Multitrait index based on factor analysis and ideotype‐design: proposal and application on elephant grass breeding for bioenergy

This study proposes a new multitrait index based on factor analysis and ideotype‐design (FAI‐BLUP index), and validates its potential on the selection of elephant grass genotypes for energy cogeneration. Factor analysis was carried out, and afterwards, factorial scores of each ideotype were designed according to the desirable and undesirable factors, and the spatial probability was estimated based on genotype‐ideotype distance, enabling genotype ranking. In order to quantify the potential of the FAI‐BLUP index, genetic gains were predicted and compared with the Smith‐Hazel classical index. The FAI‐BLUP index allows ranking the genotypes based on multitrait, free from multicollinearity, and it does not require assigning weights, as in the case of the Smith‐Hazel classical index and its derived indices. Furthermore, the genetic correlation ‐ positive or negative ‐ within each factor was taken into account, preserving their traits relationship, and giving biological meaning to the ideotypes. The FAI‐BLUP index indicated the 15 elephant grass with the highest performance for conversion to bioenergy via combustion, and predicted balanced and desirable genetic gains for all traits. In addition, the FAI‐BLUP index predicted gains of approximately 62% of direct selection, simultaneously for all traits that are desired to be increased, and approximately 33% for traits which are desired to be decreased. The genotypes selected by the FAI‐BLUP index have potential to improve all traits simultaneously, while the Smith‐Hazel classical index predicted gains of 66% for traits that are desired to be increased, and ?32% for traits that are desired to be decreased, and it does not have potential to improve all traits simultaneously. The FAI‐BLUP index provides an undoubtable selection process and can be used in any breeding programme aiming at selection based on multitrait.