Asymmetric response of early warning indicators of phytoplankton transition to and from cycles
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Phytoplankton populations often exhibit cycles associated with nuisance blooms of cyanobacteria and other algae that cause toxicity, odor problems, oxygen depletion, and fish kills. Models of phytoplankton blooms used for management and basic research often contain critical transitions from stable points to cycles, or vice-versa. It would be useful to know whether aquatic systems, especially water supplies, are close to a critical threshold for cycling blooms. Recent studies of resilience indicators have focused on alternate stable points, although theory suggests that indicators such as variance and autocorrelation should also rise prior to a transition from stable point to stable cycle. We investigated changes in variance and autocorrelation associated with transitions involving cycles using two models. Variance rose prior to the transition from a small-radius cycle (or point) to a larger radius cycle in all cases. In many but not all cases, autocorrelation increased prior to the transition. However, the transition from large-radius to small-radius cycles was not associated with discernible increases in variance or autocorrelation. Thus, indicators of changing resilience can be measured prior to the transition from stable to cyclic plankton dynamics. Such indicators are potentially useful in management. However, these same indicators do not provide useful signals of the reverse transition, which is often a goal of aquatic ecosystem restoration. Thus, the availability of resilience indicators for phytoplankton cycles is asymmetric: the indicators are seen for the transition to bloom–bust cycles but not for the reverse transition to a phytoplankton stable point.
KeywordsPhytoplankton Threshold Early warning Algae bloom Hopf bifurcation
We thank the referees for their helpful comments on the manuscript. We acknowledge support of an NSF grant to JCC, SRC, and MLP, the Hilldale Fund of the University of Wisconsin-Madison, and a NSF Graduate Research Fellowship to DAS.
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