Since pioneering work on multiple stable states and hysteresis, changes in lake clarity have often been modelled as a function of changing nutrient loads that cause a system to suddenly shift from a turbid state dominated by phytoplankton to a stable clear state with abundant macrophytes. Under some conditions, a larger change in nutrients is required to move from the turbid to the clear state than vice versa (hysteresis). As a result, large reductions in phosphorus loading would not result in any system change until a tipping point is reached, beyond which the turbid state is unstable. However, theory also suggests that systems with parameter values near those required for a change in stability may linger in the vicinity of a formerly stable state (a "ghost attractor") for very long periods. That is, we might expect very similar behaviour if the turbid state was no longer stable, but there was a long transient. Finally, a large perturbation could move a system between a turbid and clear state in both cases. We use over 40 years of data to examine these alternative hypotheses regarding the temporal patterns in phosphorus, water clarity and macrophyte density in the Bay of Quinte, Ontario
Results/Conclusions
The Bay of Quinte experienced severe eutrophication in the late 1960s and 70s. Following modification to point source inputs in the late 70s, phosphorus loading decreased dramatically to the 1990s, but there was only small recovery of macrophytes and water clarity at this time. There was a marked increase in water clarity post -1994, with the large perturbation of an invasion of zebra mussels. However, since 2003 there has been a decrease in water clarity. We model this system starting with a simple lake model stated as a stochastic differential equation and parameterized using both recent and sediment core measurements. We evaluate the four hypotheses for the system dynamics by generating probability distributions of possible behaviour (e.g., length of transient, parameter location of regime shift, effect of large perturbation under either situation). Using total phosphorus, water clarity, chlorophyll density and macrophyte coverage, we find substantial differences between variables when they are interrogated for changes in system dynamics. Whereas water clarity as measured by Secchi depth indicates a clear regime shift, dynamic behaviour indicated by water clarity as measured by a light extinction coefficient, total phosphorus and macrophyte cover are less definitive.