Data for: Top-down control and species composition non-linearly influence the short-term response of experimental food webs to a nutrient pulse perturbation

Data files

Oct 22, 2025 version files 4.34 MB

data.zip

4.31 MB
README.md

23.16 KB

Abstract

Extreme weather events intensify with global change and frequently disturb aquatic ecosystems via e.g., nutrient pulses through surface runoff. While there is accumulating evidence that the associated short-term responses of plankton communities depend on their top-down control (TC), the actual shape of TC-community response relationships remains unclear. We therefore conducted 24 flow-through (chemostat) experiments to investigate algal and rotifer biomass responses to a nutrient pulse along a gradient of TC values. To generate this gradient, we used a trait-based method instead of varying the inoculation species densities. We complemented our analysis by estimating non-measured nutrient dynamics and feeding interactions via Bayesian modelling. We found support for hump-shaped relationships. At low TC, algal species were strongly nutrient-depleted, limiting their immediate growth potential after the pulse, and thereby one of the rotifer species. At high TC, algae were not nutrient-limited, thus algae and rotifers hardly responded. At intermediate TC, responses were larger because algae immediately exploited the pulse, and rotifers exploited the increased algal biomass production without preventing an algal bloom. This study showed the importance of investigating community responses to resource pulses along a gradient of TC values, thereby improving the understanding of the ecological stability of food webs under global change.

https://doi.org/10.5061/dryad.51c59zwj5

Description of the data and file structure

Information about the datasets and the code

The aim of this study is to investigate the response in biovolume of phytoplankton (algae) and zooplankton (rotifers) after a nutrient pulse perturbation. We notably test two types of relationships:

the hump-shaped relationship between biovolume responses of algae and the top-down control at the pulse perturbation
the hump-shaped relationship between biovolume responses of rotifers and the top-down control at the pulse perturbation

First, we conducted experiments and then inferred the experimental data via Bayesian inference. Data analysis was performed in R 4.5.0 and RStudio environment using notably the libraries tidyverse, PKNCA, cmdstanr, brms, vegan, gridExtra, scales, readxl, stringr, and deSolve. To run the scripts, it is important to keep the structure with the 3 folders; otherwise, errors can emerge.

The files are organised into three folders: data containing 8 files, scripts containing 10 R scripts, and figures containing 8 PDF files. The following sections explain the aim, structure, and content of each folder. To access all three folders together, you can unzip "scripts*dataplanktonresponses*Npulse.zip". If you are only interested in looking at the folder data, you can unzip "data.zip", or if you are only interested in looking at the folder figures, you can unzip "figures.zip".

Folder data

This folder contains all the files necessary for running the R scripts. NA or empty cell values indicate that data was not available.

