Genomic Bayesian Prediction Model for Count Data with Genotype x Environment Interaction

Genomic tools allow the study of the whole genome, and facilitate the study of genotypeenvironment combinations and their relationship with phenotype. However, most genomic prediction models developed so far are appropriate for Gaussian phenotypes. For this reason, appropriate genomic prediction models are needed for count data, since the conventional regression models used on count data with a large sample size (nT ) and a small number of parameters (p) cannot be used for genomic-enabled prediction where the number of parameters (p) is larger than the sample size (nT ). Here, we propose a Bayesian mixed-negative binomial (BMNB) genomic regression model for counts that takes into account genotype by environment ðG ·EÞ interaction. We also provide all the full conditional distributions to implement a Gibbs sampler. We evaluated the proposed model using a simulated data set, and a real wheat data set from the International Maize and Wheat Improvement Center (CIMMYT) and collaborators. Results indicate that our BMNB model provides a viable option for analyzing count data.