Probabilistic Selection of Forage Hybrids Based on Biomass Yield

The development of high-yielding tropical grass hybrids is a fundamental strategy to increase forage production under contrasting environmental conditions. This study aimed to evaluate the performance and stability of Papalotla’s hybrids tested in Mexico, based on dry biomass yield data. The dataset comprised 33 genotypes evaluated across three environments, including five commercial checks, arranged in a randomized complete block design. Initially, the Best Linear Unbiased Estimators (BLUEs) were obtained from linear mixed models fitted separately for each environment, considering genotype as a fixed effect and replication as a random effect. Subsequently, the BLUEs were analyzed using a Bayesian multi-environment model implemented in the ProbBreed package in R. The application of the Bayesian multi-environment model enabled a robust estimation of hybrid performance and stability by incorporating uncertainties associated with environmental and genotype-by-environment interaction effects. From the posterior distributions of the parameters, probabilistic metrics were derived to directly support the selection process, including the Probability of superior performance (PSP) and the Pairwise Probability of Superior Performance (PPSP). PSP values close to 1 indicate strong evidence of superior performance and stability, whereas values near 0 suggest low performance or high uncertainty associated with the genotype’s response. The PPSP quantifies the probability of a specific genotype outperforming its peers. This probabilistic measure reflects how often a genotype is ranked as superior across all posterior samples. The PPSP matrix revealed marked contrasts among hybrids. Genotypes such as G18, G33, G7 and G5 stood out by showing a high probability (>0.75) of superiority over most others, reflecting high yield potential and stability across environments. In contrast, the commercial checks (G28, G29, G30 and G32) exhibited low probabilities (<0.30), indicating inferior performance and reduced adaptability compared with the new hybrids, suggesting that the experimental materials possess superior genetic potential for biomass yield. This evidence highlights the progress achieved in Papalotla’s breeding program and indicates the potential for gradually replacing traditional cultivars with more productive and stable hybrids. Therefore, the analysis of the Probability of Superior Performance provides a probabilistic and intuitive view of the relative performance of genotypes, allowing for the reliable identification of elite materials compared to approaches based solely on phenotypic means. The inclusion of this Bayesian approach supports more informed decision-making in genotype recommendation, especially under complex experimental conditions or environments with strong interactive effects.

Financial support: We acknowledge the support of the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES), the Maize Genetics and Breeding Laboratory (LGM), the “Luiz de Queiroz” College of Agriculture of the University of São Paulo (ESALQ/USP) and Papalotla Group for providing the data used in this study.