Analyzing Fish Condition Factor Index Through Skew-Gaussian Information Theory Quantifiers

Biological-fishery indicators have been widely studied. As such the condition factor (CF) index, which interprets the fatness level of a certain species based on length and weight, has been investigated, too. However, CF has been studied without considering its temporal features and distribution. In this paper, we analyze the CF time series via skew-gaussian distributions that consider the asymmetry produced by extreme events. This index is characterized by a threshold autoregressive model and corresponds to a stationary process depending on the shape parameter of the skew-gaussian distribution. Then we use the Jensen-Shannon (JS) distance to compare CF by length classes. This distance has mathematical advantages over other divergences such as Kullback-Leibler and Jeffrey's, and the triangular inequality property. Our results are applied to a biological catalogue of anchovy (Engraulis ringens) from the northern coast of Chile, for the period 1990-2010 that consider monthly CF time series by length classes and sex. We find that for high values of shape parameter, JS distance tends to be more sensible to detect discrepancies than Jeffrey's divergence. In addition, the body condition of male anchovies with higher lengths coincides with the ending of the moderate-strong El Niño event 91-92 and for both males and females, the smaller lengths coincide with the beginning of the strong El Niño event 97-98.