DOI: 10.5061/dryad.pnvx0k6xx
title: Data from: Seasonal shifts in trophic interaction strength drive stability of natural food webs

description: It remains challenging to understand why natural food webs are remarkably
 stable despite pronounced variability in environmental factors and
 population densities. We analysed the dynamics in the structure and
 stability of the pelagic food web of Lake Constance using seven years of
 high-frequency observations of biomasses and production, leading to 59
 seasonally resolved quantitative food web descriptions. We analysed the
 dynamics in asymptotic food web stability using maximum loop weight, which
 revealed mechanisms governing stability. Maximum loop weight showed a
 recurrent seasonal pattern while indicating consistently high stability
 despite pronounced dynamics in biomasses and fluxes. This arose from
 rewiring of the food web structure along seasons, which counteracted
 destabilization by enhanced productivity. The rewiring originated from
 energetic constraints within loops and how loops were embedded into food
 web structure. The stabilizing dynamics originated from the counter-acting
 effect between high metabolic activity and competitiveness/susceptibility
 to predation within a diverse grazer community.
description: For a general description of Lake Constance, the overall data
 set, the raw data to obtain the biomasses, the production rates of
 phytoplankton and bacteria, and the corresponding measurement techniques
 see https://fred.igb-berlin.de/Lakebase and literature provided therein.
 Plankton was sampled weekly during the growing season and approximately
 every second week in winter up to 20 years. Biomasses were calculated from
 taxonomically resolved microscopic counting of all plankton groups.
 Production rates were measured in in situ using advanced techniques. This
 data set was used to establish 59 mass-balanced food web models on which
 the present study is based.
description: # Seasonal shifts in trophic interaction strength drive stability of
 natural food webs
 [https://doi.org/10.5061/dryad.pnvx0k6xx](https://doi.org/10.5061/dryad.pnvx0k6xx) ## Description of the data and file structure ### Files, variables and code For a general description of Lake Constance and its food web, the overall data set, the raw data to obtain the biomasses, the production rates of phytoplankton and bacteria, and the corresponding measurement techniques see [https://fred.igb-berlin.de/Lakebase](https://fred.igb-berlin.de/Lakebase) and literature provided therein. More data and documentation will be provided in a data paper (Gaedke, in prep, intended as publication in Data Science). The present study is based on 59 mass-balanced food web models established by Gaedke et al. (2002) (described by the fluxes among the compartments which also provide the gross growth efficiencies) and further measurements like plankton biomasses and production which have mostly been published in principle elsewhere but e.g. with different resolutions in time. Using this data base we calculated the interaction strengths (Jacobian matrices), measures of stability (Re(λmax), *loop weights*) and different types of openness in this study. The data describing the 59 mass-balanced food web models and those underlying the figures in the main text and the appendices are provided in the following data sets: The data set ***flux_IS.xlsx*** provides for the 59 phases (first two columns, providing the year and the phase number) and each prey and predator guild (column 3 and 4): 1.     the fluxes between all living compartments in units of mg C m-2 d-1 describing the mass-balanced food webs. The compartments are numbered as: 1 - phytoplankton, 2 – bacteria, 3 - heterotrophic flagellates, 4 - ciliates, 5 - rotifers, 6 - predominantly herbivorous crustaceans (daphnids, *Bosmina* sp., *Eudiaptomus* sp.), 7 - predominantly carnivorous crustaceans (cyclopoid copepods including their herbivorous nauplii, *Leptodora kindtii*, *Bythotrephes longimanus*) and 8 – fish. 2.     the negative interaction strengths between all living compartments (d-1), and 3.     the positive interaction strengths between all living compartments (d-1). The negative and positive interaction strengths are the off-diagonal values of the Jacobian matrices (the diagonal values were set to 0). The file ***Jacobian_matrices.xlsx*** provides for each year and phase the same negative and positive interaction strengths as given in the data set ***flux_IS.xlsx*** but in a matrix format, which is more convenient for some but not for all further studies which may use these data. For the name of the compartments see above. The data set ***biomass_stability***.***xlsx*** provides for the 59 phases (first columns, providing the year and the phase number): 1.     