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

A unified framework model of the H/P ratio

Based on the Lotka–Volterra equations^24,25, the biomass dynamics of primary producers (P) and herbivores (H) are described as follows:

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:

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:

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:

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 nutrients^26,27,28,29. Thus, k can be expressed as:

where α_nut 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:

where α_edi 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

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:

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. (5–8) to Eq. (4), effects of factors on the H*/P* biomass ratio is formulated as:

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 (α_edi), and nutrient contents (α_nut) of producers as well as by predation by carnivores (θ), we expect non-zero values for ε₁–ε₄. 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

The experiment was carried out at two ponds (pond ID 217 and 218) located at the Cornell University Experimental Ponds Facility in Ithaca, NY, USA during 4 June to 28 August 2016 (Fig. 1). Each pond has a 0.09 ha surface area (30 × 30 m) and is 1.5 m deep. To initiate the experiment, we equally divided each of the two ponds into four sections using vinyl-coated canvas curtains, and randomly assigned the four sections to either high-shade (64% shading), mid-shade (47% shading), low-shade (33% shading), or no-shade treatments (no shading). Shading in each treatment was made using opaque floating mats (6 m diameter; Solar-cell SunBlanket, Century Products, Inc., Georgia, USA)³¹. The floating mats were deployed silvered side up to reflect sunlight and blue side down to avoid pond heating. Sampling was performed biweekly for water chemistry and abundance of phytoplankton and zooplankton with measurements of vertical profiles of water temperature, dissolved oxygen (DO) concentration and photosynthetic active radiation (PAR).

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 (α_edi) 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 (α_edi) (Fig. 3a; n = 8, r = 0.241, p = 0.565), mean seston carbon to phosphorus ratio (α_nut) (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 α_edi, α_nut, 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 (α_nut) while it did not significantly differ from one for edible phytoplankton frequency (α_edi) 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 α_edi, α_nut, μ, and θ, we estimated standardized regression coefficients. The absolute value of the coefficients for H*/P* was highest for θ, followed by α_nut (Table 1).

Source: Ecology - nature.com