Causal networks reveal the dominance of bottom-up interactions in large, deep lakes

Ecological dynamics often exhibit significant temporal variability and sudden shifts that characterize their non-equilibrium and nonlinear nature, challenging our ability to understand and predict their trajectories. Among a set of ecological time series originating from the long-term monitoring of three large and deep lakes, nonlinear forecasting methods (Simplex projection and S-map) indicated that most of the time series exhibited hallmarks of complex dynamics in the form of nonlinear behaviors. Convergent Cross Mapping (CCM) was used to estimate the causal relationships among these time series by considering different time lags. The significant causal relationships were then used to construct causal networks from which nodes were characterized using PageRank and CheiRank. For the three lakes, the dominance of bottom-up control was revealed and was mostly indirect (i.e., nutrient-forcing zooplankton). This result likely evidences the transitivity of the causal relationships obtained by CCM as well as the mixed phytoplankton diet of zooplankton species limiting the identification of causal relationships among these two ecological components. Complementarily, the consistence of causal relationships for the different time lags may highlight a temporal transitivity by which the instantaneous causal signal was transmitted over time. The dual representation of both PageRank and CheiRank provided a straightforward classification of each node and enabled their thorough implications in the information flow within the causal networks. The complementary use of CCM and network metrics constituted an efficient way to delineate ecological causation using a high-resolution time series, for which linear methods performed poorly, and provided insights into the dynamic hierarchy of the different ecological variables in aquatic ecosystems.