the biomasses (mg C m-2) of all living compartments (trophic guilds, phyt - phytoplankton, bac – bacteria, HF - heterotrophic flagellates, cil - ciliates, rot - rotifers, herb.cru. -predominantly herbivorous crustaceans, carn.cru - predominantly carnivorous crustaceans) and the total plankton biomass averaged across all measurements conducted during the respective phase (the fish biomass is not provided per phase and year as it was kept constant at 752 mg C m-2), 2.     the real part of the leading eigenvalues, *Re(λmax) (d-1)* , of the respective Jacobian matrices, called Real(lambda), 3.     the weight of the heaviest loop in the food web of any length, LWmax (d-1), 4.     the weight of the heaviest loop in the food web with length 3, called LWmax-3(d-1). This weight was used in the present analysis. It is three times slightly lower than that of a longer loop. Which loop of length 3 was the heaviest during a distinct phase is provided in Appendix Table 1, 5.     the weight of the ciliate-flagellate-phytoplankton loop (d-1), called LWC-F-P, 6.     the net primary production (i.e., the production of the resource guild) called Phyt Prod in mg C m-2 d-1, and 7.     the gross growth efficiencies of the consumers (i.e., the ratio between production and ingestion), labelled HF Efficiency, …, Fish Efficiency (dimensionless).  They are used to calculate loop weight (d-1). The data set ***25_loops_IS_weight.xlsx*** provides for each year and phase (first two columns) for the 25 positive loops of length 3 1.     the three interaction strengths within the respective loop. For each loop the interaction strength IS-12 provides the negative interaction between the intermediate consumer and the resource guild, IS-23 stands for the negative interaction between the top predator and the intermediate consumer, and IS-13 for the positive interaction between the resource guild and the top predator, and 2.     the loop weight. The loops are coded according to their 3 trophic guilds going from the resource guild via the intermediate consumer to the top predator: 1- phytoplankton, 2 – bacteria, 3 - heterotrophic flagellates, 4 - ciliates, 5 - rotifers, 6 - predominantly herbivorous crustaceans, 7 predominantly carnivorous crustaceans. For example, the loop called “1-3-4” is the ciliates-flagellates-phytoplankton loop. The data set ***openness.xlsx*** provides for each year and phase (first two columns) for the 6 loops which became the heaviest during individual phases 1.     the overall openness OO of the entire loop (cf. methods in the main text) and 2.     the openness in respect to the 4 in- or outgoing fluxes (O1 to O4) (both dimensionless). The loops are coded according to their 3 trophic guilds going from the resource guild via the intermediate consumer to the top predator: 1- phytoplankton, 2 – bacteria, 3 - heterotrophic flagellates, 4 - ciliates, 5 - rotifers, 6 - predominantly herbivorous crustaceans, 7 predominantly carnivorous crustaceans. **Data for individual figures** The data for the figures in the main text are provided in the following way (the hash tagged numbers “#x” refer to the descriptions under point x of the respective data set, e.g., #4 of ***biomass_stability.xlsx*** refers to point 4 “the weight of the heaviest loop…”): 1.     Fig. 2 by ***biomass_stability***.***xlsx***  #4, 2.     Fig. 3 by ***25_loops_IS_weight.xlsx*** #2, 3.     Fig. 4 by ***biomass_stability.xlsx***  #5 and ***openness***.xlsx, and 4.     Fig. 5 by ***biomass_stability.xlsx***  #1, ***flux_IS***.***xlsx*** #1, 2 and 3 and ***openness.xlsx*** #1. The data for the table and figures in the appendices are provided in the following way: 1.     Table 1 by ***25_loops_IS_weight.xlsx*** #2, 2.     Fig. A1 by ***biomass_stability.xlsx*** #1 and ***flux IS.xlsx*** #1, 3.     Fig. A2 by ***biomass_stability***.***xlsx***  #1 and #6, and ***flux IS***.***xlsx*** # 2 and 3, 4.     Fig. A4 by ***biomass_stability***.***xlsx***  #2 and 4, 5.     Fig. A6 by Table A1, ***biomass_stability***.***xlsx***  #2, 4 and 6, 6.     Fig. A7 by ***openness***.***xlsx*** #1 and ***25_loops_IS_weight.xlsx*** #2, 7.     Fig. A8 by ***flux_IS***.***xlsx*** #1 and ***25_loops_IS_weight.xlsx*** #2, and 8.     Fig. A9 by ***flux_IS.xlsx*** #2, #3 and ***25_loops_IS_weight.xlsx*** #2. The **following code** was used: 1.     To identify all possible loops in the food webs and to calculate the loop weight the programme "Program_identify_loops_and_calculate\_ LW.R" was used. It uses the data file "BodenseeCdef.txt" as input file, containing the interaction matrices (fwnr - number of the food web (n=59), P - phytoplankton, B - bacteria, HF - heterotrophic flagellates, Cil - ciliates, R - rotifers, HC - herbivorous crustaceans, CC - carnivorous crustaceans, F - fish) 2.     To produce Figure 2, 3 and 4 the code Figure2.R, Figure3.R and Figure4.R was used. To calculate the correlation coefficients the code spearmancorrelation.R was used. The other calculations were done in Excel and the other figures with Powerpoint. **Reference** Gaedke, U., S. Hochstädter & D. Straile (2002) Interplay between energy limitation and nutritional deficiency: Empirical data and food web models. Ecological Monographs 72: 251-270.