL287 Fig. S4 first mention, after Fig. S5 (L186)\nL305 I am not convinced of making a point about a non-significant support for the Ehnes et al. proposition. In fact, I was stacked Fgg. 4 a,d, trying to see a support that is not there.\nL307-317 probably one or two sentences are enough for sating that, functionally, this is a 2D system and deviations in scaling for foraging in a 3D environment might not explain the actual here devations from expected scaling patterns (Pawar et al. 2012)\nL351-353 third time this point is stated in the discussion.\nL358-360 stated above.\nL 361 this is a main point for discussion that starts in the middle of a paragraph devoted to other ideas.\nL411 at this point of the ms it is not evident what a node is.\nRitchie, M.E. (2010) Scale, heteogeneity, and the structure and diveristy of ecological communities. Princeton University Press Princeton.", "reviewer_3": "General comments:\nThis thoughtful study uses a huge dataset to show that population energy use in soil invertebrate communities does not follow the energy equivalence principle (EEP), and that the scaling of energy use and population abundance does not follow the 3/4-power law, both considered by some to be major rules of nature. Other studies have also shown energy inequivalence for some ecological communities, but the present study is notable because it is verified by using two different measures of energy use and by showing significant effects of food-web structure. This study also clearly shows that one cannot reliably test the EEP by merely examining size-abundance patterns in communities. The authors further recommend that energy flux measurements may be more useful than measurements of metabolic rate in testing the EEP.\nHowever, I have three major concerns that I believe that the authors should address.\n(1) There seems to be a disconnect between the author’s model (Figure 1) and their collected data on body-size distribution (Figure 2). Their model assumes that secondary consumers have larger body sizes than primary consumers, on average, but their data show no obvious overall difference between these trophic levels.\n(2) The authors claim that their study is the first to compare size-abundance relationships between trophic levels, but this was done previously for aquatic macroinvertebrates, which interestingly like the present study, also show little difference in mean body size between primary and secondary consumers (Gjoni & Glazier 2020). However, to my knowledge, the present study is the first that directly tests the EEP at different trophic levels.\n(3) I am concerned about whether the authors considered that primary and secondary consumers tend to have different assimilation efficiencies, which may affect their estimates of energy fluxes based only on energy consumption rate. This should be clarified.\nSpecific comments:\nL 103-108: Note that references 9 &10 focus on the scaling of metabolic rate, not population abundance. Note also that reference 10 describes several intrinsic and extrinsic factors that affect the metabolic scaling exponent.\nL 108-109: Reference 1 shows that across life the metabolic scaling exponent is nearer to 1 than 0.75.\nL 127-131: Note that the original analysis by Damuth (1981) focused on herbivorous mammals (primary consumers) only, thus controlling trophic level.\nL 132-134, 324-325: See also the work of Gjoni and her colleagues (e.g., Gjoni et al. 2017, 2022, 2023; Gjoni & Glazier, 2020). Gjoni & Glazier (2020) have shown that size-abundance relationships for macroinvertebrate communities vary with trophic level in brackish lagoons. However, the major difference between predators and prey is the elevation of the scaling relationship, and not the slope.\nL 139-140: Using energy input (consumption) before assimilation may be an unreliable method of estimating population energy use, especially if assimilation efficiency is low and variable. Note that assimilation efficiency tends to be much higher for animal (secondary) versus plant (primary) consumers. Please clarify.\nL 153-156: If energy consumption is known at each trophic level, then I suspect that trophic transfer efficiency will be higher at the secondary consumer level because secondary consumers tend to have higher assimilation efficiencies than primary consumers. However, the efficiency of acquiring food may be lower in secondary versus primary consumers. Please clarify.\nIn any case, it is also possible that trophic-specific energy fluxes may affect consumers of all sizes in a uniform way, thus causing a change in the scaling elevation rather than the scaling slope (as observed for size-abundance relationships by Gjoni and Glazier 2020). Why is a change in slope expected? Is it because secondary consumers are expected to be larger on average than primary consumers, as shown in Figure 1a? If so, this need not be true, as observed on brackish water macroinvertebrate communities (Gjoni and Glazier 2020). Please clarify.\nL 301-305: Similar trophic level patterns have been shown by Gjoni and Glazier (2020).\nL 318: Change “are” to “is”.\nL 387-415: What was the body-size range of the invertebrates collected. Which taxa were included? Were any taxa that were present not included because they were too small or for other reasons?