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.

Population structure, effective population size and adverse effects of stocking in the endangered Australian eastern freshwater cod Maccullochella ikei

Microsatellite markers were used to examine spatio-temporal genetic variation in the endangered eastern freshwater cod Maccullochella ikei in the Clarence River system, eastern Australia. High levels of population structure were detected. A model-based clustering analysis of multilocus genotypes identified four populations that were highly differentiated by F-statistics (FST = 0· 09 − 0· 49; P < 0· 05), suggesting fragmentation and restricted dispersal particularly among upstream sites. Hatchery breeding programmes were used to re-establish locally extirpated populations and to supplement remnant populations. Bayesian and frequency-based analyses of hatchery fingerling samples provided evidence for population admixture in the hatchery, with the majority of parental stock sourced from distinct upstream sites. Comparison between historical and contemporary wild-caught samples showed a significant loss of heterozygosity (21%) and allelic richness (24%) in the Mann and Nymboida Rivers since the commencement of stocking. Fragmentation may have been a causative factor; however, temporal shifts in allele frequencies suggest swamping with hatchery-produced M. ikei has contributed to the genetic decline in the largest wild population. This study demonstrates the importance of using information on genetic variation and population structure in the management of breeding and stocking programmes, particularly for threatened species.