Inferring species interactions using Granger causality and convergent cross mapping
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ORIGINAL PAPER
Inferring species interactions using Granger causality and convergent cross mapping ´ eric ´ Barraquand1,2 Fred
· Coralie Picoche1,2
· Matteo Detto3
· Florian Hartig4
Received: 13 March 2020 / Accepted: 4 September 2020 © Springer Nature B.V. 2020
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. Keywords Time series · Interaction network · Causal inference · Feedback · Food web · Community dynamics
Introduction Inferring links between different species’ population dynamics is a statistical endeavor with profound implications for understanding coexistence mechanisms (Adler et al. 2010, 2018), food web structure and functioning (Berlow et al. 2004; Wootton and Emmerson 2005), as
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s12080-020-00482-7) contains supplementary material, which is available to authorized users. Fr´ed´eric Barraquand
[email protected] 1
Institute of Mathematics of Bordeaux, CNRS & University of Bordeaux, Talence, France
2
Integrative and Theoretical Ecology, LabEx COTE, University of Bordeaux, Pessac, France
3
Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA
4
Theoretical Ecology, University of Regensburg, Regensburg, Germany
well as management and conservation at the ecosystem level (Link 2002; Pikitch et al. 2004). However, statistically detecting such dependencies using correlative approaches can be extremely challenging (Coenen and Weitz 2018; Carr et al. 2019). Outside of the usual limitations induced by sample sizes, spatial or temporal co-occurrence (Cazelles et al. 2016) or co-abundance patterns (Stone and Roberts 1991; Loreau and de Mazancourt 2008) do not directly indicate interactions between species (Dormann et al. 2018; Blanch
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