"Chemostat_experimental*_*timeseries.xlsx" contains the experimental timeseries of species and trophic level biovolumes and of the relative abundance of algal species. The 16 columns are:
Category: the category of rotifer treatments "Monocultures" or "Polycultures" (cf. methods)
Treatment: the subcategory of treatments: "Bc" for monocultures of B. calyciflorus, "Ce" for monocultures of Cephalodella sp., "Le" for monocultures of Lecane sp.; "9d" for rotifer polycultures disturbed 9 days after inoculation, "13d" for rotifer polycultures disturbed 13 days after inoculation.
Chemostat: the name of the chemostat
Date [date DD/MM/YY]: date of the measurement
Time standardised to pulse [day]: day standardised to the day of the pulse perturbation. Negative values correspond to the days before the pulse perturbation, 0 corresponds to the day of the pulse perturbation, and positive values correspond to the days after the pulse perturbation.
Biovolume_total_algae [µm³/mL]: total biovolume of the algae species
Biovolume_Cryptomonas [µm³/mL]: biovolume of the species Cryptomonas sp.
Biovolume_Chlamydomonas [µm³/mL]: biovolume of the species C. reinhardtii
Biovolume_Monoraphidium_Chlorella [µm³/mL]: summed biovolume of the species M.minutum and C. vulgaris
Biovolume_total_rotifers [µm³/mL]: total biovolume of the rotifer species
Biovolume_Brachionus [µm³/mL]: biovolume of the species B. calyciflorus
Biovolume_Cephalodella [µm³/mL]: biovolume of the species Cephalodella sp.
Biovolume_Lecane [µm³/mL]: biovolume of the species Lecane sp.
Relative_abundance_Cryptomonas [unitless, takes values between 0 and 1]: proportion of Cryptomonas sp. in the algal total abundance
Relative_abundance_Chlamydomonas [unitless, takes values between 0 and 1]: proportion of C. reinhardtii in the algal total abundance
Relative_abundance_Monoraphidium_Chlorella [unitless, takes values between 0 and 1]: summed proportion of the species M.minutum and C. vulgaris in the algal total abundance
"plankton_response_avgOEV_TC_share.csv" contains the algal and rotifer responses to the pulse perturbation estimated from the experimental timeseries, and the top-down control at the pulse, the relative biovolume of the different species at the pulse. There are 12 columns, among which the first three columns are Category, Treatment, and Chemostat (cf. above), and the others are:
OEV_biovolume_algae [day^-1^]: the algal biovolume response per day
OEV_biovolume_rotifers [day^-1^]: the algal biovolume response per day
TC_at_pulse [unitless]: the top-down control at the pulse
Relative_Biovolume_Monoraphidium_Chlorella_at_pulse [unitless, takes values between 0 and 1]: the summed share of M. minutum and C. vulgaris at the pulse
Relative_Biovolume_Chlamydomonas_at_pulse [unitless, takes values between 0 and 1]: the share of C. reinhardtii at the pulse
Relative_Biovolume_Cryptomonas_at_pulse [unitless, takes values between 0 and 1]: the share of Cryptomonas sp. at the pulse
Relative_Biovolume_Brachionus_at_pulse [unitless, takes values between 0 and 1]: the share of B. calyciflorus at the pulse
Relative_Biovolume_Cephalodella_at_pulse [unitless, takes values between 0 and 1]: the share of Cephalodella sp. at the pulse
Relative_Biovolume_Lecane_at_pulse [unitless, takes values between 0 and 1]: the share of Lecane sp. at the pulse
"algae_no-rotifer_chemostat_preliminary_experiments.xlsx": contains the preliminary experimental timeseries of algal species and trophic level biovolumes and of the relative abundance of algal species. These experiments were conducted in the absence of rotifers to have indicative insights about the algal species' behaviour. These datasets are not used in the main analyses of the study or are only used as supplementary material. The structure of the dataset is similar to the one described for "Chemostat_experimental*_*timeseries.xlsx".
