Multifractal patterns in the daily catch time series of smooth pink shrimp (Pandalus jordani) from the west coast of Vancouver Island, Canada

Abstract

There is an urgent need for indicators that anticipate changes in populations of exploited marine species. We modelled the complex patterns of variability found in fisheries time series that are not detected using classical models. We applied fractal analyses to detect time-invariant scaling symmetries in daily catch time series from the smooth pink shrimp ( Pandalus jordani ) fishery from the west coast of Vancouver Island, British Columbia, Canada. A universal multifractal model, which accounts for intermittent fluctuations and extreme values in a time series, provided a better fit to daily catches than a monofractal model. Multifractality is an indication of multiple scaling patterns and suggests that more than one process is affecting the variability of catches. Fractal dynamics in catch time series were found for a range of scales between 16 and 120 fishing days. To our knowledge, this is the first time that multifractality has been demonstrated for an invertebrate fishery. The multifractal model has the potential to provide an in-season estimate (up to 120 fishing days) of the variability of shrimp catches based on the variability at time scales less than 1 month. Changes in these fractal patterns may provide an early warning that conditions underlying this fishery are changing.