# A unified framework for herbivore-to-producer biomass ratio reveals the relative influence of four ecological factors

## Abstract

The biomass ratio of herbivores to primary producers reflects the structure of a community. Four primary factors have been proposed to affect this ratio, including production rate, defense traits and nutrient contents of producers, and predation by carnivores. However, identifying the joint effects of these factors across natural communities has been elusive, in part because of the lack of a framework for examining their effects simultaneously. Here, we develop a framework based on Lotka–Volterra equations for examining the effects of these factors on the biomass ratio. We then utilize it to test if these factors simultaneously affect the biomass ratio of freshwater plankton communities. We found that all four factors contributed significantly to the biomass ratio, with carnivore abundance having the greatest effect, followed by producer stoichiometric nutrient content. Thus, the present framework should be useful for examining the multiple factors shaping various types of communities, both aquatic and terrestrial.

## Introduction

The biomass ratio of herbivores (H) to primary producers (P) in nature varies by four orders of magnitude (10−4~101)1,2. Because it reflects the structure of a community and ecosystem properties, such as energy flow from producers to higher trophic levels and nutrient cycling1,2,3,4, a large number of studies have empirically and theoretically examined the H/P biomass ratio and have shown that factors related with either bottom–up or top–down control may play crucial roles. These factors are production rate5,6,7, defense traits8,9,10,11, and nutrient content of the producers2,4, and predation rate by carnivores including food-chain length12,13,14. However, it has been difficult to quantify how these factors act together to affect the H/P biomass ratio in natural communities, because few studies have considered a theoretical framework for examining these effects simultaneously.

Top–down control of trophic structure is determined by the feeding rate and the abundance of consumers at higher trophic levels15,16, whereas bottom–up control is determined by the primary production rate regulated by nutrient supply17,18 and light19. In addition, both for terrestrial and aquatic producers including vascular plants and algae, chemical and physical defense traits are well documented as factors limiting herbivory9,20,21, indicating that edibility of primary producers is a crucial factor in determining the biomass ratio9,11. The nutrient content of producers is also viewed as a primary factor in regulating H/P mass ratio2,4,22,23. Depending on the supply rates of light and nutrients, the contents of biologically important elements such as nitrogen and phosphorus relative to carbon vary widely among primary producers4. As herbivore growth strongly depends on the elemental content of primary producers22,23, the stoichiometric mismatch in carbon to phosphorus or carbon to nitrogen ratios between primary producers and herbivores likely results in a decrease in the H/P ratio2,4,22. However, no study has yet examined how such a stoichiometric mismatch combined with other factors jointly affect the H/P biomass ratio.

In this study, we used classic Lotka–Volterra equations24,25 to develop a framework that simultaneously assesses the effects of primary production rate, producer defense traits and producer nutrient content, and predation rate on the H/P ratio in natural communities. We then test the model using data from communities inhabiting freshwater experimental ponds. In the ponds, the bottom–up factor (light) was manipulated by shading, while the top–down factor (fish predation) was quantified regularly. We show that, for pond plankton communities, top–down control and the stoichiometry of primary producers played pivotal roles in determining the H/P ratio, followed by defense traits and the rate of primary production.

## Results

### A unified framework model of the H/P ratio

Based on the Lotka–Volterra equations24,25, the biomass dynamics of primary producers (P) and herbivores (H) are described as follows:

$$\begin{array}{l}dP/dt = g\left( P \right)P - xP - f\left( P \right)PH,\\ dH/dt = kf\left( P \right)PH - mH\end{array}$$
(1)

where g(P) is biomass-specific primary production (gC gC−1 d−1) and may be a function of P (gC m−2) owing to density-dependent growth, f(P) is per capita grazing rate of herbivores (m2 gC−1 d−1) and also may be function of P depending on the functional response, x is biomass-specific loss rate of primary producers other than due to grazing loss (gC gC−1 d−1), k is the conversion efficiency of herbivores as a fraction of ingested food converted into herbivore biomass (dimensionless: 0~1), and m is per capita mortality rate of herbivores owing to predation and other factors (gC gC−1 d−1). A list of model variables is listed in Supplementary Table 1. If we assume both g(P) and f(P) are constants, Eq. (1) is basically the Lotka–Volterra model, whereas it is an expansion of the Rosenzweig–MacArthur model if we assume logistic growth for g(P) and Michaelis–Menten (Holling type II) functional responses for f(P)24. At the equilibrium state, i.e., dP/dt = 0 and dH/dt= 0, the abundance of producers (P*) and consumers (H*) can be represented as:

$$H \ast /P \ast = \left\{ {\left[ {g\left( {P \ast } \right) - x} \right]} \right./\left. {\left. {f\left( {P \ast } \right)} \right]} \right\}/\left\{ {{\mathrm{m/}}\left[ {kf\left( {P \ast } \right)} \right]} \right\}$$
(2)

Thus, the relationship between H and P is not affected by the types of the functional response in herbivores (f(P)). If we set g(P) as the biomass-specific primary production rate at equilibrium, as in simple Lotka–Volterra equations (i.e., g(P*) = g), then the H/P ratio can be expressed with log transformation as:

$${\mathrm{log}}\left( {H \ast /P \ast } \right) = {\mathrm{log}}\left( k \right) + {\mathrm{log}}(g - x) - {\mathrm{log}}\left( m \right)$$
(3)

