[Paper Review] A Framework for Building Enviromics Matrices in Mixed Models

Bruno Achcar Trevisan, Vilela Junqueira+4 more|arXiv (Cornell University)|Jan 7, 2025

Genetics and Plant Breeding3 citations

TL;DR

The paper presents a framework to build enviromics matrices in mixed models to integrate genetic and environmental data, enhancing phenotypic predictions in plant breeding. It explains construction of block-diagonal design matrices and Kronecker-structured covariances, plus frequentist and Bayesian implementations.

ABSTRACT

This study introduces a framework for constructing enviromics matrices in mixed models to integrate genetic and environmental data to enhance phenotypic predictions in plant breeding. Enviromics utilizes diverse data sources, such as climate and soil, to characterize genotype-by-environment (GxE) interactions. The approach employs block-diagonal structures in the design matrix to incorporate random effects from genetic and envirotypic covariates across trials. The covariance structure is modeled using the Kronecker product of the genetic relationship matrix and an identity matrix representing envirotypic effects, capturing genetic and environmental variability. This dual representation enables more accurate crop performance predictions across environments, improving selection strategies in breeding programs. The framework is compatible with existing mixed model software, including rrBLUP and BGLR, and can be extended for more complex interactions. By combining genetic relationships and environmental influences, this approach offers a powerful tool for advancing GxE studies and accelerating the development of improved crop varieties.

Motivation & Objective

• Introduce a framework to construct enviromics matrices for integrating genetic and environmental data in mixed models.
• Explain how block-diagonal design matrices capture random effects across genotypes and environments.
• Describe a Kronecker-product covariance structure combining kinship and envirotypic effects to improve phenotypic predictions.
• Show how the framework integrates with rrBLUP and BGLR and discuss extensions to more complex GxE interactions.

Proposed method

• Construct a block-diagonal design matrix Z to include random effects for each genotype and envirotypic covariate across trials.
• Define a covariance structure using Sigma d7 A or equivalently K = A
  d7 I to model envirotypic and genetic variance components.
• Use a kernel (K) as the Kronecker product of the kinship matrix A and an identity matrix to expand genetic relationships across envirotypic effects.
• Provide frequentist estimation via rrBLUP and Bayesian estimation via BGLR, including handling of convergence with ensemble/grouping of ECs and MCMC settings.
• Demonstrate construction steps on a toy dataset with sample code in R and discuss interpretation of outputs (BLUE/BLUP) and predictions.

Experimental results

Research questions

• RQ1 How can enviromic covariates be integrated with genetic relationships in a mixed model framework?
• RQ2 What is the effect of using a block-diagonal Z and a Kronecker-structured K on predicting phenotypes across environments?
• RQ3 How do frequentist (rrBLUP) and Bayesian (BGLR) approaches compare in this enviromics setting?
• RQ4 Can the framework accommodate many envirotypic covariates and complex G interactions while remaining implementable in standard software?

Key findings

• A block-diagonal Z can accommodate random effects for multiple genotypes across envirotypes.
• The Kronecker-product kernel K = A 7 I expands the kinship matrix to include envirotypic effects, capturing genetic and environmental covariance.
• Frequentist (rrBLUP) and Bayesian (BGLR) approaches yield highly concordant predictions (correlation ~0.973 in the example).
• The framework supports integration with rrBLUP and BGLR and can be extended for more complex G interactions.
• Enviromics improves phenotypic predictions across environments by combining genetic relationships with envirotypic covariates.