Splines e modelo funcional em bins: abordagens integradas à seleção genômica

Abstract

The continuous genome model for dimensionality and multicollinearity reduction is based on the dividing genome into windows (bins) and then it assumes a functional model in which the gene expression in a marker is an unknown function of the position in the genome (signal function). The main challenge is to obtain a functional form by relating phenotypes to marker genotypes (seen as thousands of covariates) and to genetic values. The simplest approach is to use the average genotype status of the marker within the bins as an information measure to predict genomic values of new individuals. This study proposed two alternatives: the first one was to incorporate the idea of weights into the effects within bins using the relative frequency with which each marker is sampled in a Markov chain, along with the functional model in bins, to classic genomic selection methods; the second one was to obtain a polynomial expression, by means of functional data analysis techniques, that represents the gene expression in the genomic selection. The adaptation of the RR-BLUP, Bayes A, and Bayes B methods was illustrated under the Bayesian version of the functional model, and their original forms were used as standards for comparisons. In addition, B-Spline functions were used to estimate the signal function. Both alternatives presented satisfactory results, returning analyzes in less computational time compared to the originals. Functional models are very attractive and can be used as unifying principles for selection and localization of genes.