Measuring trends and signals of sustainability in oyster population and production data

Resilience research often includes time series analysis in search of trend shifts. Recently statistical signals including changes in variance and autocorrelation, were proven to be universal indicators of stability. In this paper the suitability of those early warning signals was tested on two case studies: oysters production of France (case study 1) and catch rates of the native oyster in the Solent, UK (case study 2). First, trend analyses were performed and their association to the evolution of the North Atlantic Oscillation (NAO) index was assessed. For the French oyster production, two sinusoidal waves were found in the first and second order residuals with periods of 33 and 8 years. In the Solent, the trend depiction showed after an initial increase, the catch rates of oysters declined over time from West to East. A positive relationship was apparent between NAO and both the production and population data, with a significant correlation in case study 2. Furthermore, a high and significant spectral coherency in the 8 year period of case study 1 revealed a near phase opposition between the influence of NAO and the French oyster production. For the first and second case study, the early warning signals calculated were lag-1 autocorrelation and variance, respectively. In case study 1, the stability of the low frequency wave of the first order residuals could not be assed, the trend of lag 1 autocorrelation was thus not conclusive. However the high but stable lag-1 autocorrelation of the second residuals, revealed a probable underlying stability. In case study 2 significant increase in variance reflected the instability prior to the decline. It is discussed that in periodic signals the number of residual fluctuations needs to be sufficient to allow the generation of an autocorrelation trend within the limits of the sliding window, used for its calculation. The importance of time scale and appropriate de-trending is also questioned when calculating and interpreting early warning signals as indicators of underlying (in)stability. Finally besides their scientific use, also the utility of early warning signals in managerial settings are discussed.