Category: the category of rotifer treatments "No herbivore" (cf. methods)
Treatment: the subcategory of treatments: "Mi" for the polycultures of the four algal species, "Cr" for the monocultures of Cryptomonas sp., "Ca" for the monocultures of C. reinhardtii, "Mo" for the monocultures of M.minutum and "Co" for the monocultures of C. vulgaris.
Chemostat: the name of the chemostat
Date [date DD/MM/YY]: date of the measurement
Time standardised to pulse [day]: day standardised to the day of the pulse perturbation. Negative values correspond to the days before the pulse perturbation, 0 corresponds to the day of the pulse perturbation, and positive values correspond to the days after the pulse perturbation.
Biovolume_total_algae [µm³/mL]: total biovolume of the algae species
Biovolume_Cryptomonas [µm³/mL]: biovolume of the species Cryptomonas sp.
Biovolume_Chlamydomonas [µm³/mL]: biovolume of the species C. reinhardtii
Biovolume_Monoraphidium_Chlorella [µm³/mL]: summed biovolume of the species M.minutum and C. vulgaris
Biovolume_total_rotifers [µm³/mL]: total biovolume of the rotifer species
Biovolume_Brachionus [µm³/mL]: biovolume of the species B. calyciflorus
Biovolume_Cephalodella [µm³/mL]: biovolume of the species Cephalodella sp.
Biovolume_Lecane [µm³/mL]: biovolume of the species Lecane sp.
Relative_abundance_Cryptomonas [unitless, takes values between 0 and 1]: proportion of Cryptomonas sp. in the algal total abundance
Relative_abundance_Chlamydomonas [unitless, takes values between 0 and 1]: proportion of C. reinhardtii in the algal total abundance
Relative_abundance_Monoraphidium_Chlorella [unitless, takes values between 0 and 1]: summed proportion of the species M. minutum and C. vulgaris in the algal total abundance
"algae_stoichiometry_preliminary_experiments.xlsx": contains the preliminary experimental timeseries of nitrogen content, carbon content, C/N ratio, cell volume, density, and biovolume of algal species. These experiments were conducted in the absence of rotifers to have indicative insights about the algal species' behaviour. These datasets are not used in the main analyses of the study or are only used as supplementary material. There are 9 columns:
Date [date DD/MM/YY]: date of the measurement
Time standardised to pulse [day]: day standardised to the day of the pulse perturbation. Negative values correspond to the days before the pulse perturbation, 0 corresponds to the day of the pulse perturbation, and positive values correspond to the days after the pulse perturbation.
Algae: the algae species present in the experiment. "Cr" is Cryptomonas sp., "Ca" is C. reinhardtii, "Mo" is M. minutum, "Co" is C. vulgaris and "Mi" is the four algal species together.
N [pmol/cell]: nitrogen content
C [pmol/cell]: carbon content
C/N Ratio [molar]: ratio between N and C in [pmol/cell]/[pmol/cell]
Cell volume [µm³]: algal cell volume
Density [cells/mL]: algal density
Biovolume [µm³/mL]: algal biovolume
"fit_monocultures.rds" is the file containing the a priori distributions of the parameters of the equation-based model used for the Bayesian inference. It was used to generate the predicted timeseries of nitrogen dynamics, algal biovolume, and rotifer biovolume of "Monocultures", which is contained in "bayesian_predictions_monocultures.csv". The file is composed of five columns:
variable: name of the fitted variable: eAlog the log value of the conversion factor between nitrogen concentration and algal biovolume in μm³ ⋅ mL ⁻¹ /μmol N ⋅ L ⁻¹, b the algal maximum growth rate in d ⁻¹, Klog the log value of the algal half-saturation constant in μmol N ⋅L ⁻¹, alog[1] the log value of the attack rate of B. calyciflorus in mL/μm³⋅day, alog[2] the log value of the attack rate of Cephalodella sp. in mL/μm³⋅day, alog[3] the log value of the attack rate of Lecane sp. in mL/μm³⋅day, hlog[1] the log value of the handling time of B. calyciflorus in day, hlog[2] the log value of the handling time of Cephalodella sp. in day, hlog[3] the log value of the handling time of Lecane sp. in day, eR[1] the conversion factor between algae and B. calyciflorus (unitless), eR[2] the conversion factor between algae and Cephalodella sp. (unitless), eR[3] the conversion factor between algae and Lecane sp. (unitless), m[1] the mortality rate of B. calyciflorus in day ^-1, m[2] the mortality rate of Cephalodella sp. * *in day ^-1, m[3] the mortality rate of Lecane sp. in day ^-1.
