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

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. 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.

Genotype by environment interactions in forest tree breeding: review of methodology and perspectives on research and application

“…Eberhart and Russell 1966;Finlay and Wilkinson 1963;Huehn 1990). Type-B genetic correlation (Burdon 1977) and factor analytic models characterise patterns of ranking changes of genotypes across multiple environments (Cullis et al 2014). Likelihood ratio tests now provide robust tests of interaction in departures from perfect type-B correlations.…”

“…Factor analytic (FA) models can provide a reliable, parsimonious and holistic approach for estimation of genetic correlations between all pairs of trials (Cullis et al 2014;Smith et al 2015) and provide a natural framework for modelling G×E patterns in complex multi-environment experiments (Meyer 2009). The FA model is the most useful for making decisions of selection for breeding populations and decisions of deployment for production populations.…”

“…The use of FA models in multi-environment trials is based on the use of eigenvectors from PCA (Jolliffe 1986;Smith et al 2001) and extended to accommodate both additive and non-additive effects (Oakey et al 2006a, b). Cullis et al (2014) used FA models to accommodate a large number of environments and poor connectivity between environments with a reduced animal model. The FA models aim to identify the statistical common factors that give rise to correlations between variables (Mrode 2014).…”

“…Increased awareness of the magnitude and nature of G×E helps tree breeders and foresters to see the opportunities to increase genetic gain in the forests (Cullis et al 2014;Ivković et al 2013a, b). With this awareness comes a transition from thinking about G×E mainly in relation to selection and structuring of breeding populations to thinking more about G×E also in relation to deployment.…”

“…For deployment, however, concern among tree-growing businesses in New Zealand over the realisation of genetic gain on some sites led to a reappraisal of the situation by the Radiata Pine Breeding Company (RPBC) (Butcher, 2015, personal communication). Application of multi-environment factor analytic models has also given a new level of statistical efficiency and evidence that there are additional genetic gains possible by deploying the right genotypes on the right sites (Cullis et al 2014).…”