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Power laws in species’ biotic interaction networks can be inferred from co-occurrence data

Nature Ecology & Evolution volume 8, pages 209–217 (2024)Cite this article

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Abstract

Inferring biotic interactions from species co-occurrence patterns has long intrigued ecologists. Yet recent research revealed that co-occurrences may not reliably represent pairwise biotic interactions. We propose that examining network-level co-occurrence patterns can provide valuable insights into community structure and assembly. Analysing ten bipartite networks of empirically sampled biotic interactions and associated species spatial distribution, we find that approximately 20% of co-occurrences correspond to actual interactions. Moreover, the degree distribution shifts from exponential in co-occurrence networks to power laws in networks of biotic interactions. This shift results from a strong interplay between species’ biotic (their interacting partners) and abiotic (their environmental requirements) niches, and is accurately predicted by considering co-occurrence frequencies. Our work offers a mechanistic understanding of the assembly of ecological communities and suggests simple ways to infer fundamental biotic interaction network characteristics from co-occurrence data.

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Fig. 1: Visual representation of a network of co-occurrence and the corresponding network of biotic interactions and their degree distribution.
Fig. 2: Comparison of the frequency distributions of consumer’s degree among co-occurrence networks and realized biotic interactions networks.
Fig. 3: The role of super-generalist species in the emergence of power-law degree distributions.
Fig. 4: Relationship between the number of potential interactions (based on co-occurrences) and the number of realized interactions for consumer species.
Fig. 5: Relationship between the number of potential interactions of consumer species and the average frequency of co-occurrence with their potential resources.
Fig. 6: Model predictions for the degree distribution of consumer interactions based on the frequency of species co-occurrences.

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Data availability

The data supporting the study results can be found at https://doi.org/10.5281/zenodo.8402455.

Code availability

The code used to analyse the data and generate the results can be found at https://doi.org/10.5281/zenodo.8402455.

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Acknowledgements

N.G. received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement BIOFOODWEB (no. 101025471). M.B.A. acknowledges funding from the Spanish Ministry of Science, Innovation and Universities through the PredWeb project (PGC2018–099363-B-I00) and, together with A.R., from the European Union’s Horizon 2020 research and innovation programme under grant agreement AQUACOSM-Plus (no. 871081). J.-F.A. was supported by the Laboratoires d’Excellences (LABEX) TULIP (ANR-10-LABX-41).

Author information

Author notes

  1. These authors contributed equally: Nuria Galiana, Jean-François Arnoldi.

Authors and Affiliations

  1. Department of Biogeography and Global Change, National Museum of Natural Sciences, Madrid, Spain

    Nuria Galiana & Miguel B. Araújo

  2. Centre National de la Recherche Scientifique, Experimental and Theoretical Ecology Station, Moulis, France

    Jean-François Arnoldi

  3. Rui Nabeiro Biodiversity Chair, Mediterranean Institute for Agriculture, Environment and Development, University of Évora, Évora, Portugal

    Frederico Mestre, Alejandro Rozenfeld & Miguel B. Araújo

  4. INTELYMEC Group, Centro de Investigaciones en Física e Ingeniería del Centro Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires – Universidad Nacional del Centro de la Provincia de Buenos Aires – Consejo Nacional de Investigaciones Científicas y Técnicas, Olavarría, Argentina

    Alejandro Rozenfeld

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Contributions

N.G., J.-F.A. and M.B.A. designed the research. N.G. performed the research and analysed the data. J-F.A. and N.G. developed the theoretical framework. N.G. wrote the manuscript with feedback from J.-F.A. and M.B.A., and comments from F.M. and A.R.

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Correspondence to Nuria Galiana.

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Nature Ecology & Evolution thanks Kevin Cazelles and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data

Extended Data Fig. 1 Comparison of the frequency distributions of resources degree among co-occurrence networks and realised biotic interactions networks.

Red lines represent co-occurrence networks and yellow lines represent realised biotic interactions networks in the 10 datasets investigated. Top row are plant-pollinator networks and bottom row are host-parasite networks. Black dashed lines indicate the more parsimonious functions among all tested (see Methods).

Extended Data Fig. 2 Relationship between the number of potential interactions and the number of realised interactions and model prediction for resource species.

Top row are plant-pollinator networks and bottom row are host-parasite interactions. Each black point represents a species in the empirical system and the green line and points indicate the predicted proportion of realised interactions by the proposed model based on the frequency of co-occurrences. Green lines represent the mean tendency and shaded areas represent 95% confidence intervals.

Extended Data Fig. 3 Relationship between number of potential interactions for resource species and the mean frequency of co-occurrence with their consumers.

Top row are plant-pollinator networks and bottom row are host-parasite interactions. Each black point represents a species in the empirical system. Blue lines represent a gam fit only for visualisation purposes and shaded areas represent 95% confidence intervals.

Extended Data Fig. 4 Relationship between the number of expected interactions based on the frequencies of species co-occurrences and the number of realised interactions for each species.

(a) Shows the relationship from the consumer’s perspective (that is indegree is the number of resources each consumer has) while (b) represents the resources perspective (that is outdegree corresponds to the number of consumers each resource has). Each point represents a species in the empirical system. Black line shows the 1:1 line indicating a perfect relationship between the predicted and the realised number of interactions.

Extended Data Fig. 5 Comparison of the degree distributions of resource species among co-occurrence networks, realised biotic interactions networks and our theoretical predictions accounting for the frequency of interactions.

Red lines represent co-occurrence networks, yellow lines represent realised biotic interactions networks and our theoretical predictions accounting for the frequency of interactions are represented in multicolor (each color represents a replicate) in the 10 datasets investigated. Top row are plant-pollinator networks and bottom row are host-parasite networks.

Extended Data Fig. 6 Comparison of the degree distributions among co-occurrence networks, realised biotic interactions networks and the null model predictions.

Red lines represent co-occurrence networks, yellow lines represent realised biotic interactions networks and the null model predictions are represented in multicolor (each color represents a replicate) for the 10 datasets investigated. The null model prunes the co-occurrence networks using a constant proportion of links to keep across species. Therefore, it results in a random pruning of the co-occurrence network. Top rows correspond to consumers and bottom rows correspond to resource species.

Extended Data Fig. 7 Relationship between the per-site interactions rate (p) and the proportion of realised links (f) across datasets.

Each color represents a different dataset.

Supplementary information

Supplementary Information

Supplementary Text 1. Dataset description. Table 1. Basic network properties of each dataset. Text 2. Mathematical transformations of degree distributions: how to get from an exponential to a power law. Table 2. Values of the per-site interaction rate (P) for each dataset. Table 3. Degree distribution fits for each dataset.

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Galiana, N., Arnoldi, JF., Mestre, F. et al. Power laws in species’ biotic interaction networks can be inferred from co-occurrence data. Nat Ecol Evol 8, 209–217 (2024). https://doi.org/10.1038/s41559-023-02254-y

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