Abstract-The von Bertalanffygrowth function is the model most widely applied to describe growth in fish populations. Parameters describing this function usually are estimated from observed lengths at different ages by using maximum likelihood and by assuming Gaussian distributed errors. In harvested populations, observed length at age usually involves a high level of skewness and extreme values because of the size-selective sampling process. Some approaches, based on the maximum-likelihood method for making inferences, have been developed to resolve such issues. We propose a Bayesian framework for estimating growth parameters for nonlinear regression models-a framework that is based on the family of log-skew-t distributions and which provides an approach that is flexible enough for modeling the presence of asymmetries and heavy tails. This framework based on a method in which 1) the error accounts for both skewness and heavy-tailed distributions of a log-skew-t model, and 2) the observed length at each age has a heteroscedastic error distribution. The proposed method was applied and compared with the methods of previous models by using observed length-at-age data for the southern blue whiting (Micromesistius australis), an important fish species harvested in the southeast Pacific. Comparisons indicated that the proposed model is the best for describing data on southern blue whiting.
Abstract-Natural mortality (M) is one of the most important life history attributes of functioning fish populations. The most common methods to estimate M in fish populations provide point estimates which are usually constant across sizes and ages. In this article, we propose a framework for incorporating uncertainty into the length-based estimator of mortality that is based on von Bertalanffy growth function (VBGF) parameters determined with Bayesian analysis and asymmetric error distributions. Two methods to incorporate uncertainty in M estimates are evaluated. First, we use Markov chains of the estimated VBGF parameters directly when computing M and second, we simulate the posterior distribution of VBGF parameters with the copula method. These 2 approaches were applied and compared by using the extensive database available on age and growth for southern blue whiting (Micromesistius australis) harvested in the southeast Pacific. The copula approach provides advantages over Markov chains and requires far less computational time, while conserving the underlying dependence structure in the posterior distribution of the VBGF parameters. The incorporation of uncertainty into length-based estimates of mortality provides a promising way for modeling fish population dynamics.
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.
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