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.

Assessment of internal quality attributes of mandarin fruit. 1. NIR calibration model development

The utility of near infrared spectroscopy as a non-invasive technique for the assessment of internal eating quality parameters of mandarin fruit (Citrus reticulata cv. Imperial) was assessed. The calibration procedure for the attributes of TSS (total soluble solids) and DM (dry matter) was optimised with respect to a reference sampling technique, scan averaging, spectral window, data pre-treatment (in terms of derivative treatment and scatter correction routine) and regression procedure. The recommended procedure involved sampling of an equatorial position on the fruit with 1 scan per spectrum, and modified partial least squares model development on a 720–950-nm window, pre-treated as first derivative absorbance data (gap size of 4 data points) with standard normal variance and detrend scatter correction. Calibration model performance for the attributes of TSS and DM content was encouraging (typical Rc2 of >0.75 and 0.90, respectively; typical root mean squared standard error of calibration of <0.4 and 0.6%, respectively), whereas that for juiciness and total acidity was unacceptable. The robustness of the TSS and DM calibrations across new populations of fruit is documented in a companion study.

Spatial model of site index based on Y-ray spectrometry and a digital elevation model for two Pinus species in Tuan Toolara State Forest, Queensland, Australia

Site index prediction models are an important aid for forest management and planning activities. This paper introduces a multiple regression model for spatially mapping and comparing site indices for two Pinus species (Pinus elliottii Engelm. and Queensland hybrid, a P. elliottii x Pinus caribaea Morelet hybrid) based on independent variables derived from two major sources: g-ray spectrometry (potassium (K), thorium (Th), and uranium (U)) and a digital elevation model (elevation, slope, curvature, hillshade, flow accumulation, and distance to streams). In addition, interpolated rainfall was tested. Species were coded as a dichotomous dummy variable; interaction effects between species and the g-ray spectrometric and geomorphologic variables were considered. The model explained up to 60% of the variance of site index and the standard error of estimate was 1.9 m. Uranium, elevation, distance to streams, thorium, and flow accumulation significantly correlate to the spatial variation of the site index of both species, and hillshade, curvature, elevation and slope accounted for the extra variability of one species over the other. The predicted site indices varied between 20.0 and 27.3 m for P. elliottii, and between 23.1 and 33.1 m for Queensland hybrid; the advantage of Queensland hybrid over P. elliottii ranged from 1.8 to 6.8 m, with the mean at 4.0 m. This compartment-based prediction and comparison study provides not only an overview of forest productivity of the whole plantation area studied but also a management tool at compartment scale.

The accuracy of varietal selection using factor analytic models for multi-environment plant breeding trials

Modeling of cultivar x trial effects for multienvironment trials (METs) within a mixed model framework is now common practice in many plant breeding programs. The factor analytic (FA) model is a parsimonious form used to approximate the fully unstructured form of the genetic variance-covariance matrix in the model for MET data. In this study, we demonstrate that the FA model is generally the model of best fit across a range of data sets taken from early generation trials in a breeding program. In addition, we demonstrate the superiority of the FA model in achieving the most common aim of METs, namely the selection of superior genotypes. Selection is achieved using best linear unbiased predictions (BLUPs) of cultivar effects at each environment, considered either individually or as a weighted average across environments. In practice, empirical BLUPs (E-BLUPs) of cultivar effects must be used instead of BLUPs since variance parameters in the model must be estimated rather than assumed known. While the optimal properties of minimum mean squared error of prediction (MSEP) and maximum correlation between true and predicted effects possessed by BLUPs do not hold for E-BLUPs, a simulation study shows that E-BLUPs perform well in terms of MSEP.