\nL 415: Change “Ehnes” to “Ehnes et al.”?\nL 437: Was assimilation efficiency adjusted to trophic level? Primary consumers tend to have lower assimilation efficiencies than secondary consumers.\nL 450: Change “supplementary for full methods” to “supplementary information for full methods”.\nL 495-505: Why are scaling slopes predicted to be more negative for secondary consumers? This need not be so (see e.g., Gjoni & Glazier 2020).\nL 507-510: On the X-axis, shouldn’t “body size” be “body mass”? Also is it dry or wet body mass?\nLiterature cited:\nDamuth, J. (1981). Population density and body size in mammals. Nature, 290(5808), 699-700.\nGjoni, V., Cozzoli, F., Rosati, I., & Basset, A. (2017). Size–density relationships: A cross-community approach to benthic macroinvertebrates in Mediterranean and Black Sea lagoons. Estuaries and Coasts, 40, 1142-1158.\nGjoni, V., & Glazier, D. S. (2020). A perspective on body size and abundance relationships across ecological communities. Biology, 9(3), 42.\nGjoni, V., Glazier, D. S., Wesner, J. S., Ibelings, B. W., & Thomas, M. K. (2023). Temperature, resources and predation interact to shape phytoplankton size–abundance relationships at a continental scale. Global Ecology and Biogeography, 32(11), 2006-2016.\nGjoni, V., Marle, P., Ibelings, B. W., & Castella, E. (2022). Size–Abundance Relationships of Freshwater Macroinvertebrates in Two Contrasting Floodplain Channels of Rhone River. Water, 14(5), 794."}, "author_response": "Response: We thank you for your very positive and constructive assessment of our work!\nYour comments are highly insightful and have helped to significantly improve clarity around\nthe implications of our findings.\nOn the basis of these strengths the study qualifies to be published in a high quality scientific\njournal.\nBut I have the following concerns regarding the present manuscript.\n1. The introduction could have been clearer regarding the state-of-the-art in this field of\nresearch. Then it becomes also clearer what the novelty of the study is and how it stands out\nfrom other studies. An important piece of novelty is the consideration of aspects of food web\narchitecture and the trophic position of the species. In the manuscript lines 132 -134 states\nthat variation in food web architecture is unexplored, but this statement should be made\nmore explicit. There is a number of studies in which the EER is applied to datasets including\nfood webs. In one of these studies a large number of soil food webs is analysed (ref 20). And\nin another study (ref. 1) categories of species are distinguished in part based on their trophic\nposition. It would be helpful when the present study is contrasted to such studies. For\nexample, in terms of what they did and found rather than only mentioning that they have\nbeen done.\nIn this context I like to mention a study not referred to in the present manuscript, i.e.\nEvolution of body size in food webs: does the energetic equivalence rule hold? by Nicolas\nLoeuille and Michel Loreau in Ecology Letters, (2006) 9: 171–178. In this study the authors\nmodel how food web structure evolves from body-size and ecological interactions. The study\nmight be relevant for sharpening the research question.\nResponse: Thank you for bringing this lack of clarity to our attention. To address this issue,\nwe restructured our introduction to emphasise the novelty of the manuscript early on, as well\nas highlighting the key advance in determining the influence of food web structure and\ntrophic position on EER scaling relationships (see lines 84-93). Additionally, when referring\nto past studies, we have clarified what they are lacking that we have addressed in our study\n(e.g., lines 105-110, 112-119, 126-130). Thank you for bringing the Loeuille & Loreau paper\nto our attention; it has now been included in the introduction.\n2. I am a little uncertain whether I fully understood the results, but what I see is that the soil\nfood webs deviate very strongly from the EER. The size-density index is found to be -0.174\ninstead of -0.75 (correct?). This is a lot. If the indexes for size-population metabolism and the\nsize-energy flux are 0.134 and 0.204 respectively, then the index for individual size-\nmetabolism should be around 0.5, i.e. smaller than 0.75, but less deviating than the index for\nsize-density. I would emphasize this finding more. This makes the paper more challenging\nas to me the soil food webs do confirm the EER (at all).\nResponse: This is an important point of the study that we have now made clearer, see lines\n277-280, 318-321. We found important differences between the whole food web results and\ntrophic–level specific results. We also agree that there is a disconnect between the size–\ndensity and size–energy use scaling that provides evidence that size–density scaling alone\nis not an indicator of energetic equivalence in soil food webs at all. This is especially true for\nwhole soil food webs. These results are also more clearly highlighted in the new Figure 5.\n3. I miss a discussion of how the present results relate to the findings for the soil food webs\nexamined in ref. 20. Also, a comparison with the results given in ref 1. seems relevant.