median: the median value of the a priori distribution of the variable considered in the unit of the variable considered (cf variable above)
sd: the standard deviation value of the a priori distribution of the variable considered in the unit of the variable considered (cf variable above)
q5: the 5th-quantile value of the a priori distribution of the variable considered in the unit of the variable considered (cf variable above)
q95: the 95th-quantile value of the a priori distribution of the variable considered in the unit of the variable considered (cf variable above)
"fit_polycultures.rds" is the file containing the a priori distributions of the parameters of the equation-based model used for the Bayesian inference. It was used to generate the predicted timeseries of nitrogen dynamics, algal biovolume, and rotifer biovolume of "Polycultures", which is contained in "bayesian_predictions_polycultures.csv". The file is composed of five columns:
variable: name of the fitted variable: eAlog the log value of the conversion factor between nitrogen concentration and algal biovolume in μm³ ⋅ mL ⁻¹ /μmol N ⋅ L ⁻¹, b the algal maximum growth rate in d ⁻¹, Klog the log value of the algal half-saturation constant in μmol N ⋅L ⁻¹, alog the log value of the attack rate of rotifers in mL/μm³⋅day, hlog the log value of the handling time of rotifers in day, eR the conversion factor between algae and rotifers (unitless)*, m the mortality rate of rotifers *in day ^-1.
median: the median value of the a priori distribution of the variable considered in the unit of the variable considered (cf variable above)
sd: the standard deviation value of the a priori distribution of the variable considered in the unit of the variable considered (cf variable above)
q5: the 5th-quantile value of the a priori distribution of the variable considered in the unit of the variable considered (cf variable above)
q95: the 95th-quantile value of the a priori distribution of the variable considered in the unit of the variable considered (cf variable above)
"bayesian_predictions_monocultures.csv": contains the predicted timeseries of nitrogen dynamics, algal biovolume, and rotifer biovolume of "Monocultures". There are 11 columns:
Chemostat: the name of the chemostat
Time standardised to pulse [day]: day standardised to the day of the pulse perturbation. Negative values correspond to the days before the pulse perturbation, 0 corresponds to the day of the pulse perturbation, and positive values correspond to the days after the pulse perturbation.
N.Q1 [µmol N/L]: the first quantile value of the predicted nitrogen concentration
N.Q2 [µmol N/L]: the second quantile value of the predicted nitrogen concentration
N.Q3 [µmol N/L]: the third quantile value of the predicted nitrogen concentration
Biovolume.Q1_A [µm³/mL]: the first quantile value of the predicted algal biovolume
Biovolume.Q2_A [µm³/mL]: the second quantile value of the predicted algal biovolume
Biovolume.Q3_A [µm³/mL]: the third quantile value of the predicted algal biovolume
Biovolume.Q1_R [µm³/mL]: the first quantile value of the predicted rotifer biovolume
Biovolume.Q2_R [µm³/mL]: the second quantile value of the predicted rotifer biovolume
Biovolume.Q3_R [µm³/mL]: the third quantile value of the predicted rotifer biovolume
"bayesian_predictions_polycultures.csv": same as "bayesian_predictions_monocultures.csv" for "Polycultures".

