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  1. Extreme daily values of precipitation (1939–2021), discharge (1991–2021), phosphorus (P) load (1994–2021), and phycocyanin, a pigment of Cyanobacteria (June 1–September 15 of 2008–2021) are clustered as multi-day events for Lake Mendota, Wisconsin. Long-range dependence, or memory, is the shortest for precipitation and the longest for phycocyanin. Extremes are clustered for all variates and those of P load and phycocyanin are most strongly clustered. Extremes of P load are predictable from extremes of precipitation, and precipitation and P load are correlated with later concentrations of phycocyanin. However, time delays from 1 to 60 d were found between P load extremes and the next extreme phycocyanin event within the same year of observation. Although most of the lake’s P enters in extreme events, blooms of Cyanobacteria may be sustained by recycling and food web processes. 
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  2. Abstract Transformation toward a sustainable future requires an earth stewardship approach to shift society from its current goal of increasing material wealth to a vision of sustaining built, natural, human, and social capital—equitably distributed across society, within and among nations. Widespread concern about earth’s current trajectory and support for actions that would foster more sustainable pathways suggests potential social tipping points in public demand for an earth stewardship vision. Here, we draw on empirical studies and theory to show that movement toward a stewardship vision can be facilitated by changes in either policy incentives or social norms. Our novel contribution is to point out that both norms and incentives must change and can do so interactively. This can be facilitated through leverage points and complementarities across policy areas, based on values, system design, and agency. Potential catalysts include novel democratic institutions and engagement of non-governmental actors, such as businesses, civic leaders, and social movements as agents for redistribution of power. Because no single intervention will transform the world, a key challenge is to align actions to be synergistic, persistent, and scalable. 
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  4. Abstract The COVID-19 pandemic has exposed an interconnected and tightly coupled globalized world in rapid change. This article sets the scientific stage for understanding and responding to such change for global sustainability and resilient societies. We provide a systemic overview of the current situation where people and nature are dynamically intertwined and embedded in the biosphere, placing shocks and extreme events as part of this dynamic; humanity has become the major force in shaping the future of the Earth system as a whole; and the scale and pace of the human dimension have caused climate change, rapid loss of biodiversity, growing inequalities, and loss of resilience to deal with uncertainty and surprise. Taken together, human actions are challenging the biosphere foundation for a prosperous development of civilizations. The Anthropocene reality—of rising system-wide turbulence—calls for transformative change towards sustainable futures. Emerging technologies, social innovations, broader shifts in cultural repertoires, as well as a diverse portfolio of active stewardship of human actions in support of a resilient biosphere are highlighted as essential parts of such transformations. 
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  5. 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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  6. Ecological resilience is the magnitude of the largest perturbation from which a system can still recover to its original state. However, a transition into another state may often be invoked by a series of minor synergistic perturbations rather than a single big one. We show how resilience can be estimated in terms of average life expectancy, accounting for this natural regime of variability. We use time series to fit a model that captures the stochastic as well as the deterministic components. The model is then used to estimate the mean exit time from the basin of attraction. This approach offers a fresh angle to anticipating the chance of a critical transition at a time when high-resolution time series are becoming increasingly available.

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