At equilibrium, (g − x)P* is the amount of primary production that herbivores consume per unit of time (f(P*)P*H*). Thus, if this amount is divided by primary production per unit of time (P*g), it corresponds to the fraction of primary production that herbivores consume (0~1). We define it as β (= 1 − x/g). Large β values imply that producers are efficiently grazed at the equilibrium state. Thus, β is a gauge of inefficiency in the producers’ defensive traits. Using these parameters, the H*/P* ratio can be expressed as:

$${\mathrm{log}}\left( {H \ast /P \ast } \right) = {\mathrm{log}}\left( k \right) + {\mathrm{log}}\left( \beta \right) + {\mathrm{log}}\left( g \right) - {\mathrm{log}}\left( m \right)$$
(4)

This equation implies that the H*/P* biomass ratio on a log scale is affected additively by the specific primary production rate (log(g)), the grazeable fraction of primary production (log(β)), the conversion efficiency (log(k)), and the mortality rate of herbivores (log(m)). According to this equation, communities with relatively low carnivore abundance would have a correspondingly low value of m and will exhibit high herbivore biomass relative to producer biomass (H*/P*), whereas those with low primary production (with low value of g) owing to, for example, low light supply will have a low H*/P* ratio. An increase in defended producers such as armored plants or a decrease in edible producers will decrease β by increasing the loss rate x owing to the cost of defense, and will result in a decreased H*/P* ratio. Finally, when the nutritional value of producers decreases, the conversion efficiency of herbivores (k) should be low, which in turn decreases the H*/P*biomass ratio.

### The model for a test with plankton communities

To apply Eq. (4) to a natural community, some modifications are necessary. Here, we consider a plankton community composed of algae and zooplankton. A theory of ecological stoichiometry suggests that the carbon content of primary producers relative to their nutrient content such as nitrogen or phosphorus is an important property affecting growth efficiency in herbivores4. Supporting the theory, a number of studies have shown that growth rate in terms of carbon accumulation relative to ingestion rate strongly depends on the carbon contents of the food relative to nutrients26,27,28,29. Thus, k can be expressed as:

$$k = q_1 \times a_{{\mathrm{nut}}}^{\varepsilon 1}$$
(5)

where αnut is carbon content relative to nutrient content of primary producers and q1 is the conversion factor adjusting to biomass units. In this study, we applied a power function with coefficient of ε1 as a first order approximation because effects of this factor on the H*/P* biomass ratio may not be proportionally related to plant nutrient content. For example, if ε1 is much smaller than zero, it means that negative effects of the carbon to phosphorus ratio of algal food on an herbivore’s k are more substantial when the carbon to phosphorus ratio is high compared with the case when the carbon to phosphorus ratio is low. However, if this factor does not affect the H*/P* biomass ratio, ε1 = 0 and k is constant.

As herbivorous zooplankton cannot efficiently graze on larger phytoplankton due to gape limitation30, the feeding efficiency of herbivores or the defense efficiency of the producers’ resistance traits, β, would be related to the fraction of edible algae in terms of size as follows:

$$\beta = q_2 \times a_{{\mathrm{edi}}}^{\varepsilon 2}$$
(6)

where αedi is a trait determining producer edibility, q2 is a factor for converting the traits to edible efficiency, and ε2 is how effective the trait is in defending against grazing. We expect ε2 = 0 if this factor does not matter in regulating the H*/P* biomass ratio but ε2 > 0 if it has a role. Similarly, g can be described as

$$g = q_3 \times \mu ^{\varepsilon 3}$$
(7)

where μ is the specific growth rate of producers, q3 is a conversion factor, and ε3 is the effect of µ on growth rate. Again, we expect that ε3 ≠ 0 if g has a role in determining the H*/P* ratio. Finally, assuming a Holling type I functional response of carnivores, the mortality rate of herbivores, m, is expressed as:

$$m = q_4 \times \theta ^{\varepsilon 4}$$
(8)

where θ is abundance of carnivores, q4 is specific predation rate, and ε4 is the effect size of carnivore abundance on m.

By inserting Eqs. (58) to Eq. (4), effects of factors on the H*/P* biomass ratio is formulated as:

$${\!}{\mathrm{log}}\left( {H \ast /P \ast } \right) {\!}= \varepsilon _1{\mathrm{log}}(a_{{\mathrm{nut}}}) + \varepsilon _2{\mathrm{log}}(a_{{\mathrm{edi}}}) + \varepsilon _3{\mathrm{log}}(\mu ) - \varepsilon _4{\mathrm{log}}(\theta ) + \gamma$$
(9)

where γ is log(q1) + log(q2) + log(q3) − log(q4). If differences in the H*/P* ratio among communities are regulated by growth rate (μ), edibility (αedi), and nutrient contents (αnut) of producers as well as by predation by carnivores (θ), we expect non-zero values for ε1ε4. Thus, Eq. (9) can be used to evaluate the relative importance of the four hypothesized agents if all of them simultaneously affect the H*/P* ratio. Here we undertake this analysis using data for natural plankton communities in experimental ponds where primary production rate was manipulated with different abundance of carnivore fish.

### Experimental test by plankton communities

PAR in the water column was lower in the sections with larger shaded areas throughout the experiment (Fig. 2b). Water temperature varied from 18 to 25 °C during the experiment but showed no notable differences in mean values of the water columns or the vertical profiles among the four treatments of the two ponds regardless of the shading treatment (Supplementary Fig. 1a, Supplementary Fig. 2). In all treatments, pH values gradually decreased towards the end of experiment and were higher in pond 218 (Supplementary Fig. 1b). DO concentration varied among the treatments and between the ponds, but were within the range of 5–12 mg L−1 (Supplementary Fig. 1c).

