Statistics - serving plant science for generations
Predicting the performance of novel plant genotypes in different environments is essential for developing cultivars with superior economically important traits (such as yield) and resilience to environmental stresses (such as drought).
The Radiata Pine Breeding Company Ltd.” runs breeding programmes to improve the productivity and quality of wood from radiata pine trees for the Australasian forestry industry. Candidate pine trees (i.e. different genotypes) are tested in a multi-environment trial (MET), a series of experiments conducted across a range of geographic locations in New Zealand and Australia over multiple years. The set of experiments within and across years is designed to provide a range of growing conditions, or “environments”. From these trials, the genetic and environmental effects on the performance of the candidate pine trees can be estimated. This information is then used by radiata pine breeders to select trees for crossing, with the aim of further genetic improvement, and by growers of radiata pine for selecting genotypes predicted to perform well at their site.
Plant breeders use multi-environment trial (MET) data to evaluate genotypes across a range of environments. However, the relative performance of the genotypes often varies between environments, a phenomenon known as the genotype by environment (G×E) interaction. The G×E interaction can be exploited to identify genotypes that perform well in all environments (i.e. are suitable for broad use) and those with exceptional performance in specific environments (i.e. are well suited for use in certain growing conditions).
Today, linear mixed models are widely used in the analysis of MET data. The linear mixed model framework accommodates the analysis of genetically and/or experimentally correlated data, heterogeneous variances and unbalanced data sets, enabling the accurate prediction of genotype performance within all environments in the data set. In addition, the ability to formally test statistical hypotheses provides greater insight into the nature of the G×E interaction.
An established method for analysing MET data involves a linear mixed model that adopts multiplicative factor analytic (FA) variance structures for the G×E effects. The FA model provides a parsimonious, yet flexible, method of describing the G×E interaction. For example, it allows for genetic variance heterogeneity between trials and different genetic correlation across trials. It can also be extended to include genetic relationship information (e.g. pedigrees) so that the genetic effects can be partitioned into additive and non-additive components. Furthermore, it typically has higher predictive accuracy than alternative models when there is substantial G×E interaction.
A Brief History of MET Analysis
A powerful, efficient and reliable software solution for fitting linear mixed models is ASReml-R. It is particularly well suited to the analysis of MET data. With over 4500 citations, ASReml-R is a popular choice by MET data analysts due to:
Case Study Continued…
Biometricians from the University of Wollongong, Australia, have analysed MET data for the Radiata Pine Breeding Company Ltd. Over 360,000 progeny trees were grown in 111 trials. Pedigree information was available for the 2948 parental lines. Their aim was to produce predicted breeding values (i.e. additive genetic effects) of the parental trees. A linear mixed model adopting a fa ctor analytic (FA) model for the G×E effects was fitted using ASReml-R.
The breeding values predicted by the statistical model are now publicly available on the Radiata Pine Breeding Company Ltd. website for use by radiata pine breeders and growers.
For readers new to linear mixed models or ASReml-R, MMA (Mixed Model Academy) provides a simple and user-friendly tool to help you