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.

根据种群密度的时间序列确定物种之间的定向相互作用在生态学中有许多用途。这主要统计任务等同于因果时间序列推断，它连接到格兰杰因果关系（GC）的概念：X导致Ÿ如果X改善的预测ÿ在动态模型中。但是，非线性生态系统的纠缠性质引发了对格兰杰因果关系是否适当的质疑，特别是在其经典的线性多元自回归（MAR）模型形式中。收敛交叉映射（CCM）是为确定性动力学系统开发的一种非参数方法，已被建议作为替代方案。在这里，我们证明了线性GC和CCM能够发现具有惊人相似性能的相互作用，包括捕食者－捕食者循环，​​2种确定性（混沌）或随机竞争以及10和20种相互作用网络。我们发现动力学非线性程度与哪种方法效果最好之间没有对应关系。因此，我们的结果表明，即使在线性MAR（p）公式，是推断非线性生态网络中相互作用的有效方法；可以根据分析的目的和具体情况决定使用GC还是CCM（或同时使用两者）。