Phytoplankton biomass (mg C L−1) correlated significantly with chlorophyll a (µg L−1) (r = 0.702, p < 0.001), varied temporally (Supplementary Fig. 3), and was generally higher in the no-shade treatments, followed by the low-shade treatments in both Pond 217 and 218 (Fig. 2a). Zooplankton biomass also varied temporally (Supplementary Fig. 4) and was generally lower in low-shade treatments compared with other treatments (Fig. 2a). Although sampling began on 31 May, to remove effects of the initial conditions, we calculated mean phytoplankton (P) and zooplankton biomasses (H) in samples collected during the period from 10 June to 28 August 28 (Supplementary Table 2). Phytoplankton biomass was lower in Pond 218 regardless of the treatments, but such a notable difference between the ponds was not found in zooplankton biomass. Accordingly, no significant relationship was found between the mean values of phytoplankton and zooplankton biomass (Fig. 2a).

Both for zooplankton and phytoplankton, community composition was similar among the four treatments within the same pond (permutational multivariate analysis of variance (PERMANOVA), F = 0.993, p = 0.42 for algae; F = 1.23, p = 0.34 for zooplankton) but differed significantly between the two ponds (F = 1.59, p = 0.017 for algae; F = 3.82, p = 0.047 for zooplankton). In zooplankton communities, copepods dominated in pond 217, whereas large cladocerans including Daphnia occurred abundantly in pond 218 (Supplementary Fig. 5). In phytoplankton communities, Euglenophyceae and Chrysophyceae occurred abundantly in pond 217, and Euglenophyceae and Dinoflagellata dominated in pond 218 (Supplementary Fig. 6). In all treatments, cyanobacteria biomass was <20%. According to previous knowledge30, we defined phytoplankton smaller than 30 µm (along the major axis of the cell or colony) as edible. Then, we calculated the fraction of the edible phytoplankton (αedi) as the ratio of edible phytoplankton biomass to total phytoplankton biomass, which varied from near zero to almost one in all the treatments of both ponds (Supplementary Fig. 3). The seston carbon to phosphorus ratio varied from 90 to 310 (Supplementary Fig. 7) and was higher for treatments with less shade in pond 217, whereas in pond 218 the seston carbon to phosphorus ratio did not vary among the treatments (Fig. 3b).

The chlorophyll a specific daily production rate estimated from the photosynthesis–PAR curve (Supplementary Fig. 8) varied temporally depending on weather conditions but was, in general, higher in treatments with less shade (Fig. 3(c)). Daily primary production rates also varied and were higher in treatments with less shade in pond 217, although in pond 218 the levels were similar among the treatments (Supplementary Fig. 4).

Fish abundance in each treatment section, determined as catch per unit of effort (CPUE) using minnow traps, showed that banded killifish (Fundulus diaphanus) and fathead minnow (Pimephales promelas) were present (Supplementary Fig. 9). Both fish species were collected on all sampling dates in pond 217 but were not caught after June 21 in pond 218 (Supplementary Fig. 4). Thus, mean abundance of these fish species was higher in pond 217 than in pond 218 (Fig. 3d). In the former pond, fish abundance also varied among the treatments, and was greater in no-shade treatments than in any of other treatments. Neither mean zooplankton biomass (n = 8, r = 0.310, p = 0.45) nor mean specific production rate (μ) (n = 8, r = 0.247, p = 0.56) was significantly related to mean fish abundance (θ).

Throughout the study period, the mass ratio of zooplankton to phytoplankton varied temporally (Supplementary Fig. 4). Among treatments, the temporal mean of this ratio (H*/P*) was highest in the mid-shade treatment and lowest in the low-shade treatment in both ponds (Fig. 2(b)). However, H*/P* was higher in pond 218 than in pond 217. A significant relationship was not detected between the H*/P* and mean PAR in the water column (Fig. 2b; n = 8, r = 0.155, p = 0.714), mean fraction of edible phytoplankton (αedi) (Fig. 3a; n = 8, r = 0.241, p = 0.565), mean seston carbon to phosphorus ratio (αnut) (Fig. 3b; n = 8, r = −0.265, p = 0.523), and mean specific production rate (μ) (Fig. 3c; n = 8, r = 0.081, p = 0.849), whilst a significantly negative relationship was detected between the H*/P* mass ratio and mean of fish abundance (CPUE) (Fig. 3d; n = 8, r = −0.818, p = 0.013).