\nResponse: We have elaborated on suggested areas in both the introduction and discussion\nas mentioned in your previous comments (lines 126-130, 277-280). We now feel these\npoints have been discussed more thoroughly.\n4. The results that discriminate between types of consumers are interesting, make sense,\nand are discussed well. But they might also be viewed in the context of the deviating values\nfor the food webs as a whole.\nResponse: We completely agree and would like to bring to the reviewer’s attention that the\nwhole food web models testing the effects of food web properties on the deviation of scaling\nexponents from EER expectations are included in the supplementary information (Figure\nS3). We decided to not include these additional results in the main text as these general\nrelationships are not central to our focus on determining trophic-level-dependent EER\nscaling relationships. However, we see now that we missed any discussion of these whole-\nfood web level effects, despite presenting these findings in the results section. Therefore, we\nhave now touched on these findings in our discussion as well (see lines 334-337, 341-343).\nFurthermore, these results are now better highlighted and compared to scaling relationships\nfor specific trophic levels in the new synthesis figure (Fig 5).\n5. EER is seen as a rule, but it can also be seen as a hypothesis. The present study\nformulates hypotheses regarding trophic position, competition and ways to quantify\npopulation energy use, so we have hypotheses on top of the EER hypothesis, which makes\nit sometimes difficult to see what ‘expectations’ mean.\nResponse: Thank you for bringing this source of confusion to our attention. We have now\nclarified throughout the manuscript whether we are referring to EER expectations versus\nspecific hypotheses from our study.\n6. The conclusion drawn in lines 364-368 I find too mild. I don’t think that deviations from the\nEER is the most promising way to understand population dynamics in soil ecosystems. In\nthe discussion numerous factors and processes are mentioned that influence these\ndynamics in fundamental ways. And soil populations are known for their large variation in\nnumbers among soils and within soils over time and space. Isn’t it possible to simply reject\nthe EER for soil food webs. We then should not throw away the baby with the washing water\nof course. The rejection comes from the assumed relationship between body-size and\nabundance, which to me is the weaker part of the EER (see also ref. 25 and Isaac et al.\nGlobal Ecology and Biogeography, 2013, 22, 1–5). The relationship between body-size and\nindividual metabolism though is well based on biological/physiological arguments and has\nproven to be of value for understanding food web structure and also the structure of soil food\nwebs.\nResponse: As suggested, we have emphasised the novelty of our study throughout the\nintroduction and discussion which was also suggested by the other reviewers (e.g., see lines\n364-366). We have also included a synthesis figure (Fig. 5) to emphasize the overall findings\nof our study. This has helped to better communicate the overarching findings that, while we\nfind almost no evidence for the EER based on size-density scaling, there is considerably\nmore support for EER expectations based on size-energy use scaling, though this varies\nmarkedly with the estimator of energy use, trophic level, and food web structure.\nHope my comments are helpful in making the positioning of the study somewhat clearer and\nthe implications of the findings somewhat more pronounced.\nResponse: Thank you, your comments have been most helpful for identifying areas of\nimprovement!\nReviewer #2 (Remarks to the Author):\nI truly appreciate the opportunity to read this manuscript. It is well written and provides a\nsignificant contribution with a mass of evidence about density-body size and energy use –\nbody size. This is a significant landmark about the empirical support or not for sound\necological rules. The authors analyzed the most comprehensive data set of individual body\nsize in terrestrial food webs, covering 183 food webs from different geographic regions. The\nresults are not confirmatory, clearly indicating that the increase in density with body size is\nusually more positive than expected by the main theories and that in most cases energetic\nuse is predominantly associated with body size. This qualitative result was consistent with\nthe estimate of energy use from the expected metabolic rate or with the estimate of energy\nflux. However, the estimated exponents differed between these estimations. This is a point\nto highlight because of the lack of support for the general use of metabolic scaling to assess\nenergetic equibalance. In this sense, the focus on the energy flux represents a relevant\nmethodological and conceptual advance that might challenge the accumulated evidence.\nDifferences were detected between scaling patterns in primary and secondary consumers\nsupporting the role of the food web structure in energy use and scaling with body size.\nResponse: We are very grateful for your highly positive and constructive assessment of our\nstudy! Your comments have challenged us to critically assess our approach and how we\npresent our overarching findings.