Folder figures

This folder contains all the PDF files generated by the R scripts. In the following, we provide the caption of the figure and which script that was used to generate it.

"figure2.pdf"
Caption: Relationships between a) log2 algal response (avgOEVA) or b) log2 rotifer response (avgOEVR) and top-down control TC. We fitted quadratic regressions for the 24 chemostats together (orange solid line), for the 12 rotifer monocultures (blue dotted curve and symbols: circles for B. calyciflorus, squares for Cephalodella sp., and diamonds for Lecane sp.), for the 12 rotifer polycultures (black dashed curve and symbols: down-triangles for chemostats perturbed 9 days after inoculation and up-triangles for chemostats perturbed 13 days after inoculation). The shadowed areas are the 90% credible intervals. Full summary statistics are available in the Appendix S5.
Script: "figure2.R"
"figure3.pdf"
Caption: Time series of dissolved nitrogen concentration (dotted grey curve), algal biovolume (dashed green curve), and rotifer biovolume (solid magenta curve) in eight chemostats: four rotifer monocultures of Lecane sp. (a), Cephalodella sp. (b), or B. calyciflorus (c and d), and four rotifer polycultures (e-h) differing in top-down control (TC) at the pulse (t = 0). Upper panels are chemostats with lower TC values. Dots are experimental data, whereas the curves and shaded areas show the respective means and 90% credible intervals of posterior predictive distributions from Bayesian inference. To fit the experimental timeseries, we first predicted pre-pulse dynamics and then post-pulse dynamics, which explains the jumps in the predictions at t = 0 (see details in the Appendix S4-S5). Time series of the other chemostats are available in the Appendix (Figs. S5.3-S5.4).
Script: "figure3.R"
"figure4.pdf"
Caption: (a) Per-capita net growth rates of rotifers predicted by Bayesian inference for B. calyciflorus monoculture (Bc) in dark red with circles, Cephalodella sp. monoculture (Ce) in red with squares, Lecane sp. monoculture (Le) in orange with diamonds, and rotifer polycultures in black (Poly), and (b) algal nutrient uptake rate in rotifer monocultures (Mono; solid, blue curve) and rotifer polycultures (Poly; dashed, black curve). Curves and shaded areas show means and 90% credible intervals, respectively, of the posterior predictive distribution from Bayesian inference (see Appendix S4 for details).
Script: "figure4.R"
"figureS2_1.pdf"
Caption: Biovolume timeseries in chemostats with monocultures of C. vulgaris (Co), M. minutum (Mo), C. reinhardtii (Ca), and Cryptomonas sp. (Cr), and with all the algal species together (polyculture). In all the panels, solid and dashed curves distinguish two replicates, and the vertical black line marks the day of the pulse. In polycultures M. minutum and C. vulgaris could not be distinguished (cf. Appendix S3), thus their biovolumes were summed (Mo+Co), and Crytomonas sp. biovolume was not displayed because it was several orders of magnitude lower than the biovolume of the other species (< 10⁵ μm³ ⋅ mL ⁻¹), but this species persisted until the end of the experiment.
Script: "figureS2_1.R"
"figureS2_2.pdf"
Caption: Time series of C:N ratios (a), cell densities (b), biovolumes (c), and cell volumes (d) for monocultures of C. vulgaris (Co in solid, light green curve), M. minutum (Mo in solid, dark green curve), C. reinhardtii (Ca in dashed, light blue curve) and Cryptomonas sp. (Cr in dashed, dark blue curve). Monocultures were cultivated semi-continuously and pulsed the day marked by a vertical, black line by increasing the nitrogen concentration from 80 to 400 μmol N/L.
Script: "figureS2_2.R"
"figureS5_1.pdf"
Caption: Biovolume timeseries of rotifer monocultures of B. calyciflorus (Bc1-4), Cephalodella sp. (Ce1-4) or Lecane sp. (Le1-4). Algae are in full dots and dashed curves – M. minutum and C. vulgaris in green, C. reinhardtii in light blue, Cryptomonas sp. in dark blue – and rotifers in empty dots and solid curves – B. calyciflorus in dark red, Cephalodella sp. in red and Lecane sp. in orange.
Script: "figuresS5_1_and_S5_2.R"
"figureS5_2.pdf"
Caption: Biovolume timeseries of rotifer polycultures differing in the timing of the pulse (9d or 13d after inoculation) and thus TC values (cf. Table S5.1). Colors and markers are the same as in Figure 3 and S5.1.
Script: "figuresS5_1_and_S5_2.R"
"figureS5_3.pdf"
Caption: Biovolume timeseries of rotifer monocultures of B. calyciflorus (Bc1-4), Cephalodella sp. (Ce1-4) or Lecane sp. (Le1-4) fitted via Bayesian inference. Nitrogen concentration is in the dotted grey curve, algal total biovolume is in the dashed green curve, and rotifer total biovolume is in the solid magenta curve. The green empty circles and the magenta full circles are the experimental data of algae and rotifers, respectively.
Script: "figuresS5_3_and_S5_4.R"
"figureS5_4.pdf"
Caption: Biovolume timeseries of rotifer polycultures differing in the timing of the pulse (9d or 13d after inoculation) fitted via Bayesian inference. The figure layout is the same as in Figures 3 and S5.3.
Script: "figuresS5_3_and_S5_4.R"
"figureS5_5.pdf"
Caption: Differences in algal response (a) and rotifer response between rotifer monocultures (low diversity, in blue) and rotifer polycultures (high diversity, in black). No significant differences were observed (p-value > 0.05 for all the Wilcoxon sum rank tests).
Script: "figureS5_5.R

Folder scripts

This folder contains all the R scripts for generating the figures and performing the analyses of this study. In the following, we provide the aim of the script, which datasets are uploaded, and which figures or datasets are generated. The scripts are presented in the order that they should be run:

