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UBC Theses and Dissertations

Fractal analysis of fisheries and environmental time series for the development of early warning indicators Montes-Aste, Rodrigo Marco


Fractal theory has been used in aquatic sciences to quantify scale-invariant relationships under the form of scaling or power laws, which represent patterns that help to understand the complex structure of exploited marine ecosystems and their populations through time. Fisheries time series are inherently variable and complex because they represent the interaction between population dynamics, oceanographic forcing’s and anthropogenic pressure (exploitation rates). Thus, to better understand the temporal dynamics of fisheries time series under the framework of fractal theory, smooth pink shrimp (Pandalus jordani) daily catch time series, daily sea surface temperature and wind stress time series from the west coast off Vancouver Island were analyzed. The ultimate goal of this thesis was the early detection of changes and critical thresholds levels over which a fishery move to a depleted or unhealthy state. This is a highly desirable objective because it gives fishery managers time to intervene in order to avoid a fishery collapse. I identified fractal patterns in smooth pink shrimp daily catches, sea surface temperature and wind stress time series. Those patterns were quantified through the Hurst coefficient (H), which integrates time series’ long-range dependence and intermittency into a single index. Inter-annual changes in Hurst coefficients from sea surface temperature appear to be related with major oceanographic anomalous conditions such regime shifts and El Niño events. Long-range dependence and intermittency were estimated for catch time series using the fractionally differenced parameter d and the Lévy index α and then combined into a single index (1/LHE indicator). Our proposed indicator, calculated using rolling windows across the history of the fishery, tracks well the vulnerable biomass for all years, which means that it is possible to have an indicator of major changes in the biomass of Pandalus jordani at the beginning and during the progress of each fishing season.

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