Resilience and the reliability of spectral entropy to assess ecosystem stability.

Abstract

Zurlini et al. (2014) formulated interesting thoughts on our recent publication dealing with the assessment of ecosystem stability using remote sensing time series (De Keersmaecker et al., 2014). Their main concerns can be summarized as follows: (i) the normalized spectral entropy (HSn; Zaccarelli et al., 2013) that was used to quantify resilience, should be interpreted as a metric for structural irregularity, rather than regularity and (ii) our focus was on local stability and the ability to return to a stable point or trajectory only (i.e., engineering resilience), whereas stability metrics are commonly used to assess the adaptive capacity to remain within the same stability domain (i.e., ecological resilience) (Pimm, 1984; Holling, 1996; Dakos et al., 2012). First, since we applied HSn to anomaly time series instead of to original Normalized DifferenceVegetation Index (NDVI) time series, the interpretation of the HSn metric also changes from structural irregularity to regularity. For example, when a large disturbance results in vegetation response persistent anomalies, the time series regularity would decrease (i.e., increase in HSn) but also the irregularity of the anomaly time series would decrease (i.e., decrease in HSn). Although we believe that both interpretations of HSn are valid, we based our analysis on the anomaly time series as it avoids the sensitivity of HSn to shape effects. Shape effects can have strong impact on the interpretation of HSn as a regularity metric as is illustrated in Fig. 1. Both time series shown are equally regular, but have different HSn values, which complicates the interpretation of regularity, whereas this is not the case for the anomaly time series with equal HSn values. Second, we agree that De Keersmaecker et al. (2014) focuses on local stability, whereas other stability measures can be important as well (Holling, 1996). However, these other stability measures are difficult to quantify based on metrics that assume stationarity and consequently do not account for multiple stable states [e.g., HSn is based on a Fourier transformation which assumes stationarity (Zaccarelli et al., 2013)]. For example, it is difficult to interpret HSn as an indicator of ecological resilience without knowing when the time series switches from one local stability regime to another. This is illustrated in Fig. 2, which shows two time series with similar HSn values but different stability regimes (i.e. time series A flips between two regimes, whereas time series B has only one regime). Therefore, we believe that detecting tipping points is imperative before assessing other stability measures. The interpretation of the stability metrics described in De Keersmaecker et al. (2014) is therefore only useful within a regime of local stability. Finally, we want to stress that the conclusion of De Keersmaecker et al. (2014) was exactly that understanding the reliability of stability metrics is essential when assessing ecosystem stability. This is especially true because time series properties (e.g., the presence of multiple stable states and the use of original vs. anomaly time series, as demonstrated here) can highly affect the interpretation of these metrics.