Early Detection of Ecosystem Regime Shifts Table 1. Assessment of early-detection methods in terms of (i) the potential for detecting early-warnings signals in the selected time series, (ii) how far in advance early-warning signals could potentially be detected (i.e., in number of years before the regime shift), (iii) major associated methodological assumptions and drawbacks influencing early-warning detection and (iv) applicability to real ecosystem monitoring and management in terms of data needs. 1. Indicators of critical slowing down Method A. Temporal variance B. Temporal AR(1) C. Spatial variance D. Spatial r (Moran’s I) 2. Trend analysis A. Temporal GAM (I) B. Temporal GAM (II) 3. Shiftograms A. Shiftogram (AICC) B. Shiftogram (p-joint) C. Alertogram i Medium Low Low Medium Low Low High High Medium ii 1–2 0–1 0–1 1 (1) (1) 2–4 2–4 1 iii Size of window, Length of time series Size of window, Length of time series Uneven sampling (No./distribution) Uneven sampling (No./distribution) Degrees of smoothers, ‘‘retrospective’’ (f ’’) ‘‘retrospective’’ analysis, f ’’ calculation (t+1) iv Long-term data, slow variables Long-term data, slow variables Spatial data, consistent design Spatial data, consistent design Recent trend, pressures/drivers Recent trend, pressures/drivers Gradual/rapid decrease, global vs local minima Time series, contrasts/variability Broad local minima, timing of shift Slope, power, significance of shifts in AICC Time series, contrasts/variability Time series, contrasts/variability doi:10.1371/journal.pone.0038410.t001 (Figure 4). When refitted to the time-period preceding the regime shift (1960–1987), significant change points were detected between 1986 and 1987 (Figure S4), while when excluding year 1987 no change was detected before the regime shift. In the complimentary trend analysis [35], applying a routine for selecting the optimal numbers of regression splines, a significant increase in the rate of decline was indicated between 1985 and 1987 (Table S1), as illustrated by a negative f9 (slope) and a positive f99 (acceleration). As in the previous example, no significant trend or change point was detected when excluding also 1987. The trend analysis seems to be highly dependent on the length of time series and the numbers of regression splines used during fitting of the generalized additive models (GAMs; Figure 4). These assumptions influence the degree to which potential signals may resemble true early-warning signals, hence limiting the robustness of advice originating from such analysis. As an example of potential methodological bias, the choice of the numbers of regression splines results in differences in the number of change points detected, as well as in the timing of these changes (Figure 4). Even when statistically optimizing the number of splines [35], the length of the time series may influence the number and timing of significant change points being detected. However, it should be noted that trend analysis approaches were not primarily designed for early detection of regime shifts, but as an highly effective tool for detecting recent trends and change points in ecological time series [34,35]. Shiftograms The shiftogram generally resulted in an early detection of regime changes well in advance of the regime shift. For Pseudocalanus acuspes both the Akaike’s information criterion (AICC) and the p-joint significance test showed a gradual transition towards a local minimum (i.e., structural break point) 3–4 years before the regime shift (Figure 5A), while for Acartia spp. an abrupt transition occurred only 2 years in advance (Figure 5B). This was the case regardless of fitting to the entire time series or to the time- period preceding the regime shift. In both cases, the p-joint statistics decreased before the AICC and remained on low values over a longer time-period. In addition, performing tests on false positive and negative warnings using a slope F test based on the AICC (alertogram), shows that two years before the local minimum in 1987 was reached, the negative decrease towards a break becomes highly significant (p,,0.05) in terms of the estimated slopes (Figure 5C). Thus, the year 1985 sharply marks the beginning of a gradual shift in Pseudocalanus acuspes with a clear alert signal. In addition, both type I and II errors exceed their upper significance limits before 1985 and after 1987, indicating that false positive and negative warnings occur outside the 1985– 1987 period (Figure 5E). In contrast, the Acartia spp. time series displayed a significant alert signal first in 1990 (Figure 5D), despite a pronounced decrease in AICC and p-joint prior to the regime shift (Figure 5B). The shiftogram approach appeared to be promising in detecting structural breakpoints well in advance before the regime shift. However, the way these metrics approach a local minimum are influenced by the type of transition at hand in the time series. Sudden (pulse) transitions or more gradual changes strongly influence the shape (e.g., steepness and size) of the local minimum and hence the degree to which these transitions can be detected sufficiently in advance; a difference illustrated by the abrupt decrease in Acartia spp. (Figure 5B) and the more gradual decline in Pseudocalanus acuspes (Figure 5A). In addition, a local minimum of considerable width and little steepness may saturate the value and hence the reliability of the derived early-warning signal. However, the use of alertograms may compliment the shiftogram approach by adding valuable information for decision support, such as the strength of the negative slope of the AICC, as well as the significance (false positive signals) and the power (false negative signals) of this slope. Because the alertogram displays the false warning probabilities along with the false no-warning probabilities it aids in evaluating the urgency of potential management actions. Conclusions The versatility of methods for early detection of regime shifts in ecological time series provide an important toolbox for scientists and ecosystem managers. As learned from our example, no ‘one- size-fits all’ solution to deriving and interpreting spatio-temporal patterns announcing critical transitions exists [3]. Given by the PLoS ONE | www.plosone.org 7 July 2012 | Volume 7 | Issue 7 | e38410