Mixture of time-dependent growth models with an application to blue swimmer crab length-frequency data

Understanding how aquatic species grow is fundamental in fisheries because stock assessment often relies on growth dependent statistical models. Length-frequency-based methods become important when more applicable data for growth model estimation are either not available or very expensive. In this article, we develop a new framework for growth estimation from length-frequency data using a generalized von Bertalanffy growth model (VBGM) framework that allows for time-dependent covariates to be incorporated. A finite mixture of normal distributions is used to model the length-frequency cohorts of each month with the means constrained to follow a VBGM. The variances of the finite mixture components are constrained to be a function of mean length, reducing the number of parameters and allowing for an estimate of the variance at any length. To optimize the likelihood, we use a minorization–maximization (MM) algorithm with a Nelder–Mead sub-step. This work was motivated by the decline in catches of the blue swimmer crab (BSC) (Portunus armatus) off the east coast of Queensland, Australia. We test the method with a simulation study and then apply it to the BSC fishery data.

Assessment of a data-limited, multi-species shark fishery in the Great Barrier Reef Marine Park and south-east Queensland

The status of five species of commercially exploited sharks within the Great Barrier Reef Marine Park (GBRMP) and south-east Queensland was assessed using a data-limited approach. Annual harvest rate, U, estimated empirically from tagging between 2011 and 2013, was compared with an analytically-derived proxy for optimal equilibrium harvest rate, UMSY Lim. Median estimates of U for three principal retained species, Australian blacktip shark, Carcharhinus tilstoni, spot-tail shark, Carcharhinus sorrah, and spinner shark, Carcharhinus brevipinna, were 0.10, 0.06 and 0.07 year-1, respectively. Median U for two retained, non-target species, pigeye shark, Carcharhinus amboinensis and Australian sharpnose shark, Rhizoprionodon taylori, were 0.27 and 0.01 year-1, respectively. For all species except the Australian blacktip the median ratio of U/UMSY Lim was <1. The high vulnerability of this species to fishing combined with life history characteristics meant UMSY Lim was low (0.04-0.07 year-1) and that U/UMSY Lim was likely to be > 1. Harvest of the Australian blacktip shark above UMSY could place this species at a greater risk of localised depletion in parts of the GBRMP. Results of the study indicated that much higher catches, and presumably higher U, during the early 2000s were likely unsustainable. The unexpectedly high level of U on the pigeye shark indicated that output-based management controls may not have been effective in reducing harvest levels on all species, particularly those caught incidentally by other fishing sectors including the recreational sector. © 2016 Elsevier B.V.