A framework for building enviromics matrices in mixed models

Abstract

This study unravels a framework for constructing enviromics matrices within mixed models to integrategenetic and envirotypic data, enhancing phenotypic predictions in plant breeding. Enviromics leveragesdiverse data sources, such as climate and soil, to characterize genotype-by-environment (G×E) interac-tions. The approach uses block-diagonal structures in the design matrixZto incorporate random effectsfrom genetic and envirotypic covariates across trials. The covariance structure is modeled through theKronecker product of the genetic relationship matrixAand an identity matrixIrepresenting envirotypiceffects, effectively capturing both genetic and environmental variability. This dual representation facili-tates more accurate predictions of crop performance (y) across environments, enabling improved selectionstrategies in breeding programs. The framework is compatible with widely used mixed model software,including rrBLUP and BGLR, and is adaptable to account for more complex interactions. By integrat-ing genetic relationships (A) and environmental influences (Z), this approach provides a robust tool foradvancing G×E studies and accelerating the development of superior crop varieties.