Quantifying ecosystem states and state transitions of the Upper Mississippi River System using topological data analysis.

Aquatic systems worldwide can exist in multiple ecosystem states (i.e., a recurring collection of biological and chemical attributes), and effectively characterizing multidimensionality will aid protection of desirable states and guide rehabilitation. The Upper Mississippi River System is composed of a large floodplain river system spanning 2200 km and multiple federal, state, tribal and local governmental units. Multiple ecosystem states may occur within the system, and characterization of the variables that define these ecosystem states could guide river rehabilitation. We coupled a long-term (30-year) highly dimensional water quality monitoring dataset with multiple topological data analysis (TDA) techniques to classify ecosystem states, identify state variables, and detect state transitions over 30 years in the river to guide conservation. Across the entire system, TDA identified five ecosystem states. State 1 was characterized by exceptionally clear, clean, and cold-water conditions typical of winter (i.e., a clear-water state); State 2 had the greatest range of environmental conditions and contained most the data (i.e., a status-quo state); and States 3, 4, and 5 had extremely high concentrations of suspended solids (i.e., turbid states, with State 5 as the most turbid). The TDA mapped clear patterns of the ecosystem states across several riverine navigation reaches and seasons that furthered ecological understanding. State variables were identified as suspended solids, chlorophyll a, and total phosphorus, which are also state variables of shallow lakes worldwide. The TDA change detection function showed short-term state transitions based on seasonality and episodic events, and provided evidence of gradual, long-term changes due to water quality improvements over three decades. These results can inform decision making and guide actions for regulatory and restoration agencies by assessing the status and trends of this important river and provide quantitative targets for state variables. The TDA change detection function may serve as a new tool for predicting the vulnerability to undesirable state transitions in this system and other ecosystems with sufficient data. Coupling ecosystem state concepts and TDA tools can be transferred to any ecosystem with large data to help classify states and understand their vulnerability to state transitions.