Variance as a Leading Indicator of Regime Shift in Ecosystem Services

Many environmental conflicts involve pollutants such as greenhouse gas emissions that are dispersed through space and cause losses of ecosystem services. As pollutant emissions rise in one place, a spatial cascade of declining ecosystem services can spread across a larger landscape because of the dispersion of the pollutant. This paper considers the problem of anticipating such spatial regime shifts by monitoring time series of the pollutant or associated ecosystem services. Using such data, it is possible to construct indicators that rise sharply in advance of regime shifts. Specifically, the maximum eigenvalue of the variance-covariance matrix of the multivariate time series of pollutants and ecosystem services rises prior to the regime shift. No specific knowledge of the mechanisms underlying the regime shift is needed to construct the indicator. Such leading indicators of regime shifts could provide useful signals to management agencies or to investors in ecosystem service markets.