Multivariate Models with Random Effects for Mixed Nature Components: an Application in Genomic Prediction from Multivariate Phenotypes

Abstract

The literature in plant breeding, such as for grasses like sugarcane and forage, indicates that conducting genetic improvement for multiple phenotypes simultaneously has an advantage over individual and separately modeled phenotypes. However, a common practice is to model multiple phenotypes through a multivariate Gaussian distribution, introducing inferential bias when the variable does not have a Gaussian nature. In this sense, from a statistical perspective, the goal is to formulate a class of models for mixed-nature multivariate responses, considering accommodating responses on continuous support (not necessarily with a Gaussian distribution) and discrete support (count, ordered or unordered categorical). To accommodate marginal correlation between phenotypes, we consider random effects. In the context of improvement, random effects will be represented by environmental and genetic effects. The proposed model considers two levels of plant genetic effects, one of which typically incorporates information on kinship between plants and the other considers information at the molecular level, in this study represented by Single Nucleotide Polymorphisms (SNPs). The estimation of these effects will be done simultaneously through a Bayesian approach. Thus, in the context of genetic improvement, the goal is to obtain the most accurate prediction of genetic vectors, aiming to improve the selection process. We will illustrate the method using a real and public dataset of grasses to assess the gain of our proposal in the genetic improvement of the forage species Megathyrsus maximus compared to the models used so far. We intend to use production and nutritional value as agronomic phenotypic traits of interest.