Usefulness and limitations of convergent cross sorting and continuity scaling methods for their application in simulated and real-world time series.

Causality detection methods are valuable tools for detecting causal links in complex systems. The efficiency of continuity scaling (CS) and the convergent cross sorting (CSS) methods to detect causality was analysed. Usefulness and limitations of both methods in their application to simulated and real-world time series was explored under different scenarios. We find that CS is more robust and efficient than the CSS method for all simulated systems, even when increasing noise levels were considered. Both methods were not able to infer causality when time series with a marked difference in their main frequencies were analysed. Minimum time-series length required for the detection of a causal link depends on intrinsic system dynamics and on the method selected to detect it. Using simulated time series, only the CS method was capable to detect bidirectional causality. Causality detection, using the CS method, should at least include: (i) causality strength convergence analysis, (ii) statistical tests of significance, (iii) time-series standardization, and (iv) causality strength ratios as a strength indicator of relative causality between systems. Causality cannot be detected by either method in simulated time series that exhibit generalized synchronization.

Quantifying harmful algal bloom thresholds for farmed salmon in southern Chile.

Harmful algal blooms (HABs) have affected salmon farms in Chile since the early 1970's, causing massive losses in fish. Two large HABs occurred in 2002 and 2009, during which Alexandrium catenella blooms killed tons of salmon over an extended geographic area in southern Chile. At the beginning of 2016, high and persistent densities of Pseudochattonella cf. verruculosa and A. catenella were detected in the estuarine and marine ecosystems of southern Chile. Mortality for this latter event reached 27 million salmon and trout (i.e. 39,000 tons). Unfortunately, the threshold concentrations of algae that could be harmful to the health of farmed salmon in southern Chile have not yet been quantified. Here, to protect fish farms from HABs, critical concentration levels, i.e. thresholds at which the behavior of farmed Salmo salar is affected by harmful algae were quantified using generalized linear mixed models (GLMM). An extensive database from southern Chile covering the period from 1989 to 2016 was analyzed. The database included salmon behavior, cell abundance of microalgae and oceanographic factors. For both species analyzed, the higher the cell abundance, the greater the probability of detecting anomalous behavior. A threshold of 397 cells/mL was estimated for A. catenella, although it can increase up to ca. >975 cells/mL at a Secchi depth >6 m and up to 874 cells/mL during flood tide. A threshold value <1 cell/mL for Pseudochattonella cf. verruculosa was found to be associated with anomalous salmon behavior, which significantly increased at a water temperature of 11 °C. Evidence for a relationship between fish behavior and mortality is provided.