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.

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.

The climate change risk management matrix for the grazing industry of northern Australia

The complexity, variability and vastness of the northern Australian rangelands make it difficult to assess the risks associated with climate change. In this paper we present a methodology to help industry and primary producers assess risks associated with climate change and to assess the effectiveness of adaptation options in managing those risks. Our assessment involved three steps. Initially, the impacts and adaptation responses were documented in matrices by ‘experts’ (rangeland and climate scientists). Then, a modified risk management framework was used to develop risk management matrices that identified important impacts, areas of greatest vulnerability (combination of potential impact and adaptive capacity) and priority areas for action at the industry level. The process was easy to implement and useful for arranging and analysing large amounts of information (both complex and interacting). Lastly, regional extension officers (after minimal ‘climate literacy’ training) could build on existing knowledge provided here and implement the risk management process in workshops with rangeland land managers. Their participation is likely to identify relevant and robust adaptive responses that are most likely to be included in regional and property management decisions. The process developed here for the grazing industry could be modified and used in other industries and sectors. By 2030, some areas of northern Australia will experience more droughts and lower summer rainfall. This poses a serious threat to the rangelands. Although the impacts and adaptive responses will vary between ecological and geographic systems, climate change is expected to have noticeable detrimental effects: reduced pasture growth and surface water availability; increased competition from woody vegetation; decreased production per head (beef and wool) and gross margin; and adverse impacts on biodiversity. Further research and development is needed to identify the most vulnerable regions, and to inform policy in time to facilitate transitional change and enable land managers to implement those changes.