Early Detection of Ecosystem Regime Shifts Figure 2. Temporal indicators of critical slowing down. Temporal variance (estimated as standard deviations, SD) and the first-order autocorrelation coefficient (AR(1)) for Pseudocalanus acuspes (A, C) and Acartia spp. (B, D) estimated within sliding windows of 10 years. Vertical dashed lines mark the timing of the regime shift in the late 1980s and grey solid lines the upper and lower 95% confidence intervals. doi:10.1371/journal.pone.0038410.g002 the coefficient of variation (CV; 100*SD/mean) [17] correcting for the mean across all stations from the entire sampling area (Figure S1). Similar to temporal variance it has been shown that spatial variance or the coefficient of variation increases before a catastrophic shift [13,15]. In addition, spatial correlation may also change close to a shift [16]. Here, we estimated spatial correlation across sampling stations using the Moran’s I test [32]. In order to reduce bias from uneven sampling between years, we randomly selected 6, 8 and 10 stations per year and estimated the mean correlation coefficient and associated p-value for each year after 1000 random draws. Trend Analysis In a second set of methods we applied statistical methods for assessing recent trends in the zooplankton time series. Although not specifically designed for early detection of regime shifts, the idea of using trend analysis as an early-warning signal lies in the possibility of detecting a slight increase in the rate of change (either in an upward or downward trend) in advance of a critical transition in an ecological time series. The approach is based on fitting non-linear Generalized Additive Models (GAM) [33] and estimating second derivatives (f99) as a proxy for statistically significant acceleration in the rate of change (slope) of ecological time series [34,35]. While the first approach relies on an a priori specified degree of smoothing [34], the second method [35] applies a routine for selecting optimal numbers of regression splines (degree of smoothing; df). In order to reduce potential bias due to the selection of regression splines, we performed the trend analysis using two levels of degrees of freedom (df = 10 and 20). Shiftograms The third approach was not primarily designed for early detection either, but rather for the identification and detection of regime shift. It is based on the evaluation of statistical time series models including structural breaks and combines several statistical indicators into a so-called ‘‘shiftogram’’ [36]. The shiftogram approach is an iterative procedure combining econometric time series analysis and quantile methods displaying the gradual or rapid transition towards a local minimum (i.e., structural break- point) by making use of time series features and quality-of-fit criteria, such as the corrected Akaike’s information criterion (AICC) and a joint significance test (p-joint) of all parameters related to a particular type of structural break. These quality-of-fit criteria may be regarded as indicators of an imminent shift, illustrated by a potential decrease in AICC and p-joint statistics prior to a shift. Moreover, we used the AICC and p-joint test into an ‘‘alertogram’’ that primarily uses the negative slope of the AICC or p-joint values prior to a potential structural break by PLoS ONE | www.plosone.org 3 July 2012 | Volume 7 | Issue 7 | e38410