\nI have different comments to consider by the authors.\nThere is a methodological point that represents the most important concern. There is\nevidence that the selected method, binning the data, provides a biased estimation of the true\nexponent and that Maximum Likelihood estimation based on the individual size distribution\nmust be used (Clauset et al., 2009; Newman, 2005; White et al., 2008). ML estimation on the\nsize distribution provides an unbiased estimation and also requires the finding of the\nminimum and maximum individual sizes within which the estimation has to be performed\n(see Fig. 3.3 in Clauset et al., 2009). Note that energetic constraints to density and the effect\nof body size on energy flow are not expected to operate equally in all body sizes, expecting\nnonlinear relationships and ranges of different body sizes with different scaling\n(Arim et al., 2011; Clauset et al., 2009; Newman, 2005).). However, I have to say that I\nunderstand the authors´ decision to use a widely used method in ecology (even after the\nreport on its shortcomings) and that the discrepancy of ML on estimation of the scaling in the\nsize distribution with alternative methods is a point of attention. However, so far I know, there is\nno evidence supporting binning methods over ML on the size distribution, nor is there\nevidence supporting that binning methods are not biased, particularly for the amount of\ninformation available in ecological studies. Regrettably, discrepancies between energy use\nand density scaling can be affected by the selected method.\nResponse: Thank you for raising this point for discussion, as we have also thought about this\na great deal while developing the study. We would like to clarify that we used maximum\nlikelihood estimation of individual size distributions for size–density scaling (see lines 280-\n284, 405-409 and supplementary information). While we acknowledge some of the\nlimitations of the size binning and OLS approach, we are unaware of an equivalent method\nto estimate the relationship between body size and energy use. This is because we must\ninspect the relationship between average body size and population energy use, which does\nnot allow for an individual size distribution analysis like we employed for the size-density\nscaling (as body size must be compared against a population measure of energy\nconsumption). Therefore, the closest analogue was to apply the size binning approach with\nsummed individual metabolic rates. That said, we have additionally relanalysed the size-\nenergy use scaling relationships with ranged major axis regression (see supplementary\ninformation) and still found that findings appear to be robust to the model fitting approach\nused. Furthermore, we have pointed out that direct comparisons between size-density and\nsize-energy use scaling from our analyses require a high degree of caution, due to the\ndifferent model fitting procedures used for these scaling relationships.\nThe rest of my comments do not represent major concerns:\n1. Along the introduction, I think that some points could be further highlighted. The\ndensity and energy rules were generally supported at large geographic scale, but not\nin local communities; which is the scale of the present study (White et al., 2007). In\naddition to the soil studies mentioned by the authors, other studies considered the\nexistence of an effect of local conditions and biotic organization on scaling (e.g.\nCyr et al., 1997a; Cyr et al., 1997b).\nResponse: Thank you for bringing these studies to our attention, as well as the\nimportant nuance around local and global size-density relationships. We have\nintegrated these studies, as well as highlighting the points mentioned into the\nintroduction as suggested (see lines 110-113, 119-125, 271-273).\n2. I find the discussion to be a bit long and repetitive in some ideas. For example,\nparagraphs 2-3 focus on the performance of energy flux and similar methodological\nissues; probably they can be reduced and merged in half of its actual extension. In\naddition, I found some sections unnecessarily speculative with general comments but\nnot explicit attention to the underlying mechanisms (e.g. the mention to the habitat\ncomplexity hypothesis of Pawar et al.; the mechanisms through which richness affect\nscaling, the potential evaluation of alternative scaling methods, etc.). Previous\nstudies on EER and Damuth in particular highlighted the lack of an energetic\nadvantage associated with body size, and the fact that this difference did not evolve\nwas surprising (Damuth, 2007). However, the present results contradict this view,\nindicating the need to consider the ecological and evolutionary mechanisms involved\nin the existence of systematic differences in the use of energy by the population\nassociated with body size. I think this should be a matter of discussion here.\nResponse: We agree with the reviewer, and have removed sections of the discussion\nthat were long and repetitive, particularly where we felt that we have been overly\nspeculative. We have also included the distinction mentioned between our findings\nand those in Damuth 2007 (lines 324-330). We believe this has greatly streamlined\nthe discussion and better emphasized the key findings of our study, thank you.