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.

Modelling predicts positive and negative interactions between three Australian tropical tree species in monoculture and binary mixture

Computer modelling promises to be an important tool for analysing and predicting interactions between trees within mixed species forest plantations. This study explored the use of an individual-based mechanistic model as a predictive tool for designing mixed species plantations of Australian tropical trees. The `spatially explicit individually based-forest simulator' (SeXI-FS) modelling system was used to describe the spatial interaction of individual tree crowns within a binary mixed-species experiment. The three-dimensional model was developed and verified with field data from three forest tree species grown in tropical Australia. The model predicted the interactions within monocultures and binary mixtures of Flindersia brayleyana, Eucalyptus pellita and Elaeocarpus grandis, accounting for an average of 42% of the growth variation exhibited by species in different treatments. The model requires only structural dimensions and shade tolerance as species parameters. By modelling interactions in existing tree mixtures, the model predicted both increases and reductions in the growth of mixtures (up to +/-50% of stem volume at 7 years) compared to monocultures. This modelling approach may be useful for designing mixed tree plantations.