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Inferring species interactions using Granger causality and convergent cross mapping

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Abstract

Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC) concept: x causes y if x improves the prediction of y in a dynamic model. However, the entangled nature of nonlinear ecological systems has led to question the appropriateness of Granger causality, especially in its classical linear multivariate autoregressive (MAR) model form. Convergent cross mapping (CCM), a nonparametric method developed for deterministic dynamical systems, has been suggested as an alternative. Here, we show that linear GC and CCM are able to uncover interactions with surprisingly similar performance, for predator-prey cycles, 2-species deterministic (chaotic), or stochastic competition, as well as 10- and 20-species interaction networks. We found no correspondence between the degree of nonlinearity of the dynamics and which method performs best. Our results therefore imply that Granger causality, even in its linear MAR(p) formulation, is a valid method for inferring interactions in nonlinear ecological networks; using GC or CCM (or both) can instead be decided based on the aims and specifics of the analysis.

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Acknowledgments

FB thank Julien Chiquet and Camille Charbonnier for advice on the structured LASSO and Grégoire Certain for discussions on MAR modelling. FB and CP were supported by the French ANR through LabEx COTE (ANR-10-LABX-45). We thank Ethan Deyle, Adam Clark and Hao Ye for feedback, notably regarding surrogate time series testing for CCM. Constructive referee suggestions improved the manuscript, notably the figures.

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Authors and Affiliations

  1. Institute of Mathematics of Bordeaux, CNRS & University of Bordeaux, Talence, France

    Frédéric Barraquand & Coralie Picoche

  2. Integrative and Theoretical Ecology, LabEx COTE, University of Bordeaux, Pessac, France

    Frédéric Barraquand & Coralie Picoche

  3. Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA

    Matteo Detto

  4. Theoretical Ecology, University of Regensburg, Regensburg, Germany

    Florian Hartig

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  1. Frédéric Barraquand
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Correspondence to Frédéric Barraquand.

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Author contributions

All authors contributed to the project design. FB and CP constructed the case studies, wrote the computer code, and analyzed the real and simulated data. All authors contributed to the interpretation of the results. FB wrote a first draft of the manuscript, which was then edited by all authors.

Data availability

Codes for the analyses presented in this paper are available at https://github.com/fbarraquand/GCausality and are published at Zenodo with DOI https://doi.org/10.5281/zenodo.3967591 (Barraquand and Picoche, 2020).

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Barraquand, F., Picoche, C., Detto, M. et al. Inferring species interactions using Granger causality and convergent cross mapping. Theor Ecol 14, 87–105 (2021). https://doi.org/10.1007/s12080-020-00482-7

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