Quantifying and exploring state-dependent ecological interactions from time series data using Gaussian process regression.

Ecological interactions in natural communities are often highly nonlinear; that is, interaction strengths can fluctuate temporally depending on community states. An effective and reliable tool to infer state-dependent interactions from empirical data is crucial to ecological studies. Here, we propose a novel non-parametric inference method based on Gaussian process regression to quantify interaction strengths from nonlinear time series data. We introduce the method by extending the Gaussian process empirical dynamic modelling (GP-EDM) approach in ecology. To confirm its applicability, we investigated the performance of the proposed method, using both synthetic and real-time series data. The results highlight that the proposed method possesses several distinct features. First, throughout performance comparison with existing methods (S-map and regularized S-map), the proposed method achieves higher inference accuracy for noisy time series data. Second, the proposed method analytically accounts for the dependence of interaction strengths on community states. This enables us to locally evaluate state-dependent changes in interaction strengths by exploring hypothetical community states. Moreover, because the posterior function is derived analytically, the proposed method can easily evaluate the inference uncertainty (e.g. credible interval), resulting in more reliable inference outcomes. The proposed method provides a basis for addressing state dependence in analyses of species interactions.