\nSpecific Comments\n3. Contribution, particularly along the discussion section. There are several important\nresults, and in some points the synthesis could be difficult for a first reader, figures\nhelp, but I wonder if a synthesis figure resuming results can improve the clarity of the\nmain massage; may be expanding Figure 1?.\nResponse: This is an excellent suggestion. We have now included a synthesis figure\n(see Figure 5) that is based on Figure 1, which ties together our hypothesis with our\noverarching findings.\n4. About the hypotheses. Consumers not only lose available energy at higher trophic\nposition because of the low efficiency in energy flow available energy can also\nincrease by other mechanisms. Attenuation in gape limitation, an increase in the\nspatial scale of movement of individuals, a larger prey richness, and the access to\nnovel energy source can also compensate for the loss of energy at higher trophic\npositions (Arim et al., 2010; Rooney et al., 2008). Even along primary consumers, the\nwell-reported increase in prey richness with body size can increase the amount of\navailable energy, by means of the above-mentioned mechanisms (Arim et al. 2010).\nResponse: We have now included these potential contrasting influences on energetic\nconstraints with increasing body size in our hypotheses (see lines 172-175). Indeed,\nthis could help to explain our findings of weaker-than-expected energetic constraints\n(size-density scaling exponents > -0.75 and positive size-energy use exponents),\nparticularly for primary consumers and at the whole food web scale. We have\nintegrated this into our discussion accordingly (see lines 336-343).\n5. L159 More competition will affect the scaling only if competition changes with body\nsize and/or differentially affect species efficiency or predation at different body sizes\n(Ritchie, 2010) Hypotheses about the effect of richness and complementary trophics\nare also expected for this section.\nResponse: Thank you for bringing this lack of clarity and of hypotheses to our\nattention. We have revised this section accordingly and included explicit hypotheses\nabout how variation in food web properties could influence deviation of food webs\nfrom EER expectations (lines 175-189).\n6. I agree with the use of kurtosis, but it is not clear why not use variance, since a\nsimilar kurtosis level can mask different variances.\nResponse: Variance as well as kurtosis values have now been included throughout\nthe results section (including figures).\n7. For energy use scaling, I appreciate having a histogram reporting the R2 values.\nResponse: We have now added these model summaries. See Figure S6 and S7 in\nsupplementary information.\nMinor:\n1. L 88 “population [density] n biomass”.\nResponse: Added ‘density’ to sentence.\n2. L 89 if possible try to add citations in words and not following exponents.\nResponse: Edited citations where applicable\n.\n3. L 93. Perhaps some references would be added here.\nResponse: References added.\n4. L157 it is difficult that a whole trophic level is represented by a single guild\nResponse: We have clarified this within the text (line 175-178).\n5. L182 This is the first time that the node richness appears in ms. I think the motivation\nfor considering node richness should be stated in the Introduction. In addition, until\nthis line, I consider that each node was the population of single species, probably\nsome mention to tropho species or node aggregation can also help.\\\nResponse: Added to introduction (see lines 165-169).\n6. L184 What is the trophic similarity? Is it estimated within or between nodes?\nResponse: Trophic similarity describes the similarity among the diets of consumers,\nwhich is estimated by the mean Jaccard similarity between consumer nodes, based\non their interactions with their resources, per food web. We have now included its\ndefinition within this sentence, and have elaborated on how this is calculated in the\nsupplementary information.\n7. L287 Fig. S4 first mention, after Fig. S5 (L186)\nResponse: Order of figure citation fixed.\n8. L305 I am not convinced of making a point about a non-significant support for the\nEhnes et al. proposition. In fact, I was stacked Fgg. 4 a,d, trying to see a support that\nis not there.\nResponse: We found that secondary consumers had slightly more negative size–\ndensity scaling relationships than primary consumers and more negative than\nexpected size–energy use scaling (particularly compared to primary consumers).\nThis point has also been made clearer in the new Figure 5.\n9. L307-317 probably one or two sentences are enough for sating that, functionally, this\nis a 2D system and deviations in scaling for foraging in a 3D environment might not\nexplain the actual here devations from expected scaling patterns (Pawar et al. 2012)\nResponse: We have now removed this section of the discussion from the manuscript\nas it was highly speculative and distracts from the central findings of our research.\n10. L351-353 third time this point is stated in the discussion.\nResponse: Sentence removed.\n11. L358-360 stated above.\nResponse: Sentence removed.\n12. L 361 this is a main point for discussion that starts in the middle of a paragraph\ndevoted to other ideas.