Structural instability, multiple stable states, and hysteresis in periphyton driven by phosphorus enrichment in the Everglades

Periphyton is a key component of the Everglades ecosystems. It is a major primary producer, providing food and habitat for a variety of organisms, contributing material to the surface soil, and regulating water chemistry. Periphyton is sensitive to the phosphorus (P) supply and P enrichment has caused dramatic changes in the native Everglades periphyton assemblages. Periphyton also affects P availability by removing P from the water column and depositing a refractory portion into sediment. A quantitative understanding of the response of periphyton assemblages to P supply and its effects on P cycling could provide critical supports to decision making in the conservation and restoration of the Everglades. We constructed a model to examine the interaction between periphyton and P dynamics. The model contains two differential equations: P uptake and periphyton growth are assumed to follow the Monod equation and are limited by a modified logistic equation. Equilibrium and stability analyses suggest that P loading is the driving force and determines the system behavior. The position and number of steady states and the stability also depend upon the rate of sloughing, through which periphyton deposits refractory P into sediment. Multiple equilibria may exist, with two stable equilibria separated by an unstable equilibrium. Due to nonlinear interplay of periphyton and P in this model, catastrophe and hysteresis are likely to occur.