We fitted H*/P* by αedi, αnut, μ, and θ among treatments in the two ponds using a multiple regression linear model. As fish were often not collected, we used $$\theta = {\mathrm{CPUE}} + 1$$ as a relative measure of fish abundance. The variance inflation factors (VIFs) for these explanatory variables ranged from 1.05 to 2.38, indicating a low probability of multicollinearity among explanatory variables. An analysis with the generalized linear model showed that the model including all of these parameters had the lowest Akaike’s Information criterion (Supplementary Table 3), indicating that it was the best model. The multiple regression analysis revealed that all four variables were significant: 95% confidence intervals (CI) were smaller or larger than zero, and explained 95% of variance in H*/P* (Table 1). The regression coefficient was significantly less than zero for seston carbon to phosphorus ratio (αnut) while it did not significantly differ from one for edible phytoplankton frequency (αedi) and specific production rate (μ), and was smaller than one but larger than zero for fish abundance (θ). Because sample size (two ponds × four treatments) was limited relative to the number of parameters in the multiple regression, the results may not be reliable due to low statistical power. Therefore, we examined the effects of these parameters separately using the partial regression analysis, and found that all the partial correlation coefficients of these factors were statistically significant (Fig. 4), indicating that these explanatory variables affected the H*/P* independently. Finally, to examine sensitivities of H*/P* to changes in αedi, αnut, μ, and θ, we estimated standardized regression coefficients. The absolute value of the coefficients for H*/P* was highest for θ, followed by αnut (Table 1).

## Discussion

Starting with the green world hypothesis proposed by Hairston Sr. et al.12 and the counterpoint by Ehrlich and Birch32, a number of studies have examined the effects of primary production and predation6,7,13,14,16,33, and those of anti-herbivory defense or edibility of producers8,9,10,11,20 on herbivore abundance relative to producer abundance (the H/P ratio). Although the elemental stoichiometry of primary producers has often been considered as a factor that determines herbivore biomass2,4,26, only a few studies have examined whether nutrient content can regulate herbivores relative to producer abundance using planktonic communities34,35. Moreover, to the best of our knowledge, no study has simultaneously examined the effects of these putative factors on the H/P ratio in nature, presumably because no theoretical framework has been developed for examining their effects in a comparable way. This is the first study to examine simultaneously the effects of those four factors on H*/P* in a single natural community. By fitting our observed data to a modified Lotka–Volterra-based model, we have shown that in addition to primary production and predation, which were repeatedly pointed out as fundamental factors affecting the community structure, edibility, and stoichiometry of primary producers also play pivotal roles in regulating H*/P*. In other words, this study showed that the importance of a producer’s stoichiometry and edibility on herbivore abundance becomes apparent only if the effects of primary production and predation are simultaneously examined.

Our model, based on Lotka–Volterra equations, is derived from the equilibrium state of a system. In this study, both phytoplankton and zooplankton biomass changed markedly in all the treatments throughout the experiment, indicating that no community in this study reached equilibrium. However, theoretically, temporal means of herbivore and producer abundances for at least one oscillation cycle should coincide with the equilibrium abundances in the Lotka–Volterra model25. Theoretical and experimental studies have also shown that a single cycle of abundance occurred within <50 days in zooplankton–phytoplankton dynamics36. Thus, the present experimental run (85 days) was longer than at least one oscillation. In addition, we sampled at regular intervals. Therefore, the temporal mean values among samples would be close to equilibrium values in zooplankton–phytoplankton dynamics.

In our experiment, H*/P* was most sensitive to changes in fish abundance among factors compared with the production, edibility, and stoichiometry of producers, suggesting that top–down control by zooplanktivorous fish is the greatest factor affecting H*/P* in our planktonic community. In all sections (treatments) of pond 217, where fish were abundant, the density of large cladocerans in the zooplankton community was low, a result in accordance with the well-known obsrvation that planktivorous fish prey selectively on larger zooplankton species13,30,33. However, the high sensitivity of H*/P* to changes in the fish abundance may reflect the possibility that the variation of fish abundance was more substantial than variation in other factors in our experimental setting. Thus, the present result does not imply that compared with predation, other factors were less critical in regulating H*/P* in nature.

Other than the direct effect of predation, several studies suggest that fish can indirectly affect zooplankton biomass by stimulating primary productivity through nutrient recycling37. However, in this study, the specific primary production rate (μ) was not related to fish abundance, suggesting that the net impact of fish abundance on H*/P was largely attributable to a direct top–down force on zooplankton biomass rather than indirect bottom–up forcing through nutrient cycling.

A number of studies have argued that H*/P* is regulated by the efficacy of the producer’s anti-predator defense8,10,11. In this study, occurrence of phytoplankton, such as cyanobacteria, that might have contained compounds toxic to zooplankton18,30 was limited. Therefore, we have focused on the physical defense traits of phytoplankton. As most herbivorous plankton cannot efficiently graze phytoplankton species with a cellular or colony size larger than 30 µm30, enlargement of cellular or colony size can be viewed as a defense trait against herbivory21. Therefore, we examined effects of the edible phytoplankton fraction (αedi) on H*/P*. No significant relationship was detected between these. However, if we considered only the treatments in pond 218 where fish abundance was limited, H*/P* tended to increase with this fraction. Indeed, αedi was significantly related with the mass ratio when other factors, such as fish abundance, were simultaneously considered in the multiple regression analysis. These results indicate that edibility, or a defense trait such as enlargement of cellular or colony size, indeed has a role in regulating H*/P* in nature.

Other than the defense traits, nutritional value or nutrient content of producers have often been proposed as crucial factors determining the abundance of herbivores relative to that of producers2,4,22,23. In this study, cyanobacteria biomass was <20%, suggesting that a deficiency of polyunsaturated fatty acids and sterol was not a prime factor affecting the quality of phytoplankton food for zooplankton27. Cebrian22 argued that a lower H*/P* in terrestrial communities compared with aquatic communities is attributable to lower nitrogen and phosphorus contents relative to carbon in terrestrial producers. In this study, we focused on phosphorus as the main nutrient since phosphorus limitation of herbivore growth at an individual level has been repeatedly pointed out as an outcome of ecological stoichiometry4,38. Indeed, this study has shown that the seston carbon to phosphorus ratio was a significant factor affecting H*/P* across communities with different taxonomic compositions of phytoplankton and zooplankton. This result is consistent with theoretical predictions of ecological stoichiometry, which states that the relative abundance of herbivores to producers changes depending on the stoichiometric mismatch between them4.