"get_responses_to_pulse.R"
Aim: For each chemostat experiment, calculate the biovolume responses of algae and rotifers to the pulse perturbation, the top-down control at the pulse perturbation, and the relative biovolume of each species per trophic level.
Uploaded data: "Chemostat_experimental_timeseries.xlsx"
Generated output: "plankton_response_avgOEV_TC_share.csv"
"get_bayesian_predictions_monocultures.R"
Aim: Predicts the time series of the nitrogen concentration, algal total biovolume, and rotifer total biovolume of each chemostat of the "Monocultures" treatment using Bayesian inference
Uploaded data: "fit_monocultures.rds"
Generated output: "bayesian_predictions_monocultures.csv"
"get_bayesian_predictions_polycultures.R"
Aim: Predicts the time series of the nitrogen concentration, algal total biovolume, and rotifer total biovolume of each chemostat of the "Polycultures" treatment using Bayesian inference
Uploaded data: "fit_polycultures.rds"
Generated output: "bayesian_predictions_polycultures.csv"
"figure2.R"
Aim: Investigating the relationships between plankton responses and the hypothesized drivers (top-down control, the relative biovolume of the opportunist species per trophic level)
Uploaded data: "plankton_response_avgOEV_TC_share.csv"
Generated output: "figure2.pdf"
"figure3.R"
Aim: Plotting experimental timeseries and the associated predicted timeseries via Bayesian modelling for different chemostats
Uploaded data: "Chemostat_experimental_timeseries.xlsx", "bayesian_predictions_monocultures.csv", "bayesian_predictions_polycultures.csv"
Generated output: "figure3.pdf"
"figure4.R"
Aim: plotting the nitrogen uptake rate of algae and the rotifer per-capita net growth rates predicted by Bayesian modelling
Uploaded data: "fit_monocultures.rds", "fit_polycultures.rds"
Generated output: "figure4.pdf"
"figureS2_1.R"
Aim: Plotting the biovolume timeseries of the preliminary experiments run in the absence of rotifers
Uploaded data: "algae_no-rotifer_chemostat_preliminary_experiments.xlsx"
Generated output: "figureS2_1.pdf"
"figureS2_2.R"
Aim: Plotting the timeseries of nitrogen content, carbon content, C/N ratio, cell volume, density, biovolume of algal species for the preliminary experiments run in the absence of rotifers.
Uploaded data: "algae_stoichiometry_preliminary_experiments.xlsx"
Generated output: "figureS2_2.pdf"
"figuresS5_1_and_S5_2.R"
Aim: Plotting the experimental biovolume timeseries of plankton species for all chemostats
Uploaded data: "Chemostat_experimental_timeseries.xlsx"
Generated output(s): "figureS5_1.pdf", "figureS5_2.pdf"
"figuresS5_3_and_S5_4.R"
Aim: Plotting the fitted biovolume timeseries of plankton species for all chemostats
Uploaded data: "Chemostat_experimental_timeseries.xlsx", "bayesian_predictions_monocultures.csv", "bayesian_predictions_polycultures.csv"
Generated output(s): "figureS5_3.pdf", "figureS5_4.pdf"
"figureS5_5.R"
Aim: Investigating the differences in plankton responses between rotifer monocultures and polycultures
Uploaded data: "plankton_response_avgOEV_TC_share.csv"
Generated output(s): "figureS5_5.pdf"

The aim of this study is to investigate the response in biovolume of phytoplankton (algae) and zooplankton (rotifers) after a nutrient pulse perturbation. We notably test two types of relationships:

the hump-shaped relationship between biovolume responses of algae and the top-down control at the pulse perturbation
the hump-shaped relationship between biovolume responses of rotifers and the top-down control at the pulse perturbation

In the following, you can find a summary of the methods. Please see the published study for more details.

We cultivated the four algal species Chlamydomonas reinhardtii (strain No. SAG 11-32b), Monoraphidium minutum (SAG 243-1), Chlorella vulgaris (SAG 211-11b), and Cryptomonas sp. (SAG 26-80), and the three herbivorous rotifer species Brachionus calyciflorus sensu strictu (isolated from the Milwaukee Harbor, Wisconsin, USA), Cephalodella sp. (obtained from Florian Altermatt, Campus pond), and Lecane sp. (isolated by Christina Schirmer, Löschteich Golm, Potsdam, Germany). Stock cultures were reared in 300-mL flasks containing 200 mL of Woods Hole Culture medium (WC medium) at pH 7, 19.5°C, and a 16:8 hour day:night cycle. B. calyciflorus and Cephalodella sp. were fed once per week with C. reinhardtii, and Lecane sp. with C. vulgaris. Three days before inoculation, we diluted algal stock cultures with fresh medium to guarantee exponential growth.

