Florian Hartig

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Inferring species interactions using Granger causality and convergent cross mapping

Frédéric Barraquand, Coralie Picoche, Matteo Detto & Florian Hartig

Theoretical Ecology, 14(1), 87–105 (2021)
Cite this
@article{barraquand2021inferring,
  author = {Frédéric Barraquand and Coralie Picoche and Matteo Detto and Florian Hartig},
  title = {Inferring species interactions using Granger causality and convergent cross mapping},
  journal = {Theoretical Ecology},
  volume = {14},
  number = {1},
  pages = {87--105},
  year = {2021},
  doi = {10.1007/s12080-020-00482-7},
}

DOI: 10.1007/s12080-020-00482-7
Citation statistics: 75 (Google Scholar) · 56 (OpenAlex), as of 29 October 2026

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Funding

This study was supported through funding by French ANR through LabEx COTE (ANR-10-LABX-45).

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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.

What the paper shows and why it matters

(AI-generated)

Ecologists often want to know which species affect one another’s populations from time series of abundances. This is a causal-inference problem, and the classical statistical answer is Granger causality: one series “causes” another if its past values improve the prediction of the other’s future. It is often tested with linear multivariate autoregressive (MAR) models, in which each species depends on the earlier abundances of all species. Sugihara et al. (2012) argued that Granger causality is best suited to linear systems dominated by random noise and not strongly nonlinear deterministic ones, which call for convergent cross mapping (CCM), a method that reconstructs the system’s dynamics from the series themselves. Their concern has a basis: in a deterministic system, a driver leaves a trace in the affected species’ own past values. Many later CCM studies adopted this view, which suggests choosing the method by how nonlinear a system is. The paper puts this assumption to the test.

The paper shows that linear Granger causality and convergent cross mapping infer species interactions from time series with similar performance, and that which method does better does not follow the degree of nonlinearity. This holds when the model is fitted to log abundances and the number of past time steps included (the lags) is chosen with information criteria. Both methods detect the two-way coupling in Veilleux’s predator–prey data. In a chaotic two-species model, both detect the strong interaction in all simulations and find roughly half of the weak one. In 20-species networks with weaker interactions, Granger causality tends to do better, because CCM yields more false positives. When two species share an environmental driver, both struggle: CCM gives many false positives and Granger causality misses a weak interaction.

The results imply that Granger causality, even in its linear form, is a valid way to infer interactions in nonlinear ecological communities, and that the choice between it, CCM or both can rest on the aims and data of the analysis rather than on assumed nonlinearity. What matters more, the paper argues, are details such as lag selection (for Granger causality) and the definition of p-values (for CCM), and which confounders, such as a shared environmental driver, are included in the model. Lidgard et al. (2021) cite the paper when applying Granger causality to fossil time series of bryozoan diversification.

References

  • Sugihara et al. (2012). Detecting Causality in Complex Ecosystems. Science 338, 496–500. doi:10.1126/science.1227079
  • Lidgard et al. (2021). When fossil clades ‘compete’: local dominance, global diversification dynamics and causation. Proceedings of the Royal Society B: Biological Sciences 288, 20211632. doi:10.1098/rspb.2021.1632