Causal feedback loops modify lake chlorophyll a–nutrient relationships over two decades of nutrient reductions and climate warming

Abstract Understanding how the causal feedback between phytoplankton and environmental drivers controlling the chlorophyll a (Chl a , as a proxy of phytoplankton biomass)–nutrient relationships are modulated under different ecosystem conditions is a major challenge in aquatic ecology. Using an empirical dynamic model (convergent cross mapping) on a 20‐yr dataset on 20 Danish lakes, we quantified hypothesized causal feedback networks for each lake and related them to lake system properties (e.g., mean water depth, nutrient concentrations and extent of reduction, climate warming) vs. the Chl a –nutrient relationship (estimated from generalized least square models). The results showed prevalent causal feedback across the studied lakes, which demonstrated clear patterns for the tested ecosystem variations. Weaker causal feedbacks were found in deeper lakes and lakes with larger warming trends, while stronger causal feedbacks appeared in lakes experiencing greater reductions of TP (total phosphorus) and TN (total nitrogen). Moreover, these causal feedbacks showed a strong and positive coupled pattern. Most of the causal feedbacks worked as enhancement loops, which promote the sensitivity of phytoplankton to TP, not least in shallow lakes with a high TP reduction, and as regulatory loops, which force a shift in the Chl a –TN relationship from a more negative slope in lakes experiencing a high nutrient reduction and weak warming to a positive slope in lakes with low nutrient reduction and stronger warming. Our findings suggest a mechanistic explanation of how internal feedbacks regulate the Chl a –nutrient relationships across a broad gradient of nutrient reductions, climate warming, and lake morphologies.