FW: An R Package for Finlay–Wilkinson Regression that Incorporates Genomic/Pedigree Information and Covariance Structures Between Environments

The Finlay-Wilkinson regression (FW) is a popular method among plant breeders to describe genotype by environment interaction. The standard implementation is a two-step procedure that uses environment (sample) means as covariates in a within-line ordinary least squares (OLS) regression. This procedure can be suboptimal for at least four reasons: (1) in the first step environmental means are typically estimated without considering genetic-by-environment interactions, (2) in the second step uncertainty about the environmental means is ignored, (3) estimation is performed regarding lines and environment as fixed effects, and (4) the procedure does not incorporate genetic (either pedigree-derived or marker-derived) relationships. Su et al. proposed to address these problems using a Bayesian method that allows simultaneous estimation of environmental and genotype parameters, and allows incorporation of pedigree information. In this article we: (1) extend the model presented by Su et al. to allow integration of genomic information [e.g., single nucleotide polymorphism (SNP)] and covariance between environments, (2) present an R package (FW) that implements these methods, and (3) illustrate the use of the package using examples based on real data. The FW R package implements both the two-step OLS method and a full Bayesian approach for Finlay-Wilkinson regression with a very simple interface. Using a real wheat data set we demonstrate that the prediction accuracy of the Bayesian approach is consistently higher than the one achieved by the two-step OLS method.