Aspectos Computacionais da Estimação e Predição em Modelos Lineares Mistos para Seleção de Híbridos de Milho em Ensaios Premilinares - Marçal, Tiago de Souza (2016)
Maize (Zea mays L.), is a specie from the Poaceae family, diploid and allogamous. In this culture, there is an increase with the accumulation of heterozygous loci, thus justifying hybrids productions. Due to drastic predictions of climate change and population growth in the coming years, it is necessary to adopt, develop and enhance methods that allow a greater efficiency in the selection and achieve greater genetic progress in crop improvement programs of agriculture importance that can help mitigation of challenges to sustain the food security of this century. Therefore, the objective of this study was to implement the algorithms of first and second derivatives for the REML (restricted maximum likelihood) method in R, generalizable for different mixed linear models and enable incorporate arrays of relationship. Moreover, to evaluate the impact of mathematical simplifications, sparse matrices and different convergence error rates in computational efficiency of these algorithms aiming to minimize the computational cost to enable REML in studies with a great number of maize hybrids and complex models, in computers with simple setup. The experimental data used in this study was obtained from harvest 2013/14 conducted in a randomized block design with five controls and 3352 simple maize hybrids in Embrapa (Empresa Brasileira de Pesquisa Agropecuária) Maize and Sorghum in the city of Sete Lagoas- MG. The analyzed variable was grain yield, which is subjected to analysis using mixed models with and without pedigree of incorporation using different REML algorithms, in R. Computation response evaluated the convergence criteria, error rates convergence, sparse matrices, computers with different processing capabilities, different initial estimates of variance components and increasing number of EM (Expectation Maximization) steps in combined algorithms. The proposed algorithms were equivalent for the tested software (ASReml, Selegen and Ime4) and the estimates of variance components indicating their coherence. Furthermore, the use of sparse matrices in association with the proposed optimizations, reduced the computational cost of the algorithms using coefficients of determination as a convergence criteria and convergence error rate equal to 10-5. The hybrid combination of EM algorithm, in ten steps, with NR (Newton Raphson) reduced the computational cost and increased the average convergence percentage. Although, it was observed that uniform weights for the initial estimates of the variance components should be avoided.