Factor analytic and reduced animal models for the investigation of additive genotype-by-environment interaction in outcrossing plant species with application to a Pinus radiata breeding programme

Abstract

Key message

Modelling additive genotype-by-environment interaction is best achieved with the use of factor analytic models. With numerous environments and for outcrossing plant species, computation is facilitated using reduced animal models.

Abstract

The development of efficient plant breeding strategies requires a knowledge of the magnitude and structure of genotype-by-environment interaction. This information can be obtained from appropriate linear mixed model analyses of phenotypic data from multi-environment trials. The use of factor analytic models for genotype-by-environment effects is known to provide a reliable, parsimonious and holistic approach for obtaining estimates of genetic correlations between all pairs of trials. When breeding for outcrossing species the focus is on estimating additive genetic correlations and effects which is achieved by including pedigree information in the analysis. The use of factor analytic models in this setting may be computationally prohibitive when the number of environments is moderate to large. In this paper, we present an approach that uses an approximate reduced animal model to overcome the computational issues associated with factor analytic models for additive genotype-by-environment effects. The approach is illustrated using a Pinus radiata breeding dataset involving 77 trials, located in environments across New Zealand and south eastern Australia, and with pedigree information on 315,581 trees. Using this approach we demonstrate the existence of substantial additive genotype-by-environment interaction for the trait of stem diameter measured at breast height. This finding has potentially significant implications for both breeding and deployment strategies. Although our approach has been developed for forest tree breeding programmes, it is directly applicable for other outcrossing plant species, including sugarcane, maize and numerous horticultural crops.

Appendix

Below is the ASReml-R syntax to fit the FA3 model. The ASReml-R function has numerous arguments which are described in detail in the user manual which is distributed with the package. The approach we use to fit an FA3 model is to use the REML estimates of the variance parameters from the FA2 model as starting values for the iterative fitting process for the FA3 model. We have found that this improves the chance of convergence without manual intervention. The first call to ASReml-R sets up a template which can then be populated with the appropriate starting values.

Note the formation of the design matrix for the additive effects of the parental and forward selection trees using the and constructor function.

The additional terms in the random model formula are terms which relate to the blocking structure of the trials. For example, the set of trials which were multi-tree plot trials is found in the data vector pplt, while the set of trials which were incomplete block designs is found in the data vector pblk. The relationship matrices for additive effects is provided in the ginverse argument, we require a very large amount of workspace and the term which is fitted as a sparse term is a factor with $K$ levels where $K$ is one more than the number of trees whose female parent was a control tree. Lastly the factor TExpt is a copy of the trial factor for those trials which are clonal trials else is it set to missing value indicator (NA).