Abstract

Time series of exploited marine populations tend to exhibit reddened spectra, where fluctuations in density or abundance are a combination of high frequency variability (short term variation) on top of a dominant low frequency oscillation (long-term variation). Several factors contribute to redden the spectra, but there is general agreement that the major causes are environmental fluctuations, demographic processes (e.g., density-dependence) and their interactions. Traditional analyses focus on the use of Box-Jenkins (BJ), univariate (ARIMA), and multivariate (e.g., Transfer Function Noise) models to quantify the effect of these factors on the dynamics of fisheries time series. BJ models are inappropriate to detect and model the effect of low frequency oscillations of the environment on fisheries time series. In the present work, long-term memory patterns (i.e., long-term correlations) were detected and quantified in: i) daily catch (DC) time series from the smooth pink shrimp (Pandalus jordani) fishery off the west coast of Vancouver Island, and ii) daily sea surface temperature (DSST) observations measured at Amphitrite Point lighthouse (approx. 48°55'N; 125°32'W), using fractal models. A time series with a fractal structure reveals the existence of long-term memory patterns (scaling dynamics). A single parameter (Hurst coefficient) was not able to quantify these scaling patterns in DC and DSST time series due to the existence of scaling relationships that vary through time (multi-scaling or multifractal dynamics). A multifractal model was used to quantify these multiple scaling patterns and to investigate the potential relationship between smooth pink shrimp catches and SST.