Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately
Ascertaining and characterizing causation in various ecological systems of interacting species. (a, b) Unidirectional causation of two coupled species. In (a), the values of the slope associated with the causal relation are approximately 0.0004, 0.1167, 0.1203, and 0.1238 for four different values of the coupling parameter . (b) Near zero slope values for , indicating its nonexistence. (c, d) Inferred causal network of five species whose interacting structure is, respectively, that of a ring: () and of a tree: (), where the estimated slope values are color-coded. Results of a statistical analysis of the accuracy and reliability of the determined causal interactions are presented in SI Section III. Time series of length are used in all these simulations. The embedding parameters are and with .