Estimation in a multiplicative mixed model involving a genetic relationship matrix.

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.

Telomere dynamics in the Sydney rock oyster (Saccostrea glomerata): an investigation into the effects of age, tissue type, location and time of sampling.

Telomere length has been purported as a biomarker for age and could offer a non-lethal method for determining the age of wild-caught individuals. Molluscs, including oysters and abalone, are the basis of important fisheries globally and have been problematic to accurately age. To determine whether telomere length could provide an alternative means of ageing molluscs, we evaluated the relationship between telomere length and age using the commercially important Sydney rock oyster (Saccostrea glomerata). Telomere lengths were estimated from tissues of known age individuals from different age classes, locations and at different sampling times. Telomere length tended to decrease with age only in young oysters less than 18 months old, but no decrease was observed in older oysters aged 2-4 years. Regional and temporal differences in telomere attrition rates were also observed. The relationship between telomere length and age was weak, however, with individuals of identical age varying significantly in their telomere length making it an imprecise age biomarker in oysters.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).