In conclusion, the theoretical framework presented in this study showed that herbivore biomass relative to producer biomass is related significantly with the abundance of carnivores, producer stoichiometry, producer defense traits, and primary production rate in plankton communities. The experimental results support our hypothesis that these factors can simultaneously regulate community structure in nature. In this study, we considered the size and phosphorus stoichiometry of phytoplankton as the defense trait and nutritional quality of primary producers, respectively. However, it is also possible to consider the effects of other chemical and physical defenses such as secondary metabolites, toxins and thorns, and nutritional substances such as protein and essential fatty acid contents in Eq. (4). In our theoretical framework, we did not consider organisms’ size or temperature, which would affect the biomass ratio of herbivores to producers through differences in their size- and temperature-specific metabolic rates39. Thus, caution is needed to apply the present model to communities for which size structures differ over several orders of magnitude. Under such conditions, our theoretical framework (Eqs. (4) and (9)) can incorporate multiple factors, so that application of the model to various terrestrial and aquatic communities is possible. Thus, the present theoretical framework may serve to generalize the relative importance among production rate, defense traits and stoichiometric nutrient content of producers, and predation in various ecosystems.

## Methods

### Samplings

Phytoplankton and zooplankton were collected biweekly during the experiment. In each treatment (section) of the two ponds, 11-L water was collected in duplicate from the bottom to surface with the repeated deployment of a 2.2-L tube sampler (5 cm in diameter × 112 cm in length). These were used for measuring water chemistry and abundance of phytoplankton and small zooplankton (copepod nauplii and rotifers). In addition to these samples, crustacean plankton were collected by filtering 30-L of vertically integrated water from three different sites in each section with a 100 μm mesh net, and fixed with 99% ethanol for enumeration. During sampling, we measured vertical profiles of water temperature, DO concentration, conductivity and pH using a multiparameter probe (600XLM, YSI) at each section of both ponds. We also measured PAR using a spherical quantum sensor (LI-193; LiCor, Inc.) at 10-cm intervals from the surface to bottom and calculated extinction coefficients of PAR in the water.

### Chemical analyses and enumeration of plankton

In the laboratory, sestonic particles in the water, including phytoplankton, were concentrated onto pre-combusted GF/F (0.7 µm pore size) filters. Seston carbon was determined with a CN analyzer (model 2400; Perkin-Elmer, Inc.). Seston phosphorus concentrations were determined by the ascorbate-reduced molybdenum-blue method41. Chlorophyll a was extracted by 90% ethanol for 24 hours in the dark and quantified using a fluorometer (TD-700; Turner Designs, Inc.). For phytoplankton and small zooplankton samples, 250-mL and 500 mL, respectively, of the collected water were fixed with dilute Lugol’s solution. These samples were settled by gravity for >24 hours and concentrated into 20 mL prior to analysis. For each phytoplankton taxon, the number of cells in 0.2–1.0 mL of the concentrated sample were counted and the sizes of 20–50 cells were measured for estimating the cell volume, which was made based on geometric shapes. For small zooplankton, we counted all individuals in 1 mL according to taxa with measurements of body length and width. For crustacean zooplankton, we concentrated the samples into 10 mL. For each of the crustacean taxa, we categorized size classes according to body length and counted individuals of each size category in 1 mL of the concentrated sample.

### Biomass estimation

We estimated carbon biomass of phytoplankton from the cell biovolume (μm3) using conversion factors presented by Menden-Deuer & Lessard42. Although large zooplankton individuals can graze on algae up to ~ 70 µm in size33, most zooplankton including small cladocerans and copepods are known to graze efficiently on algae smaller than 30 µm in size30. Therefore, we estimated the fraction of phytoplankton smaller than 30 µm for the major axis of the cell or colony in the total phytoplankton biomass as edible fraction (αedi). Carbon biomass of cladocerans and copepods were determined using individual abundance and length-weight relationships43 with a conversion factor of 0.48 g C per g DW. For rotifers, species-specific biovolume was estimated44. Then, carbon biomass of rotifers was estimated using individual abundance, specific biovolume and conversion factors of 0.024 g C per g WW except for Asplanchna and Keratella, which were determined by species-specific carbon weight for each of these taxa45,46.

### Primary production rate

For estimating the daily production rate, we measured changes in O2 concentration rate per unit of chlorophyll a (μg O2 μg chl-a−1 h−1) using the light and dark bottle method41 on 14 June, 11 July, and 22 August. Pond water from each pond section was poured into each of 16 100-ml DO bottles. An aliquot of the water was also collected for quantifying the chlorophyll a concentration as described above. In each treatment, two of these bottles were fixed immediately to quantify the initial DO concentration. Two of these bottles were wrapped in aluminum foil, incubated at 0.5 m depth and used for measuring community respiration rate. The remaining 12 bottles were incubated at various depths from the surface to bottom in the no-shade treatment section of pond 218. Simultaneously, we measured PAR at depths where the bottles were incubated. After six hours incubation from 10:00 to 16:00, we measured O2 concentrations in all the DO bottles by the Winkler method. Then, according to Wetzel and Likens41, chlorophyll a-specific photosynthetic rate (g C g chl-a−1 min−1) was calculated by assuming that C fixation and O2 production occurred in a 1:1 stoichiometric ratio.