We ran chemostats (i.e., flow-through systems) in 1-L bottles filled with 800 mL of nitrogen-reduced WC medium (inorganic nitrogen N0 = 80 μmol N ⋅ L ⁻¹ rather than 1 mmol N ⋅ L ⁻¹) at 19.5° C, under constant light conditions, and with a dilution rate δ = 0.2 d ⁻¹. After one to two weeks, we spiked the nitrogen concentration to a total of 400 μmol N ⋅ L ⁻¹ and the phosphorus concentration in the same ratio to avoid a shift in the limiting macronutrient. Then, we measured the short-term responses of algae and rotifers over 12 days.

We conducted a total of 24 chemostats comprising the four algal species, differing in the identity and number of rotifer species, and timing of the pulse. Varying these factors generated a gradient of top-down control (TC). With this information in mind, we designed two treatments: (i) rotifer monocultures pulsed 17 days after inoculation (12 chemostats, i.e., 4 per rotifer species); and (ii) rotifer polycultures comprising all the rotifer species and pulsed 9 or 13 days after inoculation (12 chemostats, i.e., 6 per date).

To obtain time series of species biovolumes, we sampled 25 mL of each chemostat three times a week, and daily during the first five days after the perturbation. A 10 mL subsample fixed with Lugol’s solution was used to determine algal density and size spectra with a particle counter (CASY; Schärfe, Germany), and rotifer density with a microscope (Zeiss Axioskop 2, Germany). Then, we calculated algal and rotifer biomass as their respective total biovolume (in μm³ ⋅ mL ⁻¹) using densities and size spectra for algae, and densities and fixed species-specific volumes for rotifers (1.85 ⋅ 10⁶ μm³ for B. calyciflorus, 7.37 ⋅ 10⁴ μm³ for Cephalodella sp., and 3.45 ⋅ 10⁴ μm³ for Lecane sp.). Algal species composition was analysed via flow cytometry (BD Accuri C6 Flow Cytometer, BD Biosciences), accounting for differences in algal morphology and pigmentation. Distinguishing M. minutum from C. vulgaris was not possible, hence they were considered together as one morphological group in the analyses.

Following the framework of Hillebrand et al (2018) and Urrutia-Cordero et al (2022), biomass responses were quantified using the metric of overall ecological vulnerability (OEV), which integrates multiple dimensions of ecological stability such as resistance, resilience, and recovery. A large OEV value means that a trophic level or a community strongly reacts to a perturbation because of pronounced biomass changes in comparison to the pre-perturbation conditions. The trophic level or community is thus vulnerable to a perturbation, indicating low ecological stability. We quantified the short-term responses over a maximum of 12 days after the pulse and standardised these responses by the sampling period of each chemostat and obtained thereby the average biomass responses per day.

We expect biomass responses of algae and rotifers to be influenced by the top-down control (TC). TC is the log2 value of the ratio between the total algal biomass per chemostat with rotifers at the pulse and the average total algal biomass in the absence of rotifers at the pulse (i.e., carrying capacity of 4 ⋅ 10⁷ μm³ ⋅ mL ⁻¹). We also determined the relative biomasses, i.e., the species biomasses divided by the trophic level biomass.

Data analysis was performed in R 4.5.0 and RStudio environment using notably the libraries tidyverse, PKNCA, cmdstanr, vegan, brms, gridExtra, scales, readxl, stringr, and deSolve. For each trophic level and each treatment separately (12 rotifer monocultures or 12 rotifer polycultures) or both treatments together, we fitted quadratic regressions (y ∼ a + bx + cx2 ) to log2 avgOEV and TC data. Because of the small number of observations, we used Bayesian inference, which produces accurate estimates of parameter uncertainty even in small datasets. We considered a relationship as hump-shaped if (i) the quadratic term c of the regression was negative, and (ii) if the predicted maximum $-b/2c was located within the observed range of TC. We calculated posterior probabilities as

P(shape)=P(c<0 AND TC_min < -b/2c < TC_max).

Furthermore, we obtained insights into non-measurable nutrient dynamics and species interactions, and, thus, into top-down and bottom-up control, via Bayesian inference. For this, we fitted the predictions of a differential equation model to the experimental timeseries of trophic level biomasses, and estimated posterior probability distributions of all the model parameters.