title: Mixture of time-dependent growth models with an application to blue swimmer crab length-frequency data.
abstract: 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.
authors.affiliation: Centre for Neurogenetics and Statistical Genomics, Queensland Brain Institute, University of Queensland, St Lucia, Brisbane, Queensland 4072, Australia.
authors.forename: Luke R
authors.initials: LR
authors.lastname: Lloyd-Jones
authors.affiliation: School of Mathematics and Physics, University of Queensland, St Lucia, Brisbane, Queensland 4072, Australia.
authors.forename: Hien D
authors.initials: HD
authors.lastname: Nguyen
authors.affiliation: School of Mathematics and Physics, University of Queensland, St Lucia, Brisbane, Queensland 4072, Australia.
authors.forename: Geoffrey J
authors.initials: GJ
authors.lastname: McLachlan
authors.affiliation: Queensland Department of Agriculture and Fisheries, Ecosciences Precinct, Joe Baker St, Dutton Park, Brisbane, Queensland 4102, Australia.
authors.forename: Wayne
authors.initials: W
authors.lastname: Sumpton
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland 4000, Australia.
authors.forename: You-Gan
authors.initials: YG
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D000818:Animals; D003386:Brachyura / Q000254:growth & development*; D005398:Fisheries / Q000706:statistics & numerical data*; D008954:Models, Biological; D015233:Models, Statistical; D016011:Normal Distribution; D013997:Time Factors
keywords: Blue swimmer crab; Growth model estimation; Length-frequency data; Minorization-maximization algorithm; Mixture modeling