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Abstract Resilience, measured by the distribution of passage times between alternate states, indicates persistence of a state in stochastic dynamic systems such as blooms of cyanobacteria in lakes. We used high‐frequency datasets to compare the resilience of low and high states of phycocyanin, a pigment indicator of cyanobacteria, in Lake Mendota, Wisconsin, USA, for three growing seasons that ranged sevenfold in external phosphorus (P) load. Each year we observed 139–265 passage times across the unstable threshold that separated the low‐ from high‐phycocyanin states. Each sample of passage times is highly skewed with low median, larger mean, much larger SD, and wide tails extending to long lifetimes of a state. About 25% of events, whether low or high phycocyanin, lasted a day or more. Among these 3 years of contrasting external P load, there were no discernible differences in the resilience of either ecosystem state. We attribute this lack of contrast to the sustained recycling of P from sediments and the high stochasticity of phycocyanin in this lake.
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Resilience of phytoplankton dynamics to trophic cascades and nutrient enrichment
Abstract Resilience was compared for alternate states of phytoplankton pigment concentration in two multiyear whole‐lake experiments designed to shift the manipulated ecosystem between alternate states. Mean exit time, the average time between threshold crossings, was calculated from automated measurements every 5 min during summer stratification. Alternate states were clearly identified, and equilibria showed narrow variation in bootstrap analysis of uncertainty. Mean exit times ranged from 13 to 290 h. In the reference ecosystem, Paul Lake, mean exit time of the low‐pigment state was about 100 h longer than mean exit time of the high‐pigment state. In the manipulated ecosystem, Peter Lake, mean exit time of the high‐pigment state exceeded that of the low‐pigment state by 30 h in the cascade experiment. In the enrichment experiment mean exit time of the low‐pigment state was longer than that of the high‐pigment state by about 100 h. Mean exit time is a useful measure of resilience for stochastic ecosystems where high‐frequency measurements are made by consistent methods over the full range of ecosystem states.
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- PAR ID:
- 10446957
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Limnology and Oceanography
- Volume:
- 67
- Issue:
- S1
- ISSN:
- 0024-3590
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Concentrations of phycocyanin, a pigment of Cyanobacteria, were measured at 1‐min intervals during the ice‐free seasons of 2008–2018 by automated sensors suspended from a buoy at a central station in Lake Mendota, Wisconsin, U.S.A. In each year, stochastic‐dynamic models fitted to time series of log‐transformed phycocyanin concentration revealed two alternative stable states and random factors that were much larger than the difference between the alternate stable states. Transitions between low and high states were abrupt and apparently driven by stochasticity. Variation in annual magnitudes of the alternate states and the stochastic factors were not correlated with annual phosphorus input to the lake. At daily time scales, however, phycocyanin concentration was correlated with phosphorus input, precipitation, and wind velocity for time lags of 1–15 d. Multiple years of high‐frequency data were needed to discern these patterns in the noise‐dominated dynamics of Cyanobacteria.more » « less
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