To estimate PAR during the bottle incubation, the light extinction coefficient (λ: Supplementary Fig. 1(d)) was calculated by fitting photon flux density (I) against depth (z) in the no-shade treatment section of pond 218 according to the following equation:

$${\mathrm{I}}\left( {\mathrm{z}} \right) = {\mathrm{I}}\left( 0 \right){\mathrm{exp}}\left( {-{\mathit{\lambda}} \,{\mathrm{z}}} \right).$$
(10)

Mean PAR during the incubation was calculated using λ and temporal changes in I(0) that were estimated from ambient PAR in air (PARair). The PARair was obtained from Guterman Research Center at Cornell University, near CUEPF, where PARair was monitored every 2 minutes. Then, in each of the pond sections with different treatments in the two ponds, specific photosynthetic rates were plotted against the mean PAR and fitted to non-rectangular hyperbola models by the function nls() in R 3.2.147 to obtain the photosynthesis–PAR curve (Supplementary Fig. 8). Using the photosynthesis– PAR curve and daily PAR in the water column, we estimated chlorophyll a specific daily production rate. The daily PAR in each pond section was derived from PARair, and λ (Supplementary Fig. 2) at the time of sampling. To minimize specificity in light conditions at the measurement date, we estimated chlorophyll a specific daily production rate using the temporal profile of PAR for 3 days before each sampling date. Then the average value for these 3 days was used in our analysis. On the date when photosynthetic rate was not measured, we used the photosynthesis–PAR curve obtained for the closest measured date. Because we used carbon biomass of phytoplankton for estimating the H/P mass ratio, we used chlorophyll a specific daily production rate as a surrogate of the specific production rate (μ) to avoid autocorrection between this and the H/P ratio.

### Fish abundance

In each of the different treatment sections, fish were sampled using minnow traps with carp bait. The traps were placed 3–5 days before the regular plankton samplings in each section of the ponds. Then, we collected the traps at the plankton samplings and measured total wet weight of the collected fish (g) as CPUE. Note that, although shading may have affected the number of fish collected by the traps, CPUE can nevertheless be viewed as a measure of fish activity and, therefore, an indication of relative predation pressure48. Work with fish was permitted under Cornell University’s Institutional Animal Care and Use Committee protocol 2016-0095.

### Statistics and reproducibility

In each treatment (n = 8: four treatments × two ponds) of the field experiment, we used mean values from June 10 to August 27 (n = 7 sampling dates) for all variables in the following statistical analyses (Table S2). Relationships among phytoplankton and zooplankton biomasses, specific production rate and fish abundance were examined by correlation analysis. To test differences in phytoplankton and zooplankton community composition among the treatments and between the two ponds, PERMANOVA was performed by the adonis() function in R package “vegan”49. In this test, we used 999 permutations and the Euclidean distance both for phytoplankton and zooplankton communities as an index of dissimilarity in the community.

We used mean phytoplankton carbon biomass, zooplankton carbon biomass, fish abundance, specific production rate and fraction of edible phytoplankton (n = 8: four treatments × two ponds) for P, H, θ, μ, and αedi in Eq. (9), respectively. As our traps often contained no fish, we used $$\theta = {\mathrm{CPUE}} + 1$$. For αnut, we focused on phosphorus since freshwater limnetic ecosystems are primarily phosphorus limited17,18 and as growth of zooplankton is affected by relative phosphorus in algae26,27,28,29. Specifically, we used the carbon to phosphorus ratio of seston as a surrogate for αnut because this ratio has been generally used in consideration of ecological stoichiometry in freshwater4. Thus, we expected lower H*/P* at larger values of seston carbon to phosphorus ratio. To examine effects of these explanatory variables on the H/P ratio, a simple regression analysis was performed. Then, after checking multicollinearity among the explanatory variables by VIFs50, we fitted these data to Eq. (9) using a lm function of R 3.2.147 followed by examination of Akaike’s Information Criterion. In this analysis, 95% CIs of the regression coefficients were estimated using bootstrapping with a residual resampling procedure51 and 1999 replicates. Because Eq. (9) indicates an a priori effect direction of a given variable, we estimated upper or lower one-tailed 95% CIs (100 and 5 percentiles) for the explanatory variables according to negative or positive effects predicted by Eq. (9). Effect sizes of these explanatory variables were assessed using standardized regression coefficients of the multiple regression. Finally, to examine whether effects of explanatory variables on the H/P mass ratio were independent of each other and significant, we performed partial regression analysis with residual leverage plot according to Sall52 using leveragePlots() in R package “car”53.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

## Data availability

Data used in this study are summarized in supplementary Table 2 and available at the Dryad repository https://doi.org/10.5061/dryad.p8cz8w9ms54.

## Code availability

The codes used this study are available at the Dryad repository https://doi.org/10.5061/dryad.p8cz8w9ms54.

## References

1. 1.

Odum, E. P., & Barrett, G. W. Fundamentals of ecology (Vol. 3). (Saunders, Philadelphia, 1971).

2. 2.

Cebrian, J. et al. Producer nutritional quality controls ecosystem trophic structure. PLOS ONE 4, e4929 (2009).