\nResponse: Moved further up in the discussion as suggested.\n13. L411 at this point of the ms it is not evident what a node is.\nResponse: Now mentioned further up what a node is. In “Soil invertebrate community\ndata collection and preparation” paragraph\nResponse: We have now included the definition of a node earlier in the manuscript.\nRitchie, M.E. (2010) Scale, heteogeneity, and the structure and diveristy of ecological\ncommunities. Princeton University Press Princeton.\nReviewer #3 (Remarks to the Author):\nGeneral comments:\nThis thoughtful study uses a huge dataset to show that population energy use in soil\ninvertebrate communities does not follow the energy equivalence principle (EEP), and that\nthe scaling of energy use and population abundance does not follow the 3/4-power law, both\nconsidered by some to be major rules of nature. Other studies have also shown energy\ninequivalence for some ecological communities, but the present study is notable because it\nis verified by using two different measures of energy use and by showing significant effects\nof food-web structure. This study also clearly shows that one cannot reliably test the EEP by\nmerely examining size-abundance patterns in communities. The authors further recommend\nthat energy flux measurements may be more useful than measurements of metabolic rate in\ntesting the EEP.\nWe thank you for your positive and constructive thoughts and suggestions on our\nmanuscript. We have made every effort to address your points, as shown in our responses\nbelow.\nHowever, I have three major concerns that I believe that the authors should address.\n(1) There seems to be a disconnect between the author’s model (Figure 1) and their\ncollected data on body-size distribution (Figure 2). Their model assumes that secondary\nconsumers have larger body sizes than primary consumers, on average, but their data show\nno obvious overall difference between these trophic levels.\nResponse: Thank you for bringing this point to our attention. We have now bridged this\ndisconnect between Fig. 1 and Fig. 2 by redrawing the hypothetical scaling relationships\nexpected across primary and secondary consumers. Specifically, our original hypotheses\nwere based on general ecological theory (irrespective of ecosystem type) that assumes\npredators are, on average, larger than their prey. While this is often the case in belowground\necosystems, soil food webs also contain many primary consumer 'trophic whales' that reach\nexceptionally large body sizes (e.g. earthworms and some millipedes), though the majority of\nprimary consumers are still very small. Predators on the other hand, are usually larger than\ntheir prey, but there are also few (or even none) that eat large–bodied detritivores. Thus, a\nmore appropriate expectation of body size structure for soil food webs would be that the\nupper body size range of primary and secondary consumers are similar, while the lower\nrange for primary consumers extends beyond that of secondary consumers (as now shown\nin Fig. 1).This revised expectation now better describes the typical body size structure of soil\nfood webs, but without altering the overarching hypotheses and interpretation of findings in\nour study related to the EER.\n(2) The authors claim that their study is the first to compare size-abundance relationships\nbetween trophic levels, but this was done previously for aquatic macroinvertebrates, which\ninterestingly like the present study, also show little difference in mean body size between\nprimary and secondary consumers (Gjoni & Glazier 2020). However, to my knowledge, the\npresent study is the first that directly tests the EEP at different trophic levels.\nResponse: We agree with the reviewer that our study is the first to directly investigate the\nEER across multiple trophic levels within a food web context, and to also compare different\nmeasures of energy use. We believe this novel approach addresses a critical gap in the\ncurrent literature. We have carefully revised our novelty statements throughout the\nmanuscript to this effect.\n(3) I am concerned about whether the authors considered that primary and secondary\nconsumers tend to have different assimilation efficiencies, which may affect their estimates\nof energy fluxes based only on energy consumption rate. This should be clarified.\nResponse: We apologise for the lack of clarity on this key aspect. We have indeed\naccounted for differing assimilation efficiencies across trophic levels, as well as scaling\norganism efficiency with environmental temperature (sensu Lang et al. 2017 Oikos; see\nsupplementary information). We have added an additional sentence into the Methods\nsection (see lines 437-441) to improve clarity. Additionally, for a more comprehensive\nmethodology please refer to the “Food web reconstruction” section in the supplementary\ninformation.\nSpecific comments:\n1. L 103-108: Note that references 9 &10 focus on the scaling of metabolic rate, not\npopulation abundance. Note also that reference 10 describes several intrinsic and\nextrinsic factors that affect the metabolic scaling exponent.\nResponse: References removed.\n2. L 108-109: Reference 1 shows that across life the metabolic scaling exponent is\nnearer to 1 than 0.75.