A framework for simulating genotype-by-environment interaction using multiplicative models.

Key message: The simulation of genotype-by-environment interaction using multiplicative models provides a general and scalable framework to generate realistic multi-environment datasets and model plant breeding programmes. Plant breeding has been historically shaped by genotype-by-environment interaction (GEI). Despite its importance, however, many current simulations do not adequately capture the complexity of GEI inherent to plant breeding. The framework developed in this paper simulates GEI with desirable structure using multiplicative models. The framework can be used to simulate a hypothetical target population of environments (TPE), from which many different multi-environment trial (MET) datasets can be sampled. Measures of variance explained and expected accuracy are developed to tune the simulation of non-crossover and crossover GEI and quantify the MET-TPE alignment. The framework has been implemented within the R package FieldSimR, and is demonstrated here using two working examples supported by R code. The first example embeds the framework into a linear mixed model to generate MET datasets with low, moderate and high GEI, which are used to compare several popular statistical models applied to plant breeding. The prediction accuracy generally increases as the level of GEI decreases or the number of environments sampled in the MET increases. The second example integrates the framework into a breeding programme simulation to compare genomic and phenotypic selection strategies over time. Genomic selection outperforms phenotypic selection by $\sim$ 50-70% in the TPE, depending on the level of GEI. These examples demonstrate how the new framework can be used to generate realistic MET datasets and model plant breeding programmes that better reflect the complexity of real-world settings, making it a valuable tool for optimising a wide range of breeding methodologies.