3. 3.

Hairston, N. G. Jr & Hairston Sr, N. G. Cause-effect relationships in energy flow, trophic structure, and interspecific interactions. Am. Nat. 142, 379–411 (1993).

4. 4.

Sterner, R. W. & Elser, J. J., 2002. Ecological stoichiometry: the biology of elements from molecules to the biosphere. Princeton University Press, Princeton, NJ, 2002).

5. 5.

Coe, M. J., Cumming, D. H. & Phillipson, J. Biomass and production of large African herbivores in relation to rainfall and primary production. Oecologia 22, 341–354 (1976).

6. 6.

Power, M. top–down and bottom–up forces in food webs: do plants have primacy. Ecology 73, 733–746 (1992).

7. 7.

Ward, C., McCann, K. & Rooney, N. HSS revisited: multi-channel processes mediate trophic control across a productivity gradient. Ecol. Lett. 18, 1190–1197 (2015).

8. 8.

Coley, P. D., Bryant, J. P. & Chapin, F. S. Resource availability and plant antiherbivore defense. Science 230, 895–899 (1985).

9. 9.

Wolfe, G. V., Steinke, M. & Kirst, G. O. Grazing-activated chemical defence in a unicellular marine alga. Nature 387, 894–897 (1997).

10. 10.

Poelman, E. H., van Loon, J. J. & Dicke, M. Consequences of variation in plant defense for biodiversity at higher trophic levels. Trends Plant Sci. 13, 534–541 (2008).

11. 11.

Mooney, K. A., Halitschke, R., Kessler, A. & Agrawal, A. A. Evolutionary trade-offs in plants mediate the strength of trophic cascades. Science 327, 1642–1644 (2010).

12. 12.

Hairston, N. G., Smith, F. E. & Slobodkin, L. B. Community structure, population control, and competition. Am. Nat. 94, 421–425 (1960).

13. 13.

Carpenter, S. R., Kitchell, J. F. & Hodgson, J. R. Cascading trophic interactions and lake productivity. BioScience 35, 634–639 (1985).

14. 14.

Hanley, T. C. & La Pierre, K. J., Eds. Trophic Ecology: bottom–up and top–down interactions across aquatic and terrestrial systems (Cambridge University Press, Cambridge, UK, 2015).

15. 15.

Vanni, M. J. et al. Effects on lower trophic levels of massive fish mortality. Nature 344, 333–335 (1990).

16. 16.

Shurin, J. B. et al. A cross-ecosystem comparison of the strength of trophic cascades. Ecol. Lett. 5, 785–791 (2002).

17. 17.

Schindler, D. W. Eutrophication and recovery in experimental lakes: implications for lake management. Science 184, 897–899 (1974).

18. 18.

Smith, V. H. & Schindler, D. W. Eutrophication science: where do we go from here? Trends Ecol. Evol. 24, 201–207 (2009).

19. 19.

Karlsson, J. et al. Light limitation of nutrient-poor lake ecosystems. Nature 460, 506–509 (2009).

20. 20.

Agrawal, A. A. & Fishbein, M. Plant defense syndromes. Ecology 87, S132–S149 (2006).

21. 21.

Pančić, M. & Kiørboe, T. Phytoplankton defence mechanisms: traits and trade‐offs. Biol. Rev. 93, 1269–1303 (2018).

22. 22.

Cebrian, J. Patterns in the fate of production in plant communities. Am. Nat. 154, 449–468 (1999).

23. 23.

Konno, K. A general parameterized mathematical food web model that predicts a stable green world in the terrestrial ecosystem. Ecol. Monogr. 86, 190–214 (2016).

24. 24.

Rosenzweig, M. & MacArthur, R. Graphical representation and stability conditions of predator-prey interaction. Am. Nat. 97, 209–222 (1963).

25. 25.

Haberman, R. Mathematical models: population dynamics: mechanical vibrations, population dynamics, and traffic flow. (Prentice Hall Inc., New Jersey, 1977).

26. 26.

Frost, P. C. et al. Threshold elemental ratios of carbon and phosphorus in aquatic consumers. Ecol. Lett. 9, 774–779 (2006).

27. 27.

Urabe, J., Shimizu, Y. & Yamaguchi, T. Understanding the stoichiometric limitation of herbivore growth: the importance of feeding and assimilation flexibilities. Ecol. Lett. 21, 197–206 (2018).

28. 28.

Mathews, L., Faithfull, C. L., Lenz, P. H. & Nelson, C. E. The effects of food stoichiometry and temperature on copepods are mediated by ontogeny. Oecologia 188, 75–84 (2018).

29. 29.

Zhou, L. & Declerck, S. A. Maternal effects in zooplankton consumers are not only mediated by direct but also by indirect effects of phosphorus limitation. Oikos 129, 766–774 (2020).

30. 30.

Lampert, W. & Sommer, U. Limnoecology: the ecology of lakes and streams, 2nd edn (Oxford University Press, Oxford, UK, 2007).

31. 31.

Yamamichi, M. et al. A shady phytoplankton paradox: when phytoplankton increases under low light. Proc. R. Soc. B. 285, 20181067 (2018).

32. 32.

Ehrlich, P. R. & Birch, L. C. The” balance of nature” and” population control”. Am. Nat. 101, 97–107 (1967).

33. 33.

