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Coupling strength between omnivory loops and their one-species-delete subloops drives real food web stability

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Abstract

A central and fundamental issue in ecology is to understand the relationship between complexity and stability. Increased empirical evidences demonstrated no clear relationships between complexity metrics and stability, and recent food web loop analyses suggested that maximum loop weight as well as the summation ratio between 3- and 2-link feedback loop weights could be better estimators of system stability. However, the importance of longer loops than 3-link on the stability remains unclear. Here, we use 127 marine food webs and the matrix product and trace method to investigate the relationship between loops with maximum of 7 links and food web stability. We found that feedback metrics \(| a_{2n+1}/a_{2n} |\), i.e., the ratio of the sums of (2n + 1)-link and 2n-link loop weights, are strongly related with stability. These sum weight ratios can be regarded as the coupling strength between omnivory loops and their one-species-delete subloops, including the smallest three species and high-level omnivory ones. Further theoretical simulations of bioenergetic consumer-resource models with allometric constraints strengthen this finding. These results suggest that both longer loops and omnivory are important drivers of the food web stability.

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Data accessibility statement

Data available from the Figshare Digital Repository: https://doi.org/10.6084/m9.figshare.16622305.v1. The code supporting the results (mainly R scripts and partly Python code for graph cycles) should be archived in Zenodo, and the DOI will be included at the end of the article if the manuscript is accepted.

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Funding

This work was supported by the [National Key Research and Development Program of China] (Grant numbers 2019YFE0122300 and 2018YFC1406403).

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Author notes

  1. Jianfeng Feng and Shengpeng Li contributed equally to this work and should be considered as co-first authors.

Authors and Affiliations

  1. Tianjin Key Laboratory of Environmental Technology for Complex Trans-Media Pollution and Tianjin International Joint Research Center for Environmental Biogeochemical Technology, College of Environmental Science and Engineering, Nankai University, Tianjin, China

    Jianfeng Feng, Yueming Jiang & Ruyue Wang

  2. School of General Education, Tianjin Foreign Studies University, Tianjin, China

    Shengpeng Li

  3. State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing, China

    Xiaoxiao Li, Wei Yang & Tao Sun

  4. Center for Combinatorics and LPMC, Nankai University, Tianjin, China

    Xianhao Meng & Yongtang Shi

  5. Institute of Biochemistry and Biology, University of Potsdam, Potsdam, Germany

    Peter C. de Ruiter

  6. Biometris, Wageningen University, Wageningen, The Netherlands

    Peter C. de Ruiter

  7. Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Amsterdam, The Netherlands

    Peter C. de Ruiter

  8. Department of Biology, University of Oslo, Oslo, Norway

    Nils Chr. Stenseth

Authors
  1. Jianfeng Feng
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  2. Shengpeng Li
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  3. Xiaoxiao Li
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  7. Wei Yang
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  8. Tao Sun
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  11. Nils Chr. Stenseth
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Contributions

J.F. designed the research and discussed the framework with S.L. and R.W. S.L., J.F., and X.L. conducted research. Y.J., R.W., X.M., W.Y., T.S., P.R., and Y.S. contributed to the analysis. S.L. and J.F. wrote the paper, and T.S. and P.R. edited the paper, as well as input from all co-authors.

Corresponding author

Correspondence to Jianfeng Feng.

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Feng, J., Li, S., Li, X. et al. Coupling strength between omnivory loops and their one-species-delete subloops drives real food web stability. Theor Ecol 16, 327–338 (2023). https://doi.org/10.1007/s12080-023-00568-y

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