\nResponse: Reference removed.\n3. L 127-131: Note that the original analysis by Damuth (1981) focused on herbivorous\nmammals (primary consumers) only, thus controlling trophic level.\nResponse: We appreciate the point that Damuth (1981), as an example, did in fact\ncontrol for cross-trophic level variation in EER scaling. However, this study did not\ndiscriminate between trophic levels or describe differences in scaling relationships\nexpected due to varying energetic constraints across trophic levels, which is what we\naddress in our present study.\n4. L 132-134, 324-325: See also the work of Gjoni and her colleagues (e.g., Gjoni et al.\n2017, 2022, 2023; Gjoni & Glazier, 2020). Gjoni & Glazier (2020) have shown that\nsize-abundance relationships for macroinvertebrate communities vary with trophic\nlevel in brackish lagoons. However, the major difference between predators and prey\nis the elevation of the scaling relationship, and not the slope.\nResponse: These suggested studies have been added, where relevant, to the\nmanuscript. Thank you for bringing these to our attention.\n5. L 139-140: Using energy input (consumption) before assimilation may be an\nunreliable method of estimating population energy use, especially if assimilation\nefficiency is low and variable. Note that assimilation efficiency tends to be much\nhigher for animal (secondary) versus plant (primary) consumers. Please clarify.\nReponse: We took much care in accounting for assimilation efficiency in energy\nintake calculations. Please see section “Food web reconstruction and consumer\nenergy flux calculation” within the supplementary information. Energy intake before\nassimilation quantifies total resource consumption, taking into account the different\nenergetic demands of consumers due to different assimilation efficiencies of\norganisms at different trophic levels. If we were to rather use energy intake after\nassimilation, this would not account for the proportionately greater consumption rates\nof lower trophic level organisms (e.g. detritivores) needed to balance their energetic\ndemands, as compared to predators that have relatively high assimilation\nefficiencies. Therefore, we calculate energy intake per population by scaling\nconsumption rates according to varying assimilation efficiencies among trophic\nlevels. This is necessary because energetic equivalence will depend on competition\namong consumers for resources based on total rates of exploitation of those\nresources, rather than the proportion of energy that is eventually assimilated by\nconsumers. \n6. L 153-156: If energy consumption is known at each trophic level, then I suspect that\ntrophic transfer efficiency will be higher at the secondary consumer level because\nsecondary consumers tend to have higher assimilation efficiencies than primary\nconsumers. However, the efficiency of acquiring food may be lower in secondary\nversus primary consumers. Please clarify.\nResponse: We appreciate the reviewer's feedback on the clarity of our hypotheses.\nWe have now revised this point, ensuring the hypotheses are clearly stated without\nunnecessary detail. See lines 130-131, 172-175. Please note, we do account for\ntrophic-level specific assimilation efficiencies in our energy intake calculations. To do\nso, energy fluxes are scaled up proportionately to the efficiency of the given energy\ntransfer from resource to consumer. See supplementary information for details.\n7. In any case, it is also possible that trophic-specific energy fluxes may affect\nconsumers of all sizes in a uniform way, thus causing a change in the scaling\nelevation rather than the scaling slope (as observed for size-abundance relationships\nby Gjoni and Glazier 2020). Why is a change in slope expected? Is it because\nsecondary consumers are expected to be larger on average than primary consumers,\nas shown in Figure 1a? If so, this need not be true, as observed on brackish water\nmacroinvertebrate communities (Gjoni and Glazier 2020). Please clarify.\nResponse: A change in slope is expected due to the proportionately increasing\nenergetic demand with body size for secondary versus primary consumers because\nof the greater energetic constraints faced by secondary consumers. We believe this\nis well covered and already discussed in multiple areas throughout the introduction\n(first stated in lines 126-127, 134-138) and discussion. However, we have done our\nbest to elaborate where possible throughout the manuscript.\n8. L 301-305: Similar trophic level patterns have been shown by Gjoni and Glazier\n(2020).\nResponse: Thank you for this suggestion. We have now cited this interesting study.\n9. L 318: Change “are” to “is”.\nResponse: Changed.\n10. L 387-415: What was the body-size range of the invertebrates collected. Which taxa\nwere included? Were any taxa that were present not included because they were too\nsmall or for other reasons?\nResponse: See lines 400 for body size range. Please see supplementary information\nfor taxa included in our analyses e.g., Table S2, S3. As well as the “Statistical\nanalysis” section for exclusion/inclusion criteria.\n11. L 415: Change “Ehnes” to “Ehnes et al.”?\nResponse: Fixed\n12. L 437: Was assimilation efficiency adjusted to trophic level? Primary consumers tend\nto have lower assimilation efficiencies than secondary consumers.