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.