# Optimizing the single-step model for predicting fumonisins resistance in maize hybrids accounting for the genotype-by-environment interaction

## TL;DR

This study explores how to predict resistance to harmful fumonisins in maize hybrids by combining genetic and environmental data in Brazil's tropical regions.

## Contribution

The study introduces a cross-validation approach to optimize the hyper-parameter w in the B-matrix model for predicting fumonisins resistance in tropical maize.

## Key findings

- Using the B-matrix in five tested linear models increased predictive ability compared to pedigree or genomic data alone.
- Under CV1, larger training sets improved predictive accuracy, while under CV2, better covariance structures were more important.
- The study is the first to apply the B-matrix approach for predicting fumonisins resistance in tropical maize breeding.

## Abstract

In Brazil, disease outbreaks in plant cultivars are common in tropical zones. For example, the fungus Fusarium verticillioides produces mycotoxins called fumonisins (FUMO) which are harmful to human and animal health. Besides the genetic component, the expression of this polygenic trait is regulated by interactions between genes and environmental factors (G × E). Genomic selection (GS) emerges as a promising approach to address the influence of multiple loci on resistance. We examined different manners to conduct the prediction of FUMO contamination using genomic and pedigree data, and combinations of these two via the single step model (B-matrix) which also offers the possibility of increasing training set sizes. This is the first study to apply the B-matrix approach for predicting FUMO in tropical maize breeding programs. Our research introduced a cross-validation approach to optimize the hyper-parameter w, which represents the fraction of total additive variance captured by the markers. We demonstrated the importance of selecting optimal w by environment in unbalanced datasets. A total of 13 predictive models considering General Combining Ability (GCA) and Specific Combining Ability (SCA) effects, resulted from five linear predictors and three different covariance structures including the single-step approach. Two cross-validation scenarios were considered to evaluate the model’s proficiency: CV1 simulated the prediction of completely untested hybrids, where the individuals in the validation set had no phenotypic records in the training set; and CV2 simulated the prediction of partially tested hybrids, where individuals had been evaluated in some environments but not in the target environment. Results showed that using the B-matrix in the five tested linear models increased the predictive ability compared to pedigree or genomic information. Under CV1, increasing training set sizes exhibit superior predictive accuracy. On the other hand, under CV2 the advantages of increasing the training set size are unclear and the improvements are due to better covariance structures. These insights can be applied to plant breeding programs where the GCA, SCA, and G × E interactions are of interest and pedigree information is accessible, but constraints related to genotyping costs for the entire population exist.