Inferring species interactions using Granger causality and convergent cross mapping

TL;DR

This study compares Granger causality and convergent cross mapping for inferring species interactions from ecological time series, finding both methods perform similarly across various nonlinear and stochastic systems, supporting GC's validity.

Contribution

The paper demonstrates that linear Granger causality is as effective as convergent cross mapping in detecting ecological interactions, challenging assumptions about nonlinearity requirements.

Findings

GC and CCM perform similarly across tested systems

No link between nonlinearity degree and method performance

GC is validated for nonlinear ecological networks

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. There is 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.