Towards Age Determination of Southern King Crab (Lithodes santolla) Off Southern Chile Using Flexible Mixture Modeling

Abstract

This study addresses the problem of age determination of the southern king crab (Lithodes santolla). Given that recapture is difficult for this species and, thus, age cannot be directly determined with the help of the annual marks on the shell, the von Bertalanffy growth function (vBGF) cannot be used to directly model length-frequency data (LFD). To determine age classes, some researchers have proposed using the MIX algorithm that consists of sampling realization of a finite mixture of normal (FMN) distributions for each LFD. However, normality assumption in age-length data has been questioned in several works related to fish growth analysis. For this study, we considered the biological information of the southern king crab for the period 2007–2015 and localization between 50 ∘ 06 ′ – 53 ∘ 15 ′ S and 76 ∘ 36 ′ – 72 ∘ 18 ′ W. We assumed that LFD could be modelled by the novel class of finite mixture of skew-t (FMST). Assigned age classes were used to estimate the vBGF parameters. The estimated vBGF parameters were L ∞ = 176.756 cm, K = 0.151 year − 1 , t 0 = − 1.678 year for males, and L ∞ = 134.799 cm, K = 0.220 year − 1 , t 0 = − 1.302 year for females. This study concludes that (a) FMST modal decomposition can detect a group of younger individuals at age 2, given that those individuals have LFD with a left heavy-tail and asymmetry; (b) FMST produces a better representation of LFD than the FMN model; (c) males have bigger L ∞ but grow slower than females; and (d) as expected, a high correlation exists among the vBGF estimates.

Sampling Procedure for Establishing Criteria for Sea Urchin (Loxechinus albus) Proportion under the Legal Minimum Length of landings

“…The sampling method based on individual weights did not necessarily assume a linear weight-age relationship, such as in the von Bertalanffy growth models used for fish catches based on the age-length relationship (see, e.g., [23,24]). This was because some old and young sea urchins with equal lengths could have similar weight.…”

Poincaré and Log–Sobolev Inequalities for Mixtures

“…Recently, the investigation of mixtures can be found in many different applications, and the main results of this work may be useful to the investigation of asymmetric Kalman filter estimates [ 10 ], the study of asymmetric mixtures in Marine Biology [ 11 ], Econometrics [ 12 ], Gradient-quadratic and fixed-point iteration algorithms [ 7 ] and estimates of multivariate Gaussian mixtures [ 13 ].…”

Robust Mixture Modeling Based on Two-Piece Scale Mixtures of Normal Family

“…In fact, by considering the estimated (posterior) probabilities, we can assign such observation points to given groups. However, some atypical data have an undesirable effect to suitable clustering (see e.g., [1,2,8]). In our models, we consider the skewness and use the clustering as a base on them to show the robustness on the clustering of atypical data in components.…”

“…In addition, a robust extension of the FM-SN model to robust finite mixture of skew-t (FM-ST) has been done in the influential works of [3,[5][6][7]. The FM-ST components, too, capture both skewness and extreme observations due to their flexibility [8].…”