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.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs12080-023-00568-y/MediaObjects/12080_2023_568_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs12080-023-00568-y/MediaObjects/12080_2023_568_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs12080-023-00568-y/MediaObjects/12080_2023_568_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs12080-023-00568-y/MediaObjects/12080_2023_568_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs12080-023-00568-y/MediaObjects/12080_2023_568_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs12080-023-00568-y/MediaObjects/12080_2023_568_Fig6_HTML.png)
Similar content being viewed by others
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.
References
Allesina S, Tang S (2012) Stability criteria for complex ecosystems. Nature 483:205–8
Altena C, Hemerik L, Heesterbeek J, Ruiter P (2014) Patterns in intraspecific interaction strengths and the stability of food webs. Theor Ecol 9
Arim M, Marquet PA (2004) Intraguild predation: a widespread interaction related to species biology. Ecol Lett 7:557–564
Bascompte J, Melián CJ (2005) Simple trophic modules for complex food webs. Ecology 86:2868–2873
Brose U, Williams RJ, Martinez ND (2006) Allometric scaling enhances stability in complex food webs. Ecol Lett 9:1228–1236
Butler S, O’Dwyer JP (2018) Stability criteria for complex microbial communities. Nat Commun 9:2970
Camacho J, Stouffer D, Amaral L (2007) Quantitative analysis of the local structure of food webs. J Theor Biol 246:260–268
Colléter M, Valls A, Guitton J, Morissette L, Arregun-Snchez F, Christensen V, Pauly D (2013) EcoBase: a repository solution to gather and communicate information from EwE models. Fish Cent Res Rep 21:60pp
Colléter M, Valls A, Guitton J, Gascuel D, Pauly D, Christensen V (2015) Global overview of the applications of the Ecopath with Ecosim modeling approach using the EcoBase models repository. Ecol Model 302:42–53
de Vries FT, Thébault E, Liiri M et al (2013) Soil food web properties explain ecosystem services across European land use systems. Proc Natl Acad Sci 110:14296–14301
Domínguez-García V, Dakos V, Kéfi S (2019) Unveiling dimensions of stability in complex ecological networks. Proc Natl Acad Sci 116:25714–25720
Gardner M, Ashby W (1970) Connectance of large dynamic (cybernetic) systems: critical values for stability. Nature 228:784. https://doi.org/10.1038/228784a0
Hofbauer J, Sigmund K (1988) The theory of evolution and dynamical systems: mathematical aspects of selection. Cambridge University Press, pp. 193, 204-206
Holt RD, Huxel GR (2007) Alternative prey and the dynamics of intraguild predation: theoretical perspectives. Ecology 88:2706–2712
Holt RD, Polis GA (1997) A theoretical framework for intraguild predation. Am Nat 149:745–764
Jacquet C, Moritz C, Morissette L, Legagneux P, Massol F, Archambault P, Gravel D (2016) No complexity-stability relationship in empirical ecosystems. Nat Commun 7:12573
Johnson D (1977) Efficient algorithms for shortest paths in sparse networks. Journal of the ACM (JACM) 24:1–13. https://doi.org/10.1145/321992.321993
Kuiper J, Altena C, Ruiter P, van Gerven L, Janse J, Mooij W (2015) Food-web stability signals critical transitions in temperate shallow lakes. Nat Commun 6:7727. https://doi.org/10.1038/ncomms8727
Laska MS, Wootton JT (1998) Theoretical concepts and empirical approaches to measuring interaction strength. Ecology 79:461–476
Levins R (1974) Discussion paper: the qualitative analysis of partially specified systems. Ann N Y Acad Sci 231:123–138
Li X, Yang W, Gaedke U, de Ruiter PC (2021) Energetic constraints imposed on trophic interaction strengths enhance resilience in empirical and model food webs. J Anim Ecol n/a:1–12
MacArthur R (1955) Fluctuations of animal populations and a measure of community stability. Ecology 36:533–536
May R (1972) Will a large complex system be stable. Nature 238:413–4
McCann K (2000) The diversity-stability debate. Nature 405:228–233
McLeod AM, Leroux SJ (2021) The multiple meanings of omnivory influence empirical, modular theory and whole food web stability relationships. J Anim Ecol 90:447–459
Michalska-Smith M, Sander E, Barabs G, Allesina S (2015) Stability and feedback levels in food web models. Ecol Lett
Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298:824–7. https://doi.org/10.1126/science.298.5594.824
Mitchell E, Neutel AM (2012) Feedback spectra of soil food webs across a complexity gradient, and the importance of three-species loops to stability. Theo Ecol 5
Mougi A (2018) Spatial compartmentation and food web stability. Sci Rep 8. https://doi.org/10.1038/s41598-018-34716-w
Mougi A, Kondoh M (2016) Food-web complexity, meta-community complexity and community stability. Sci Rep 6:24478. https://doi.org/10.1038/srep24478
Neutel A, Thorne MAS (2016) Beyond connectedness: why pairwise metrics cannot capture community stability. Ecol Evol 6:7199–7206
Neutel AM, Thorne M (2015) Linking saturation, stability and sustainability in food webs with observed equilibrium structure. Theo Ecol 9
Neutel A-M, Thorne MA (2014) Interaction strengths in balanced carbon cycles and the absence of a relation between ecosystem complexity and stability. Ecol Lett 17:651–661
Neutel A-M, Heesterbeek JAP, de Ruiter PC (2002) Stability in real food webs: weak links in long loops. Science 296:1120–1123
Neutel A-M, Heesterbeek J, van de Koppel J, Hoenderboom G, Vos A, Kaldeway C, Berendse F, Ruiter P (2007) Reconciling complexity with stability in naturally assembling food webs. Nature 449:599–602
Paine R (1966) Food web complexity and species diversity. Am Nat 100:65–75
Paulau P, Feenders C, Blasius B (2015) Motif analysis in directed ordered networks and applications to food webs. Sci Rep 5. https://doi.org/10.1038/srep11926
Rip JMK, McCann KS (2011) Cross-ecosystem differences in stability and the principle of energy flux. Ecol Lett 14:733–740
Stouffer DB, Bascompte J (2010) Understanding food-web persistence from local to global scales. Ecol Lett 13:154–161
Tang S, Pawar S, Allesina S (2014) Correlation between interaction strengths drives stability in large ecological networks. Ecol Lett 17:1094–1100
Tsehaye I, Nagelkerke LA (2008) Exploring optimal fishing scenarios for the multispecies artisanal fisheries of Eritrea using a trophic model. Ecol Model 212:319–333
Tu C, Suweis S, Grilli J, Formentin M, Maritan A (2019) Reconciling cooperation, biodiversity and stability in complex ecological communities. Sci Rep 9:1–10
Williams R, Martinez N (2000) Simple rules yield complex food webs. Nature 404:180–3
Wootton KL (2017) Omnivory and stability in freshwater habitats: does theory match reality? Freshw Biol 62:821–832
Funding
This work was supported by the [National Key Research and Development Program of China] (Grant numbers 2019YFE0122300 and 2018YFC1406403).
Author information
Authors and Affiliations
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
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12080-023-00568-y