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

Abstract

Communicated by Andras DerBiological-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 skewgaussian 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.

Bounds on Rényi and Shannon Entropies for Finite Mixtures of Multivariate Skew-Normal Distributions: Application to Swordfish (Xiphias gladius Linnaeus)

“…To study the behavior of the Shannon entropy bounds of Proposition 2 and the Rényi entropy bounds of Equation (13) and Lemma 1, some examples are simulated for the cases d = 1, 2 and 3: 20,35),Ω = (9, 16, 9), and η = (5, 3, 6); [26]. Examples 5 and 6 are represented in 3D plots, according to [27].…”

“…Following [35] (and references therein), we briefly describe the length-weight function. This function explains the increments in weight of species in terms of their length by the non-linear relationship…”

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

“…Given that the calculus of negentropy presents a computational challenge, where the integral involves the pdf of Z [16,18], different approximations of negentropy are used, such as cumulants' expansion series [17,19]. Withers and Nadarajah [19] provided exact and explicit series expansions for the SE and negentropy of a standardized pdf f on R, in terms of cumulants.…”

“…Thus, this model satisfies all the standard regularity conditions of Salicrú et al [27], leading to consistence and asymptotic normality of the MLEs under the null hypothesis of normality. Therefore, the MSN model serves to test the null hypothesis of normality using (18). Hence, the symmetry null hypothesis H 0 : τ = 0 is rejected at level…”

“…In both cases, we compare the SE and negentropies obtained from their series expansions with their corresponding "exact" versions computed from the Quadpack numerical integration method of Piessens et al [31]. More precisely, the "exact" expected values E{ζ 0 (τZ τ )} and E{ζ 0 (τZ * τ )} are computed using the Quadpack method as in Arellano-Valle et al [16], Contreras-Reyes and Arellano-Valle [6] or Contreras-Reyes [18]. From the series expansions, the SE and negentropies were carried out for k = 12 as in Withers and Nadarajah [19].…”