\nResponse: Yes, trophic-level specific assimilation efficiency is a key parameter\nincluded in energy flux calculations. Please see section “Food web reconstruction\nand consumer energy flux calculation” within the supplementary information.\n13. L 450: Change “supplementary for full methods” to “supplementary information for full\nmethods”.\nResponse: Changed\n14. L 495-505: Why are scaling slopes predicted to be more negative for secondary\nconsumers? This need not be so (see e.g., Gjoni & Glazier 2020).\nResponse: Based on the broader literature, we hypothesised that secondary\nconsumers should have the steepest exponents due to increasing energetic\nconstraints at higher trophic levels. This expectation is covered on lines 129-138,\nalthough we now acknowledge there are documented exceptions, as found in Gjoni &\nGlazier 2020 (lines 136-137). In line with our hypotheses, we found the size–density\nand size–energy use scaling exponents were more negative for secondary\nconsumers (see Fig. 5).\n15. L 507-510: On the X-axis, shouldn’t “body size” be “body mass”? Also is it dry or wet\nbody mass?\nResponse: We used estimates of live, fresh body size (mg) (synonymous with ‘wet\nbody mass’; see lines 392-394). More generally, we use body size throughout the\nmanuscript, but have now clearly defined this on line 156.\nLiterature cited:\nDamuth, J. (1981). Population density and body size in mammals. Nature, 290(5808), 699-\n700.\nGjoni, V., Cozzoli, F., Rosati, I., & Basset, A. (2017). Size–density relationships: A cross-\ncommunity approach to benthic macroinvertebrates in Mediterranean and Black Sea\nlagoons. Estuaries and Coasts, 40, 1142-1158.\nGjoni, V., & Glazier, D. S. (2020). A perspective on body size and abundance relationships\nacross ecological communities. Biology, 9(3), 42.\nGjoni, V., Glazier, D. S., Wesner, J. S., Ibelings, B. W., & Thomas, M. K. (2023).\nTemperature, resources and predation interact to shape phytoplankton size–abundance\nrelationships at a continental scale. Global Ecology and Biogeography, 32(11), 2006-2016.\nGjoni, V., Marle, P., Ibelings, B. W., & Castella, E. (2022). Size–Abundance Relationships of\nFreshwater Macroinvertebrates in Two Contrasting Floodplain Channels of Rhone River.\nWater, 14(5), 794."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors addressed my comments satisfactorily. I was already quite positive about the original manuscript, and I still am.\nI have still one concern, and that is how the presented results are comparable with other studies. In my review I referred to ref. 20, in which the EER is studied in 146 soil food webs. In the response to the reviewers the authors refer to lines 277-280, but I do not see these lines being clearly connected to the soil food web findings of Reuman et al. If there will be a second round of revision, I would like the authors to take a look at this again.", "reviewer_2": "I appreciate the serious attention devoted by the authors to all my comments and those stated by the other reviewers. As I mentioned in the first review, I really like the study and the opportunity to have an early view of this contribution. Having attended all my comments and suggestions, I have no further point to be considered.", "reviewer_3": "I am happy with the authors' responses to my previous comments. Excellent study!\nDoug Glazier"}, "author_response": "Reviewer #1 (Remarks to the Author):\nThe authors addressed my comments satisfactorily. I was already quite positive about the\noriginal manuscript, and I still am.\nI have still one concern, and that is how the presented results are comparable with other\nstudies. In my review I referred to ref. 20, in which the EER is studied in 146 soil food webs.\nIn the response to the reviewers the authors refer to lines 277-280, but I do not see these\nlines being clearly connected to the soil food web findings of Reuman et al. If there will be a\nsecond round of revision, I would like the authors to take a look at this again.\nResponse: We thank the reviewer for their helpful feedback and positive assessment. The\nsentence referencing to ref. 20 has been removed in the final version, so this concern is no\nlonger applicable.\nReviewer #2 (Remarks to the Author):\nI appreciate the serious attention devoted by the authors to all my comments and those\nstated by the other reviewers. As I mentioned in the first review, I really like the study and the\nopportunity to have an early view of this contribution. Having attended all my comments and\nsuggestions, I have no further point to be considered.\nResponse: We sincerely thank the reviewer for their positive feedback and thoughtful\nengagement throughout the review process. We are grateful for their constructive\ncomments, which have helped improve the clarity and quality of our manuscript.\nReviewer #3 (Remarks to the Author):\nI am happy with the authors' responses to my previous comments. Excellent study!\nDoug Glazier\nReviewer #3 (Remarks on code availability):\nDid not review.\nResponse: Thank you Dr. Glazier for your feedback and encouraging words. We greatly\nappreciate your thoughtful review and valuable comments, which have helped strengthen\nthe manuscript."}]

Decision letter