Hambright, K. D., Hairston, N. G., Schaffner, W. R. & Howarth, R. W. Grazer control of nitrogen fixation: synergisms in the feeding ecology of two freshwater crustaceans. Arch. Hydrobiol. 170, 89–101 (2007).

34. 34.

Urabe, J. et al. Reduced light increases herbivore production due to stoichiometric effects of light/nutrient balance. Ecology 83, 619–627 (2002).

35. 35.

Laspoumaderes, C. et al. Glacier melting and stoichiometric implications for lake community structure: zooplankton species distributions across a natural light gradient. Glob. Change Biol. 19, 316–326 (2013).

36. 36.

McCauley, E. & Murdoch, W. W. Predator-prey dynamics in environments rich and poor in nutrients. Nature 343, 455–457 (1990).

37. 37.

Williamson, T. J. et al. The importance of nutrient supply by fish excretion and watershed streams to a eutrophic lake varies with temporal scale over 19 years. Biogeochemistry 140, 233–253 (2018).

38. 38.

Elser, J. J., Dobberfuhl, D. R., MacKay, N. A. & Schampel, J. H. Organism size, life history, and N: P stoichiometry: toward a unified view of cellular and ecosystem processes. BioScience 46, 674–684 (1996).

39. 39.

Enquist, B. J. et al. Scaling from traits to ecosystems: developing a general trait driver theory via integrating trait-based and metabolic scaling theories. Adv. Ecol. Res. 52, 249–318 (2015).

40. 40.

Hambright, K. D. Morphological constraints in the piscivore-planktivore interaction: implications for the trophic cascade hypothesis. Limnol. Oceanogr. 39, 897–912 (1994).

41. 41.

Wetzel, R. G. & Likens, G. E. Limnological Analyses, 3rd edn (Springer, New York, NY, 2010).

42. 42.

Menden-Deuer, S. & Lessard, E. J. Carbon to volume relationships for dinoflagellates, diatoms and other protist plankton. Limnol. Oceanogr. 45, 569–579 (2000).

43. 43.

McCauley, E. The estimation of the abundance and biomass of zooplankton in samples in: A Manual on Methods for the Assessment of Secondary Productivity in Fresh Waters, J. A. Downing, F. H. Rigler, Eds. (Blackwell Scientific Publications, Oxford, UK, 1984), pp. 228–265.

44. 44.

Ruttner-Kolisko, A. Suggestions for biomass calculations of planktonic rotifers. Arch. Hydrobiol. Ergeb. Limnol. 21, 71–76 (1977).

45. 45.

Salonen, K. & Latja, R. Variation in the carbon content of two Asplanchna species. Hydrobiologia 162, 79–87 (1988).

46. 46.

Telesh, I. V., Rahkola, M. & Viljanen, M. Carbon content of some freshwater rotifers. Hydrobiologia 387–388, 355–360 (1998).

47. 47.

43 R Core Team, 2018. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna.

48. 48.

Hairston, N. G. Jr. Diapause as a predator avoidance adaptation, in Predation: Direct and Indirect Impacts on Aquatic Communities, W. C., Kerfoot, A. Sih, Eds. (University Press of New England, Hanover, NE, 1987), pp. 281–290.

49. 49.

Oksanen, J. et al. 2018. The vegan package. Community Ecol. package 10, 631–637 (2018).

50. 50.

Kennedy, P., Ed. A guide to econometrics, 6th edn (Blackwell Publisher, Malden, MA, 2008).

51. 51.

Moulton, L. H. & Zeger, S. L. Bootstrapping generalized linear models. Computational Stat. Data Anal. 11, 56–63 (1991).

52. 52.

Sall, J. Leverage plots for general linear hypotheses. Am. Stat. 44, 308–315 (1990).

53. 53.

Fox, J. & Weisberg, S. An R. Companion to Applied Regression, 2nd edn (Sage Publications, Thousand Oaks, CA, 2011).

54. 54.

Urabe, J., et al. Raw data used in “A unified framework for herbivore-to-producer biomass ratio reveals the relative influence of four ecological factor”. Dryad https://doi.org/10.5061/dryad.p8cz8w9ms (2020).

## Acknowledgements

We thank N. Hamm and R. L. Johnson for managing the experimental ponds, L.R. Schaffner for helping with laboratory and fieldwork and M. Kyle for discussion. This project was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI) 15H02642 to J.U., M.Y., I.K., H.D., and T.Y., 16H02522 and 20H03315 to J.U., and 16K18618, 16H04846, and 18H02509 to M.Y.

## Author information

Authors

### Contributions

J.U., T.K., and N.G.H. planned and designed the enclosure experiment. N.G.H. arranged use of CUEPF ponds for the experiment. T.K., J.U., K.T., X.Y., M.Y., I.K., H.D., T.Y., and N. G. H. contributed to the experimental setup and carried out the experiment. T.K., K.T., and X.Y. performed chemical analyses, enumerated plankton, and measured primary production rates. J.U. and M.Y performed theoretical modeling and J.U. and T.K. performed statistical analyses. J.U., T.K., M.Y., and N.G.H. wrote the draft and all authors contributed to the final manuscript.

### Corresponding author

Correspondence to Jotaro Urabe.

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### Competing interests

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Kazama, T., Urabe, J., Yamamichi, M. et al. A unified framework for herbivore-to-producer biomass ratio reveals the relative influence of four ecological factors. Commun Biol 4, 49 (2021). https://doi.org/10.1038/s42003-020-01587-9

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